Students can access the CBSE Sample Papers for Class 10 English with Solutions and marking scheme Term 2 Set 1 will help students in understanding the difficulty level of the exam.

CBSE Sample Papers for Class 10 English Term 2 Set 1 with Solutions

Time Allowed: 2 Hours
Maximum Marks: 40

General Instructions:

• The Question Paper contains THREE sections—READING, WRITING & GRAMMAR and LITERATURE.
• Attempt questions based on specific instructions for each part.

SECTION – A
Reading [10 marks]

Question 1.
Read the passage given below.
Technology is making advancements at a rapid rate but at the cost of a valued tradition—the crafts industry. The traditional crafts industry is losing a lot of its trained and skilled craftsmen. With that, the art of embellishing brass and 5. copper utensils with fine engravings is also disappearing. The government has identified around 35 crafts as languishing craft.

The speciality of handcrafted items is its design, an association with long traditions belonging to a specific region. The word ‘handcrafted’ does not imply the involvement of dexterous human fingers or an agile mind with a moving 10. spirit anymore. Lessening drudgery, increasing production and promoting efficiency have taken precedence. The labour-saving devices are taking the place of handcrafted tools and this has jeopardized the skills of these artisans.

Mechanisation has made its way into 15. everything-cutting, polishing, edging, designing etc. Ideally, the use of machinery should be negligible and the handicrafts should be made purely by hand with a distinguishable artistic appeal. However, with the exception of small-scale industries, the export units are mostly operated by machines. The heavily computerised designs contribute to a faster production at lower costs.

20. Although mechanization of crafts poses a challenge to safeguarding traditional crafts, the artisans are lured with incentives in order to impart handicrafts training. Some makers do see machines as a time-saving blessing since they are now able to accomplish difficult and demanding tasks with relative ease.

25. These machines might give a better finesse to these products but they don’t stand out as handcrafted. Quantity has overtaken quality in this industry.
A need to highlight the importance of the hand-made aspect is required by both the government and private sectors, in order to amplify awareness and also support the culture of making handicrafts. A few artisans 30. are still trying their best to rejuvenate and revive their culture and heritage but it’s an uphill task competing with the machine- made goods. A multitude of artisans have changed their professions and are encouraging their progeny to follow suit. There are others who have stayed their ground but are clearly inclined towards buying machines.

35. Nearly two decades ago, there were around 65 lakh artisans in the country. Three years ago, when the government started the process of granting a unique number to the artisans based on the Aadhaar card, 25 lakhs were identified. Loss of traditional crafts is clearly a worrying issue, but it stands to reason that forcing any artisan to follow old ways when concerns of livelihood overrule other considerations, is unfair.

On the basis of your understanding of the passage, answer ANY FIVE questions from the six given below. (1 × 5 )
(A) What does the writer mean by calling handicrafts a ‘valued tradition’? (1)
Answer:

• valued – showcase talents that are associated with artisans’ lifestyle and history
• tradition – represent rich our artistic culture / heritage / tradition

Detail Explanation:
The writer calls handicrafts a ‘valued tradition’ as it shows the talents of the artisans and represents their rich artistic culture, life style, heritage and tradition.

(B) Rewrite the following sentence by replacing the underlined phrase with a word that means the same from lines (5-15).
If it continues, the workcation (work + vacation) trend will be a powerful boost to domestic tourism operators failing to make progress in the economic slump caused due to the pandemic. (1)
Answer:
If it continues, the workcation (work + vacation) trend will be a powerful boost to domestic tourism operators languishing in the economic slump caused due to the pandemic.

Detail Explanation:
If it continues, the workcation (work + vacation) trend will be a powerful boost to domestic tourism operators failing to make progress in the economic slump caused due to the pandemic.

(C) State any two reasons why artisans are choosing to work via machines rather than handcrafted tools. (1)
Answer:
Saves labour / reduces drudgery / increases production / finesse / effciency

Detail Explanation:
Artisans choose to work via machines as they can now accomplish difficult and demanding tasks relatively easily. The machines save them time and labour, reduce drudgery and increase production. Besides, the machines sometimes give a better finesse to these products.

(D) Why do the artisans need to be ‘lured with incentives’ to impart handicrafts training? (1)
Answer:
Because if artisans impart training to mass/bulk producers, they run the risk of losing their traditional livelihood to them and hence need to be tempted via benefits or rewards, to do so.
Detail Explanation: Though imparting training to mass/bulk producers runs the risk of losing their traditional livelihood, artisans have to be Lured with incentives to provide handicrafts training and keep the custom alive.

(E) List one likely impact of the support of government and private sectors towards the culture of making handicrafts. (1)
Answer:
Creation of awareness and public support for the artisans and their work / more artisans would be incentivised to continue their tradition / artisans wouldn’t change their professions seeking better livelihood

Detail Explanation:
Government and private sectors have been discreetly creating support and public awareness to support the artisans and their work. This way artisans would be incentivised to continue with their profession and tradition and wouldn’t change their professions seeking better livelihood.

(F) How does the writer justify an artist’s act of abandoning her/his traditional craft for a more lucrative option? 1
Answer:
Via the argument that the artisans cannot be expected to continue their profession if it is not profitable, even though the loss of traditional crafts is perturbing.

Detail Explanation:
To justify the artisans’ act of abandoning his/her traditional craft for a more lucrative option, the writer puts up the argument that the artisans cannot be expected to continue their profession if it is not profitable, even though the loss of traditional crafts is disturbing.

Question 2.
Read the following excerpt from a case study titled Impacts of Festivities on Ecology.
Festivals are synonymous with celebration, ceremony and joy. Howeve festivals bring to fore the flip side of celebrations – pollution – air, water, soil and noise. This led to the need of assessing the awareness level among people about ecological pollution during festivals. So, a study was conducted by scholars of an 5. esteemed university in India. This study was titled “Awareness Towards Impact Festivals on Ecology.”

There were two main objectives of the study. The first one was to assess the awareness level among people about ecological protection during festivities, exploring solutions to bring awareness about celebrating festivals without 10. harming ecology was the second objective. The method used to collect data was a simple questionnaire containing 6 questions, shared with 50 respondents across four selected districts of a state in the southern region of India.

The research began by understanding the socio-economic conditions of the respondents before sharing the questionnaire. Once the 15. responses were received, the data collected was tabulated (Table 1), for analysis.

Table-1: Awareness level among respondents

The study recommended the imposition of strict rules and regulations as opposed to a total ban on all festive activities which have a drastic impact on our environment. The researchers believed that such measures would help in harnessing some ill-effects that add to the growing pollution and suggest 20. further studies be taken up across the country to assess awareness about ecological degradation.

The observations made in the study pointed to the environmental groups and eco-clubs fighting a losing battle due to city traffic issues, disposal of plastics, garbage dumping and all sorts of ecological degradation. The 25. researchers stressed that the need of the hour is increasing awareness among reduce ecological pollution which can be facilitated by celebrating all festivals in an eco-friendly manner.

On the basis of your understanding of the passage, answer ANY FIVE questions from the six given below. (1 × 5)
(A) Why do the researchers call pollution the ‘flip side’ of festivals? (1)
Answer:
because the accepted norm is that festivals are synonymous with celebration/joy and people fail to see the other side, which is pollution
OR
festivals and pollution are two sides of the same coin currently/ polar opposites/ completely in contrast, yet together with each other—where we associate festivals with joy and celebration, we can’t deny that pollution is an ignored reality

Detail Explanation:
Unfortunately, festivals and pollution go hand-in-hand. Though festivals are all about celebrations, fun and laughter, today it is (in many ways) traumatizing the mother earth with the litter left after celebrations. Festivals and pollution are two sides of the same coin, where the latter is an ignored reality.

(B) Comment on the significance of the second objective of the study with reference to lines 7-12. (1)
Answer:

• Second objective- Exploring solutions
• Significance- important for knowing steps that need to be taken to address the problem investigated in the research/ knowing what are the immediate actions that need to be implemented to address the issue studied/ helps focus on what needs to be corrected and what needs to be avoided to solve the problem focused on in the research

Detail Explanation:
Second objective is exploring solutions, to bring awareness about celebrating festivals without harming the ecology. To understand and focus on what needs to be corrected and what needs to be avoided, and then give the solution for the problem focused on in the research.

(C) Justify the researchers’ recommendation for limiting the drastic impact of festival pollution on the environment with reference to lines 16-21. (1)
Answer:

• Researcher’s recommendation: Strict rules
• Justification: Strict rules are better than a total ban because banning does not serve the purpose of awareness/ people do not generally conform to banning and tend to revolt/ strict rules pose some restrictions but still give the needed freedom.

Detail Explanation:
Researchers recommend enfo. sing strict ruLes to limit the drastic impact of festival pollution. Government should resort to strict rules instead of total ban because people do not conform to banning and tend to oppose it. So also, banning does put the people under some restrictions but gives the much needed freedom.

(D) Why do the researchers feel that environmental groups and eco-clubs are fighting a losing battle in the given scenario? (1)
Answer:

• the festivals cause pollution along with other issues (give examples) that add to it.
• awareness is the only solution but the lack of it only adds to the problem.

Detail Explanation:
In the study, the environmental groups and eco-clubs aren’t succeeding in their battle against pollution because of unregulated disposal of plastics, garbage dumping, city traffic issues and all sorts of ecological degradation that happens during the festival season. The need of the hour is to sensitize the masses and increase the awareness on celebrating the festivals in an eco-friendly manner.

(E) Even though a larger number of people say ‘no’ to bursting crackers than those who say ‘yes’, festival pollution persists. How does evidence from Table 1 support this statement? (1)
Answer:

• a large percentage of people (72%) abuse environmental resources to celebrate festivals.
• a high percentage of people (82%) use crackers to celebrate festivals in order to live up to the expectation of their social status.

Detail Explanation:
A large percentage of people (72%) abuse environmental resources to celebrate festivals. In spite of a large number of people saying no’ to crackers, pollutions persists as a high percentage of people (82%) use crackers to celebrate festivals in order to live up to the expectation of their social status. It adds to the festival pollution.

(F) What purpose does the ‘Can’t Say’ column serve in the questionnaire (Table 1)? (1)
Answer:
gives a provision to/ allows the respondents to choose not to express/ not to answer/ allows an option to those who lack clarity/ are unwilling to respond.

Detail Explanation:
Other than the obvious ‘Yes’ and ’No’ column, ‘Can’t Say’ aLlows the respondents to choose not to express their opinion on something they are uninterested in, lack of clarity on the topic or doesn’t wish to respond.

SECTION – B
Writing and Grammar [10 marks]

Question 3.
(A) Study the concept chart from the seLf-heLp magazine section of a monthLy pubLication.

Write a paragraph in not more than 120 words, analysing the listed responses to the situation when one faces setbacks. (5)
Answer:
The question tests the folLowing writing LOs:

• convey ideas convincingly using appropriate Language.
• organize the content and structure the ideas Logically, sequentially, cohesively
• use a range of vocabulary and sentence structure appropriate to the content and context
• use of fùnctional Language to show comparison, contrast, emphasis, conclusion, etc.

Detail Explanation:
Setbacks often leave us with a feeling of disappointment and may even lead to acute depression. There are two ways to handle any setback-one for the better, i.e. healthy and the other for the worse, i.e. unhealthy. When we take the setback in a healthy way, we learn from it and let go of the emotions inside. The optimistic approach provides an ability to feel, reflect and align. In other words, we observe the pattern of the setback, especially assess the difficulty of work and possibility of future success by doing the work.

In particular, the person reaches a healing state to transform anxiety, shunning away bitter life experiences that are the results of not meeting some particular expectations. On the contrary, a negative approach to setback gives rise to a feeling of inadequacy and incompetency and the affected person is unable to accept the situation. It leads to a vicious cycle of undesirable feelings and the person becomes a victim to self-criticism and self-doubt as opposed to a person with a positive response to setbacks.

The victim even resorts to blaming others and sees everything as a danger and threat. So, it is imperative to channelize the thoughts in the right direction and avoid anger, anxiety and depression. A healthy response to setbacks must be seen as a learning opportunity, though it may require some time and efforts.

(B) You are Samina Zaveri, Class X, Vadodara, Gujarat. You come across the following information on a local library’s notice board.

You wish to participate but require more information. Write a letter to Teen- Toggle Games Pvt. Ltd. in about 120 words, enquiring about rules, scholarship details and deadlines. Also enquire about specifications for solo or group entries. (5)
Answer:
Reference to the source of information

• Conveying interest
• Seeking information about rules
• Enquiring about scholarship details
• Asking about defined articles
• Confirm type of entries allowed (Any other relevant information)

Detail Explanation:
Samina Zaveri, Class X Vadodra, Gujarat
20th June, 20XX

The Manager
Teen-Toggle Games Pvt. Ltd.
307, Satija building, Colaba
Mumbai

Subject: Seeking information about board game competition
Dear Sir/Madam
I came across your advertisement on the notice board of a local library. I wish to participate in the board game competition. I need to participate in the competition but need some more information regarding the competition. Kindly provide the following details:

• Age limit
• Specific requirement
• Topic or theme
• Scholarship details
• Are the entries solo or group?

Kindly provide the above details as soon as possible so that I can apply for the same.
Thanking you
Yours sincerely
Samina Zaveri

Question 4.
The following paragraph has not been edited. There is one error in each Une. Identify the error and write its correction against the correct blank number. Remember to underline the correction. The first one has been done for you. (1 × 3)

Have you ever [earn from a mistake you have made? Many shouLdn’t admit doing so. For those who do, there was no need for guilt. We often make mistakes white taking risks, but alt brush them aside and Learn. With that, they usually don’t make mistakes the next time.

Answer:
Hove you ever Learn from a mistake you hove made? Many shouldn’t admit doing so. For those who do. there was no need for guilt. We often make mistakes while taking risks, but aLt brush them aside and learn. With that, they usually don’t make mistakes the next time.

Explanation:
(a) The sentence is in present perfect tense and we use 3rd form of the verb with has/ have. So, learn is not the correct word and we use ‘learnt’.
(b) The sentence is in present tense and there is no sense of advice or suggestion. So, should is the wrong word and we will use won’t/don’t.
(c) The complete extract is in present tense, so ‘was’ is the wrong word and the correct word is ‘is’.
(d) If we understand the sense of the sentence, we will know that the right word is some/ many not all.

Question 5.
Read the conversation between a teacher and student and complete the passage that follows. (1 × 2)
Biology Teacher: I instructed you to draw the diagram of bacteria. Why did you submit a blank sheet?

Sameer: Sir, I had drawn the diagram of bacteria, but you can’t see it because it is not visible to the naked eye.
The biology teacher had instructed Sameer to draw the diagram of a bacterial cell and asked him
(a) …………… a blank sheet. Sameer respectfully answered that he had drawn the diagram but
Answer:
why he had submitted

Detail Explanation:
If the sentence in the direct speech is in past tense, the verb changes to past perfect tense. The pronoun ‘you changes to ‘he’, hence, did you submit changes to ‘he had submitted’.

(b) ………….. to the naked eye. (1 + 1)
Answer:
he/ the teacher couldn’t see it because it was not visible

Detail Explanation:
In the first part of the sentence, there is no change in the indirect speech as it already uses past perfect change and that is not changed. In the second part of the sentence, can’t is changed to ‘couldn’t’ and the pronoun you is changed to ‘he’.

Section – C
Literature [20 marks]

Question 6.
Answer ANY SIX questions in 30-40 words each. (2 × 6)
(A) What is the significance of the Buddha’s request for a handful of mustard seeds and the addition of a condition to it? (2)3
Answer:

• added condition – must be procured from a house where no one had Lost a child, husband, parent or friend
• made Kisa Gotami realize the universal nature of death

Detail Explanation:
Kisa Gotami came to Buddha asking him to bring back his dead son to life. Buddha asked her to go to the village and bring some mustard seeds from a house where no death had been occured. The condition held a significant meaning that death is universal. One who is born is sure to die. It was only after that that Kisa Gotami realized her folly and came to terms with the will of God.

(B) Justify how ‘Animals’ by Walt Whitman is a criticism of mankind and its ways. (2)
Answer:

• human beings seem to have dropped/ shed their values/virtues/attributes
• human society blemished by ego, hypocrisy, hatred, materialism, fake display
• profusion of complaints, race for greed and lack of contentment
• the poet wishes to leave the human world and join animals as he finds them better than humans (a testimony)

Detail Explanation:
The poet appreciates the virtues animals possess and that, they were once human virtues. But, now the human beings have forgotten all virtues and have become the victims to innumerable vices such as ego, hypocrisy, hatred, materialism, greed, show off, dissatisfaction, etc. For all these reasons, the poet wishes to live with animals.

(C) Comment on the tone of the speaker when she says ‘Will you please look at me when I’m speaking to you, Amanda!’.
Answer:

• Tone
• exasperated
• irritated
• frustrated
• annoyed

Or words with similar meanings Illustration- Exclamation mark, suggestive of the inherent emotion

Detail Explanation:
The speaker sounds exasperated, irritated, frustrated and annoyed while speaking to the little girl Amanda. Amanda was fed up of constant rebukes and questionings and doesn’t want to answer or pay attention to the speaker.

(D) A ballad includes the telling of a tale as well as a surprise ending. Using evidence from the poem, explain how these features are included in ‘The Tale of Custard the Dragon’. (2)
Answer:
Tale: The poem tells the story of Custard, the dragon (setting, characters, rising action, climax, resolution).

• portrays his life with Belinda and the other pets where he is considered a coward.
• Surprise ending: The end of the poem shows how Custard rose to the occasion; gobbled the pirate and proved his bravery.

Detail Explanation:
A ballad is a story in a poem form where there is a main character and other supporting characters as well. It follows all the elements of a story like setting, characters, rising action, climax and resolution. The poem is about a dragon who was considered coward by Belinda and other pets. But, at the end, it was custard who saved everyone from the pirate.

(E) Which two issues about himself convinced Lomov of his decision to get married? (2)
Answer:
He is expected to marry and cannot stay unmarried

• He ought to lead a quiet, settled and regular life at his age (‘critical age’/ thirty- five).
• He needs a partner as he suffers from palpitations and is always getting upset.

Detail Explanation:
Lomov decided to get married as he couldn’t stay unmarried for long. He was of age, when he thought, he must be leading a settled life. He also suffered from anxiety attacks and palpitations and needed someone to take care of him.

(F) Briefly state how Matilda invited ‘a dreadful life of necessity’ into her family. (2)
Answer:
Matilda’s extreme self-indulgence-dreams of a luxurious life, riches and jewellery

• Doesn’t pay heed to the advice of wearing natural flowers-borrows the necklace- loses it
• In paying for the necklace invited a horrible life of necessity and deprivation/ a life that resulted in a hand-to-mouth existence, Or any other relevant point

Detail Explanation:
Matilda always dreamed of a luxurious life and was not satisfied with her middle- class life. She longed to have riches. She invited misery upon herself when she borrowed her friend’s necklace and lost it. Now, the life became ill for the couple. They borrowed money to compensate the loss and consequently, had to live a life full of hardship and struggle to pay back the loan.

(G) The hack driver successfully trapped the narrator in his web of words. Comment. (2)
Answer:
Hack driver – a conversationalist, cheerful, friendly, open

• befriends the narrator who trusts him for everything he says and does
• asks the narrator to stay behind, himself makes inquiries, offers home-made lunch, mints money
• befools and outwits the narrator in the guise of help

Detail Explanation:
The lawyer was new to the town and the hack driver came across as a friendly, cheerful and an open person, who impressed the lawyer with his sweet talks. The lawyer fully trusted him and did what he said. He never gave a chance to the lawyer to come to the front and ask about the offender. He was a cunning man who outwits the narrator in the guise of help.

Question 7.
Answer ANY TWO of the following in about 120 words each. (4 × 2)
(A) Parents play a crucial role in the upbringing of their children. Critically examine the parents of Bholi and Ebright, highlighting their impact on their children’s lives. (4)
Answer:
Introductory sentence:

• crucial and indelible role played by parents
• parents influence their children both implicitly (indirectly) and explicitly (directly)
• are role models, first teachers, friends, companions, guides

Critical examination (any 3 – 4)

• Richard H. Ebright’s mother- loving, caring, understanding, a friend, a companion
• filled the vacuum in Ebright’s life in his father’s absence
• invested time and energy in his upbringing which made him see heights ofsuccess
• Bholi’s parents—uncaring, indifferent, biased, insensitive, had a patriarchal mindset
• traditional outlook—did not believe in the education of girls, totally indifferent to Bholi and her needs, negLected her
• did not bother to groom her (oil her hair, give her good clothes to wear)
• sent her to school not to educate her but to save their own face
• despite their prosperity, they left Bholi to her own misery, worst was when they decided to marry her off to Bishamber (Accept any other relevant content point that lends itself to critical examination)

Concluding thought:
The contribution and companionship of parents cannot be denied. Love, care, and guidance from parents make a difference, sculpt children and shapes their future.

Detail Explanation:
It is rightly said that home is the first school for a child and it paves the way for future successes. Richard’s mother was highly compassionate, caring, understanding and supportive. She raised Richard alone and she always was like a companion to him. She was the one who developed in him a curiosity and interest about the world around him. She brought him books that inspired Richard. On the other hand, Bholi’s parents were uneducated, biased and uncaring. The totally neglected Bholi was a simple-looking girl. They didn’t believe in educating girls but sent Bholi to school to save themselves from embarrassment. Though they were prosperous enough, they never gave Bholi good clothes or food. And above all that, they decided to marry Bholi to Bishamber, a man almost twice her age. But thanks to her teacher, Bholi was able to get education and could oppose all the wrongs done to her.

It is evident from both the incidents that parents really play a crucial role in shaping the lives of their children. They are the one who guide and motivate their child/children.

(B) Pranjol and Rajvir discuss their next vacation destination. They shortlist Coorg and Goa. Rajvir is keen on Coorg and tries to convince Pranjol. Develop a conversation between the two, based on your understanding of Glimpses of India.
You may begin like this:

• Rajvir: Hey Pranjol! I think we should be visiting Coorg. It is a beautiful place with coffee plantations. I can smell the aroma already!
• Pranjol: I gave you the opportunity to explore a tea plantation last year, in Assam; I want to… (4)
  Answer:
• Rajvir: Hey Pranjol! I think we should be visiting Coorg. It is a beautiful place with coffee plantations. I can smell the aroma already! Pranjol: I gave you the opportunity to explore a tea plantation last year, in Assam; I want to…
• Rajvir: There is a lot more to do in Coorg than smelling the coffee! The place has rainforests, so the megafauna will be worth watching. Not just this, Coorg provides opportunities to indulge in adventure sports like river rafting, rappelling, mountain biking, to name a few. Pranjol: That sounds interesting, but 1 would prefer some serene moments too, away from this post-pandemic hustle-bustle.
• Rajvir: Oh! The answer is Coorg again!
• Pranjol: Oh, come on! You can’t be serious..
• Rajvir: Believe me, I am. Coorg is the place. It has beautiful natural walking trails and the Brahmagiri hills offer a panoramic view I read that the place has the largest Tibetan settlement, so the environment will reflect peace and spirituality, I’m sure.
• Pranjol: Have to say, you’ve presented a fine case in favour of Coorg and convinced me. Let’s plan to leave for Coorg next Wednesday!

(C) Farce is a kind of comedy that includes situations and dialogues that are ridiculous, exaggerated and even absurd. Evaluate the play, ‘The Proposal’, as a farce. (4)
Answer
Introductory sentence:
farcical characters, their ridiculous and odd behaviour, unlikely and exaggerated situations (profuse in the play)

Evaluation: (any 3 – 4)

• humour in the play, improbable situations, childish behaviour of the characters (making a mountain out of a molehill), arguments and quarrels
• hurling of accusations and insults without a second thought
• resolving the differences and fighting again over another topic
• Lomov’s nerve problems and other ailments
• Chubukov’s theatrical statements
• Natalaya’s impulsive and belligerent remarks (Any other relevant evidence)

Concluding Statement:
the manner in which the final proposal is made amidst all the chaos, makes the play a farce.

Detail Explanation:
The play The Proposal’ is a farce were the characters behave oddly and in a ridiculous manner. The events are highly exaggerated giving rise to humour. Though the characters are grown up persons, they behave in a childish manner and are indulged in fights and arguments. They start on a good note but ultimately end up hurling abuses at each other. They insult each other like anything over trivial matters. As soon as one controversial topic ends they come up with another. Lomov’s nervous panic attacks, Chubukov’s theatrical statements and reactions, Natalya’s impulsive remarks all add to the humour.

Finally, the way the proposal is made amidst all the chaos makes the play a farce.

The post CBSE Sample Papers for Class 10 English Term 2 Set 1 with Solutions appeared first on Learn CBSE.

Students can access the CBSE Sample Papers for Class 10 English with Solutions and marking scheme Term 2 Set 2 will help students in understanding the difficulty level of the exam.

CBSE Sample Papers for Class 10 English Term 2 Set 2 with Solutions

Time Allowed: 2 Hours
Maximum Marks: 40

General Instructions:

• The Question Paper contains THREE sections—READING, WRITING & GRAMMAR and LITERATURE.
• Attempt questions based on specific instructions for each part.

SECTION – A
Reading [10 marks]

Question 1.
Read the passage given below.
Call it a blessing or a curse of Mother Nature, we have to breathe in over 10,000 litres of air in a day (more than four million litres in a year) to remain alive. By making it essential for life, God wanted us to keep the air we breathe clean. Everyone can see the food that is not clean and perhaps refrain from eating it, but one cannot stop breathing even if one can feel the air to be polluted.

5. Several harmful and noxious substances can contaminate the air we breathe. Generally, much is said and written about outdoor air pollution, most of which is due to vehicular and industrial exhausts. Given the fact that most of us spend most of our time indoors, it is most important to recognise that the air we breathe in at home or in offices can be polluted. It can be a cause of ill-health. Air pollutants that are generally present in very low concentrations

10. can assume significance in closed ill- ventilated places. .The indoor air pollution can lead to allergic reactions and cause irritation to the skin, the eyes and the nose. But as is logical to assume, the brunt of insult by pollutants is borne by the lungs. It can lead to the development of fresh breathing problems, especially in those who have allergic tendencies, or it can worsen the existing respiratory illnesses like asthma and bronchitis. There can be several sources of indoor air pollution. Tobacco smoke is one of the most

15. important air pollutants in closed places. “Passive smoking” or environmental tobacco smoke (ETS) pollution can lead to all the harmful effects of tobacco smoking seen in the smokers in their non-smoking companions. ETS as a health hazard has been unequivocally proven and is also getting social recognition now. One can occasionally see signs displaying the all-important message: “Your smoking is injurious to my health” in offices and homes.

20. The children of smoking parents are among the worst affected persons. The exposure of young children to ETS leads to increased respiratory problems and hospital admissions as compared to non-exposed children. Several studies, including those done at the PGI, have shown an increased risk of lung cancer among women exposed to passive smoking. ETS also worsens the existing lung diseases like asthma and bronchitis. It may be responsible for the development of asthma in children.

25. The gases are very toxic in high concentrations as may be encountered during industrial accidents, but even in very minimal amounts, as may be prevalent in homes and offices, they can cause irritation to the skin or the eyes, rashes, headache, dizziness and nausea. Improving the ventilation is an important preventive measure, besides trying to eliminate the source that may not be always feasible. Other indoor pollutants are toxic chemicals like cleansing agents, 30.pesticides, paints, solvents and inferior quality personal-care products, especially aerosols. Very old crumbling pipes, boilers, insulation or false roofing can also be important sources. Asbestos is a hazardous product that can cause cancer in humans. It is important to realise that the air we breathe at home may not be clean always and we must try to eliminate the source of pollution. We should give due consideration to ventilation..

Based on your understanding of the passage, answer ANY FIVE questions from the six given below. (1 × 5)
(A) What does the writer mean by using the quote “Your smoking is injurious to my health”? (1)
Answer:
The given phrase is a witty version of ‘Smoking is injurious to health’. By this, the writer means that smoking is risky for the ‘non-smokers’ who inhale the fumes passed on by the ‘smokers’.

(B) Rewrite the following sentence by replacing the underlined phrase with a word that means the same from lines 15-20.
Shalini, without a doubt, is a Manchester City fan. She even got the stadium tickets to go watch the live series. (1)
Answer:
Shalini, unequivocally, is a Manchester City fan. She even got the stadium tickets to go watch the live series.

(C) State a reason for air being contaminated with noxious substances. (1)
Answer:
The chemical industries emitting noxious substances into the air make it contaminated.

(D) Why are the children of smoking parents more prone to ‘hospital admissions’? (1)
Answer:
The children of smoking parents are exposed to ETS which leads to several respiratory disorders. This is why they are more prone to ‘hospital admissions’.

(E) List one reason as to why we should give ‘due consideration to ventilation’? (1)
Answer:
We should give ‘due consideration to ventilation’ because on an average, we spend most of our time indoors, inhaling the trapped contaminated air.

(F) How does the writer justify emphasising ventilation over eliminating the source of pollutant? (1)
Answer:
The writer justifies the given argument by saying that eliminating the sources of pollutants is not feasible as we cannot control the toxic air outside, but can release that trapped air through ventilation from our houses.

Question 2
Read the following excerpt from a case study titled “what is a healthy diet?”
“What is a healthy diet?” Many clinicians find themselves at a loss to answer this common question from patients. The difficulty of offering a simple answer is understandable. The overwhelming volume of data generated by food and nutrition researchers coupled with sometimes contradictory findings, the seeming flip-flops in

5. recommendations, and the flood of misinformation in diet books and the media can make it seem as though explaining the essentials of healthy eating is akin to describing the intricacies of particle physics. That is unfortunate, because there are now enough solid strands of evidence from reliable sources to weave simple but compelling recommendations about diet.

10. In the United States and other developed countries, the average woman can expect to live 80 years or more. With such longevity, it isn’t enough merely to consume the calories needed to sustain the body, build it, and repair it. The foods that supply these calories can influence the risk of developing chronic conditions, which range from heart disease and cancer to osteoporosis and age-related vision loss.

15. Although much remains to be learned about the role of specific nutrients in decreasing the risk of chronic disease, a large body of evidence supports the utility of healthy dietary patterns that emphasize whole-grain foods, legumes, vegetables, and fruits, and that limit refined starches, red meat, full-fat dairy products, and foods and beverages high in added sugars. Such diets have been associated with decreased risk of a variety of chronic diseases.

20. Diet, of course, is just one approach to preventing illness. Limiting caloric intake to maintain a healthy weight, exercising regularly, and not smoking are three other essential strategies. Compelling data from the Nurses’ Health Study which was collected through a questionnaire of 5 questions shared with 100 respondents, show that women who followed a healthy lifestyle pattern that includes these four strategies were 80% less likely to develop cardiovascular disease over a 14-year period. The responses were tabulated (Table 1), for analysis.

Table-1: Awareness level among respondents

25. A companion study, the Health Professionals Follow-up Study, showed that similar healthy choices were beneficial in men, even among those who were taking medications to lower blood pressure or cholesterol. Although much solid information on optimal diets has emerged, the full picture of the relationships between diet and health will take years of further research to fill in. Yet several fundamentals have been established and are unlikely to change significantly.

On the basis of your understanding of the passage, answer ANY FIVE questions from the six given below. (1 × 5)
(A) Why do the food researchers get data coupled with ‘contradictory findings’? (1)
Answer:
The food researchers get data coupled with ‘contradictory findings’ because the data is overwhelmingly wide and may contradict in results from person to person.

(B) Comment on the approaches to prevent illness in line 20-21. (1)
Answer:
The four approaches to prevent illness are dieting, limiting caloric intake, exercising regularly, and quitting smoking.

(C) Why do researchers feel that several fundamentals have been established and are unlikely to change significantly? (1)
Answer:
The researchers feel so because there are many fundamentals of diet which have been studied upon for years and have been proven clinically as well.

(D) Justify the researchers’ suggestions of healthy dietary patterns leading to low risk of chronic diseases. (1)
Answer:
Researchers have done several studies over the years which provided them with a large body of evidence that healthy dietary patterns lead to decreased chronic diseases in people.

(E) Healthy diet helps to prevent the risk of cardiovascular diseases. How does evidence from Table 1 support this statement? (1)
Answer:
In Table 1, we can see that the number of healthy eaters is more than the people who don’t eat healthy diet on a daily basis. This leads to 80% of people saying ‘no’ to ever being diagnosed with cardiovascular diseases.

(F) What purpose does the ‘Can’t Say’ column serve in Q1 of the questionnaire (Table 1)? (1)
Answer:
The ‘Can’t Say’ column is for the people who are unsure of the parameters of the diet being healthy.

SECTION – B
Writing and Grammar (10 marks)

Question 3.
Attempt ANY ONE from (A) and (B).
(A) Study the concept chart from the sports magazine section of a monthly publication.

Write a paragraph in not more than 120 words, analysing the listed situations due to the global pandemic. (5)
Answer:
In recent times, people had become more conscious about their health and started • to change their lifestyle. Doing yoga, going to a gym, seeking alternative therapies are some of the activities that people of all age groups indulge in to keep themselves fit and healthy. Moreover, after a stressful day, it is considered a good idea to unwind by going to theatre with friends or family. Flowever, COVID-19 has drastically changed the way we live today.

Due to the global pandemic, all these activities have become the things of the past. Keeping indoors is the new norm to be healthy. What about those outdoor enthusiasts who miss their routine of going for a morning walk or weekly outings with friends? The sports industry is on the top of the list, getting badly affected due to the restrictions on sports activity.

But we can still take care of our health by indulging in some activities that we can do at home. You can exercise in the garden or backyard of the house. Those who live in apartments can walk in the balcony or on terrace. Doing pranayama or breathing exercises is also highly beneficial in keeping us fit. Furthermore, there are many apps that provide online classes in yoga and other workouts both free and paid. So while we hope for the good time to return, let’s not miss out on our favourite activities.

(B) You are Somya/Sahil, a resident of Modern Colony, Kanpur. You come across the following information on a local library’s notice board.

As you want to be a choreographer, write a letter to the Director, National School of Dance, Kanpur, in about 120 words, seeking information about their courses, duration, admission procedure, eligibility criteria and other details. (5)
Answer:
B-23, Modern Colony
Kanpur
10^th August, 20XX
The Director
National School of Dance
Kanpur
Subject: Inquiry regarding a choreography course

Dear Sir/Madam
I came across your advertisement regarding the courses in choreography offered by your institute and want to state that I have passed my higher secondary exams. I am very much interested in dancing and want to learn the classical dance. I have heard much about your institution and the classes.

Kindly send me the prospectus and the application form so that I can choose the timings best suited to me. I would be thankful if you could provide me with the following information:

• Timings
• Fees
• Admission procedure
• Eligibility criteria

Hope to get the information soon.
Thanking you

Yours sincerely
Somya/Sahil

Question 4.
The following paragraph has not been edited. There is one error in each line. Identify the error and write its correction against the correct blank number. Remember to underline the correction. The first one has been done for you. (1 × 3)

The students that were fighting for The flowers or fruits that they plucked all both the things were in plenty, the Teacher called the student and asked him to

Answer:

Explanation:
(a) The students plucked both the flowers and the fruits, not any one of them. Hence, this is the right answer.
(b) ‘As’ both the things were in plenty, the students were fighting to get them. All makes no sense here. Hence, this is the right answer.
(c) The teacher didn’t call any specific student. It could be any random person. Hence, this is the right answer.

Question 5.
Read the conversation between a teacher and student and complete the passage that follows.

John was annoyed as he couldn’t enjoy the Cars monthly issue digitally.
So, his mom (a) ………………… She knew that
John was (b) ………………… so she went to the store and got that book for him. John got happy and thanked his mother. (1 + 1)
Answer:
(a) surprised him with a physical book
(b) annoyed with the e-book

SECTION – C
Literature (20 marks)

Question 6.
Answer ANY SIX questions in 30-40 words each. (2)

(A) What were Valli’s emotions when the elderly man expressed concern that she was standing on the bus seat? (2)
Answer:
Valli was fairly displeased when the elderly man expressed concern that she was standing on the bus seat. She was annoyed by the way she was treated like a little child in the bus.

(B) Custard’s reaction was different from that of others, on seeing the pirate. Using evidence from the poem, explain how this difference is represented in ‘The Tale of Custard the Dragon’. (2)
Answer:
Belinda’s other pets always teased Custard and called him a coward, but Custard was the only one who stood up to fight the pirate when he broke in. The others ran away to save themselves.

(C) Justify the poet’s allusion to Rapunzel in the poem ‘Amanda’. (2)
Answer:
The poet in the poem ’Amanda’, uses allusion to depict that Amanda knows that as Rapunzel let her hair down, she was freed from the confines of the castle. However, Amanda wishes to live alone without any disturbance so unlike Rapunzel, she doesn’t want to escape.

(D) What does the poet Walt Whitman suggest by saying that ‘they do not sweat and whine about their condition’ in the poem ‘Animals’? (2)
Answer:
In the poem, the poet Walt Whitman said this phrase with reference to the animals. By this, he suggests that animals are satisfied and content with whatever they have in their lives. They do not cry about the situation they deal with.

(E) When the writer says, ‘Baking was indeed a profitable profession in the old days’, what did he mean? (2)
Answer:
Through the given statement, the writer wants us to know that the eaters of the Portuguese bread have reduced in numbers today. This indicates that baking as a profession is now no longer that profitable which it used to be in the olden days.

(F) Comment on the tone of Mme Frostier when said to Matilda, “Choose, my dear”. (2)
Answer:
The tone of Mme Frostier was benevolent. When Frostier heard the story of Matildas distress, she felt the desire to help and thus, offered her jewels box to choose from.

(G) Mr Weiherer was pleased that Richard Ebright not only put in the nightly research hours towards butterflies, but also his other interests. Comment. (2)
Answer:
Mr Weiherer was pleased that Richard was able to balance his academics along with his hobbies. He was impressed with both Richard’s commitment to work and his hobbies. He wanted Richard to grow as a well-rounded personality.

Question 7.
Answer ANY TWO of the following in about 120 words each. (4 × 2 = 8)
(A) Natalya and Ivan argued about the ownership of Oxen Meadows and the superiority of their respective dogs in the play, The Proposal. Based on your understanding of the personality traits reflected through the given points of arguments of Natalya and Ivan, develop a conversation, showcasing another argument between them.
You may begin like this:
Natalya: Hello, Ivan. I wasn’t expecting you to be here.
Ivan: Hello, I am equally surprised to see you here.
Natalya: Why are you surprised? …………………. (4)
Answer:

• Natalya: Hello, Ivan. I wasn’t expecting you to be here.
• Ivan: Hello, I am equally surprised to see you here.
• Natalya: Why are you surprised? I come here often, rather I thought this wasn’t something a person like you would like. Ivan: Well, if you come here often then you should have known that I am a member of the book club here. How much you do Like to lie! What else can one expect from someone who likes to stake claim to things belonging to others.
• Natalya: Are you sure you are not talking about yourself? After all, you lay false claim to own Oxen Meadows which have been in our family for generations. And I don’t believe you come here often, as they have a policy against allowing drunks in here.
• Ivan: That’s it. I am going to take this matter to court now.
• Natalya: Yes and then the truth will come out!

(B) Bholi’s evolution from a ‘dumb cow’ to saying ‘no’ to marry Bishamber was a great journey. Examine her journey highlighting her stand for herself. (4)
Answer:
The journey of Bholi’s evolution from a ‘dumb cow’ to a ‘masterpiece’ clearly showcases the idea of being an individual who is not being exploited by people or circumstances. Initially, Bholi was considered a simpleton and people compared her to a dumb cow. Bholi could not speak till she was five, and when at last she learnt to speak, she stammered. Children made fun of her which had an adverse effect on her self-confidence. Bholi’s teacher understood her need for love and gently guided her. Under her teacher’s gentle guidance, Bholi blossomed into a confident young girl who believed in her own self-worth. Eventually, she was able to stand up for herself and raise her voice against the social evil of dowry. Hence, she at once said no to the proposal of the greedy Bishambhar who asked money to marry her.

(C) It is a bitter truth that death is immortal and would come to all. Evaluate the chapter ‘Sermon at Benaras’ with reference to the given statement. (4)
Answer:
In the chapter, ‘Sermon at Benaras’, Kisa Gotami was completely beset with grief after the loss of her only son. All the people made her learn that her grief and lament could not bring his son back to life. She has to bear the loss to live in peace. Yet, Kisa failed to learn the lesson. Then, to get his son back, Kisa went to Buddha, who told her to get mustard seed from a house that had never lost any one to death and once she would get that, he would bring her son back to life.

When she went looking for the mustard seeds, she learnt that each house had lost a loved one to death. She finally learnt in the second time that if one wants peace, then he/she must get rid of lamentation, complaint and grief as death is immortal and would come to all.

The post CBSE Sample Papers for Class 10 English Term 2 Set 2 with Solutions appeared first on Learn CBSE.

Students can access the CBSE Sample Papers for Class 10 English with Solutions and marking scheme Term 2 Set 3 will help students in understanding the difficulty level of the exam.

CBSE Sample Papers for Class 10 English Term 2 Set 3 with Solutions

Time Allowed: 2 Hours
Maximum Marks: 40

General Instructions:

• The Question Paper contains THREE sections—READING, WRITING & GRAMMAR and LITERATURE.
• Attempt questions based on specific instructions for each part.

SECTION – A
Reading [10 marks]

Question 1.
Read the passage given below.
Have you ever failed at something so miserably that the thought of attempting to do it again was the last thing on your mind?
If your answer is yes, then you should understand that you are not a robot. Unlike robots, we human beings have feelings, emotions, and dreams. We are all meant to grow despite

5. our circumstances and limitations. Flourishing and trying to make our dreams come true feels great when life goes our way. But what happens when it does not? What happens when you fail despite all your hard work? Do you stay down and accept defeat or do you get up again? If you tend to persevere and keep going, you have what experts call grit’.

10. Falling down or failing is one of the most agonising, embarrassing, and scary human experiences. But it is also one of the most educational, empowering, and essential parts of living a successful and fulfilling life. Did you know that perseverance (grit) is one of the seven qualities that has been described as the key to personal success and betterment in society? The other six are curiosity, gratitude, optimism, self-control, social intelligence, and zest.

15. Thomas Edison is an example of grit for trying more than 1,000 times to invent the light bulb. If you are reading this with the lights on in your room, you will realise the importance of his success. When asked why he kept going despite hundreds of failures, he merely stated that they had not been failures, they were hundreds of attempts towards creating the light bulb. This statement not only revealed his grit but also his optimism for looking at the bright side.

20. Grit can be learnt to help you become more successful. One of the techniques that help is mindfulness. Mindfulness is a practice that makes an individual stay at the moment by bringing awareness of his or her experience without judgement. This practice has been used to quieten the noise of fears and doubts. Through this simple practice of mindfulness, individuals have the ability to stop the self¬sabotaging downward spiral of hopelessness, despair, and frustration.

25. What did you do to overcome the negative and self-sabotaging feelings of failure? Reflect on what you did, and try to use those same powerful resources to help you today..
On the basis of your understanding of the passage, answer ANY FIVE questions from the six given below. (1 × 5)
(A) What does the writer mean by saying that it feels great when ‘life goes our way’? (1)
Answer:
By the given phrase, the writer means that a human feels great when his life goes according to his plans and expectations.

(B) Rewrite the following sentence by replacing the underlined phrase with a word that means the same from lines (20-25).
Amit’s behavior of preventing himself from reaching his goals purposely, will make him regret in future. (1)
Answer:
Amit’s behaviour of self-sabotaging, will make him regret in future.

(C) State the meaning of ‘social intelligence’ as implied in the passage. (1)
Answer:
In the passage, ‘social intelligence’ means knowing oneself and others. It includes an individual’s ability to understand, and act on, the feelings, thoughts, and behaviours of other people in the society.

(D) How does mindfulness helps in ‘quietening the noise of fears and doubts’? (1)
Answer:
Mindfulness focuses one’s awareness on the present moment, while calmly acknowledging and accepting one’s feelings, thoughts, and bodily sensations, used as a therapeutic technique. This way it helps in ‘quietening the noise of fears and doubts’ in one’s mind.

(E) List two reasons as to why humans are ‘unlike robots’. (1)
Answer:
Humans are ‘unlike robots’ as humans have emotions and they have their own thought-process which robots do not possess.

(F) How does the writer justify ‘failure’ in a positive light? (1)
Answer:
The writer justifies ‘failure’ in a positive Light by saying that failure is the road to success. It makes a person full of grit to work upon himself in order to achieve success in life.

Question 2.
Read the following excerpt from a case study titled ‘The Rising Obesity’.
An epidemic of obesity or being overweight is affecting many countries in the world; more than 300 million people are obese or overweight. Obesity could be for a particular reason. In India, some people tend to be overweight because of their high calorie diet and lack of physical activities. In the United States, obesity is more prevalent in lower income groups. Obesity is now well recognised as a disease in its own right.

5. Though obesity commonly means being overweight, it is defined as an excess amount of body weight that includes muscles, bones, fat and water. Obesity’ specifically refers to an excess amount of body fat. A certain amount of body fat is needed to store energy, keep warm and absorb the shocks. Usually men with more than 25% body fat and women with more than 3.5% body fat are regarded as obese. Obesity tends to run in families suggesting a genetic cause. Environmental factors include lifestyle behavior such as

10. what a person eats and his or her level of physical activity. So, one should choose more nutritious food which is low in fat, and helps us to become more active.

There are psychological factors like negative emotions such as boredom, sadness and anger which act as the main culprits. Then there is also ‘binge eating’, i.e. when people eat large amounts of food thinking that it is beyond their control how much they eat. A study was collected through a questionnaire of 5 questions shared with 120 respondents, show that those with the most severe binge eating problem are also likely to have more
symptoms of depression and low self-esteem. The responses were tabulated (Table 1), for analysis of Obesity in people.

15. Obesity is a health hazard giving rise to many serious medical conditions like type 2 diabetes, heart disease, high blood pressure and stroke. Obesity is also linked to a higher rate of certain types of cancer. There are many ways of losing weight but exercise is the best way to do this as it is free from any type of harmful side effects.

On the basis of your understanding of the passage, answer ANY FIVE questions from the six given below. (1 × 5)
(A) Why does the writer call obesity an ‘epidemic’? (1)
Answer:
The writer calls obesity an ‘epidemic’ as it is spreading in many countries of the world at a fast pace, affecting millions of people.

(B) Comment on the significance of physical activity’ in the lines 9-11. (1)
Answer:
‘Physical activity’ is a crucial environ-mental factor that makes a person more active and less likely to turn obese.

(C) Justify the writer’s recommendation of choosing exercise over other means of losing weight in the lines 15-18. (1)
Answer:
The writer has fushfied his recommendation by calling it free of any harmful side-effects which other forms of weight loss might show.

(D) Why does the writer feel that psychological factors are the main culprit for giving birth to ‘obesity’? (1)
Answer:
The writer feels so because psychological factors like anger, sadness and boredom lead a person to opt for eating more in order to satisfy or ignore these bad feelings. It’s in itself a psychological phenomenon.

(E) Often people with obesity believe that they are not in control of their desire to eat. How does evidence from Table 1 support this statement? (1)
Answer:
In Table 1, we can see that the number of people saying ’no’ when asked if they can controL their cravings to eat are more, proves that majority of them feel that they can’t control their desire to eat.

(F) What purpose does the ‘Can’t Say’ column serve in Q5 of the questionnaire (Table 1)? (1)
Answer:
The ‘Can’t Say’ column is for the people who don’t know how exactly do they feel or what is the right name for the feeling that they have on mind.

Section – B
Writing And Grammar (10 marks)

Question 3.
Attempt ANY ONE from (A) and (B).
(A) Study the concept chart from the HIS Market Analysis of the number of Americans travelling for the thanksgiving holiday in the years 2020 and 2022 and their comparison.

Write a paragraph in not more than 120 words, analysing the given information. (5)
Answer:
Given the topsy-turvy times of the Covid-19 . pandemic, the number of Americans who are planning to travel home for Thanksgiving has been reduced to 5% in the year 2021, in comparison to the year 2020 where the number was 16%. There is a sharp decline in using other modes of travel in the year 2021 as well due to the safety reasons. Despite the pandemic, airplane travel in 2020 was still 50 per cent lower than pre-pandemic. Moreover, Americans are more likely to feel safe and comfortable driving during the pandemic than take public transportation. By far, car travel—the most popular mode of travel during Thanksgiving—was the least affected in the year 2020 and 2021. The fear of COVID-19 continues to linger even after two years. Therefore, it is advised to attend gatherings only with vaccinated friends and family, follow proper hygiene protocols and wear masks when in a crowded indoor setting too.

(B) You are Amit/Amita, Secretary of Delhi Public school, Preet Vihar, New Delhi. You come across the following information on an advertisement.

You need some sports material for the Sports Club of your school. Write a letter to the Manager of Arena Sports Goods, in about 120 words, placing an order for the same. Provide and enquire about all required details. (5)
Answer:
Delhi Public School
PreetVihar
New Delhi

19th January 20XX
The Manager
Arena Sports Goods
Darya Ganj
New Delhi

Subject: Ordering for sports goods Dear Sir/Ma’am
We are in need of some sports items for the Sports Club of our school. Kindly send the following items at the earliest.

Please check that all the items should be of good quaLity, fine condition, well-packed and delivered soon. The payment will be mode by cash once we receive the items. We hope to get the goods as per our specifications mentioned in the mail.
Yours sincerely
Amit/Arnito

Question 4.
The following paragraph has not been edited. There is one error in each line. Identify the error and write its correction against the correct blank number. Remember to underline the correction. The first one has been done for you. (1 × 3)

I can’t never forget my P. T. teacher who had for the healthy habit of daily morning walk. He should get up early and shall go out for a brisk walk.
Even when he wouldn’t be fit, nothing can stop him from going fot it.

Answer:

(a) Explanation: ‘should’ represents what is to be done while ‘would’ represents what was done. Hence, this is the right answer.
(b) Explanation: As the person is describing the teachers past routine, would will be used. Hence. this is the right answer.
(c) Explanation: Since the sentence is in the past tense, this is the right answer.

Question 5.
Read the conversation between a teacher and student and domplete the passage that follows.
Grandpa: Do you know that our ancestors were not much different from us? ALSO, learning from first-hand experience such as visiting a historical site or a museum helps one gain more information.
Salma: Oh yes Grandpa! I can easily recall facts aboutthe things that I learnt at the City History Museum.
Salim: We were shocked by looking at the actual size of a Mammoth there!
Salim and Salma were talking to their grandfather. He was telling them about their ancestors. He told them that they were not different from them.
He (a) ……………..learning from first-hand experience like visiting a historical site or a Museum helps one gain more information. To this, Salima
(b) …………….what she learnt about the City History Museum. (1 + 1)
Answer:
(a) also told them that
(b) added that she remembers

Section -C
Literature (20 marks)

Question 6.
Answer ANY SIX questions in 30-40 words each.
(A) What is the significance of the line that a baker enjoys in a Goan village? (2)
Answer:
A baker or a pader is of great significance in a Goan village as no important occasion or festival is complete without the use of bread or cakes from the baker.

(B) Justify the message for the parents that the poet is trying to convey through the poem ‘Amanda’. (2)
Answer:
The poet conveys a very important message to the parents through ‘Amanda’. The way Amanda is being constantly nagged, she feels that her freedom has been curtailed. Children must be allowed more liberty by parents. Excessive nagging makes them defiant and they turn a deaf ear to the instructions of the elders.

(C) Comment on the tone of Belinda when she cried, “Help! Help!”. (2)
Answer:
The tone of Belinda when she cried was anticipation. She was anticipating for help because she was afraid of the pirate and there was none around to help her as they ran away.

(D) Animals are greedy in nature, unlike humans. Using evidence from the poem, explain how this quality is represented in ‘Animals’. (2)
Answer:
In the poem, ‘Animals’, the poet says that not one animal is demented with ‘the mania of owning things’. This means that animals are not dissatisfied like humans who are greedy and materialistic in nature.

(E) How did Buddha teach Kisa Gotami the truth of life? (2)
Answer:
Buddha asked Kisa Gotami to bring a handful of mustard seeds on a condition that the seeds must be from a house where people had not lost a loved one to death. Kisa Gotami’s futile search made her realise the bitter truth that losses and sorrows are par-t and parcel of life and one can attain peace only by acceptance.

(F) Briefly state why did the lawyer ‘hate’ his work. (2)
Answer:
The lawyer hated his work as he was offered the unpleasant job of serving the summons to criminals who used to live in the dirty and shadowy corners of the city. He would even get beaten up sometimes on his job.

(G) Matilda’s expectation of a rich ife made her suffer incessantly. Comment. (2)
Answer:
Matilda believed that she deserved a better life. She expected to have her life filled with all delicacies and luxuries. But, in reality, she suffered from poverty and lived in a house with shabby walls and worn chairs that made her’ angry and suffer incessantly.

Question 7.
Answer ANY TWO of the following in about 120 words each.
(A) The concept of ‘marriage of convenience’ is still practised in different parts of world. Critically examine the relation between Lomov and Natalya, highlighting their stance on it. (4)
Answer:
A ‘marriage or convenience’ is a marriage where two people come into a relationship out of a specific reason and circumstances. They do not base their relation on any bond of love or courtesy. Under such marriages, people have a planned motive that could be anything like a political move, economic move or others. In such marriages, the demerits of the partners are overlooked. The relation between Lomov and Natalya was also a ‘marriage of convenience’. Even though both of them hated each other, they were ready to get married to each other only because of their prevailing circumstances. Lomov was a mature man of thirty-five years who had several ailments. He decided to compromise by marrying Natalya. Natalya, on the other hand, was a twenty-five year old lady who desperately wanted to get married to anybody. Hence, both decided to go for this ‘marriage of convenience.

(B) Rajvir was so excited with his first-ever experience of visiting Assam. As his brother could not accompany him on the trip, Rajvir shares his experience to his brother. Develop a conversation where Rajvir shares the details to his brother about his holidays with Pranjol in Assam, on returning home, based on your reading of the chapter, ‘Tea from Assam’. (4)
Answer:

• Rajvir: Oh dear, what a fun-filled trip it was! Although I had researched a lot about tea and its consumption before going to Assam but I learned even more about it when I saw it with my own eyes.
• Rajvir’s Brother: Brother, tell me some facts about tea.
• Rajvir: Sure! Do you know that the world’s largest concentration of tea plantations is in Assam? One can see tea gardens everywhere there. Also, the best yield of tea is in the second-flush or sprouting season, i.e. between May and July.
• Rajvir’s Brother: That’s wonderful!
• Rajvir: Certainly. It’s an art. I’m glad I took the decision to join Pranjol and his family for this trip.
• Rajvir’s Sister: Yes, but next time, take me along with you too.
• Rajvir: Okay

(C) “Life isn’t about finding yourself. Life
is about creating yourself.” Reflecting on George Bernard Shaw’s message as given above, evaluate on how the story of ‘Bholi’ highlights the condition of girls across the country and gives out a strong message. (4)
Answer:
Bholi is a shy and timid girl who faces ridicule on account of her looks. Her parents consider her a burden as they feel her looks will make it difficult for them to find a suitable match for her. Her parents don’t send her to school as they think she is dumb and hence, call her ‘Bholi’, which means stupid. However, Bholi proves everyone wrong and blossoms under the nurturing of her teacher. Her parents still follow the old traditions and fix her marriage with a lame old man. True to the hypocritical practice of the society, the old man asks for dowry as Bholi is not pretty. The same is seen in our society on a regular basis. Girls are married off without consent or tortured for not bringing sufficient dowry. Bholi stands up for herself and refuses to marry the old man, giving the strong message that girls must become independent and self-reliant. Thus, she rises above the material and social conditions of the society she inhabited and created a unique identity for herself by believing in the value of self-reliance.

The post CBSE Sample Papers for Class 10 English Term 2 Set 3 with Solutions appeared first on Learn CBSE.

Students can access the CBSE Sample Papers for Class 10 English with Solutions and marking scheme Term 2 Set 4 will help students in understanding the difficulty level of the exam.

CBSE Sample Papers for Class 10 English Term 2 Set 4 with Solutions

Time Allowed: 2 Hours
Maximum Marks: 40

General Instructions:

• The Question Paper contains THREE sections—READING, WRITING & GRAMMAR and LITERATURE.
• Attempt questions based on specific instructions for each part.

SECTION – A
Reading (10 Marks)

Question 1.
Read the passage given below.
Evolution has designated vultures to be the ultimate scavengers. Enormous wingspans allow them to circle in the air for hours. Their beaks, while rather horrifying, are weak by bird standards, made to scoop and eat flesh. However, unappealing they may seem, vultures serve an important role in the ecological cycle: processing the dead bodies of animals.

5. Only 20 years ago, India had plenty of vultures-flocks so enormous they darkened the skies. But by 1999, their numbers had dropped due to a mysterious kidney ailment. By 2008, 99.9 per cent of India’s vultures were gone. It was finally discovered that they had been killed by a drug called diclofenac (a pain reliever along the lines of aspirin or ibuprofen). Indians revere their cows, and when a cow showed signs of pain, they treated it with

10. diclofenac After the animal died, the vultures would eat the corpse. And though they boast perhaps the world’s most efficient digestive system, vultures cannot digest the drug.
India banned the use of diclofenac for veterinary use in 2006, but it’s still widely used. The near-extinction of vultures has caused disease in the country, as rats and dogs moved in to take their place—spreading pathogens that would have otherwise been destroyed by the vultures.

15. Vultures need large ranges to scan for food and undisturbed areas in which to nest. They also need an abundance of prey species since they rely more on chance than their own hunting skills to eat All of these things have been reduced by human activity. Meanwhile, there is a dramatic increase in secondary poisoning. Vultures feed on carcasses laced with poison, intended to kill jackals or other predatory carnivores So, they are poisoned by the 20. lead in animals left behind by hunters.

Based on your understanding of the passage, answer ANY FIVE questions from the six given below. (1 × 5)
(A) What does the writer mean bg saging that vultures’ flock once “darkened the skies”? (1)
Answer:
By the given phrase, the writer means that there was a time when flocks of vultures used to be so large that the sky would appear black due to the huge number of the black big birds flying together.

(B) Rewrite the following sentence bg replacing the underlined phrase with a word that means the same from lines 15-20.
The gift box was filled in with a varietg of exotic chocolates. It made her dag! (1)
Answer:
The gift box was laced with a variety of exotic chocolates. It made her day

(C) State the meaning of ‘moved in to take their place’ as implied in the passage. (1)
Answer:
In the passage, ‘moved in to take their place’ means that the near-extinction of vultures has made the rats and dogs move in or replace the vultures to take their place of dismantling the dead carcasses.

(D) How did the extinction of vultures promote the “spread of pathogens”? (1)
Answer:
After the vultures’ extinction, rats and dogs moved in to take their places, spreading pathogens that would have otherwise been destroyed by the vultures.

(E) List two reasons as to why vultures got extinct. (1)
Answer:
Vultures got extinct as they fed upon the dead bodies of animals that had ‘diclofenac’ in their bodies. The other reason is their feeding on dead carcasses of predatory carnivores, laced with poisons which were intended to kill the later.

(F) How does the writer justify the world’s most efficient digestive sgstem’s ‘failure’? (1)
Answer:
The writer justifies the world’s most efficient digestive system’s ‘failure’ by saying that even after eating the deadly corpses, vultures’ digestive system couldn’t sustain the dreadful drug ‘diclofenac’.

Question 2.
Read the following excerpt from a case study titled sustainable Tourism.
The UN’s 2017 International Year tells that sustainable tourism is an important tool for development, most importantly in poor communities and countries. Today sustainability – environmental, social, and economic – is increasingly recognised as the benchmark for all tourism business. As noted by the UN World Tourism Organisation, 57% of international tourist arrivals will be in emerging economies, by 2030.

5. The various ‘Tourism Terms’ are defined as follows:


On the basis of data collected by a survey by Travel Bureau, the following market profile of an ecotourist was constructed:
Age: 35-54 years old, although age varied with activity and other factors such as cost.
Gender: 50% female and 50% male, although clear differences based on activity were found.
Education: 82% were college graduates, a shift in interest in ecotourism from those who

10. have high levels of education to those with less education was also found, indicating an expansion into mainstream markets.
Household composition: No major differences were found between general tourists and experienced ecotourists**
Party composition: A majority (60%) of experienced ecotourism respondents stated

15. they prefer to travel as a couple, with only 15% stating they preferred to travel with their families, and 13% preferring to travel alone. (** experienced ecotourists = Tourists that had been on at least one “ecotourism” oriented trip.)
Trip duration: The largest group of experienced ecotourists – (50%) preferred trips lasting 8-14 days.

20. Expenditure: Experienced ecotourists were willing to spend more than general tourists, the Largest group (26%).

Important elements of trip: Experienced ecotourists top three responses were: (a) wilderness setting, (b) wildlife viewing, (c) hiking/trekking.
Motivations for taking next trip: Experienced ecotourists top two responses were (a) enjoy 25. scenery/nature, (b) new experiences/places.

On the basis of your understanding of the passage, answer ANY FIVE questions from the six given below. (1 × 5)
(A) Why does the writer call sustainability the ‘benchmark’ for all tourism business? (1)
Answer:
The writer calls sustainability the ‘benchmark’ for all tourism business as it is recognised as a standard or referral point for comparison within the different communities or countries.

(B) Comment on the significance of ‘gender ratio’ as given in the line 8. (1)
Answer:
‘Gender ratio’ shows a great significance in the equality among both the male and female visitor as the ratio is 1:1.

(C) Justify the survey’s information of increase in ecotourism from the lines 9-11. (1)
Answer:
The survey justifies the information of increase in ecotourism by stating that a shift in interest in ecotourism from those who have high levels of education to those with less education was also found, indicating an expansion into mainstream markets.

(D) Why do you feel that experienced ecotourists prefer travelling in couples to travelling alone? (1)
Answer:
I feel that experienced eco-tourists prefer travelling in couples to travelling alone as the trip offers adventures like hiking, wildlife viewing, trekking, etc., which is more enjoyable with partners than doing these activities all alone.

(E) The tourism to a destination that makes its poor people earn benefit, has a whole separate category of tourism. How does evidence from Table 1 support this statement? (1)
Answer:
In Table 1, we can see that the tourism that results in increased net benefit for the poor people in a destination falls under a separate category known as ‘Pro-poor tourism’.

(F) What idea does the table in the passage highlight? (1)
Answer:
The idea highlighted by the table in the passage is the diversity in the field of tourism.

SECTION – B:
WRITING AND GRAMMAR (10 marks)

Question 3.
Attempt ANY ONE from (A) and (B).
(A) Study the concept chart from the survey done by the Entertainment Software Association in 2020, that was found that age doesn’t have anything to do when it comes to playing video games.

Write a paragraph in not more than 120 words, analysing the given information. (5)
Answer:
A very common myth that revolves around video games is that it is restricted to primarily kids, young or only male audiences. However, as you can see in the flow chart provided by the survey that was conducted on the people that play video games, the picture is far different. According to the Entertainment Software Association, video games are neither a youth hobby nor a male-dominated activity. In fact, women account for 41% of all gamers in the world. People between the age group of 18 to 34 years hold the largest share of game enthusiasts. And, the average age bar of video game players is between 35 and 44 years old.

Furthermore, there were 214 million+ video game users in the world in the year 2020. This helps to explain why video games have become the most popular and the fastest-growing form of entertainment in the recent years, not only for young kids and males but also for older generation and females.

(B) You are Jyoti/Jaivik, the Manager of a famous coaching institute, Pune. You come across the following advertisement of a furniture house.

Write a letter to Comfort Furniture House placing order for some furniture items to be supplied immediately in about 120 words. (5)
Answer:
Singhal Coaching Classes
New Friends’ Colony
New Delhi

25^th February 20XX

The Manager
Comfort Furniture House
New Delhi

Subject: Placing an order for furniture
Dear Sir
I am writing this Letter to order some furniture items for my coaching centre. Kindly send the best rate list for the following items urgently at the mail address mentioned below:
Singhall098@yahoomail.com

Please ensure that all the items are of best quality and of good finish. Take care to furnish us with the quotation as soon as possible as we need these items urgently. We hope to have a positive and suitable response.
Thanking you
Yours sincerely
Jyotika/Jaivik

Question 4.
The following paragraph has not been edited. There is one error in each line. Identify the error and write its correction against the correct blank number. Remember to underline the correction. The first one has been done for you. (1 × 3)

My father shall insist on taking greens everyday
Children may consume it regularly
otherwise they should suffer from
iron deficiency. Elders will also take it every day
but there are some individuals who do not like it.
Answer:
(a)

Explanation: ‘may’ represents choice while here, the father suggests that children should definitely take the greens. So, ‘must’ is the right answer.

(b)

Explanation: As the statement is a future expectation, ‘will’ will be used. Hence, this is the right answer.

(c)

Explanation: As for elders, it is only a recommendation; ‘should’ is the right answer.

Question 5.
Read the conversation between a teacher and student and complete the passage that follows.
Tim: My wife’s angry!
Max: why?
Tim: She never tells me the reason, she rather gives me the silent treatment. That used to bother me earlier, but now I just look at it as a brief holiday!

Tim told Max that (a) …………. When Max asked him about the reason, he said that she (b) …………… she was angry and rather gave him the silent treatment. He also said that earlier it bothered him but now he look at it like a brief holiday. (1 + 1)
Answer:
(A) his wife was angry at him
(B) never told him the reason when

Section – C:
Literature (20 Marks)

Question 6.
Answer ANY SIX questions in 30-40 words each. (2 × 6)

(A) What was the significance of Oliver Lutkins’ shrewdness? (2)
Answer:
The lawyer from New Mullion who was assigned the task of serving summon on Lutkins could not serve.

(B) Justify the children’s excitement about the bread. (2)
Answer:
The children looked forward to the baker’s visit and as soon as he would come, they would surround him. When they were not able to see what was inside the basket, they would climb on a bench and peep into the basket to get the sweet fragrance of the bread.

(C) Comment on the tone of Ramlal when he said to Bholi, “What’s the matter with you, you fool?” (2)
Answer:
The tone of Ramlal in the given statement is frustration. This was because Rampal hoped that Bholi would oblige him and would go to school but she refused to go to school in fear.

(D) People often make judgments about others on the basis of their superficial characteristics or appearances which are not always correct. Using evidence from the poem, explain how this concept is represented in ‘A Tale of Custard the Dragon’. (2)
Answer:
In the poem, ‘A Tale of Custard the Dragon’, Belinda and her pets believed Custard to be a coward. But, in reality, when the pirate broke in the house, it was Custard who saved Belinda and her pets from him buy fighting very bravely, proving the judgment wrong.

(E) What special privilege has been accorded to the people of Coorg? (2)
Answer:
There is a special privilege that people of Coorg has been accorded. They do not need to acquire licence to carry weapons with them because they were permitted to carry fire arms without licence.

(F) Briefly state why the poet in ‘Animals’ believed the animals to be successful to carry virtues that man lost. (2)
Answer:
According to the poet in ‘Animals’, man used to have values and qualities. But, with the passage of time, he shed all those good qualities that he possessed and became an uncivilized beast. However, the animals have been successful to carry the similar virtues that they had in them.

(G) Amanda is a school-going girl who is constantly nagged by her mother. Comment. (2)
Answer:
Amanda is a young school-going girl who is constantly nagged by her mother. Amanda is being given instructions with a long list of dos and don’ts that she is asked to follow every now and then. As a result, she felt that her freedom had been limited by her mother.

Question 7.
Answer ANY TWO of the following in about 120 words each.
(A) People accept males with a lot of shortcomings but females are always neglected if they have a single disability. Critically examine the given concept based on your reading of ‘Bholi’, highlighting how Bholi’s take on it. (4)
Answer:
It is a generic nature of the society that it accepts a falty male easily bt it never accepts a less-able female. In the chapter, ‘Bholi’, Bholi was considered dumb and had marks on her face so, her parents were worried that no one would marry an ordinary-looking girl who had pock marks on her face.

(B) Valli sneaked out of the house when her mother was asleep. Her mother didn’t get to know that Valli was out for a bus ride all alone. Develop a conversation between Valli and her mother on Valli’s return to home, based on your understanding of ‘Madam Rides the Bus’. (4)
Answer:

• Mother: Valli! Where were you the whole afternoon?
• Valli: Amma, I was at our neighbour’s house. I had gone to play with their children.
• Mother: Don’t you lie Valli! I asked the neighbours about you but they had no idea. I searched for you everywhere. Tell me, where were you the whole time?
• Valli: (frightened) Amma, I L.had gone for
  a bus ride in the same bus that goes to the nearest town every day. I didn’t want to tell you as I thought you wouldn’t let me do it. Mother: (angrily) I am shocked, Valli. Don’t you ever think of travelling alone. I won’t tolerate this ever again.
• Valli: I am so sorry Amma. I won’t ever repeat it.

(C) Chekov has used humour and exaggeration in the play to comment on courtship in his times. Evaluate with examples from the lesson, ‘The Proposal.’ Also mention the values, you think, any healthy relationship requires. (4)
Answer:
“The Proposal” is one of Anton Chekov’s famous plays where he uses humour and exaggeration in the play to provide a commentary on courtship in his times. Chekov has used several stereotypes that help play the character’s part beautifully in the portray. Lomov, Natalya ‘the shrew’, Chubukov ‘the hypocrite father’ all help in adding humour to the play.

Lomov uses exaggerated actions that, sometimes exceeds the limits of common sense like, Lomov gulping down water, putting his hand to the heart or running to the door and staggering out. Another interesting aspect of this storytelling is how the story progresses from cordiality to the hurling of insults which is seen when Lomov called Chubukov ’a swindle’ and Chubukov promptly called Lomov an ‘intriguer’. The elements of exaggeration and absurdity set the tone of ridicule, which mars the elements of love and romance that is intended in the play.

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Students can access the CBSE Sample Papers for Class 10 English with Solutions and marking scheme Term 2 Set 5 will help students in understanding the difficulty level of the exam.

CBSE Sample Papers for Class 10 English Term 2 Set 5 with Solutions

Time Allowed: 2 Hours
Maximum Marks: 40

General Instructions:

• The Question Paper contains THREE sections—READING, WRITING & GRAMMAR and LITERATURE.
• Attempt questions based on specific instructions for each part.

Section – A
Reading [10 Marks]

Question 1.
Read the passage given below.
The choices we make on a daily basis— wearing a seatbelt, lifting heavy objects correctly or purposely staying out of any dangerous situation—can either ensure our safety or bring about potentially harmful circumstances.

You and I need to make a decision that we are going to get our lives in order. Exercising
5. self-control, self-discipline and establishing boundaries and borders in our lives are some of the most important things we can do. A life without discipline is one that’s filled with carelessness.

We can think it’s kind of exciting to live life on the edge. We like the image of “Yeah! That’s me! Living on the edge! Woo-hoo!” It’s become a popular way to look at life. But if you see, even highways have lines, which provide margins for our safety while we’re driving. If we go

10. over one side, we’ll go into the ditch. If we cross over the line in the middle, we could get killed. And we tike those tines because they help to keep us safe. Sometimes we don’t even realize how lines help to keep us safe.
I’m not proud of this, but for the first 20 years of my life at work, l ignored my limits. I felt horrible, physically, most of the time. I used to tell myself “I know I have limits and that I’ve 15. reached them, but I’m going to ignore them and see if or how long I can get by with it.” I ran to doctors, trying to make myself feel better through pills, vitamins, natural stuff and anything I could get my hands on. Some of the doctors would tell me, “It’s just stress.” That just made me mad. I thought stress meant you don’t tike what you do or can’t handle life, and I love what I do. But I kept pushing myself travelling, doing speaking engagements and so 20. on— simply exhausting myself.

Finally, I understood I was living an unsustainable life and needed to make some changes in my outlook and lifestyle.
On the basis of your understanding of the passage, answer ANY FIVE questions from the six given below. (1 × 5)
(A) What does the writer mean by saying to get our lives in order’? (1)
Answer:
By the given phrase, the writer means that we should organize our life properly in such a way that it doesn’t pose any danger, risk or threat to us. We should get our life organized well.

(B) Rewrite the following sentence by replacing the underlined phrase with a word that means the same from lines 15-20.
The Government will possibly in the near future enforce a lockdown again considering the number of patients of virus in the nation. (1)
Answer:
The Government will potentially enforce a lockdown again considering the number of patients of virus in the nation.

(C) State the meaning of ‘an unsustainable life as implied in the passage. (1)
Answer:
If something is ‘unsustainable’, we cannot prolong it or continue with it as it is harmful for us. In the passage, the writer wanted to conclude that with an unsustainable lifestyle, as it was, he could not continue with it. He wanted to have a better lifestyle.

(D) How has the writer used colloquial language in this write-up? (1)
Answer:
The writer has used colloquial language in this write-up by using the words like “yeah” and “Woohoo!”

(E) List two reasons as to the writer wanted to come up with this write-up. (1)
Answer:
The writer wants us to stay out of danger by being meticulous for the choices that we make on a daily basis. He also wants us to stay out of danger and organize our lives properly in order to remain safe.

(F) How does the writer justify the high-ways’ lines as a ‘measure of safety’? (1)
Answer:
The writer justifies the highways’ lines as a ‘measure of safety’ by saying that the highway lines provide margins for our safety, while we are driving. They are meant to keep the drivers safe.

Question 2.
Read the following excerpt from a case study titled ‘Marie Curie’.
Marie was bom in 1867 in Warsaw, Poland, where her father was a Professor of Physics. At an early age, she displayed a brilliant mind and a blithe personality. Her great exuberance for learning, prompted her to continue with her studies after high school. She became disgruntled, however, when she
5. learned that the University of Warsaw was closed to women. Determined to receive a higher education, she defiantly left Poland and in 1891, entered the Sorbonne, a French university, where she earned her master’s degree and doctorate in physics.

Marie was fortunate to have studied at the Sorbonne with some of the greatest scientists of her days, one of whom was Pierre Curie. 10. Marie and Pierre were married in 1895 and spent many productive years working together in the physics laboratory.
A short time after they discovered radium, Pierre was killed by a horse-drawn wagon in 1906. Marie was stunned by this horrible misfortune and endured heartbreaking anguish. Despondently she recalled their close relationship and the joy that they had shared in scientific research. The fact that she had two young daughters to raise by herself greatly increased her distress.

15. Curie’s feeling of desolation finally began to fade when she was asked to succeed her husband as a physics professor at the Sorbonne. She was the first woman to be given a professorship at the world famous university. In 1911, she received the Nobel Prize in chemistry for isolating radium. Although Marie Curie eventually suffered a fatal illness from her long exposure to radium, she never became disillusioned about her work.
20. Regardless of the consequences, she had dedicated herself to science and to revealing the mysteries of the physical world.
On the basis of your understanding of the passage, answer ANY FIVE questions from the six given below. (1 × 5)
(A) Why does the writer mean by saying that the University of Warsaw was ‘closed to women’? (1)
Answer:
By saying that the University of Warsaw was ‘closed to women’, the writer wanted to tell that the university didn’t accept admission of any female candidate. It was not open for women.

(B) Comment on the significance of ‘professorship’ provided to Marie as given in the lines 14-17. (1)
Answer:
When the physics professorship was given to Marie, she became the first-ever woman to be given a professorship at the world famous university. The offer also significantly removed her feeling of desolation.

(C) Justify the Marie’s dedication towards her work from the lines 18-20. (1)
Answer:
Marie was extremely dedicated towards her work. Despite her life-threatening ailment due to radium exposure, she dedicated herself to the research.

(D) How can you say that Marie was ‘determined’ for her higher studies? (1)
Answer:
Marie was ‘determined’ for her higher studies as she did not resist the denial of her admission into the University of Warsaw. Instead, she left Poland and applied to a French University of her master’s degree and doctorate in physics.

(E) Curie’s mother died of ‘grief’. How does evidence from table support this statement? (1)
Answer:
From the table, we can see that in the year 1876, Marie’s sisters Bronya and Zosia became ill and Zosia passed away in ailment. Subsequently, in the year 1878, Marie’s mother died of the grief which aroused from her daughter’s death.

(F) What is the purpose of giving the ‘Year’ tab in the table for Marie? (1)
Answer:
The ‘Year’ tab provides a timeline of Marie’s historical life.

Section – B
Writing And Grammar (10 marks)

Question 3.
Attempt ANY ONE from (A) and (B).
(A) Study the concept chart from the study done by the Global Consumer Survey to know how people usually find out about new interesting products to shop in the year 2021.

Write a paragraph in not more than 120 words, analysing the given information. (5)
Answer:
With a surge of products in the market, people are always in search of something unique and useful to buy. Nothing serves better than a good rummage through the Google search results or getting a friend’s advice, when it comes to clear our buying fix. A new statistical survey by the Global Consumer shows that 40 per cent of people say by they generally happen to know about the latest via a search engine ITEMS. At the same time, 40 per cent states rely upon friends and acquaintances for an advice or inspiration. However, the power of social media should not be underestimated with 37 percent to get ideas for new purchases. Only 24 percent of shoppers use customer reviews as a source of information. Advertisement also prompts 33 per cent to shop for a particular thing and with 34 per cent of respondents opting for it. In sum, current social situation and online shopping have made a special niche for itself.

(B) You are Bindiya/Binay of Hari Nagar, New Delhi. You come across the following advertisement by the German Embassy.

You are interested in doing a German language course. Write a letter to the Director to enquire about the courses at German Embassy. (5)
Answer:
A/43, Hari Nagar
New Delhi
21st September, 20XX

The Director
German Embassy
ChankyaPuri
New Delhi

Subject: Enquiry regarding the German language course

Dear Sir/Madam
I want to join the German language courses offered exclusively to the students by the Embassy. I have just completed class XII and want to pursue a career in German. I would like to know the duration of the course, the fee structure and other eligibility criteria.

I will be grateful if you could send me the brochure to help me understand the requirements for the course and join at the earliest.
Thanking you

Yours sincerely
Bindiya/Binay

Question 4.
The following paragraph has not been edited. There is one error in each line. Identify the error and write its correction against the correct blank number. Remember to underline the correction. The first one has been done for you. (1 × 3)
Paper was first make by the Egyptians for the plant named ‘papyrus’. For a long time, papyrus were exclusively used as written material before the Chinese perfect the processes.

Answer:

Explanation: Paper was made ‘from’ Papyrus and not ‘for’ Papyrus. So, ‘from’ is the right answer.

Explanation: Papyrus is a singular noun, so ‘were’ will be used. Hence, this is the right answer.

Explanation: ‘written’ is the wrong form of the word ‘write’ here. The correct form is ’writing’. Hence, it is the right answer.

Question 5.
Read the conversation between a teacher and student and complete the passage that follows.
Alex: It feels like I’ve been inside forever! I can’t go swimming or cycling. I miss my playmates!
Alex’s Father: Don’t forget that Anne Frank and her family spent two years inside an attic.
Alex: (silent)
Alex’s Father: Yeah! I expected your silence on it.

Alex told his father that he was done (a) …………..
He added that he had been feeling sad as he couldn’t go swimming or cycling. Moreover, he missed his playmates. After listening to his son, Alex’s father told him that Anne Frank and her family spent two years in an attic. This silenced Alex. Looking at his expression, Alex’s father said that (b) …………. (1 + 1)
Answer:
(a) with being inside in-home
(b) he had expected Alex’s silence on it

Section -C
Literature (20 marks)

Question 6.
Answer ANY SIX questions in 30-40 words each. (1 × 6)
(A) What was the significance of the names of Belinda’S pets? (2)
Answer:
The names of Belindas’ pets were very significant to their personalities. Her little kitten was named Ink as it was black, the little grey mouse was named Blink as it was quick, and the little yellow dog was named Mustard due to his bright yellow color. The dragon was named as Custard because he was a coward.

(B) Justify Walt Whitman’s desire of living with animals than humans in ‘Animals’. (2)
Answer:
The poet Walt Whitman in ‘Animals’ desired to live with animals rather than humans because he feels that the animals are calm, quiet and contented. On the contrary, he feels that the humans are restless, greedy and discontent in life.

(C) Comment on the tone of Chubukov when he said, “You Lomovs have had lunacy in your family, all of you!” (2)
Answer:
The tone of Chubukov in the given statement is contempt. This is because Lomov did not behave gracefully with Chubukov and was quarreling on small issues on the ownership of Oxen Meadows and dogs.

(D) Children starts avoiding their parents when they are being constantly nagged. Using evidence from the poem, explain how this concept is represented in ‘Amanda!’. (2)
Answer:
Amanda was fed up of her mother’s constant naggings and instructions and wanted to escape into a world where she would be free to do anything. When her mother scolded her, Amanda thought about an emerald green sea that had soft lazy waves where she would be moving into the water happily in the form of a mermaid, all alone in the sea.

(E) How can you tell that the baker was an integral part of a village? (2)
Answer:
The bakers were an integral part of a village in Goa as they were a reminder of the strong impact of the Portuguese culture. The author reminisced how bakers’ breads were part of each and every occasion. Marriage gifts without the sweet bread, bol, are still considered incomplete.

(F) Briefly state why Bholi’s family compared her to their cow, Laksmi. (2)
Answer:
Lakshmi, the cow, was of no use to the family as she had become old. So, her family sold the cow. The family compared Bholi to Laksmi as Bholi too was of no use to them because she was ugly and as dumb as Lakshmi.

(G) ‘Travels of Monarch X’ changed Ebright’s life. Comment. (2)
Answer:
The book ‘The Travels of Monarch X’ opened the world of science for Richard. After reading it, he became interested in tracking the migration of butterflies and learning more about them. His interest led him to other projects and experiments. Eventually, he became a great scientist.

Question 7.
Answer ANY TWO of the following in about 120 words each. (4 × 2)
(A) India is a land that has wonderful natural beauty in its different parts. Examine the natural beauty found in Coorg and Assam, based on your reading of the chapter‘Glimpses of India.’ (4)
Answer:
The natural beauty of both Coorg and Assam is vast and amazing. Both of these places are rich in greenery and have unique traditional cultures. The chief crop in both the places is a beverage popular for its taste and flavour. Coorg gives us the most fragrant coffee while Assam gives us the best quality tea in the world. One gets the similar kind of visual delight on visiting these places.
However, there is a vast difference in their geographic location and their vegetation. Coorg has green rainforests while Assam has densely wooden hills. Coorg and Assam have different flora and fauna. Nonetheless, both of these places are a treat to eyes.

(B) Kisa Gotami runs from house to house in search of medicine for her dead child In the story, ‘The Sermon at Benares’. Based on Kisa’s trials to save her dead child, develop a conversation between kisa Gotami and a lady whom she visits to ask for the medicine. (4)
Answer:

• Kisa Gotami: (anxiously) Is anybody at home? Please help me!
• Lady: Oh dear! Who are you? And what do you need?
• Kisa Gotami: My son is dead…….he is my only child. I need medicine to cure him and bring him back to life. Please help me cure him!
• Lady: I am so sorry to hear about your loss, lady. I wish I could help you but alas! No one can help you in this as your son is dead. Please accept this harsh reality and have patience. No medicine can bring him back, dear.
• Kisa Gotami: (crying) Nooooo…..he will be alright if someone will give me the medicine to cure him. Tell me if you have that else I may ask other people. I don’t have a lot of time.
• Lady: I am sorry. I can’t help you, dear!

(C) “No legacy is so rich as honesty.” (William Shakespeare) Matilda lost her friend’s necklace and ruined her life in the process. Evaluate the given quote in the context of the lesson, ‘The Necklace’. How do you think the lesson reflects the importance of honesty? (4)
Answer:
Honesty is an important trait to possess. The story, The Necklace’ exemplifies this idea. I think that Matilda could have led a peaceful life had she controlled her social ambition, to borrow the necklace that she could ill-affbrd.

Matilda distressed herself with her unfulfilled desires to be accepted among the higher class. She was filled with wild joy at the party where she could show off her diamond necklace, borrowed from her rich friend, Mme. Forestier. After losing the necklace, she is once again unhappy, suggesting that material possessions cannot guarantee long-lasting happiness, and that greed can lead to ruin.

Had Matilda not been greedy and accepted the truth, she could have worked hard for making her own standard of living better which she always desired for. She became greedy and had to be dishonest to Mme Forestier about the necklace, which eventually ruined her entire life.

The post CBSE Sample Papers for Class 10 English Term 2 Set 5 with Solutions appeared first on Learn CBSE.

Solved CBSE Sample Paper 2021-2022 Class 10 Maths Standard and Basic with Solutions: Solving Pre Board CBSE Sample Papers for Class 10 Maths Standard and Basic with Solutions Answers 2021-2022 Pdf Download to understand the pattern of questions ask in the board exam. Know about the important concepts to be prepared for CBSE Class 10 Maths board exam and Score More marks. Here we have given CBSE Class 10 Maths Sample Papers. According to new CBSE Exam Pattern, MCQ Questions for Class 10 Maths Carries 20 Marks.

Board – Central Board of Secondary Education
Subject – CBSE Class 10 Maths
Year of Examination – 2022, 2021, 2020, 2019, 2018, 2017, 2016.

CBSE Sample Paper 2022 Class 10 Maths Standard and Basic with Solutions

CBSE Sample Paper 2022 Class 10 Maths Standard with Solutions Term 2

• CBSE Sample Papers for Class 10 Maths Standard Term 2 Set 1
• CBSE Sample Papers for Class 10 Maths Standard Term 2 Set 2
• CBSE Sample Papers for Class 10 Maths Standard Term 2 Set 3
• CBSE Sample Papers for Class 10 Maths Standard Term 2 Set 4
• CBSE Sample Papers for Class 10 Maths Standard Term 2 Set 5
• CBSE Sample Papers for Class 10 Maths Standard Term 2 Set 6 for Practice
• CBSE Sample Papers for Class 10 Maths Standard Term 2 Set 7 for Practice
• CBSE Sample Papers for Class 10 Maths Standard Term 2 Set 8 for Practice

CBSE Sample Paper 2021-2022 Class 10 Maths Basic with Solutions Term 2

• CBSE Sample Papers for Class 10 Maths Basic Term 2 Set 1
• CBSE Sample Papers for Class 10 Maths Basic Term 2 Set 2
• CBSE Sample Papers for Class 10 Maths Basic Term 2 Set 3
• CBSE Sample Papers for Class 10 Maths Basic Term 2 Set 4
• CBSE Sample Papers for Class 10 Maths Basic Term 2 Set 5
• CBSE Sample Papers for Class 10 Maths Basic Term 2 Set 6 for Practice
• CBSE Sample Papers for Class 10 Maths Basic Term 2 Set 7 for Practice
• CBSE Sample Papers for Class 10 Maths Basic Term 2 Set 8 for Practice

CBSE Sample Paper 2021 Class 10 Maths Standard with Solutions (Old Pattern)

• CBSE Sample Paper 2020 Class 10 Maths Standard with Solution Set 1
• Maths Sample Paper Class 10 2020 Standard Solution Set 2
• Sample Paper Class 10 Maths Standard with Solution Set 3
• CBSE Class 10 Maths Standard Sample Paper Set 4 for Practice
• Sample Paper of Maths Standard Class 10 Set 5 for Practice

CBSE Sample Paper 2020-2021 Class 10 Maths Basic with Solutions (Old Pattern)

• CBSE Sample Paper 2020 Class 10 Maths Basic with Solution Set 1
• Class 10 Maths Basic Sample Paper 2020 Solved Set 2
• Sample Paper of Class 10 Maths Basic Set 3
• Maths Basic Sample Paper Class 10 Set 4 for Practice
• Sample Paper for Class 10 Maths Basic Set 5 for Practice

Download Formula Book for Class 10 Maths and Science

CBSE Sample Papers 2020 Maths Basic, Maths Standard, Science, Social Science, Hindi, English, and Sanskrit

How To Take CBSE Class 10 Maths Sample Papers?

Step 1 – Download the CBSE Class 10 Sample Question Papers or Pre Board Model Papers or Previous year question papers that you want to take.

Step 2 – Take the exam seriously just like you would take the real exam.

Step 3 – Evaluate your paper – mark the questions you couldn’t answer or get incorrect.

Step 4 – Revise the related concepts and topics.

Solved CBSE Sample Papers for Class 10 Maths 2019

Solved CBSE Sample Papers for Class 10 for 2018-19 are tabulated as follows:

CBSE Previous Year Question Papers Class 10 Maths With Solutions

CBSE Previous Year Question Papers Class 10 Maths With Solutions are tabulated as follows:

• CBSE Previous Year Question Papers Class 10 Maths 2019 Outside Delhi
• CBSE Previous Year Question Papers Class 10 Maths 2019 Delhi
• CBSE Previous Year Question Papers Class 10 Maths 2018
• CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2
• CBSE Previous Year Question Papers Class 10 Maths 2017 Delhi Term 2
• CBSE Previous Year Question Papers Class 10 Maths 2016 Delhi Term 2
• CBSE Previous Year Question Papers Class 10 Maths 2015 Delhi Term 2
• CBSE Previous Year Question Papers Class 10 Maths 2014 Delhi Term 2
• CBSE Previous Year Question Papers Class 10 Maths 2013 Delhi Term 2
• CBSE Previous Year Question Papers Class 10 Maths 2012 Delhi Term 2
• CBSE Previous Year Question Papers Class 10 Maths 2011 Delhi Term 2
• CBSE Previous Year Question Papers Class 10 Maths 2016 Outside Delhi Term 2
• CBSE Previous Year Question Papers Class 10 Maths 2015 Outside Delhi Term 2
• CBSE Previous Year Question Papers Class 10 Maths 2014 Outside Delhi Term 2
• CBSE Previous Year Question Papers Class 10 Maths 2013 Outside Delhi Term 2
• CBSE Previous Year Question Papers Class 10 Maths 2012 Outside Delhi Term 2
• CBSE Previous Year Question Papers Class 10 Maths 2011 Outside Delhi Term 2

CBSE Previous Year Question Papers class 10 Maths

Last 10 Years Question Papers for Class 10 Maths are tabulated as follows:

CBSE Topper Answer Sheet Class 10 Maths

Download PDF of Last 5 Years Toppers Answer Sheet Photo Copies from the following table.

CBSE Class 10 Previous Year Question Paper Maths 2018

CBSE Class 10 Previous Year Question papers for Maths 2018 with marking scheme for main exam and compartment exam are tabulated as follows:

CBSE Previous Year Question Paper Class 10 Maths 2017

CBSE Class 10 Previous Year Question papers for Maths 2017 with marking scheme for main exam and compartment exam are tabulated as follows:

CBSE Previous Year Question Paper Class 10 Maths 2016

CBSE Class 10 Previous Year Question papers for Maths 2016 with marking scheme for main exam and compartment exam are tabulated as follows:

CBSE Previous Year Question Papers Class 10 Maths 2015

CBSE Class 10 Previous Year Question papers for Maths 2015 with marking scheme for main exam and compartment exam are tabulated as follows:

CBSE Previous Year Question Papers Class 10 Maths 2014

CBSE Class 10 Previous Year Question papers for Maths 2014 with marking scheme for main exam and compartment exam are tabulated as follows:

CBSE Sample Papers for Class 10 Maths SA2

CBSE Class 10 Sample Question papers for Maths 2017 SA2 are tabulated as follows:

Solved Papers For the Year 2017 :

• Solved CBSE Sample Paper for Class 10 SA2 Maths 2017 Set 1
• Solved CBSE Sample Paper for Class 10 SA2 Maths 2017 Set 2
• Solved CBSE Sample Paper for Class 10 SA2 Maths 2017 Set 3
• Solved CBSE Sample Paper for Class 10 SA2 Maths 2017 Set 4
• Solved CBSE Sample Paper for Class 10 SA2 Maths 2017  Set 5
• Solved CBSE Sample Paper for Class 10 SA2 Maths 2017 Set 6
• Solved CBSE Sample Paper for Class 10 SA2 Maths 2017 Set 7
• Solved CBSE Sample Paper for Class 10 SA2 Maths 2017 Set 8
• Solved CBSE Sample Paper for Class 10 SA2 Maths 2017 Set 9
• Solved CBSE Sample Paper for Class 10 SA2 Maths 2017 Set 10
• Solved CBSE Sample Paper for Class 10 SA2 Maths 2017 Set 11
• Solved CBSE Sample Paper for Class 10 SA2 Maths 2017 Set 12
• Solved CBSE Sample Paper for Class 10 SA2 Maths 2017 Set 13

Unsolved Papers:

• Sample paper for Maths Set A
• Sample paper for Maths Set B
• Sample paper for Maths Set C
• Sample paper for Maths Set D

More Resources for CBSE Class 10:

• RD Sharma Class 10 Solutions
• Lakhmir Singh Physics Class 10
• Solved Sample Papers Class 10 Science

Importance of Solving CBSE Class 10 Maths Sample Papers

1. By solving the CBSE Sample Papers for Class 10 Maths, students will get an idea of exam pattern, the types of questions asked and weightage of each section.
2. Solving CBSE Class 10 sample paper will be good practice for students.
3. These CBSE Maths Sample Papers covers all the important topics and also the questions which are repeated every year.
4. CBSE Class 10 Maths sample question paper will help the students to analyze their performance. This will also help with time management.
5. This will boost up the students’ confidence level.
6. After this much of practice, students will have a good idea about what to expect in exams.

We hope the CBSE Sample Questions papers for Class 10 Maths, help you. If you have any query regarding Maths Sample Questions papers for Class 10, drop a comment below and we will get back to you at the earliest.

The post CBSE Sample Papers for Class 10 Maths Standard and Basic with Solutions 2021-2022 appeared first on Learn CBSE.

Students can access the CBSE Sample Papers for Class 10 English with Solutions and marking scheme Term 2 Set 7 for Practice will help students in understanding the difficulty level of the exam.

CBSE Sample Papers for Class 10 English Term 2 Set 7 for Practice

Time Allowed: 2 Hours
Maximum Marks: 40

General Instructions:

• The Question Paper contains THREE sections—READING, WRITING & GRAMMAR and LITERATURE.
• Attempt questions based on specific instructions for each part.

Section – A
Reading [10 Marks]

Question 1.
Read the passage given below.
Research has shown that the human mind can process words at the rate of about 500 per minute, whereas a speaker speaks at the rate of about 150 words a minute. The difference between the two is 350, which is quite large.
So, a speaker must make every effort to retain the attention of the audience and the listener should also be careful not to let his/her mind
5. wander. Good communication calls for good listening skills.

Listening starts with hearing but goes beyond that. Hearing, in other words, is necessary but not sufficient for Listening. Listening involves hearing with attention. Listening is a process that calls for attention and concentration.
While listening, one should be observant. In other words, listening has to do with the ears as well as with the mind.
10. It calls for participation and involvement.
It is quite often a dialogue rather than a monologue. It is necessary to make it abundantly clear that one is interested in knowing what the other person has to say.

Good Listening is an art that can be cultivated.
A good listener knows the art of getting much more than what the speaker is trying to convey. He/she knows how to prompt, persuade but IS. not to cut-off or interrupt what the other person has to say. At times, the speaker may or may not be coherent, articulate and well-organised in his/her thoughts and expressions. He/she may have it in mind, yet fail to marshal the right words while communicating thoughts. Nevertheless, a good listener puts him/her at ease, helps him/her articulate his/her thoughts. For Listening to be effective, it is also necessary that barriers to listening are removed. Such 20. barriers can be both physical and psychological. Physical barriers generally relate to hindrances to proper hearing, whereas psychological barriers are more fundamental and relate to the interpretation and evaluation of the speaker and the message.

Based on your understanding of the passage, answer ANY FIVE questions out of the six given below. (1 × 5)
(A) What does the author mean when he says, “barriers to listening are removed”? (1)
(B) Mention any two characteristics of the writer as inferred from the statement, ‘Good listening is an art that can be cultivated’. (1)
(C) Rewrite the following sentence by replacing the underlined phrase with a word that means the same from lines 10-15.
His mind was as well developed and maintained as his bodily powers; he wrote well, and his observations are generally acute and accurate; he was brave, kindly and generous. (1)
(D) List one quality of a good listener that makes the listening truly effective. (1)
(E) Why does the author say that “it is quite often a dialogue rather than a monologue? (1)
(F) How does the writer differentiate between listening and hearing? (1)

Question 2.
Read the following excerpt from a case study titled ‘Stress and Covid -19.’
A new study has found that peo pie who experienced increased stress, anxiety and depression at the start of the pandemic. were at greater risk of getting Covid-19.

20. A professor says: “The significance of the work is in that it turns the debate regarding the mental health aspects of the pandemic on its head. Our data show that increased stress, anxiety and depression are not only consequences of living with the pandemic, but may also be factors that increase our risk of getting SARS-CoV-2 too. Further work is now needed to determine whether and how public health policy should change to accommodate the fact that the most distressed people in our communities appear to be at greatest risk of Covid-19 infection.”

25. Another professor of Cognitive Behavioural (Psychotherapy from King’s College) London said: “Previous work has shown a clear relationship between distress and the development of viral infections indicating a vulnerability.
30. Our study found that distress was associated with self-reported Covid-19 infection and the next step is to investigate whether this association is found in those with confirmed infection.”

On the basis of your understanding of the passage, answer ANY FIVE questions out of the six given below. (1 × 5)
(A) Why does the professor from King’s College London, say, ‘Previous work has shown a clear relationship between distress and the development of viral infections indicating a vulnerability? (1)
(B) Comment on the significance of the need to address the psychological issues with reference to lines 10-20. (1)
(C) Justify the finding that during the Covid-19 pandemic, there has been a well-documented deterioration in psychological well-being and increased social isolation. (1)
(D) Why does the narrator feel public health policy should change to accommodate the fact ‘‘that the most distressed people in our communities appear to be at greatest risk of Covid-19 infection.” (1)
(E) People who experienced increased stress, anxiety and depression at the start of the pandemic, were at greater risk of getting Covid-19. How does evidence from the table support the statement? (1)
(F) What purpose does the data in the passage seem to solve? (1)

Section – B
Writing And Grammar (10 marks)

Question 3.
Attempt ANY ONE from (A) and (B)
(A) You came across the given concept chart while searching for something on Google. You are compelled to think of the impact, that social media is leaving on young minds. Write a paragraph in about 120 words suggesting ways to deal with the problem.

Write a paragraph in not more than 120 words, analysing the given information. (5)
(B) You are the Secretary of an NGO. You have come across the following adverstisement of M/s Arora Woollen Mills.

You have decided to distribute blankets among homeless. Write a letter to place an order with M/s. Arora Woollen Mills stating your exact requirement. (5)

Question 4.
The following paragraph has not been edited. There is one error In each Line. Identify the error and write its correction against the correct b[ank number. Remember to underLine the correction. The first one has been done for you. (1 × 3)

Genetics played a key role to keep your hair healthy, But the weather, pollution, or your approach to hair care are all critical to maintained your crowning glory. A well-rounded dieting is an important factor in hair and scalp health.

Question 5.
Read the conversation and complete the passage that follows.
Simi: I do wish to get good marks in my final exams. How cari I do that?
Mother: You must devote some of your daiLy time to study at home.
Simi: Youre right mom. I am going to make a timetable to follow now.
Simi told her mother that she (a) …………. final exams and askded how she could do that. Mother replied that she must devote some of her daily time to study at home. At this, Simi replied that her mother (b) …………….. (1 + 1)

Section -C
Literature (20 marks)

Question 6.
Answer ANY SIX questions in 30-40 words each. (2 × 6)
(A) What is the significance of a baker in the Goan village, especially in celebrations? (2)
(B) Justify how Tale of the Custard the Dragon’ by Ogden Nash is funny as well as serious. (2)
(C) ‘Possessions can possess you’. Comment on the aptness of the statement with regard to the story, ‘The Necklace’. (2)
(D) Explain the reason behind Valli’s change of mood while going and coming back in the bus. (2)
(E) Which two issues as stated in the story ‘Bholi’ our society is yet to get rid of, in spite of all the advancements? (2)
(F) Briefly state the poetic aspect of the poem ‘Amanda’. (2)
(G) What does the poet Walt Whitman suggest by saying that ‘they do not sweat and whine about their condition’ in the poem ‘Animals’? (2)

Question 7.
Answer ANY TWO of the following in about 120 words each. (4 × 2)
(A) Examine and highlight the theme of the story ‘Madam Rides the Bus’. (4)
(B) Develop a conversation between the young lawyer and one of his associates regarding his experience of getting be fooled by Lutkins in the story ‘The Hack Driver’. (4)
(C) Evaluate ‘The sermon at Benares’ as an important life lesson. (4)

The post CBSE Sample Papers for Class 10 English Term 2 Set 7 for Practice appeared first on Learn CBSE.

Students can access the CBSE Sample Papers for Class 10 English with Solutions and marking scheme Term 2 Set 8 will help students in understanding the difficulty level of the exam.

CBSE Sample Papers for Class 10 English Term 2 Set 8 for Practice

Time Allowed: 2 Hours
Maximum Marks: 40

General Instructions:

• The Question Paper contains THREE sections—READING, WRITING & GRAMMAR and LITERATURE.
• Attempt questions based on specific instructions for each part.

Section – A:
READING [10 marks]

Question 1.
Read the passage given below.
“Women need more sleep than men, if not the same. The consequences of a bad sleep cycle also tend to be graver in women compared to men,” said an expert. Sleep plays a vital role in maintaining mental, physical, and emotional health. But with lockdowns imposed and offices shut yet again, people continue to work from home, a model that not only blurs the lines between office and home,

5.but also leads to increased exposure to screens. This, coupled with pandemic-induced anxiety, and lack of physical activity, not only takes a toll on one’s health, but also contributes to poor sleep quality. But it is women, especially working mothers, who are worst affected – as women need more sleep than men, say experts. “Several studies have proven that the sleep requirement may slightly vary between men and women, given their biological structure.

10. A significant factor for this is how both women and men spend their day. Research has documented the differences in the time women and men have dedicated to paid and unpaid labour, work and social responsibilities, and family caregiving,” they say. They added that women get slightly more sleep than men, approximately 11-13 minutes more, but men tend to have a much deeper sleep. Women are more likely to get up in the middle of the night to take care of

15. others in the family. Sleep works best when it is uninterrupted.
“Additionally, women are more likely to take a nap during the day, suggesting that their total sleep time may be misleading. Napping during the day adds to the sleep time (number of hours spent sleeping) and makes night-time sleep less restful,” he continued.

20. Reasons women need more (and better quality) sleep than men: Increased risk of sleep disorders: Women are 40 per cent more prone to insomnia and restless leg syndrome (RLS) which causes an uncontrollable urge to move your legs, usually because of an uncomfortable sensation disrupting sleep, requiring women to sleep a little extra to make up for the lost sleep.

25. Hormonal imbalances: Women undergo multiple hormonal changes throughout their lives. The changes create disturbances in their circadian rhythm, requiring extra sleep.
Mental health: “Women are twice more likely to suffer from depression than men. In India, women tend to face adverse mental health issues due to their professional commitments and added responsibilities of household chores. A good sleep cycle is needed for them to

30. keep their mental health in check,” said an expert.
Personal lifestyle and fitness: A good night’s sleep aids a women’s metabolism. It gives more energy to exercise, concentrate, and perform other critical daily tasks. According to researchers at the Loughborough University, UK, women need more sleep than men due to multitasking. Women need more sleep than men, if not the same. The consequences of a bad sleep cycle also tend to be much graver in women compared to men. Several studies have extensively shown that sleep-deprived women are at an increased risk of hypertension, type 2 diabetes, heart strokes, stress, and mental health issues than sleep-deprived men. Not only that, sleep deprivation can also aggravate pre-existing mood disturbances, such as anger, depression, and anxiety. It can lead to confusion, fatigue, and lack of vigour, ultimately impacting productivity. Women may also face more challenges in concentration than men.

Based on your understanding of the passage, answer ANY FIVE questions out of the six given below. (1 × 5)

(A) What does the writer mean when he/ she says, “Women need more sleep than men, if not the same”? (1)

(B) Rewrite the following sentence by replacing the underlined phrase with a word that means the same from lines 1-10.
There was so much of fog that it caused a reduction in the clarity of my vision. (1)

(C) State any two reasons for women being worst affected by lack of sleep. (1)

(D) Why is it said ‘Napping during the day adds to the sleep time (number of hours spent sleeping) and makes night-time sleep less restful’? (1)

(E) List one likely reason for women being in need of more sleep, other than a disturbed sleep cycle. (1)

(F) How does the author prove that sleep deprivation can lead to severe health issues in women? (1)

Question 2.
Read the following excerpt from a case study titled ‘Cyber Bullying’.
Cyberbullying is a serious issue affecting a large number of children and adolescents who have experienced it. Here are some stories:

5. “I have been friends with this person for 3 years now. Well best friends. I never thought she could do this to me. She’s lying and getting our friends on her side. All I can do is

10. watch. She’s called me Ugly Rag Doll! Who says these kinds of things? Only someone that is heartless and that has never been bullied before. They don’t know how it feels !

“My sixteen year old son was cyberbullied on Facebook over a period of 8 hours. The event was so traumatic it caused my son to have an acute psychotic break and to be

20. hospitalized in an adolescent psychiatric ward for almost a month. He is changed forever and will never be the same mentally.” – Parent

25. of 16 year-old boy from MN “Whenever I am on Facebook, I am in fear of my account being hacked. I can’t help but use it because I have online friends that I chat with. I just hate people who hack Facebook accounts for pleasure.”-18 year-old girl from NM

“A boy in my sixth grade math class called me mean names. Like four eyes, alien and more just

30. for wearing glasses. It made me very upset. I don’t think that kids who wear glasses shouldn’t get made fun of. It’s not someone’s fault for wearing glasses.'”‘ – 11 year-old boy from Ml

“I’ve been bullied on Twitter, by two people in the last couple weeks. After I told them to stop and leave me alone, I stopped communication with them but they still kept tweeting me. I feel

35. like I can’t say anything with someone on Twitter bullying me. I try to make it look like I don’t care and all, but it never seems to work. I’ve reported and blocked them”- 21 year-old girl from USA
“A guy I know (he is a good friend of mine now) used to be pretty cruel to me in front of my friends, mocking me. But I just want to say to every victim out there, don’t stop believing it will all get better.

40. Stand up for yourself, fight, do whatever you can. Peace.”” -14 year-old boy from IA “I think most people who bully online just do it to act tough but since they’re not saying it to someone’s face makes them seem more of a wimp.”-15 year old girl from NY

Source: https://cyberbullying.org/stories
Image source: Researchgate

On the basis of your understanding of the passage, answer ANY FIVE questions out of the six given below. (1 × 5)
(A) What does the writer mean by saying “cyber-bullying affects adolescents”? (1)

(B) Comment on the significance of the need to address the issue of cyberbullying with reference to lines 1-15. (1)

(C) Justify the statement by a mother when she says that ‘He is changed forever and will never be the same mentally’, with reference to the lines 15-20. (1)

(D) Quote an example of body shaming from the above stories and describe how it affects the victim. (1)

(E) Sending or writing rumours, cracking embarrassing jokes or gossip on social media is one of the worst types of bullying. How does evidence from the table support the statement? (1)

(F) What can be the best strategy to deal with bullies with reference to the lines 30-40? (1)

Section – B:
WRITING AND GRAMMAR (10 marks)

Question 3.
Attempt any one from (A) and (B) (5)
(A) Study the given data on ‘Cash Rlues Everything Around Christmas’ that shows things that are popluuar in giving and receiving gifts during Christmas. (3)

(B) You are David/Devi, purchase manager of a publishing house, you come cross the following adve

Write a letter to Som Safety Works in about 120 words, placing an order for some fire extinguishers that you need for your office. (5)

Question 4.
The following paragraph has not been edited. There is one error in each line. Identify the error and write its correction against the correct blank number. Remember to underline the correction. The first one has been done for you. (1 × 3)

Chess is called the game off kings.
It has being around for a long time.
People have been played it for over 500 years.
Chess was based on an even older game from India.
The chess we play today is from Europe.

Question 5.
Read the conversation and complete the passage that follows.
Teacher: Today let me share the importance of education for every person in society. If you are not properly educated you will not get any job easily.
Student: Yes sir, this is true. I have seen many people suffering due to lack of education.

The teacher told the students to let him share the importance of education for every person in society and told them
that if (a) ……………. Student replied that that was true and added that (b) ………………………. due to lack of education. (1 + 1)

Section – C:
Literature (20 Marks)

Question 6.
Answer ANY SIX questions in 30-40 words each, (2 × 6)
(A) What was the significance of Baking as indeed a profitable profession in the old days? (2)

(B) Justify how ‘The tale of Custard the Dragon’ by Ogden Nash throws light on fakeness and hypocrisy. (2)

(C) Comment on the tone of the speaker in the line: “Tell me another!” scoffed Pranjol. (2)

(D) Explain the qualities of a person that made him/her achieve what they want in life with reference to the text ‘The Making of a Scientist’. (2)

(E) Which two incidents as stated in the play ‘The Proposal’, do you find most humorous? (2)

(F) Briefly state the theme of the poem ‘Animals’. (2)

(G) Comment on the importance of being satisfied with reference to the story ‘The Necklace’. (2)

Question 7.
Answer ANY TWO of the following in about
120 words each. 4×2
(A) Critically examine and highlight the impact of sufferings seen by Siddhartha on his mind. (4)

(B) Bholi’s teacher had played a huge role in impacting Bholi in a positive light. Develop a conversation between Bholi and her teacher about the impact the teacher leaves on Bholi’s life, based on your understanding of the chapter ‘Bholi’ You may begin like: (4)

(C) The concept of‘marriage of convenience’ is still practiced in different parts of world. Evaluate the relation between Lomov and Natalya, highlighting their stance on it in the chapter ‘The Proposal’. (4)

The post CBSE Sample Papers for Class 10 English Term 2 Set 8 for Practice appeared first on Learn CBSE.

Students can access the CBSE Sample Papers for Class 10 English with Solutions and marking scheme Term 2 Set 6 will help students in understanding the difficulty level of the exam.

CBSE Sample Papers for Class 10 English Term 2 Set 6 for Practice

Time Allowed: 2 Hours
Maximum Marks: 40

General Instructions:

• The Question Paper contains THREE sections—READING, WRITING & GRAMMAR and LITERATURE.
• Attempt questions based on specific instructions for each part.

Section – A
Reading [10 Marks]

Question 1.
Read the passage given below.
Once upon a time, there lived a young boy named Sammy. He was good at studies, obedient towards his elders, more hardworking than a lot of other boys in his class and kind to everyone. Grown-ups as well as those younger than Sammy loved him very much. This aroused jealousy in some boys who longed to be as loved as him. A boy named Timmy studied in the same class as Sammy.

5. Unlike Sammy, he was not good at studies and always liked to play during school hours. He misbehaved with his parents, bullied his classmates and even ill-treated Sammy. He always tried to put Sammy down and belittled him before the other kids in class. But no matter what he did, Sammy’s grades kept getting bette. Whether in studies or in sports, Sammy kept getting accolades from everywhere. On his eighth birthday, Sammy got a beautiful pen as a gift from his parents.

10. He brought it to the school so that he could use it to take down the notes of the lectures that the teachers gave in class. When Timmy saw it, he felt jealous.
He asked Sammy, “Hey, where did you get that? Did you buy it?” “My parents gave it as a birthday gift to me,” replied Sammy. Timmy was overcome with anger and jealousy. The bad boy that he was, rarely got any presents from his parents. He decided to steal Sammy’s pen.

15. During recess, when everyone had gone out from the class, Timmy opened Sammy’s bag and took out his pen. Then he hid it inside his bag and went out to have his lunch. When Sammy came back and could not find his pen, he informed his class teacher about it. The class teacher ordered the class monitor to check every student’s bag. The missing pen was soon found from Timmy’s bag and the furious teacher asked the errant boy, “Now Timmy, what do you have to say about this?” 20. Timmy was in tears. He had nothing to say. When Sammy saw Timmy cry, he felt pity on the boy. The kind boy that he was, Sammy had no ill-feeling against his classmate. He requested his class teacher not to take any action against Timmy, now that his stolen pen was found.
On the basis of your understanding of the passage, answer ANY FIVE questions from the following. (1 × 5)
(A) What do you infer about Sammy in the following context, “He requested his class teacher not to take any action against Timmy, now that his stolen pen was found.” (1)
(B) Rewrite the following sentence by replacing the underlined phrase with a word that means the same from lines 1-10.
The wonders of nature always cause to increase my feelings towards the secret behind them. (1)
(C) State any two reasons behind Timmy’s action of stealing. (1)
(D) Why do you think Sammy forgave Timmy? (1)
(E) List one likely impact of Sammy’s kind behaviour towards Timmy. (1)
(F) Which of these quotes best justifies the central idea of the passage? Give reason.
(i) Surely it is much more generous to forgive and remember, than to forgive and forget.
(ii) A misbehaving child is a discouraged child. (1)

Question 2.
Read the following excerpt from a case study titled ‘Challenges of Remote Teaching’.
The rapid shift to e-learning, prompted by the pandemic, has exposed long-standing issues of inequality and a digital divide in India that must be addressed by future economic, education and digitalization policies. While the government endorses India as the flag-bearer of the digital revolution and acknowledges that it is a diverse and multilingual country, e-learning platforms

5. cannot replicate the various dialects, varied contexts and different lived experiences that are brought together by physical classrooms. If e-learning is to be the ‘new normal’, the NEP and related policies must go further to address the feasibility of digitalization to ensure equity and quality in education. The potential scope of e-learning is enormous and can help realize the potential of each student, but e-learning offers both opportunities and challenges for the

10. government and the private sector. The aim should be to ensure equal and adequate access to such platforms as the country continues to globalize and catch up with advanced economies. If the Indian education system aims to transit to blended education with more online learning in future, it must emphasize policies that bridge the digital divide and move the country closer to achieving the Sustainable Development Goals. In reality, the majority of government

15. schoolteachers and students currently lack the tools and infrastructure to be a part of this digitalization process – unless these core shortcomings are addressed, educational inequalities will continue to widen. These sentiments are echoed by other key actors in the education sector, such as the CEO of Azim Premji Foundation. In an interview with the BBC, he said, “The education of children cannot be done effectively online and to do so would damage education

20. deeply and exacerbate inequities. Most disadvantaged children,” he added, “did not have “any support to handle online education at home and are in families combating deep livelihood crises, making them unable to cope with other challenges.” One critical factor as countries move towards using more technology to complement classroom-based learning (or as an alternative to face-to-face teaching) is the capacity of the teachers. The digital divide for

25. teachers must be reduced, and they must be prepared, consulted and situated within an enabling ecosystem to lead this process. Students, teachers and parents are still getting used to the switch from learning in classrooms to learning from home. For the teachers, the move from interacting with a classroom 30. of around 40 students to trying to teach from their homes via mobile phones or laptops has been a learning experience fraught with challenges. From coping with the basics of internet connectivity and India’s notoriously unreliable power supply to more structural issues such as curriculum and teaching methods, educators have come under tremendous stress since India’s schools began shutting down.
Source: unicef.org
Data source: https://journals.lww.com
On the basis your understanding of the passage, answer ANY FIVE questions out of the six given below. (1 × 5)
(A) Why does the CEO say, The education of children cannot be done effectively online and to do so would damage education deeply and exacerbate inequities’? (1)
(B) Comment on the significance of the need to address the shortcomings, students in India face to be a part of the digitalization process with reference to lines 10-20. (1)
(C) Justify the finding that most disadvantaged children don’t have any support at home to handle online education with reference to the lines 20-25. (1)
(D) Why does the narrator feel that switch from learning in classroom to Learning from home is something to be Learnt gradually? (1)
(E) Class interactivity is the most affected aspect of online teaching learning process. How does evidence from the table support the statement? (1)
(F) What purpose does the data in the passage seem to solve? (1)

Section – B
Writing And Grammar [10 marks]

Question 3.
Attempt any one from (A) and (B)
(A) Study the concept chart posted under health and travel on twitter.

Based on the above cue, write a paragraph in not more than 120 words analyzing the information to keep your heart healthy and fit. (5)
(B) You are Prateek/Prerna, a resident of Modern Colony, Kanpur and wants to be a choreographer by learning dance. You come across the given advertisement regarding dance coaching.

Write a letter to the Director, Rhythm Dance Cafe, Kanpur, in about 120 words seeking information about their courses, duration, admission procedure, eligibility criteria and other details. (5)

Question 4.
The following paragraph has not been edited. There is one error in each line. Identify the error and write its correction against the correct blank number. Remember to underline the correction. The first one has been done for you. (1 × 3)

The history of chocolate began of Mesoamerica. Fermented beverages make from chocolate date back to 450 BC. The Mexico believed when cacao seeds were the gift of Quetzalcoatl, the god of wisdom, but the seeds, once, were used as a form of currency.

Question 5.
Read the conversation and complete the passage that follows.
Akhil: When will father come home?
Shweta: He will be a bit late today.
Akhil: But, he promised he whould be home for dinner and I am waiting for him.

Akhil asked his sister Shweta when (a) ……………… Shweta replied that he would be a bit late today. At this, Akhil replied that his father promised he would be home for dinner and Akhil (b) …………….. (1 + 1)

Question 6.
Answer ANY SIX questions in 30-40 words each. (2 × 6)
(A) What is the significance of the sentence -The fire in the furnaces has not yet been extinguished? (2)
(B) Justify how ‘Amanda’ by Robin Klein is a reflection of parents’ unnecessary dominance over their children and the response of the children. (2)
(C) Comment on the tone of the speaker when she says, “It’s me,” shouted Valli. “I’m the one who has to get on.” (2)
(D) How can you say that Mme. Frostier was a generous person? (2)
(E) Which two issues as stated in the poem ‘animals’, human being is suffering from, upset you most? (2)
(F) Briefly state the poetic aspect of the poem ‘The Tale of Custard the Dragon’. (2)
(G) Comment on the importance of education in one’s life with reference to the story ‘Bholi’. (2)

Question 7.
Answer any two of the following in about 120 words each. (4 × 2)
(A) Critically examine and highlight the impact of Matilda’s thoughtless action on her married life. (4)
(B) Develop a conversation between Kisa Gotami and one of the villagers, highlighting Kisa Gotami’s awareness of the truth of life-death. (4)
(C) Evaluate ‘A Baker from Goa’ as a memoir. (4)

The post CBSE Sample Papers for Class 10 English Term 2 Set 6 for Practice appeared first on Learn CBSE.

Students can access the CBSE Sample Papers for Class 10 Maths Standard with Solutions and marking scheme Set 2 will help students in understanding the difficulty level of the exam.

CBSE Sample Papers for Class 10 Maths Standard Term 2 Set 2 with Solutions

Time Allowed: 2 Hours
Maximum Marks: 40

General Instructions:

• Same instructions as given in the Sample Paper 1.

SECTION – A
(12 Marks)

Question 1.
If x = \(\frac{2}{3}\) and x = -3 are the roots of quadratic equation ax² + 7x + b = 0, find the values of a and b.
OR
Solve for x:
\(\sqrt{2 x+9}+x=13\) (2)
Answer:
Since, \(\frac{2}{3}\) and -3 are the roots of given quadratic equation,

Hence, the respective values of a and b are 3 and -6.
OR
We have,

⇒ (x – 20) (x – 8) = 0
⇒ x = 20, 8
Hence, the values of x are 8 and 20.

Question 2.
The mean of eight numbers is 23. One more number is added to it. The new mean reduced to 22. Find the number added. (2)
Answer:
Given: Mean of eight numbers = 23
Sum of eight numbers = 23 x 8
= 184

Let the newly added number be x.

Now, there are nine numbers in the set of data.

So, Sum of nine numbers = 184 + x
∴ Mean of nine numbers = \(\frac{184+x}{9}\)
But, mean of nine numbers = 22 [Given]

Hence, the number odded is 14.

Question 3.
In the given figure, AB is a chord of the circle and AOC is its diameter such that ∠ACB = 40°. If AT is a tangent to the circle at point A, find ∠BAT. (2)

Answer:
Given: ∠ACB = 40°
Since, angle in a semi-circle is a right angle
∴ ∠ABC = 90°
So, in ΔABC
∠BAC = 180° – ∠ABC – ∠ACB
= 180° – 90° – 40°
= 50°
Now,
∠OAT = 90° [∵ Tangent! Radius]
⇒ ∠OAB + ∠BAT = 90°
⇒ 50° + ∠BAT = 90°
⇒ ∠BAT = 90° – 50° = 40°

Question 4.
Given below is a cumulative frequency distribution tabLe. Find the missing vaLues a, b, c and d.

Answer:

Concept Applied
The cumulative frequency of a doss is equaL to the sum of the frequency of the class arid the cumulative frequency of the preceding class.

Question 5.
The 19^th term of an A.P. is equal to three times its sixth term. If its 9^th term is 19, find the A.P. (2)
Answer:
Let a be the first term and d be the common difference of the A.P.
Now, a₁₉ = 3a₆
⇒ a + 18 d = 3 (a + 5 d)
⇒ a + 18 d = 3 a + 15 d
⇒ 2a – 3d = 0 ………………………….. (i)
Also, a₉ = 19
⇒ a + 8d = 19 ………………………….. (ii)
Solving equations (i) and (ii), we get
a = 3, d = 2
So, the A.P. is 3, 5, 7, 9 …

Question 6.
If the total surface area of a solid hemisphere is 462 cm², find its volume. \(\left[\text { Use } \pi=\frac{22}{7}\right]\)
OR
Rakesh, a student of cLass X, kept together two cubes, each of side 5 cm, to form a cuboid. Find the surface area of the cuboid so formed. (2)
Answer:
Let the radius of the hemisphere be r cm.
Given: TSA of hemisphere = 462 cm²
⇒ 3πr² = 462

Related Theory
TSA of hemisphere = CSA of hemisphere + Area of base of hemisphere)
= 2πr² + πr²
= 3πr²
OR
When two cubes of edge 5 cm each are joined together side by side, a cuboid is formed whose dimensions are 10 cm x 5 cm x 5 cm.

SECTION – B
(12 Marks)

Question 7.
The tops of two poles of heights 20 m and 14 m are connected by a wire. If the wire makes an angle of 30° with the horizontal, find the length of the wire. (3)
Answer:
Let AB and CD be the two poles.

∴ AB = 20 m, CM = 14 m, and ∠ACM = 30°
So, AM = AB – MB
= AB – CD [∵ MB = CD]
= 20 – 14
= 6 m
Also, the wire joining the tops of two poles is AC.
So, in ΔAMC
sin 30° \(\frac{\mathrm{AM}}{\mathrm{AC}}\)
⇒ \(\frac{1}{2}=\frac{6}{A C}\)
⇒ AC = 12
Hence, the Length of the wire is 12 m.

Question 8.
Find two consecutive positive integers, sum of whose squares is 365. (3)
Answer:
Let the two consecutive positive integers be x and (x + 1).
Then, according to the question
x² + (x + 1)² = 365
⇒ 2x² + 2x + 1 = 365
⇒ 2x² + 2x – 364 =0
⇒ x² + x – 182 = 0
⇒ (x + 14) (x – 13) = 0
⇒ x = -14, 13
Since, x is a positive integer,
x = 13
So, the two consecutive positive integers are 13 and 14.

Question 9.
Draw a circle of radius 2 cm with centre O and take a point P outside the circle such that OP = 6.5 cm. From P, construct two tangents to the circle. (3)
Answer:

Steps of construction:

• Draw a circLe with centre 0 and radius 2 cm.
• Take a point P outside the circLe and join it to centre O such that OP = 6.5 cm.
• Draw perpendicuLar bisector of OP to get its mid-point M.
• Taking M as centre and OM = MP as radius, draw a circLe, intersecting the circLe drawn in step (1), at points A and B.
• Join PA and PB.
  Thus, PA and PB are the required tangents to the circLe with centre O.

Question 10.
Find the sum of all two-digit numbers which when divided by 7, leaves 2 as a remainder.
OR
Mala saved ₹ 10 in the first week of a year and then increased her weekly savings by ₹ 2. If in the nth week, her weekly savings is ₹ 68, then find the value of n. Also, find her weekly savings in 52^nd week of the year. (3)
Answer:
List of two-digit numbers which Leave remainder 2, when divided by 7 is:
(14 + 2), (21 + 2), (28 + 2) (91 + 2)
i.e. 16, 23, 30 ….. 93
This List of numbers forms an A.P. with a = 16, d = 7 and L = 93.
Let there be n terms in the A.P.
Then, L = a + (n – 1 )d
⇒ 93 = 16 + (n – 1) x 7
⇒ 7(n – 1) = 77
⇒ n – 1 = 11
⇒ n = 12

OR
Since, savings done by MaLa every week increases uniformLy by ₹ 2, so her savings form an A.P. with a = 10, d = 2 and a_n = 68.

We know,
a_n = a + (n – 1)d
⇒ 68 = 10 + (n – 1) x 2
⇒ 2(n – 1) = 58
⇒ n – 1 = 29
⇒ n = 30
So, the vaLue of n is 30.

Now,
a₅₂ = a + 51d
= 10 + 51 x 2
= 10 + 102
= 112
Hence, her savings in the 52^nd week is ₹112.

Caution
In word problems, learn to differentiate savings in the nth week and total savings in n weeks. Otherwise, error could occur.

SECTION – C
(16 Marks)

Question 11.
If median of the following frequency distribution is 32.5, find the missing values f₁ and f₂. (4)

Answer:

We have,
Sum of frequencies = 40
∴ 31 + f₁ + f₂ = 40
⇒ f₁ + f₂ = 9 ……………………………. (i)
Now,
Median = 32.5 [Given]
∴ Median class = 30 – 40
We know,

Question 12.
If the angles of elevation of the top of the candle from two coins distant a cm and b cm, (a > b), from its base and in the same straight line from it are 30° and 60°, respectively. Find the height of the candle.
OR
Two palm trees of equal heights are standing opposite to each other on either side of a river, which is 80 m wide. From a point O between them on the river, the angles of elevation of the top of the trees are 60° and 30°, respectively. Find the height of the trees and the distances of the point O from base of the trees. (4)
Answer:
Let AB be the candle and P and Q be the positions of two coins such that coin Q is nearer to the candle.

∴ ∠APB = 3O°, ∠AQB = 6O° BP = a, BQ = b.
Let height of the candle be h.
Now, in ΔABQ,

Caution
in the question, two constants namely. a and b, are given. So, the final answer must contain both the contents. Final answer, with one constant e.g. \(\sqrt{3} b\) or \(\frac{a}{\sqrt{3}}\) is incorrect.
OR
Let AB, CD be the two palm trees of equal heights.
∴ ∠OAB = 60°, ∠OCD = 30°, BD = 80m
Let BO = xm, and AB = CD = hm
Then, OD = BD – OB
= (80 – x) m

Hence, height of the trees is 20\(\sqrt{3}\) m each and distances of the trees from the point O are 20 m and (80 – 20)m, i.e. 60 m.

Question 13.
Case Study-1
A fountain is a decorative reservoir or a structure that jets water into the air for a decorative effect. Nowadays, LEDs of different colours are placed on their bases and by controlling the pressure of water, various dancing fountain shows are organized at different places.

In a society garden, a boundary was constructed around a circular fountain to restrict the children from playing with water.

Suppose the boundary was constructed in the shape of a quadrilateral ABCD, such that the walls AB, BC, CD and DA touches the fountain at points P, Q, R and S respectively.

On the basis of above information, answer the following questions.
(A) If the LED_s are placed along the boundaries of the four walls, then prove that AB + CD = BC + AD. (2)
(B) Let O be the centre of the fountain and ∠PAS = 90°, prove that ASOP is a square. (2)
Answer:
Case Study – 1
(A) We k.now, tangents drawn from an external point to a circle are equal in Length.
∴ AP = AS, BP = BQ, CR = CQ, DR = DS
Adding these equations, we get
AP + BP + CR + DR = AS + BQ + CQ + DS
⇒ (AP + BP) + (CR + DR) = (AS + DS) + (BQ + CQ)
⇒ AB + CD = AD + BC
Hence, proved.

(B) We have

∠PAS = 90°
Also, AP = AS [From part (A)]
And, OS = OP [Radii]
So, in quadrilateral OPAS, adjacent sides are equal and an angle is a right angle.

∴ OPAS is a square.
Hence, proved.

Question 14.
Case Study-2
A tent is a shelter consisting of sheets of various materials draped over, attached to o frame of poles or attached to a supporting rope.

A student adventure camp of 3 dags was organized by the school for class X students. Their accommodation was organized in tents. A group of four students was to share a tent and they were asked to prepare their own tent. The teacher asked them to prepare a conical tent of radius 7 m and for this purpose, they were provided a canvas of area 551 m² in which 1 m² is used in stitching and wasted.

Based on the given information answer the following questions:
(A) Find the height of the tent. (2)
(B) Find the amount of air required by each student in the tent. (2)
Answer:
Case Study – 2
(A) Let L h be the slant height and height of the tent, respectively.
Since, 1m2 of canvas is wasted in stitching
∴ Total canvas present in tent
= 551 – 1 = 550m²
Now, total canvas present in tent
= CSA of tent
= CSAofcone
= πrl

Hence, height of the tent is 24 m.
(B) Amount of air in  = Volume of the tent the tent
= Volume of come

Since, each tent is shared by 4 sutdents,
∴ Amount of air required by each tent

The post CBSE Sample Papers for Class 10 Maths Standard Term 2 Set 2 with Solutions appeared first on Learn CBSE.

Students can access the CBSE Sample Papers for Class 10 Maths Basic with Solutions and marking scheme Term 2 Set 1 will help students in understanding the difficulty level of the exam.

CBSE Sample Papers for Class 10 Maths BasicTerm 2 Set 1 with Solutions

Time allowed: 2 hours
Maximum Marks: 40

General Instructions:

• The question paper consists of 14 questions divided into 3 sections A, B, C.
• Section A comprises of 6 questions of 2 marks each. Internal choice has been provided in two questions.
• Section B comprises of 4 questions of 3 marks each. Internal choice has been provided in one questions.
• Section C comprises of 4 questions of 4 marks each. An internal choice has been provided in one questions. It contains two case study based questions.

Section – A (12 marks)

Question 1.
Find the roots of the quadratic equation 3x² – 7x – 6 = 0.
OR
Find the values of factor which the quadratic equation 3×2 + kx + 3 = 0 has real and equal roots. (2)
Answer:
3x² – 7x – 6 = 0
3x² – 9x.+ 2x – 6 = 0
⇒ 3x(x – 3) + 2(x – 3) = 0
⇒ (x – 3)(3x + 2) = 0
∴ x = 3, -23
OR
Since the roots are real and equal,
∴ D = b²– 4ac = 0
⇒ k² – 4 × 3 × 3 = 0
⇒ k² = 36
⇒ k = 6 or -6
Explanation: The given quadratic equation is : 3x² – 7x – 6 = 0
On splitting the middle term, we get
⇒ 3x² – 9x + 2x – 6 = 0
⇒ 3x(x – 3) + 2(x – 3) = 0
⇒ (3x + 2)(x – 3) = 0
x – 3 = 0
or 3x+ 2 = 0
∴ x = 3
or x = –\(\frac{2}{3}\)
Hence, the vaLues of x are 3 and –\(\frac{2}{3}\)
OR
Explanation: The given quadratic equation is 3x² + kx + 3 = 0.
Condition for the roots of’ equation to be real and equal is D = 0.
i.e., b² – 4ac = 0
Here, a = 3, b = -k, c = 3
Then,
k² – 4 × 3 × 3 = 0
k² = 36
k = +\(\sqrt{36}\)
k = ±6
Hence, required value of k is 6 and – 6.

Question 2.
Three cubes each of volume 64cm3 are joined end to end to form a cuboid. find the total surface area of the cuboid so formed?
Answer:
Let l be the sides of the cube and L, B, H be the dimensions of the cuboid
Since l³ = 64 cm³
∴ l = 4cm
Total surface area of cuboid is
= 2[LB + BH + HL]
Where L = 12.
B = 4
and H = 4
=2(12 × 4 + 4 × 4 + 4 × 12) cm²
= 224 cm²

Explanation: Given : volume of a cube = 64cm³
Let the side of the cube be a cm.
Then, votume of cube = a³
or a³ = 64
∴ a = (64)^1/3
= 4 cm
Here, three cubes are joined. then a cuboid is formed of dimensions.

l = 12cm, b = 4cm, h = 4cm
Then, TSA = 2(lb + bh + hl)
=2(12 × 4 + 4 × 4 + 12 × 4)
= 2(48 + 16 + 48)
= 2 × 112
= 224 cm²

Caution
When we join three cubes to form a cuboid, then its Length will be tripled but breadth and height will remain the same.

Question 3.
An inter house cricket match was organized by a school Distribution of the runs made by the students ¡s given below. Find the median runs scored. (2)

Answer:

Totat frequency (N) = 22
∴ \(\frac{N}{2}\) = 11
So 40 – 60 is the median cLass.
Median = l + \(\frac{\left(\frac{N}{2}\right)-c f}{f}\) × h
= 40 + \(\frac{11-10}{5}\) × 20
= 44 runs
Explanation: Given data is:

Total frequency, N = 22
Then \(\frac{\mathrm{N}}{2}=\frac{22}{2}\) = 11
∴ Median Class = 40 – 60

By formula.
Median = l + \(\left(\frac{\frac{N}{2}-c f}{f}\right)\) × h
Here, lower limit of median class,
l = 40
Cumulative frequency of proceeding class, c.f. = 10
Height of median class, h =20
∴ Median = 40 + \(\frac{(11-10)}{5}\) × 20
= 40 + \(\frac{20}{5}\)
= 40 + 4 = 44
Hence, median value of the data is 44 runs.

Question 4.
Find the common difference of the AP 4, 9, 14, …If the first term changes to 6 and the common difference remains the same then write the new AP. (2)
Answer:
The common difference is 9 – 4 = 5
If the first term is 6 and common difference is 5, then new AP is, 6, 6 + 5, 6 + 10…
= 6, 11, 16……….
Explanation: Here, the given AP is 4, 9,14 ….
In this A, P, a = 4, a₁ = 9, a₂ = 14
Then, common difference,
d = a₁ – a = a₂ – a₁
= 9 – 4 = 14 – 9 = 5
If first term of the AP is 6 and common difference is 5.
Then, new AP is :
6, 6 + 5, 6 + 2 × 5, 6 + 3 × 5
= 6, 11, 16, 21…
Hence, the new AP formed is 6,11,16, 21….

Concept Applied:
Common difference in an AP is the difference between the consecutive terms of the AP., which remains constant. So, by having the first term and the common difference the AP. can be formulated from the same.

Question 5.
The mode of the following frequency distribution is 38. find the value of x. (2)

Answer:
Mode = 38.
∴ The modal class is 30 – 40.
Mode = l + \(\frac{f_{1}-f_{0}}{2 f_{1}-f_{0}-f_{2}}\) × h
⇒ 30 + \(\frac{16-12}{32-12-x}\) × 10 = 38
\(\frac{4}{20-x}\) × 10 = 8
8(20 – x) = 40
20 – x = 5
x = 15
Explanation: Given, distribution is:

The mode of this distribution = 38
Then, modal class is 30 – 40.
By formula,
Mode = l + \(\frac{f_{1}-f_{0}}{2 f_{1}-f_{0}-f_{2}}\) × h

Then, lower limit of modal class,
l = 30
Frequency of modal class
f₁ = 16
Frequency of class proceeding modal class f₀ = 12
Frequency of class suceeding modal class f₀ = x
Then 38 = 30 + \(\frac{(16-12)}{32-12-x}\) × 10
⇒ 8 = \(\frac{40}{20-x}\)
⇒ (20 – x) = 5
⇒ x = 15
Hence, the value of x is 15.

Question 6.
XY and MN are the tangents drawn at the end points of the diameter DE of the circle with centre O. Prove that XY ∥ MN.

OR
In the given figure, a circle is inscribed in the quadrilateral ABCD. Given AB = 6 cm,
BC = 7cm and CD = 4 cm. Find AD. (2)

Answer:

∵ XY is the tangent to the circle at the point D
∴ OD ⊥ XY
∠ODX = 90°
⇒ ∠EDX = 90°
Also, MN is the tangent to the circle at E
OE ⊥ MN
⇒ ∠OEN = 90°
⇒ ∠DEN = 90°
⇒ ∠EDX = ∠DEN (each 90°).
which are alternate interior angles.
∴ XY ∥ MN
OR
∴ Tangent segments drawn from an external point to a circle are equal
BP = BQ
CR = CQ
DR = DS

⇒ BP + CR + DR + AP = BQ + CQ + DS + AS
⇒ AB + DC = BC + AD
∴ AD = 10^-7 = 3cm
Explanation: XY and MN are tangents at end point of diameter DE of circle with centre O.

To prove: XY ∥ MN
Proof: XY is tangent to circle at point D.
∴ ∠ODX = 90°
or ∠EDX = 90°
As tangent is perpendicular to the radius at the point of contact.
Similarly, MN is tangent to circle at point E.
∴ ∠OEN = 90°
or ∠DEN = 90°
∴ ∠EDX = ∠DEN = 90°, which are alternate interior angle
XY ∥ MN

Concept Applied
Use the property of parallel line and angles formed by transversal to get the conclusion.
OR

Given AB = 6 cm
BC = 7 cm
CD = 4cm
By the property of tangents, tangents drawn from an external point to a circle are equal.
∴ AP = AS = x
BP = BQ = y
CQ = CR = z
DR = DS = w
∴ x + y = 6 …(i)
y + z = 7 …(ii)
z + w = 4 …(iii)

Then, by (i) – (ii), we get
x – z = – 1 …(iv)
on adding (iii) and (iv), we get
x + w = 3
i.e. AS + DS =3
or
AD = 3 cm
Hence, Length of AD is 3cm.

Section – B (12 marks)

Question 7.
An AP 5, 8, 11…. has 40 terms. Find the Last term. Also find the sum of the last 10 terms. (3)
Answer:
First term of the AP, (a)= 5
Common difference (d) = 8 – 5 = 3
Last term = a₄₀
= a + (40 – 1)d
= 5 + 39 × 3 = 122
Als0 a₃₁ = a + 30d
= 5 + 30 × 3 = 95

Sum of last 10 terms
= \(\frac{n}{2}\)(a₃₁ + a₄₀)
= \(\frac{10}{2}\)(95 + 122)
= 5 × 217 = 1085

Explanation: Here, the given A.P. is 5, 8,11… number of terms,
n = 40;
first term, a = 5,
common difference, d = 8 – 5 = 3
Then, Last term,
i.e. a₄₀ = a + (40 – 1)d
[∵ a_n = a + (n – 1 )d]
= 5 + 39 × (3)
= 5 + 117
= 122
Since, the AP has total of 40 terms. Then sum of Last 10 terms means sum from 31st term to 40th term.
Then, 31st term 031 = 5 + (31 – 1) × 3
= 5 + 90 = 95

Then, sum of last 10 terms = \(\frac{n}{2}\)(a₃₁ + a₄₀)
= \(\frac{10}{2}\)(95 + 122)
= 5 × 217 = 1085

Question 8.
A tree is broken due to the storm in such a way that the top of the tree touches the ground and makes an angle of 30° with the ground. Length of the broken upper part of the tree is 8 meters. Find the height of the tree before it was broken.
OR
Two poles of equal height are standing opposite each other on either side of the road 80m wide. From a point between them on the road the angles of elevation of the top of the two poles are respectively 60° and 30°. Find the distance of the point from the two poles. 3
Answer:

Let AB be the tree broke not C
Also let AC = x
In ∆CAD,
sin 30° = \(\frac{AC}{DC}\)
⇒ 12 = \(\frac{1}{2}=\frac{x}{8}\)
∴ The length of the tree is
= 8 + 4 = 12m
OR
Let AB and CD be two poles of height h meters also let P be a point between them on the road which is x meters away from foot of first pole AB, PD = (80 – x) meters.
In ∆ABP, tan60° = \(\frac{h}{x}\)
⇒ h = x√3 ……(1)
In ∆CDP, tan30° = \(\frac{h}{80-x}\)
h = \(\frac{80-x}{\sqrt{3}}\) ……..(2)
x√3 = \(\frac{80-x}{\sqrt{3}}\)
[∵ LHS (1) = LHS (2), so equating RHS]
⇒ 3x = 80 – x
⇒ 4x = 80
x = 20m
So, 80 – x = 80 – 20 = 60m
Hence, the point is 20m from one pole and 60 meters from the other pole.

Explanation: Here, PQ is a tree, which is broken at point R and touches the ground at S.

Here, Length of broken tree
RS = 8m
Let, RQ = hm
Then, in ∆RPS
sin 30° = \(\frac{PR}{RS}\)
⇒ \(\frac{1}{2}=\frac{h}{8}\)
⇒ h = 4 m
Then, total height of tree
= PQ
= PR + RS
= 4 +8 = 12 m

Caution
The total height of the tree, is the sum of the length which is still vertical and the portion which is slanted.
OR
Explanation: Here, AB and PQ are the poles of equal height h m consider the observation point R at a distance of x m from B and at a distance of (80 – x)m from Q.

Then, in ∆RPS
tan 60° = \(\frac{h}{x}\)
⇒ √3 = \(\frac{h}{x}\)
h = √3x
Now, in ∆PQR,
tan 30° = \(\frac{\mathrm{PQ}}{\mathrm{QR}}\)
⇒ \(\frac{1}{\sqrt{3}}=\frac{h}{80-x}\)
⇒ 80 – x = √3 h
From (i) and (ii), we get
80 -x = √3 × √3x
⇒ 80 – x = 3x
⇒ 4x = 80
⇒ x = 20 m
Hence, the point is 20 m from the one pole and 60 m from the other pole.

Question 9.
PA and PB are the tangents drawn to a circle with centre O. If PA = 6 cm and ZAPB = 60°, then find the length of the chord AB. (3)

Answer:
PA = PB (tangent segments drawn to a circle from an external, point are equal)
∴ In ∆MPB,
∠PAB = ∠PBA
Also, ∠APB = 60°
In ∆APB, sum of three angles is 180°. Therefore,
∠PAB + ∠PBA = 180° – ∠APB
= 180°- 60°= 120°.
∴ ∠PAB = ∠PBA = 60° (∵ ∠PAB = ∠PBA)

∵ ∆APB is an equilateral triangle.
So, AB = 6 cm
Explanation: Here, PA and PB are tangents to a circle with centre O.

As tangents drawn from an external, point to a circle are equal
Then, PA = PB = 6 cm.
∠PAB = ∠PBA = x
(As angLes opposite to equal side are equal)
∴ In ∆APB,
∠APB + ∠PAB + ∠PBA = 180°
60° + x + x = 180°
2x= 180°—60°
= 120°
x = 600
Then, ∆APS is an equilateral triangle
AP = PB = AB = 6 cm.
Hence, length of chord AB is 6 cm.

Related Theory:
In an equilateral triangles, all the angles are equal to 60° and all the sides are also equal.

Question 10.
The sum of the squares of three positive numbers that are consecutive multiples of 5 is 725. Find the three numbers. (3)
Answer:
Let the three consecutive multiples of 5 be 5x, 5x + 5, 5x + 10.
Their squares are (5x)², (5x + 5)² and (5x + 10)².
(5x)² + (5x + 5)² + (5x + 10)² = 725
⇒ 25x² + 25x² + 50x + 25 + 25x² + 100x + 100 = 725
⇒ 75x² + 150x – 600 = 0
x² + 2x – 8 = 0
(x + 4) (x – 2) = 0
x = -4, 2
x = 2
(ignoring -ve value) So the numbers are 10, 15 and 20

Explanation: Let, three consecutive multiples of 5 be 5x, 5x + 5, 5x + 10
A.T.Q.
(5x)² + (5x + 5)² + (5x + 10)² = 725
⇒ 25x² + 25x² + 50x + 25 + 25x² + 100x + 100
⇒ 75x² + 150x – 600 = 0
⇒ x² + 2x – 8 = 0
⇒ x² + 4x – 2x – 8 = 0
⇒ x(x + 4) – 2(x + 4) = 0
⇒ (x + 4)(x – 2) = 0
⇒ x = -4, 2
∴ x = 2 (∵ x = -4,is not possible)
Hence, the required numbers are 10, 15 and 20.

Section – C (16 marks)

Question 11.
Construct two concentric circles of radii 3 cm and 7 cm. Draw two tangents to the smaller circle from a point P which lies on the bigger circle.
OR
Draw a pair of tangents to a circle of radius 6cm which are inclined to each other at an angle of 60°. Also find the length of the tangent. (4)
Answer:

Draw two concentric circles with center O and radii 3cm and 7cm respectively.
Join OP and bisect it at O’,
so PO’ = O’O
Construct circle with center O’ and radius O’O
Join PA and PB
OR

Draw a circle of radius 6cm
Draw OA and construct
∠AOB =120°
Draw ∠OAP = ∠OBP = 90°
PA and PB are required tangents.
Join OP and apply
tan ∠APO = tan30° = \(\frac{6}{P A}\)
Length of tangent = 6 √3 cm

Explanation: Steps of construction:
(1) Draw two concentric circles of radii 3 cm and 7 cm with centre 0.
(2) Join OP.
(3) Bisect OP at O’.
(4) Then, construct a circle with centre O’ and radius O’O.
(5) The circLe drawn, intersect the inner circle at A and B.
(6) Join PA and PB. .
Hence, PA and PB are the required tangents.

Explanation: Steps of construction:

• Draw a circle of radius 6 cm, with centre 0.
• Draw a radius OA and then draw ∠AOB = 120°.
• Now, draw a 90° angle at point A and B, which intersects at point P.
• So, PA and PB are the required tangents.

For finding the Length of the tangent, join OP.
In ∆OAP
∠OAP = 90°
∠OPA = 30°
∴ tan 30° = \(\frac{\mathrm{OA}}{\mathrm{AP}}\)
⇒ \(\frac{7}{\sqrt{3}}=\frac{6}{\mathrm{AP}}\)
⇒ AP = 6√3
So, length of tangent is 6√3 cm

Caution:
The construction done should be clean and tidy, with a pointed pencil and no overlapping lines.

Question 12.
The following age wise chart of 300 passengers flying from Delhi to Pune is prepared by the Airlines staff.

Find the mean age of the passengers. (4)
Answer:
Converting the cumulative frequency table into exclusive classes, we get

Mean age = x̄ = \(\frac{\Sigma f_{i} x_{i}}{\Sigma f_{i}}\)
= \(\frac{12600}{300}\)
x̄ = 42

Explanation: Given, data is:

Converting the cumulative frequency table into exclusive classes, we get

∴ Mean, x̄ = \(\frac{\Sigma f_{i} x_{i}}{\Sigma f_{i}}=\frac{12600}{300}\)
= 42

Related Theory
For finding the mean of the data, the given data is first of all converted into the form of class intervals and related frequency.

Question 13.
A lighthouse is a tall tower with light near the top. These are often built on islands, coasts or on cliffs. Lighthouses on water surface act as a navigational aid to the mariners and send warning to boats and ships for dangers. Initially wood, coal would be used as illuminators. Gradually it was replaced by candles, lanterns, electric lights. Now a days they are run by machines and remote monitoring.

Prongs Reef lighthouse of Mumbai was constructed in 1874-75. It is approximately 40 meters high and its beam can be seen at a distance of 30 kilometres. A ship and a boat are coming towards the lighthouse from opposite directions. Angles of depression of flash light from the lighthouse to the boat and the ship are 30° and 60° respectively.

(A) Which of the two, boat or the ship is nearer to the light house. Find its distance from the lighthouse? (2)
(B) Find the time taken by the boat to reach the light house if it is moving at the rate of 20 km per hour. (2)
Answer:
(A) The ship is nearer to the Lighthouse as its angle of depression is greater.

In ∆ACB,
tan 60° = \(\frac{\mathrm{AB}}{\mathrm{BC}}\)
⇒ √3 = \(\frac{40}{B C}\)
BC = \(\frac{40}{\sqrt{3}}\)
= \(\frac{40 \sqrt{3}}{3}\)m

(B) In ∆ ADB,
tan 30° = \(\frac{A B}{B D}\)
⇒ \(\frac{1}{\sqrt{3}}=\frac{40}{D B}\)
∴ DB = 40√3 m

Time taken to cover this distance = (\(\frac{60}{2000}\) × 40√3) minutes
= \(\frac{60 \sqrt{3}}{100}\)
= 2.076 minutes

Explanation:

(A) Since, angLe of depression = angle of elevation for a Line of observation
∴ ∠XAC = ∠BCA = 60°
and ∠YAD = ∠ADB = 30°
Now, ship at point C wiLt be nearer to light house, then ship at point D.
As, the ship with greater angle of depression is nearer to Light house.

Now, in ∆ACB,
tan 30° = \(\frac{A B}{B C}\)
√3 = \(\frac{40}{\mathrm{BC}}\)
BC = \(\frac{40}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}}\)
= \(\frac{40 \sqrt{3}}{\sqrt{3}}\) m

(B) Since, boat is at point D.
Now, in ∆ADB,
tan 30° = \(\frac{\mathrm{AB}}{\mathrm{BD}}\)
= BD = \(\frac{40}{\frac{1}{\sqrt{3}}}\) = 40√3m
Then, time token to cover distance

Caution:
Read the question carefully, as in the question instead of marking the points D and C they are designated as boat and ship, which can be identified by the images given.

Question 14.
Krishnanagar is a small town in Nadia District of West BengaL Knshnanagar clay dolls are unique in their realism and quality of their finish. They are created by modelling coils of clay over a metal frame. The figures are painted in natural colours and their hair ¡s made either by sheep’s wool or jute. Artisans make models starting from fruits, animals, God, goddess, farmer, fisherman, weavers to

Donald Duck and present comic characters. These creations are displayed in different national and international museums.
Here are a few images (not to scale) of some clay dolls of Krishnanagar.

The ratio of diameters of red spherical apples in Doll-1 to that of spherical oranges in Doll- 2 is 2 : 3. In Doll-3, male doll of blue colour has cylindrical body and a spherical head, the spherical head touches the cylindrical body. The radius of both the spherical head and the cylindrical body is 3 cm and the height of the cylindrical body is 8 cm.

Based on the above information answer the following question:
(A) What is the ratio of the surface areas of read spherical apples in Doll-1 to that of spherical oranges in Doll-2? (2)
(B) The blue doll of Doll-3 is melted and its clay is used to make the cylindrical drum of Doll-4. If the radius of the drum is also 3 cm, find the height of the drum. (2)
Answer:
(A) Let r₁ and r₂ be respectively the radii of apples and oranges
∴ 2r₁ :2r₂ = 2:3
⇒ r₁ : r₂ = 2 : 3
4πr₁² : 4πr₂²
= \(\left(\frac{r_{1}}{r_{2}}\right)^{2}=\left(\frac{2}{3}\right)^{2}\) = 4 : 9

(B) Let, the height of the drum be h cm
Volume of drum of drum = Volume of cylinder + Volume of sphere
3π²h = (3π² × 8 + \(\frac{4}{3}\)3π³)cm³
⇒ h = (8 + 4)cm
⇒ h = 12cm

Explanation: (A) Consider, r₁ and r₂ as the ratio of apples and oronges.

Let, the height of the drum be h cm
Volume of drum of doll. 4 = Volume of cylindrical doll 3
∴ Volume of cylinder of doll = Volume of cylinder + Volume of sphere
⇒ π × 3²h = π × 3³ × 8 + \(\frac{4}{3}\)π × 3³
⇒ h = 8 + 4
⇒ h = 12 cm

The post CBSE Sample Papers for Class 10 Maths Basic Term 2 Set 1 with Solutions appeared first on Learn CBSE.

Students can access the CBSE Sample Papers for Class 10 Maths Basic with Solutions and marking scheme Term 2 Set 4 will help students in understanding the difficulty level of the exam.

CBSE Sample Papers for Class 10 Maths BasicTerm 2 Set 4 with Solutions

Time allowed: 2 hours
Maximum Marks: 40

General Instructions:

• The question paper consists of 14 questions divided into 3 sections A, B, C.
• Section A comprises of 6 questions of 2 marks each. Internal choice has been provided in two questions.
• Section B comprises of 4 questions of 3 marks each. Internal choice has been provided in one questions.
• Section C comprises of 4 questions of 4 marks each. An internal choice has been provided in one questions. It contains two case study based questions.

Section – A (12 marks)

Question 1.
Write the equation x = \(\sqrt{6+\sqrt{6+\sqrt{6}}}\)…. in the form of a quadratic equation, where, x is a natural number.
OR
State whether the equation (x + 1) (x – 2) + x = 0 has two distinct real roots or not. Justify your answer. (2)
Answer:
We have:
x = \(\sqrt{6+\sqrt{6+\sqrt{6}}}\) ……
On squaring both sides, we get
x² = \(6+\sqrt{6+\sqrt{6+\sqrt{6}}}+\ldots .\)
x² = 6 + x
⇒ x² – x – 6 = 0,
which is the required quadratic equation.

Concept Applied:
In algebra a quadratic equation is any equation that can be rearranged in standard form as ax² + b + c = 0 where x represents an unknown variable, a, b and c represent known numbers where a ≠ 0, If a = 0, then equation is linear, not quadratic.
OR
(x + 1) (x – 2) + x = 0
⇒ x² – x – 2 + x = 0
⇒ x² – 2 = 0
We get, a = 1, b = 0 c = 2
∵ D = b² – 4ac
∴ 0 – 4 × 1 × (- 2) = 8 > 0
Hence, given equation has two district real roots.

Caution:
Convert the equation in the form ax² + bx + c = 0, to get the discriminant of the quadratic equation.

Question 2.
To make the walls of the room beautiful wallpaper is required. The wallpaper is 312 cm long and 25 cm wide. Length of the room is 7 m and its breadth is twice its height. Calculate the height of the room. (2)
Answer:
Area of wallpaper = 312 × 0.25
= 78.00 m²
Length of room = 7 m
Let, height of room be x m, then breadth is 2x
∴ Area of four walls = 2(l × h + b × h)
A.T.Q 4x² + 14x = 78
⇒ 2x² + 7x – 39 = 0
⇒ 2x² + 13x – 6x – 39 = 0
⇒ x(2x + 13) – 3(2x + 13) = 0
⇒ x = 3 or x = \(\frac{-13}{2}\) (rejected)
Hence, height of room is 3 m.

Caution:
Use the splitting of middle term method to get the value of x, in the quadratic equation formed in the condition.

Question 3.
Determine the median class for the following distribution: (2)

Answer:

Here N = 3
\(\frac{\mathrm{N}}{2}\)
= 16.5
Since \(\frac{\mathrm{N}}{2}\) = 16 – 5 Then, median class is 40-50 ’

caution:
Median class is the class having the cumulative frequency just greater than \(\frac{\mathrm{N}}{2}\).

Question 4.
If the sum of four numbers in A.P. are such that their sum is 50 and greatest number is 4 times the least, then evaluate the numbers. (2)
Answer:
Consider the numbers as a, a + d, a + 2d, a + 3d
A.T.Q., a + a + d+ a + 2d+a + 3d = 50
⇒ 4a + 6d = 50
⇒ 2a + 3d = 25 ………. (i)
and
a + 3d = 4a
3d = 3a
⇒ a = d …(ii)
From equations (i) and (ii), we get
a = d = 5
Numbers are 5, 10, 15, 20

Question 5.
Determine the mode of the following data (2)

Answer:
Here, the class with maximum frequency is 40-60
∴ Mode = l + \(\frac{f_{1}-f_{0}}{2 f_{1} f_{0}-f_{2}}\) × h
= 40 + \(\frac{18-6}{36-6-10}\) × 20
⇒ 40 + \(\frac{12 \times 20}{20}\) = 52

Question 6.
In the figure, AT is a tangent to the circle with centre O, such that OT = 8 cm and ∠OTA = 30°. What is the length of AT?

In the figure, if AB = AC, then prove that BE = EC. (2)

Answer:
Here, AT is the tangent to the circle with centre O.
∴ ∠OAT = 90° (By property of tangent)
In ∆OAT,
cos 30° = \(\frac{\mathrm{AT}}{\mathrm{OT}}\)
⇒ \(\frac{\sqrt{3}}{2}\) = \(\frac{\text { AT }}{8}\)
⇒ AT = 4√3 cm

Caution:
Use the property of tangent and trigonometric ratios to get the answer.
OR
Given: AB = AC
To Prove: BE = EC
Since, length of tangent from an external point are equal.
∴ AD = AF ….. (i)
BE = BD …(ii)
EC = CF …(iii)
But, AB = AC (Given)
AD + BD = AF + FC
⇒ AF + BD = AF + FC [from (i)]
⇒ BD = CF
⇒ EC = CF [From (ii) and (iii)]
Hence, proved.

Section – B (12 Marks)

Question 7.
The sum of n terms of an A.P., whose first term is 6 and common difference is 40 is equal to the sum of 2n terms of another A.P., whose first term is 40 and common difference is 6. Find n. (3)
Answer:
For 1^st A.P.
First term, a = 6,
Common difference, d= 40
Sum of n terms = \(\frac{n}{2}\) [2 × 6 + (n – 1) × 40]
= \(\frac{n}{2}\) [12 + 40n – 40]
= \(\frac{n}{2}\) [40n – 28]
For II^nd A.P.
First term A = 40.
Common difference, d = 6
Sum of 2n terms = \(\frac{2n}{2}\)[2 × 40 + (2n – 1)6]
= n[80 + 12n – 6]
= n[74 + 12n]
A.T.Q.,
\(\frac{n}{2}\)(40n – 28) = n(74 + 12n)
⇒ 40n – 28 = 148 + 24n
⇒ 16n = 176
n = 11

Question 8.
In the given figure, a bird is flying at the point A and two persons are standing at the point B and D, such that D is the mid-point of BC and observing the bird. Then, find the value of \(\frac{\tan x^{\circ}}{\tan y^{\circ}}\)

OR
In an experiment, some masses are hung in equilibrium as shown in the figure. AB = 40 cm, ∠CAB = 45° and ∠CBA = 30°.
Find
(A) the perpendicular distance of AB from C.
(B) the length of AC
(C) the length of BC (3)
Answer:
Here, D is the mid-point of BC

∴ BD = CD
In ∆ACD
tan x° = \(\frac{\mathrm{AC}}{\mathrm{CD}}\)
In ∆ACB
tan y° = \(\frac{\mathrm{AC}}{\mathrm{BC}}\)
= \(\frac{\mathrm{AC}}{2 \mathrm{CD}}\) (∵ BD = CD)
∴ \(\frac{\tan x^{\circ}}{\tan y^{\circ}}\) = \(\frac{A C / C D}{A C / 2 C D}\)
= \(\frac{2 C D}{C D}\)
= 2 : 1

Related Theory:
Value of tangent of an angle depends on the dimensions of perpendicular and base.
OR

(i) Draw CD ⊥ AB

In right angled ∆ADC
\(\frac{A D}{C D}\) = cot 45°
⇒ AD = CD
In right ABDC
\(\frac{B D}{C D}\) = cot 30° = √3
⇒ BD = √3 CD
Adding (i) and (ii), we get
40 = AD + BD
40 = CD + √3CD
40 = 2.732 CD
CD = \(\frac{40}{2.732}\)
= 14.64 cm
≈ 14.6 cm

(ii) In right ∆ADC
\(\frac{C D}{A C}\) = sin 45°
⇒ AC = √2CD
= 0.414 × 14.64
= 20.7 cm

(iii) In right ∆BDC
\(\frac{C D}{B C}\) = sin 45°
⇒ BC = 2 × CD
= 2 × 14.64 = 23.68
≈ 29.3 cm

Caution:
Here, drawing of line CD is important to calculate the value of the required sides as by drawing it, the right-angled triangles are obtained which are used to calculate the required sides by using trigonometric ratios.

Question 9.
In the given figure, calculate the perimeter of ∆PCD (3)

Answer:
Here, PA = 10 cm
Since, tangents from an external point are equal
∴ PA = PB = 10 cm ….(i)
Now, CA and CE are also the tangents from an external point C.
∴ CA = CE …(ii)
Similarly, DB = DE …(iii)
Perimeter of ∆ PCD = PC + CD + PD
= PC + CE + ED + PD
= PC + CA + DB + PD [Using (ii) and (iii)]
= DA + PB
= 2PA [Using (i)]
= 2 × 10 = 20 cm

Related Theory
(A) When a point lies outside the circle, then two tangents can be drawn from that point to the circle.
(B) When a point lies on the circle, then a single tangent can be drawn.
(C) When a point lies inside the circle, then no tangent can be drawn.

Question 10.
If the roots of the quadratic equation p(q – r) x² + q(r – p)x = 0 are equal, then show \(\frac{1}{p}+\frac{1}{r}=\frac{2}{q}\) (3)
Answer:
Given, quadratic equation is:
p(q – r)x² + q(r – p)x + r(p – q) = 0
On comparing the given equation with standard equation:
ax² + bx + c = 0
Here, a = p(q – r), b = q (r – q), c = r(p – q)
∴ D = b² – 4ac
= [q(r – p)]² – 4 × p(q -r) × r(p – q)
= q²(r – p)² – 4pr(q – r)(p – q)
= q²(r² + p² – 2pr) – 4pr(pq – pr – q² + qr)
= q²r² + q²p² – 2prq² – 4p²qr + 4p²r² – 4p²q
= q²r² + q²p² + 2prq² – 4p²qr + 4p²r² – 4pqrv
∴ D = (2 pr – qr – pq)²
For equal roots, = 0
(2pr – qr – qp)² = 0
⇒ 2 pr – qr – qp =0
⇒ qr + qp = 2 pr
On dividing both sides by pqr, we get
\(\frac{q r}{p q r}+\frac{q p}{p q r}\) = \(\frac{2 p r}{p q r}\)
⇒ \(\frac{1}{p}+\frac{1}{r}\) = \(\frac{2}{q}\)

Related Theory:
When, discriminant D = b² – 4ac is (positive) we get two real solutions.
When D = 0, then we get just one real solution (both answers are the same).
When it is negative, we get a pair of complex solution.

Section – C (16 marks)

Question 11.
Draw a pair of tangents to a circle of radius 5 cm which are inclined to each other at angle of 80°.
OR
Draw two concentric circles of radii 3 cm and 5 cm. Construct a tangent to smaller circle from a point on the larger circle. Also, measure its length. (4)
Answer:

Steps of construction:

1. Draw a circle with center O and radius 5cm.
2. Draw any radius OA.
3. At point O, construct ∠AOB = 100°, intersecting the circumference of the circle at B.
4. At points A and B, construct ∠OAX = ∠OBY = 90° respectively.

Let ray AX and BY intersect each other at point P.
Then, AP and BP are the required tangents to the circle, which are inclined to each other at an angle of 80°.
OR

Steps of construction:

1. Take point O. Draw 2 concentric circles of radii 3 cm and 5 cm respectively.
2. Mark point P on the circumference of the larger circle.
3. Join OP and bisect it
4. Let M be its mid-point
5. Taking M as a centre and MP as the radius, draw the arc intersecting smaller circle at A and B
6. Join PA and PB.
   Thus, PA and PB are the required tangents

Caution:
Draw the figure, with a pointed pencil, so the lines should not be overlapping and untidy.

Question 12.
The following table given production yield per hectare of wheat of 100 farms of a village

Change to the distribution a ‘less than type’ distribution and find its mean. (4)
Answer:
The given data could be converted to less than type distribution.

Now for mean,
This is the required distribution

Then, mean = A + \(\frac{\Sigma f_{i} u_{i}}{\Sigma f_{i}}\)
= 67.5 + \(\frac{180}{100}\)
= 69.3

Question 13.
Case Study-1
Sara and Hema, went to enjoy their holidays in a hill station Himachal Pradesh blessed with spectacular and gorgeous mountains and river valleys. Himachal Pradesh is India’s outdoor adventure playground. Both of the girls were thrilled about the fascinating experience of the state. During day time Sara, who is standing on the ground spots a paraglider at a distance of 24 m from him at an elevation of 30°. Her friend, Hema is also standing on the roof of a 6m high balcony, observes the same paraglider at the angle of elevation of 45°. Both of them are on the opposite sides of the paraglider.

(A) How high is the paraglider flying from the ground? (2)
Answer:
Here, paraglider is at the points D and he/ she is at a distance of DQ from the ground.
In ∆ADQ, sin 30° = \(\frac{\mathrm{DQ}}{\mathrm{AD}}\)
⇒ \(\frac{1}{2}\) = \(\frac{\mathrm{DQ}}{24}\)
⇒ DQ = 12 cm
Hence, height at which paraglider flying is 12 cm.

(B) How far is paraglider from the girl standing on the roof of the building? (2)
Answer:
The girt standing on the roof of the building is Hema.
Here, DQ = 12 m
and PQ = BC = 6 cm
∴ DP = DQ – PQ
= 12-6 = 6 m
∴ In ∆BPD, sin 45° = \(\frac{\mathrm{DP}}{\mathrm{BD}}\)
\(\frac{1}{\sqrt{2}}\) = \(\frac{6}{\mathrm{BD}}\)
⇒ BD = 6√2 m
Hence, distance between paralider and Hema is 6√2 m.

Question 14.
Case Study-2
Every one is very much excited when a New year begins with a new caiendar, Despite it is very cold on that day, but still everybody enjoy having ice-creams as desserts So, to make it fun. On the occasion of New Year, Shweta’s father bought an ice-cream brick. For making it interesting, she bought some ice-cream cones along with it, as children enjoy eating ice-cream in cones.

He bought a 1.51 ice cream brick, whose dimensions are (30 × 25 × 10) cm³. The ice¬cream is filled in the cones in the shape of hemisphere on it, whose radius is 3.5 cm. The height of the cone is 15 cm and radius is 3.5 cm.

(A) If each cone needed to be filled upto brim, then how many scoops are required to fill the cone? (2)
Answer:
Volume of a cone = \(\frac{1}{3}\) ≠ r²h
= \(\frac{1}{3}\) × \(\frac{22}{7}\) × (3.5)² × 15
= \(\frac{4042.5}{21}\)
= 192.5 cm³

Volume of one scoop = \(\frac{2}{3}\) ≠ r³
= \(\frac{2}{3}\) × \(\frac{22}{7}\) × 3.5 × 3.5 × 3.5
= \(\frac{1886.5}{21}\)
= 89.83 cm³
∴ Number of scoops required
= \(\frac{\text { Volume of cone }}{\text { Volume of one scoop }}\)
= \(\frac{192.5}{89.83}\) = 2.14 ≈ 2

(B) If the complete ice-cream in the brick is distributed in cones, how many cones will be filled by the ice-cream. (2)
Answer:
(B) Volume of ice-cream brick
= l × b × h
= 30 × 25 × 10
= 7500 cm³

Volume of 1 cone = \(\frac{1}{3}\) ≠ r²h
= \(\frac{1}{3}\) × \(\frac{22}{7}\) × 3.5 × 3.5 × 15
= 192.5 cm³
∴ Number of cones needed to distribute complete ice-cream
= \(\frac{7500}{192.5}\)
= 38.96
≈ 39 cones
Hence, total ice-cream can be distributed in 39 cones.

The post CBSE Sample Papers for Class 10 Maths Basic Term 2 Set 4 with Solutions appeared first on Learn CBSE.

Students can access the CBSE Sample Papers for Class 10 Maths Basic with Solutions and marking scheme Term 2 Set 3 will help students in understanding the difficulty level of the exam.

CBSE Sample Papers for Class 10 Maths BasicTerm 2 Set 3 with Solutions

Time allowed: 2 hours
Maximum Marks: 40

General Instructions:

• The question paper consists of 14 questions divided into 3 sections A, B, C.
• Section A comprises of 6 questions of 2 marks each. Internal choice has been provided in two questions.
• Section B comprises of 4 questions of 3 marks each. Internal choice has been provided in one questions.
• Section C comprises of 4 questions of 4 marks each. An internal choice has been provided in one questions. It contains two case study based questions.

Section – A (12 marks)

Question 1.
By mistake, the coefficient of x in quadratic equation x² + ax + b = 0 was taken as 17 in place of 13; whose roots were found to be – 2 and – 15. What are the roots of the original equation?
OR
In the equation (c² – ab) x² – 2(a² – bc)x + b² – ac = 0, if the roots are equal, then show that either q = 0 or a³ + b³ + c³ = 3abc. (2)
Answer:
When coefficient of x is 17. roots of the equation are -2 and -15.
i.e x² + 17x + b = 0
⇒ (-2)² + 17(–2) + b = 0
⇒ b = 30
Now, original equation becomes
x² + 13x + 30 = 0
x² + 10x + 3x + 30 = 0
⇒ x(x + 10) + 3(x + 10) = 0
⇒ x = -10,-3
Hence, original roots are – 3 and – 10.
OR
The given equation is;
(c² – ab)x² – 2(a² – bc)x + b² – ac = 0
Since, roots ore equal
∴ D = 0
or B² – 4AC = 0
∴ 4(a² – bc)² – 4(c² – ab) (b2 -ac) = 0
⇒ 4[a⁴ + b²c² – 2a²bc – b²c² + ac + ab³ – a²bc] = 0
⇒ a⁴ – 3a²bc + ac³ + ab³ = 0
⇒ a(a³ + b³ + c³ – 3abc) = 0
Either a = 0 or a³ + b³ + c³ = 3abc.

Question 2.
If in an A.P., the sum of first p terms is ap² + bp, then what is its common difference. (2)
Answer:
Here, S_p = ap² + bp
Then S_p-1 =a(p – 1)² + b(p – 1)
∴ a_p = S_p — S_p-1
= (ap² + bp) -[a(p – 1)² + b(p- 1)]
= ap² + bp – (ap² + a – 2ap + bp – b)
= ap² + bp – ap² – a + 2ap – bp + b)
= ap² + bp – ap² – a + 2ap – bp + b
= 2ap + b – a
a₁ = 2a + b – a, (p = 1)
= a + b
a₂ = 4a + b – a
= 3 a + b
d = a₂ – a₁
= (3o + b) – (a + b)
= 2a

Question 3.
The mean of the following data is 12, then what is the value of p? (2)

Answer:
Here, the given data is

But, mean = 12
x̄ = \(\)
12 = \(\)
12p = 348 – 204
p = \(\frac{144}{12}\) = 12

Caution
Draw the appropriate table, and use the required formula for finding the value

Question 4.
A student taking a test consisting of 10 questions is told that each question after the first question is worth 2 marks more then the preceeding questions. If third question of the test is worth 5 marks, what is the maximum score that the student can obtain by attempting 8 questions? (2)
Answer:
Here, difference between 2 questions is of 2 marks.
∴ d = 2
Numbers of questions
n = 10
And a= 5
∴a + (n – 1)d = 5
⇒ a + (3 – 1) × 2 = 5
⇒ a = 5 – 4 = 1
If n = 8, then maximum marks obtained when starting question 3 is.

S₈ = \(\frac{n}{2}\)[2a + (n – 1)d]
= \(\frac{8}{2}\) [2 × 5 + (8 – 1) × 2]
= 4(10 + 14)
= 4 × 24
= 96
Hence, 96 is the maximum marks obtained by the student.

Caution
Here, maximum marks will be obtained by solving the question of the maximum mark i.e. questions in the last.

Question 5.
Find the value x and y from the given cumulative distribution. (2)

Answer:
From the cumulative frequency distribution:
15 + x = 28
⇒ x= 28-15 = 13
and 43 + 18 = y
⇒ y = 61
Hence, value of x is 13 and y is 61.

Question 6.
A toy is in the shape of a hemisphere surmounted by a cone, as shown in the figure

What is the surface area of the complete toy ?
OR
The figure shows a wax candle in the shape of right circular cone with base radius 5 cm and height 12 cm. It takes 1 hour 40 minutes to burn completely

What is volume of the candle before it started burning? (2)
Answer:
Area of toy = C.S.A of cone + C.S.A. of hemisphere
= πrl + 2πr²

= 20.30 + 19.25
= 39.55
≅ 40 sq. cm
OR
Here, shape of the candle is a cone, whose height,
h = 12 cm and radius,
r = 5 cm
∴ Volume of the candle = πr²h
= π × 5 × 5 × 12 = 300 π cm²

Caution
Candle when not burnt, will be in the shape of a cone.

Section – B

Question 7.
If PA and PB are any two tangents drawn from a point P to a circle with centre O, touching it at A and B, then prove that OP is the perpendicular bisector of AB. (3)
Answer:
Let OP intersect AB at a point C. Here, PA and PB are the two tangents from a point P lying outside the circle, to the circle with centre O.

∠APO = ∠BPO
[∵ O Lies on the bisector of ∠APB]
Now, in ∆ACP and ∆BCP, we have
AP = BP (tangents from an external point)
PC = PC (Common)
∠APO = ∠BPO (Proved above)
⇒ ∆ACP ≅ ∆BCP [By SAS congruence axiom]
⇒ AC = BC [by c.p.ct]
And ∠ACP = ∠BCP
⇒ \(\frac{1}{2}\) × 180 = 90° [by c.p.ct]
Hence OP is the perpendicular bisector of AB.

Question 8.
A man is standing on the deck of a ship, which is 10 m above water level and observes the angle of elevation of the top of a hill as 60° and angle of depression of the base as 30°. Find the distance of the hill from the ship and height of the hill.
OR

At a point P, 20 metres above the level of water in a lake, the angle of elevation of a cloud is 30°. The angle of depression of the cloud in the lake, at P is 60°. Find the distance of the cloud from P? (3)
Answer:
Here, PQ is the deck of the ship and man is standing at the point P. AC is a hill and from point P, the angle of elevation is 60° and angle of depression is 30°

∴ In ∆PQC,
tan 30° = \(\frac{\mathrm{PQ}}{\mathrm{QC}}\)
\(\frac{1}{\sqrt{3}}=\frac{10}{Q C}\)
⇒ QC = 10√3 m
Now, QC = PB = 10√3 m

Now, in ∆ABP
tan 60° = \(\frac{AB}{PB}\)
√3 = \(\frac{\mathrm{AB}}{10 \sqrt{3}}\)
AB = 30 m

∴ Distance of hill from ship = 10√3 m
and height of the hill = AB + BC
= 30 + 10
= 40 m

Related Theory
Angie of elevation denotes the angle from the horizontal upward to an object. And angle of depression denotes the angle from the horizontal downward to an object.
OR
Let BP be x m

In ∆BPC
tan 30° = \(\frac{\mathrm{BC}}{\mathrm{BP}}\)
\(\frac{1}{\sqrt{3}}=\frac{h}{x}\)
⇒ x = √3h ………..(i)

From ∆PBO
tan 60° = \(\frac{\mathrm{BO}}{\mathrm{PB}}\)
⇒ √3 = \(\frac{20+20+h}{x}\)
x = \(\frac{40+h}{\sqrt{3}}\) ……….(ii)

From (i) and (ii)
\(\frac{40+h}{\sqrt{3}}\) = √3h
⇒ 3h = 40 + h
⇒ 2h = 40
h = 20 m
x = \(\frac{40+20}{\sqrt{3}}\)
= \(\frac{60}{\sqrt{3}}\)
= 20√3

PC = \(\sqrt{B C^{2}+P B^{2}}\)
= \(\sqrt{20^{2}+(20 \sqrt{3})^{2}}\)
= \(\sqrt{400+1200}\)
= \(\sqrt{1600}\)
= 40 m

Caution
Here, final answer that is to be calculated is the distance between cloud and the observer not the height of the cloud from the lake.

Question 9.
In the figure, ABC is a right-angled triangle with AB = 6 cm and AC = 8 cm. A circle with centre O has been inscribed inside the triangle. Calculate the value of r, the radius of the inscribed circle. (3)

Answer:
In ∆ABC, BC² = AC² + BA²
BC = \(\sqrt{8^{2}+6^{2}}=\sqrt{100}\) = 10 cm
Join OA, OB and OC
Now, area of (∆OAC + ∆OAB + ∆BOC) = Area of ∆ABC
⇒ \(\frac{1}{2}\) × 8 × r + \(\frac{1}{2}\) × 6 × r + \(\frac{1}{2}\) × 0 × r = \(\frac{1}{2}\)
⇒ 4r + 3r + 5r = 24
⇒ 12r = 24
⇒ r = 2 cm

Question 10.
Prove that the lengths of tangents drawn from an external point to a circle are equal. (3)
Answer:
Let, AP and AQ be two tangents drawn to the circle from the externaL point A.

We need to show that AP = AQ
Join OA, OP and OQ
Consider ∆OPA and ∆OQA
Here, OP = OQ (Radius of the circle)
OA = OA (Common)
∠OPA = ∠OQA = 90°
(by property of tangent)
∴ ∆OPA ≅ ∆OQA
∴ PA = QA or AP = AQ

Caution
While proving any statement, give all the necessary steps in the detailed manner, with the reason.

Question 11.
From the first floor of Qutub Minor, which is at a height of 25 m from the level ground, a man observes the top of a building at an angle of elevation of 30° and angle of depression of the base of the building to be 60°. Calculate the height of the building.
OR
Two pillars of equal height, stand on either side of a roadway which is 150 m wide. From a point on the roadway between the pillars, the elevations of the top of the pillars are 60° and 30°. Find the height of the pillars and the position of the point at which angle
of elevation is calculated. [Use √3 = 1.732] (4)
Answer:
Let, the first floor of Qutub Minar AB be at the point X.

Let MN represent the building.
Here, XT ∥ AM.

Thus, the height of the building MN = MT + TN
= (25 + \(\frac{25}{3}\))
= \(\frac{100}{3}\) m
= 33\(\frac{1}{3}\) m
OR
Let h metres be the height of each pillar and point P be x metres away from pillar AB point

In ∆PCD,
\(\frac{h}{PC}\) = tan 60° = √3
⇒ PC = \(\frac{h}{\sqrt{3}}\) …….(i)

In ∆PAB,
\(\frac{h}{PA}\) = tan 30° = \(\frac{1}{\sqrt{3}}\)
PA = √3h ……..(ii)
Now, PA + PC = 150
√3h + \(\frac{h}{\sqrt{3}}\) = 150
⇒ 3h + h = 150√3
⇒ 4h = 150√3
h = \(\frac{150 \sqrt{3}}{4}\)
= 64.875 m
Also, PA = √3h
= √3 × \(\frac{150}{4}\) × √3
= 112.5 m
Thus, the height of the pillar is 64.875 m and the position of the point is at a distance of 112.5 m from the pillar AB.

Caution
Here, point ¡s in between the two plU ors, not the mid point of AC

Question 12.
If the diameter of cross- section of a wire is decreased by 5%. By how much percent will length be increased, so that the volume remains the same ? (4)
Answer:
If R be the radius and H be the height of the wire.
∴ Original volume = πR²H
When diameter is decreased by 5%, then radius is also decrease by 5%
New radius = R – \(\frac{5 R}{100}=\frac{95 R}{100}=\frac{19 R}{20}\)
New Radius = π\(\left(\frac{19 R}{20}\right)^{2}\)H
= \(\frac{\pi H \times 361 R^{2}}{400}\)
But we have to maintain the volume at the constant level, so length H is to be multiplied by \(\frac{400}{361}\) to keep it constant.

So, new length = \(\frac{400H}{361}\)
% Increase in Length = \(\frac{\frac{400 \mathrm{H}}{361}-\mathrm{H} \times 100}{361 \mathrm{H}}\)
= \(\frac{39}{361}\) × 100
= 10.8%

Question 13.
Case Study—1
Arithmetic progression has a wider application in day-to-day Life It can be applied in real life by analysing a certain pattern. For example, AP is used in straight Line depreciation, etc. The arithmetic sequence is important in real life because this enables us to understand things with the use of patterns. It is also important in stimulating systematic events. One use of arithmetic progression is in tissue paper roll, in which the first term is the diameter of the core of the roll and twice the thickness of the paper is the common difference. If sum of first n rolls of tissue and on a roll is S_n = 0.1n² + 7.9 n then answer the following questions.

(A) What is the nth term in the given sequence? (2)
(B) What is the common difference of the progression formed by tissue rolls? (2)
Answer:
Case Study—1
(A) Here.
S_n = 0.1n² + 7.9 n
Then a_n = S_n – S_n-1
= O.1n² + 7.9n – [0.1 (n – 1)² + 79(n – 1)]
= O.1n² + 7.9n – [0.1(n² + 1 – 2n) + 79n – 7.9]
= O.1n² + 7.9n – [0.1n² + 0.1 – 0.2n + 7.9n + 7.9]
= 7.9n – 0.1 + 0.2n – 7.9n + 7.9
= 7.8n + 0.2n

(B) S₁ = a₁ = 0.1(1)² + 7.9(1)…(i)
= 8
a₂ = S₂ – S₁ = 0.1(2)² + 7.9(2) – 8
= 0.4 + 15.8 – 8
= 16.2 – 8
= 8.2
Then, d = a₂ – a₁ = 8.2 – 8 = 0.2

Question 14.
Case Study—2
National Highway Authority of India (NHAI) has installed toll tax plaza or collection centre on highway for the maintenance of roads and highways. NHAI had set up booths to collect the toll taxes. They collect the toll tax only from the four wheeler or larger vehicle drivers who pass by toll roads. The central government levy fees at such rates as may be laid down by rules made in this behalf for services or benefits rendered in relation to the use to ferries, permanent bridges and tunnels on national highways and the use of sections of national highways.

On a particular day, NHAI checked the toll tax collection of a particular toll plaza in Mathura Uttar Pradesh.
The table shows the toll tax paid by drivers and the number of vehicles on that particular day:

(A) What is the mean value of the toll tax received by NHAI on a particular day from a particular toll plaza? (2)
(B) What is the median value of the given data? (2)
Answer:

∴ Mean = \(\frac{\Sigma f_{i} x_{i}}{\Sigma f_{i}}\)
= \(\frac{21900}{420}\)
= 52.14 (approx)

(B)

Now, \(\frac{N}{2}=\frac{420}{2}\)
= 210
Median doss = 50 – 60
Then median = l + \(\frac{\frac{N}{2}-c f}{f}\) × h
= 50 + \(\frac{210-190}{110}\) × 10
= 50 + \(\frac{200}{110}\)
= 50 + 1.81
= 51.81

The post CBSE Sample Papers for Class 10 Maths Basic Term 2 Set 3 with Solutions appeared first on Learn CBSE.

Students can access the CBSE Sample Papers for Class 10 Maths Basic with Solutions and marking scheme Term 2 Set 4 will help students in understanding the difficulty level of the exam.

CBSE Sample Papers for Class 10 Maths BasicTerm 2 Set 4 with Solutions

Time allowed: 2 hours
Maximum Marks: 40

General Instructions:

• The question paper consists of 14 questions divided into 3 sections A, B, C.
• Section A comprises of 6 questions of 2 marks each. Internal choice has been provided in two questions.
• Section B comprises of 4 questions of 3 marks each. Internal choice has been provided in one questions.
• Section C comprises of 4 questions of 4 marks each. An internal choice has been provided in one questions. It contains two case study based questions.

Section – A (12 Marks)

Question 1.
If for the quadratic equation 2x² + kx – 6 = 0, 2 is one of its root, then find the value of k. Also, find the value of the other root.
OR
The sum of squares of three consecutive positive integers are 50. Then what are the three integers? (2)
Answer:
Since, x = 2 is a root of the equation. 2x² + kx – 6 = 0
∴ 2 × 2² + k × 2 – 6 = 0
⇒ 8 + 2k – 6 = 0
⇒ k = – 1
Put k = – 1 in the equation.
2x² + kx – 6 = 0
We get
2x² – x – 6 = 0
⇒ 2x² – 4x + 3x – 6 = 0
⇒ 2x(x – 2) + 3(x – 2) = 0
⇒ x = 2, \(\frac{-3}{2}\)

Caution:
First, find the value of k, to formulate the equation. Then, find the roots of the quadratic equation
OR
Consider three consecutive integer as x, x + 1 and x + 2.
A.T.Q x² + (x + 1)² + (x + 2)² = 50
⇒ x² + x² + 1 + 2x + x² + 4 + 4x = 50
⇒ 3x² + 6x – 45 =0
⇒ 3(x² + 2x – 15) = 0
⇒ x² + 2x – 15 = 0
⇒ x² + 5x – 3x – 15 = 0
⇒ x(x + 5) – 3(x + 5) =0
⇒ x = 3, – 5
x ≠ – 5 (rejected)
Hence, integers are 3, 4, 5.

Question 2.
The surface area of a sphere and a cube are equal. Then, find the ratio of their volumes. (2)
Answer:
Let, surface area of sphere be x cm²
⇒ 4πr² = x
⇒ r = \(\sqrt{\frac{x}{4 \neq}}\) cm,
where, r is the radius of the sphere Also, surface area of cube be x cm²
⇒ 6 × side² = x
⇒ side = \(\sqrt{\frac{x}{6}}\) cm

Caution:
Apply the exponents property in the end to solve the question and get the answer.

Question 3.
The daily minimum steps climbed by a man during a week were as under.

What are the mean of the steps? (2)
Answer:
Number of steps climbed in a week:
35, 30, 27, 32, 23, 28
Mean = \(\frac{\text { Sum of observations(Steps) }}{\text { Total no. of observations }}\)
= \(\frac{35+30+27+32+23+28}{6}\)
= \(\frac{175}{6}\)
= 29.17

Question 4.
The sum of first 6 terms of on AP. is 42. The ratio of its 11th term is 1: 3. CaLcuLate the first term of an AP. (2)
Answer:
Let the first term of the AP be a and common difference be ‘d’.
Now, S₆ = 42
⇒ \(\frac{6}{2}\)(2a + 5d) = 42
2a + 5d = 14
Also, \(\frac{a_{11}}{a_{33}}\) = \(\frac{1}{3}\)
⇒ \(\frac{a+10 d}{a+32 d}\) = \(\frac{1}{3}\)
⇒ 3a + 30 d = a + 32 d
⇒ 2a = 2d
⇒ a = d
Put a = d in equation (i), we get 2a + 5 = 14
a = 2
∴ First term of an AP = 2

Question 5.
Consider the following distribution:

(A) Calculate the frequency of the class 30-40.
(B) Calculate the class mark of the class (2)
Answer:

(A) So, frequency of the class 30-40 is 3.
(B) Class mark of the class 10-25
= \(\frac{10+25}{2}\) = \(\frac{35}{2}\) = 17.5

Related Theory:
Class mark can be calculated by dividing the sum of upper and lower limits by 2.

Question 6.
In the given figure, ∠APB = 90°. Then what is the length of OP?

In the figure, PQ and RS are the common tangents to two circle intersecting at O. prove that PQ = RS. (2)

Answer:
In the given figure, OA = r. AP and PB are tangents to the circle.
Then tangent is perpendicular to the radius at the point of contact.
∴ ∠OAP = 90°
And ∠APB = 90°
∴ ∠APO = 45°
(Since OP bisects ∠APB)
∴ In ∆APO
sin 45° = \(\frac{\mathrm{OA}}{\mathrm{OP}}\)
\(\frac{1}{\sqrt{2}}\) = \(\frac{r}{\mathrm{OP}}\)
⇒ OP = √2r units

Related Theory:
For the trigonometric ratio sine of an angle is equal to the \(\frac{Perpendicular}{\text { Hypotenuse }}\)
Or
Given: RQ and RS are common tangents to 2 circles intersecting at 0.
To Proof: PQ = RS
Since, tangents from an external point to a circle are equal.
∴ OP = OR …… (i)
And OS = OQ …(ii)
⇒ PQ = OP + OQ
= OR + OS
[From (i) and (ii)] = RS
Hence, proved.

Section – B (12 marks)

Question 7.
Poonam saved a portion of the pocket money. In first week, she saves ₹ 5 and then increased her weekly savings by ₹ 1.75 each week. In which week, will her weekly saving be ₹ 20.75? (3)
Answer:
Suppose amount of weekly savings will be ₹ 20.75 in the nth week. Clearly, amount of weekly savings form an AP with first term, a = 5, common difference, d = 1.75
∵ nth term = 20.75
a + (n – 1) × 1.75 = 20.75
5 + (n – 1) × 1.75 = 20.75
⇒ (n – 1) × 1.75 = 20.75 – 5
⇒ (n – 1) × 1.75 = 15.75
(n – 1) = \(\frac{15.75}{1.75}\)
(n – 1) = 9
⇒ n = 10
Hence, Poonam’s weekly saving will be ₹ 20.75 in 10 week.

Question 8.
A vertical tower stands on a horizontal plane is surmounted by a vertical flag staff of height ‘h’. At a point on the ground, the angles of elevations at the bottom and the tops of the flag staff are a and p respectively. Prove
that the height of the tower is \(\frac{h \tan \alpha}{\tan \beta-\tan \alpha}\)
OR
The figure shows two different positions P and Q of a helicopter flying horizontally at a uniform speed of 72 km/hr.

It is found that it takes the helicopter 10 min. to fly from P to Q. The angles of elevation of P and Q from point A on the ground are 45° and 60° respectively.
Find :
(A) The distance PQ.
(B) The distance AQ
(C) The height of the helicopter above the ground. (3)
Answer:
In the figure, AB and BC represent the tower and flagstaff respectively.

In ∆OAB,

OR
(A) As the helicopter is flying at the speed of 72 km/sec, So in 10 min it will fly
\(\left(\frac{72}{60} \times 10\right)\)km = 12 km

(B) Let, the height of the helicopter from the ground be ‘h’ km.
Then,
\(\frac{h}{\mathrm{AM}}\) = tan 60° and \(\frac{h}{\mathrm{AM}}\) = tan 45°
\(\frac{h}{\mathrm{AM}}\) = √3 and \(\frac{h}{\mathrm{AN}}\) = 1

h = √3 AM and h = AN
∴ √3 AM = AN
Since, AN – AM = MN = PQ = 12 cm
√3 AM = AM + 12
⇒ AM (√3 – 1) = 12
AM = \(\frac{12}{\sqrt{3}-1} \times \frac{\sqrt{3}+1}{\sqrt{3}+1}\)
= \(\frac{12(\sqrt{3}+1)}{2}\)
= 16.4 km
Now in ∆AMQ
\(\frac{A M}{A Q}\) = cos 60°
= \(\frac{1}{2}\)
⇒ AQ = 2 AM
⇒ AQ = 2 × 16.4
= 32.8 km

(C) From above, we have h = AN
= AM + 12
= 16.4 + 12
= 28.4 km

Related Theory:
Do the necessary constructions in the given figure to get the answer.

Question 9.
In the given figure, AB and CB are common tangents to the two circles of radii a and b(a > b). Prove that AB = CD (3)

Answer:
Given: Two circles of different radii such that radii of circle with centre O is a and with centre O’ is b

Construction: Join AD and BC
To Prove: AB = CD
Proof: The tangent drawn form an external point to a circle are equal in length.
If A is external point for circle having centre O’
then, AB = AD …(i)
If C is external point for circle having centre O’
then BC = CD …(ii)
Now, B is external point for circle having centre O
then, AB = BC ,..(iii)
So, from (i) (ii) and (iii), we get
AB = BC = CD
So, AB = CD
Hence proved.

Caution:
Here, circles are at a distance from each other and radii are also not equal So, use the property of tangents to get the answer.

Question 10.
What are the roots of quadratic equation 5x² – 6x – 2 = 0, by completing the square method? (3 )
Answer:
Given quadratic equation:
5x² – 6x – 2 =0 …(i)
On multiplying eq. (i) by 5, we get
25x² – 30x – 10 = 0
⇒ (5x)² – 2 × 5x × 3 – 10 = 0
On adding and subtracting 32 we get,
⇒ (5x)² – 2 × 5x × 3 + 3² – 10 – 3² = 0
⇒ (5x – 3)² – 10 – 9 = 0
[∵ (a – b)² = a² – 2ab + b²]
⇒ (5x – 3)² = 19
On taking square root on both sides, we get
⇒ (5x – 3) = ± √19
5x = 3 ± √19
On taking positive sign, we get .
x = \(\frac{3+\sqrt{19}}{5}\)
On taking negative sign we get
x = \(\frac{3-\sqrt{19}}{5}\)
Hence, \(\frac{3+\sqrt{19}}{5}\) and \(\frac{3-\sqrt{19}}{5}\) are the roots of the quadratic equations.

Related Theory:
Completing the square method is used for converting a quadratic expression of the form ax² + bx + c to the form a(x – h)² + k.

Section – C (16 marks)

Question 11.
Draw a circle of radius 5 cm. Draw two tangents to a circle, which are perpendicular to each other.
OR
Draw a circle of radius 2 cm. From a point 6 cm away from its centre, construct the pair of tangents to the circle Measure the lengths of tangents. (4)
Answer:

Steps of construction:

1. Draw a circle of radius 5 cm with centre O
2. Take, point A on the circle and join OA.
3. Draw perpendicular to OA at A
4. Draw OB, making an angle of 90° with OA.
5. Draw perpendicular to OB at point B. Let these perpendicular intersect at C.
   Hence, CA and CB are the required tangents inclined at an angle of 90°

Related Theory:
Here, quadrilateral OBCA formed is a cyclic quadrilateral. Therefore, for forming tangents inclined at 90°. The angle between the radii in the circle should also be 90°
OR

Steps of construction:

1. Draw a circle of radius 2 cm, with centre O.
2. Mark a point P at a distance of 6 cm from the centre of the circle.
3. Draw a perpendicular bisector of Line OP at P
4. From P as centre and OP’ as radius draw a circle intersecting the previous circle at M and N.
5. Join MP and NP
   MP and NP are the required tangents.

Related Theory:
Here, we apply 2 properties of circles for construction. As, tangent is perpendicular the radius and angle in a semicircle is a right angle.

Question 12.
If the median of the following distribution is 58 and sum of all the frequencies is 140. What is the value of x and y? (4)

Answer:
Given, distribution is:

And, 105 + x + y = 140
⇒ x + y = 35 (i)
Here, Median = 58
Then, median class is 55-65,
l = 55,
\(\frac{N}{2}\) = \(\frac{140}{2}\) = 70
Then, c.f. = 43 + x
Median = l + \(\left(\frac{\frac{N}{2}-c . f}{f}\right)\) × h
⇒ 58 = 55 + \(\left(\frac{70-43-x}{40}\right)\) × 10
⇒ BD = 100 m.
⇒ 3 = \(\frac{27-x}{4}\)
⇒ 12 = 27 – x
⇒ x = 27 – 12 = 15
∴ y = 35 – 15 = 20
Hence, value of x and y are 15 and 20.

Question 13.
Case Study—1
Light house is a pilLar type structure in the sea, used to give directions to ships. These are often built on the island, arts cell on cliffs. Lighthouse on water surface act as a navigational aid to the mariners and send warning to boats and ships for dangers. Traditionally, light house have been bacons of navigation for mariners for centuries, but in 21st century lighthouse are going through a major transformation as tourist destination also. India has 189 lighthouses dotting its vast coast line. A man is standing on the top of the light house.

He observes that two boats P and Q are approaching to light house from opposite direction.
He finds that angle of depression of boat P is 45° and angle of depression of boat Q is 30°.

(A) What is the distance of the boat which is nearer to the light house, at a moment? (2)
Answer:
Here, the boat at C is nearer to light house as it has lesser angle of depression i.e., angle of elevation.
∴ In ∆ACD
tan 45° = \(\frac{A D}{B D}\)
1 = \(\frac{100}{B D}\)
⇒ BD = 100 m.

(B) What is the distance between the two boats? (2)
Answer:
Distance between the 2 boats = BC
i.e., BC = BD + CD
∴ In ∆ADB, tan 30° = \(\frac{A D}{B D}\)
⇒ \(\frac{1}{\sqrt{3}}\) = \(\frac{100}{B D}\)
⇒ BD = 10o√3 m
∴ Distance between boats
= CD + BD
= 100 + 100 √3
= 100 (1 + √3) m.

Question 14.
Case Study—2
Devashish’s mother bought him a ball. He being very intellectual and always interested in finding new things, Devashish try to evaluate the radius of the ball foil calculating its volume and surface area. He tried to do it by compress seace, etc. But he was not successful. So, he saw a video on you tube, regarding the practical use of volume and surface area. Devashish decided to conduct an experiment to find the radius r of a sphere. For this he took a cylindrical container with radius, R = 7 cm and height 10 cm. He filled the container almost half by water as shown in the figure. Now he dropped the ball whose radius is to be measured in the container. After dropping the ball, the water level in the container raised by 3.4 cm.

(A) What is the approximate radius of the spherical ball dropped in the container? (2)
Answer:
5 cm

Explanation: Here, height of water raised by 3.40 cm by dropping the sphere.
The radius of container, R = 7 cm
Then, volume of the height raised = Volume of sphere
πR²h = \(\frac{4}{3}\)πr³
⇒ 7 × 7 × 3.4 = \(\frac{4}{3}\) × r³
⇒ r³ = \(\frac{7 \times 7 \times 3 \times 3.4}{4}\)
≈ 125
⇒ r = 5 cm
Hence, the radius of sphere is 5 cm.

(B) If this spherical ball is cut into two hemispherical shapes, then what is surface area of two hemispheres combined ? (2 )
Answer:
Radius of sphere = 5 cm
∴ Radius of each hemisphere = 5 cm
Surface area of one hemisphere = 2πr² + πr² = 3πr²
∴ Surface area of 2 hemisphere = 2 × 3πr²
= 6πr²
= 6 × \(\frac{22}{7}\) × 5 × 5
= 471.43 cm³

The post CBSE Sample Papers for Class 10 Maths Basic Term 2 Set 4 with Solutions appeared first on Learn CBSE.

Students can access the CBSE Sample Papers for Class 10 Maths Basic with Solutions and marking scheme Term 2 Set 7 will help students in understanding the difficulty level of the exam.

CBSE Sample Papers for Class 10 Maths BasicTerm 2 Set 2 Set 7 for Practice

Time allowed: 2 hours
Maximum Marks: 40

General Instructions:

• The question paper consists of 14 questions divided into 3 sections A, B, C.
• Section A comprises of 6 questions of 2 marks each. Internal choice has been provided in two questions.
• Section B comprises of 4 questions of 3 marks each. Internal choice has been provided in one questions.
• Section C comprises of 4 questions of 4 marks each. An internal choice has been provided in one questions. It contains two case study based questions.

Section – A (12 marks)

Question 1.
What is the value ofx, in terms, of a, b, c. (2)
\(\frac{a}{x-a}+\frac{b}{x-b}=\frac{2 c}{x-c}\) ≠ a, b, c

Question 2.
Circumference of the edge of a hemispherical bowl is 132 cm. What is the capacity of the bowl? [Use π = \(\frac{22}{7}\)]
OR
A grain storage is in the shape of a cuboid of size 8mx6mx3m. If a bag of grain occupies a space of 0.65 m3. How many bags can be stored in that granary ? (2)

Question 3.
Amira scored 36 marks in English, 44 marks in Hindi, 75 marks in Mathematics and x marks in Science. If she had scored an average of 50 marks, then find the value of x. (2)

Question 4.
Is it true to say that – 1, \(\frac{-3}{2},-2, \frac{-5}{2}\) Form an A.P.
OR
Which term of the A.P. 3,14, 25, 36, …….. is 99 more than its 25th term? (2)

Question 5.
What is the median of the following data?

Question 6.
If two tangents inclined at an angle of 60° are drawn to a circle of radius 3 cm. Then, what is the length of the tangent. (2)

Section – B (12 marks)

Question 7.
A sum of ₹ 1,000 is invested at 8% simple interest p.a. Calculate the interest at the end of 1, 2, 3… years. Is the sequence of interests, forms an A.P.? Find the interest at the end of 30 years. (3)

Question 8.
In the quadratic px² + qx + q = 0, if ratio of the roots is a : b, prove that:
\(\sqrt{\frac{a}{b}}+\sqrt{\frac{b}{a}}+\sqrt{\frac{q}{r}}\) = 0
OR
What are the roots of quadratic equation 5x² – 6x – 2 = 0, by completing the square method? (3)

Question 9.
In the given figure, if TP and TQ are two tangents to a circle with circle O, such that ∠POQ = 110°. Then, what is the measure of ∠PTQ? (3)

Question 10.
The shadow of a tower standing on a level ground is found to be 40 m longer when the Sun’s attitude is 30°, then when it is 60°, what is the height of the tower? (3)

Section – C (16 marks)

Question 11.
A sphere of diameter 6 cm is dropped in a right circular cylindrical vessel partly filled with water. The diameter of the cylindrical vessel is 12 cm. If the sphere is completely submerged in water, by how much will the level of water rise in the cylindrical vessel
OR
Water flows through a cylindrical pipe, whose inner radius is 1 cm, at the rate of 80 cm/sec in an empty cylindrical tank, the radius of whose base is 40 cm. What is the rise of water level in tank in half an hour ? (4)

Question 12.
A student begin to note the number of cars passing through a point on a road for 100 periods each of 3 min and summarized it in the table given below:

Find mode of the data and also it mean value. (4)

Question 13.
Case Study—1
Board Exams Term-ll is- shortly going to approach. The exams are going to be subjective; so a detailed understanding of all the chapters are needed for getting the good marks.
So, Mrs. sharma planned a surprise test for the students to check their knowledge of tangents and circle. She made a simple test and few questions of these test are given below:

Try to solve the following questions, to test your knowledge:
(A) If PA and PB are two tangents drawn to a circle with centre O from P such that ∠PBA = 50°, then what is the m ∠OAB? (2)
(B) In the figure below, AB is a chord of the circle and AOC is its diameter such that ∠ACB = 70°, then what is the measure of ∠BAT? (2)

Question 14.
Case Study—2
Sholu faces lots of trouble in picking the things, placed high up on the almirahs, wardrobes, etc. So she went to market, to find a solution for it. She saw a wooden stool, and found its length appropriate for her usage.

She bought that wooden bar stooL, so she could collect the things placed high.

The wooden stool has a square top of side 2 m and have a height of 6m above the ground. Also, each leg is inclined at a angle of 60° to the ground as shown in the figure.
(A) What is the length of each leg considering both are equal? (2)
(B) What is the length of side PQ as shown in the 2-D diagram of the stool? (2)

The post CBSE Sample Papers for Class 10 Maths Basic Term 2 Set 7 for Practice appeared first on Learn CBSE.

Students can access the CBSE Sample Papers for Class 10 Maths Basic with Solutions and marking scheme Term 2 Set 6 will help students in understanding the difficulty level of the exam.

CBSE Sample Papers for Class 10 Maths BasicTerm 2 Set 2 for Practice

Time allowed: 2 hours
Maximum Marks: 40

General Instructions:

• The question paper consists of 14 questions divided into 3 sections A, B, C.
• Section A comprises of 6 questions of 2 marks each. Internal choice has been provided in two questions.
• Section B comprises of 4 questions of 3 marks each. Internal choice has been provided in one questions.
• Section C comprises of 4 questions of 4 marks each. An internal choice has been provided in one questions. It contains two case study based questions.

Section – A (12 Marks)

Question 1.
Draw a line segment of length 7.8 cm and divide it in the ratio of 5 : 8.
OR
To draw a pair of tangents to a circle which are inclined to each other at an angle of 60°, it is required to draw tangents at one end points of those two radii of the circle. Then, what should be the angle between the radii?
(2)

Question 2.
If the equation x² + kx + 12 = 0 has 2 as one of its root and the equation x² + kx + q = 0 has equal roots, then what is the value of q? (2)

Question 3.
The following are the ages of 800 patients getting medical treatment in a hospital on a particular day.

Form the less than type cumulative frequency distribution table.

Question 4.
In an AP, if a = 7, a₁₃ = 35, find d and S₁₃. (2)

Question 5.
There are 2 circles of centres P and Q of radii 9 cm and 2 cm respectively. PQ the line joining the centers is 17 cm. Another circle with centre R have radius 2 cm, which touches the other two circles externally. Write an equation in terms of x, if ∠PRQ = 90°. (2)

Question 6.
A solid cube is cut into 2 cuboids of equal volumes. What is the ratio of the total surface area of the given cube to that one of the cuboid?
OR
Circumference of the edge of a hemispherical bowl is 132 cm. What is the capacity of the bowl? Use π = \(\frac{22}{7}\) (2)

Section – B (12 marks)

Question 7.
In a health check up camp of women in the age of 40+ years, the number of heart beats of women were recorded in the following table.
Number of heart beats/ minute Number of women

Find the mean of the data. (3)

Question 8.
Rohan is flying a kite. Being a student, he tried to estimate the length of the string he is using to fly that kite. The kite is flying at height of 90 m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is 60°. Then find the length of the string assuming there is no slack in the string. (3)

Question 9.
Two tangents segments BC, BD are drawn to a circle with centre O, such that ∠DBC = 120°. Prove that BO = 2BC. (3)

Question 10.
What is the median of the first ten prime numbers?
OR
60 accidents reported were randomly picked up from local evening newspaper involving the age of drivers.

Find the mode of the data (3)

Section – C (16 marks)

Question 11.
A rectangular tank is 225 m and 162 m at base. With what speed should water flow into it through an aperture 60 cm × 45 cm, so that the level of water is raised by 20 cm in 2.5 hours ? (4)

Question 12.
The angle of elevation from the top of a building from the foot of a tower is 30° and the angle of elevation of the top of the tower from the foot of the building is 60°. If the tower is 50 m high, find the height of the building.
OR
The angle of elevation of the top of a vertical tower from a point on the ground is 60°. From another point 10 m vertically above the first, its angle of elevation is 45°. Find the height of the tower. (4)

Question 13.
Case Study—1
Time is of the essence in human life. Time and tide waits for none, which means that just like tide even time does not wait for anyone. Shweta was very particular in her work and fond of buying new-new watches and clock. She went to a gift shop in which she saw a beautiful clock.

This table clock reminded Shweta of a particular shape in which a circle is inscribed inside a triangle And sides of a triangle are touching the circle as the tangents to the circle.

In the given figure, PA = 4 cm, BP = 3 cm and AC = 11 cm.
Now, answer the following question:

(A) In the given figure, calculate the length of side RC. (2)
(B) If O is the centre of the circle and length of OB is 5 cm, then what is the radius of the circle? (2)

Question 14.
Case Study—2
Akshay is a fitness freak and great athlete. He always want to make his nation proud by winning medals and prizes in the athletic activities.

An upcoming activity for athletes was going to be organised by Railways. Akshay want to participate in 200 m race. He can currently run that distance in 51 seconds. But he wants to increase his speed, so to do it in 31 seconds. With each day of practice it takes him 2 seconds less.

(A) He wants to makes his best time as 31 sec. in how many days will be able to achieve his target? (2)
(B) What will be the difference between the time taken on 5th day and 7th day. (2 )

The post CBSE Sample Papers for Class 10 Maths Basic Term 2 Set 6 for Practice appeared first on Learn CBSE.

Students can access the CBSE Sample Papers for Class 10 Maths Basic with Solutions and marking scheme Term 2 Set 8 will help students in understanding the difficulty level of the exam.

CBSE Sample Papers for Class 10 Maths BasicTerm 2 Set 2 Set 8 for Practice

Time allowed: 2 hours
Maximum Marks: 40

General Instructions:

• The question paper consists of 14 questions divided into 3 sections A, B, C.
• Section A comprises of 6 questions of 2 marks each. Internal choice has been provided in two questions.
• Section B comprises of 4 questions of 3 marks each. Internal choice has been provided in one questions.
• Section C comprises of 4 questions of 4 marks each. An internal choice has been provided in one questions. It contains two case study based questions.

Section – A (12 marks)

Question 1.
In the figure below, what is the length of PT?

OR
Two concentric circles of radii a and b(a > b) are given. Find the length of the chord of the larger circle which touches the smaller circle (2)

Question 2.
A player sitting on the wall of height 20 m sees that a ball is lying on ground and angle of depression is 60° from this point. What is the distance between the foot of the tower and the ball? (2)

Question 3.
The areas of three adjacent faces of a rectangular block are in the ratio of 2 : 3 : 4 and its volume is 9000 cu. cm, then what is the length of the shortest side ? (2)

Question 4.
A survey was conducted in a colony regarding the number of plants in a house, to promote the Go Green campainging. (2)

Question 5.
A ladder whose length is 20 m touches the wall at the height of 10 m, what is the angle made by the ladder with the ground? To solve this which trigonometric ratio is used and evaluate the value of the angle made?
OR
A helicopter is hovering over a landing pad 100 m from where Ramesh is standing. The helicopter’s angle of elevation with the ground is 30°. What is the altitude of the helicopter? (2)

Question 6.
While checking the value of 20 observations it was noted that 125 was wrongly noted as 25 while calculating the mean and then the mean was 60. What is the correct mean? (2)

Section – B (12 marks)

Question 7.
Solve the following quadratic equation for x.
9(x² + \(\frac{1}{x^{2}}\)) – 9(x + \(\frac{1}{x}\)) – 52 = 0
OR
If the roots of the quadratic equation p(q – r) x² + q(r -p)x = 0 are equal, then show

Question 8.
In a flower bed, there are 23 rose plants in the first row, 19 in the third and so on. There are 5 rose plants in the last row.
How many rows are there in the flower bed? (3)

Question 9.
In the figure below, a circle with centre O is of radius 5 cm. T is a point at a distance of 13 cm from the centre of the circle, which intersects the circle at E. If AB is a tangent to the circle at E, then what is the length of AB, where TP and TQ are two tangents to the circle (3)

Question 10.
From the top of a building 100 m high the angles of depression of 2 objects are on the same side as observed to be 45° and 60°. What is the distance between the 2 objects? (3)

Section – C (16 marks)

Question 11.
A cylindrical bucket, 32 m high with radius of base 18 cm, is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the canonical heap ¡s 24 cm, find the radius and the slant height of the heap. (4)

Question 12.
The Length of 40 Leaves of a plant are measured correct to nearest milimetre and the data obtained is represented ¡n the following table:

What is the median Length of the Leaves.
OR
A class test was conducted in the school. The marks of children out of 60 is tabulated in the table below:

Calculate mean and mode for the following distribution. (4)

Question 13.
Case Study – 1
Republic Day is our National festival celebrated on 26th January every year. On this day our constitution came into existence. In schools, parade forms an integral part of the Republic Day Celebration.
On this occassion of a march past drill need to be conducted in the scheme. On this the students were made to be stand in a way such that, there are 32 students in the first row, 30 in the second row, 28 in the third row and so on.

(A) The given sequence of students forms am A.P. then in which row there are 12 students standing? (2)
(B) What is the difference in the number of the students standing in 5th row and 8th row? (2)

Question 14.
Case Study – 2
D.P.S. school Agra is going to organise their annual function, in which many cultural activities along with a prize distribution ceremony will be organised. Along with the certificates, students who excel in various fields will also be given a momento.
A momento is need to be presented to the students for their excellence in punctuality, hard work and academics performances. This momento is in the shape of a right angled triangle inscribing a circle, such that the sides of right – angled triangle are tangents to the circle.

Here, AB = 8 cm, and BC=6 cm and r is the radius of the circle.
Now answer the following questions:
(A) If the circle inside the momento is of radius r then what is its radius. (2)
(B) What is the length of the side AP in ∆ABC? (2)

The post CBSE Sample Papers for Class 10 Maths Basic Term 2 Set 8 for Practice appeared first on Learn CBSE.

Students can access the CBSE Sample Papers for Class 10 Maths Basic with Solutions and marking scheme Term 2 Set 4 will help students in understanding the difficulty level of the exam.

CBSE Sample Papers for Class 10 Maths BasicTerm 2 Set 4 with Solutions

Time allowed: 2 hours
Maximum Marks: 40

General Instructions:

• The question paper consists of 14 questions divided into 3 sections A, B, C.
• Section A comprises of 6 questions of 2 marks each. Internal choice has been provided in two questions.
• Section B comprises of 4 questions of 3 marks each. Internal choice has been provided in one questions.
• Section C comprises of 4 questions of 4 marks each. An internal choice has been provided in one questions. It contains two case study based questions.

Section – A (12 Marks)

Question 1.
If for the quadratic equation 2x² + kx – 6 = 0, 2 is one of its root, then find the value of k. Also, find the value of the other root.
OR
The sum of squares of three consecutive positive integers are 50. Then what are the three integers? (2)
Answer:
Since, x = 2 is a root of the equation. 2x² + kx – 6 = 0
∴ 2 × 2² + k × 2 – 6 = 0
⇒ 8 + 2k – 6 = 0
⇒ k = – 1
Put k = – 1 in the equation.
2x² + kx – 6 = 0
We get
2x² – x – 6 = 0
⇒ 2x² – 4x + 3x – 6 = 0
⇒ 2x(x – 2) + 3(x – 2) = 0
⇒ x = 2, \(\frac{-3}{2}\)

Caution:
First, find the value of k, to formulate the equation. Then, find the roots of the quadratic equation
OR
Consider three consecutive integer as x, x + 1 and x + 2.
A.T.Q x² + (x + 1)² + (x + 2)² = 50
⇒ x² + x² + 1 + 2x + x² + 4 + 4x = 50
⇒ 3x² + 6x – 45 =0
⇒ 3(x² + 2x – 15) = 0
⇒ x² + 2x – 15 = 0
⇒ x² + 5x – 3x – 15 = 0
⇒ x(x + 5) – 3(x + 5) =0
⇒ x = 3, – 5
x ≠ – 5 (rejected)
Hence, integers are 3, 4, 5.

Question 2.
The surface area of a sphere and a cube are equal. Then, find the ratio of their volumes. (2)
Answer:
Let, surface area of sphere be x cm²
⇒ 4πr² = x
⇒ r = \(\sqrt{\frac{x}{4 \neq}}\) cm,
where, r is the radius of the sphere Also, surface area of cube be x cm²
⇒ 6 × side² = x
⇒ side = \(\sqrt{\frac{x}{6}}\) cm

Caution:
Apply the exponents property in the end to solve the question and get the answer.

Question 3.
The daily minimum steps climbed by a man during a week were as under.

What are the mean of the steps? (2)
Answer:
Number of steps climbed in a week:
35, 30, 27, 32, 23, 28
Mean = \(\frac{\text { Sum of observations(Steps) }}{\text { Total no. of observations }}\)
= \(\frac{35+30+27+32+23+28}{6}\)
= \(\frac{175}{6}\)
= 29.17

Question 4.
The sum of first 6 terms of on AP. is 42. The ratio of its 11th term is 1: 3. CaLcuLate the first term of an AP. (2)
Answer:
Let the first term of the AP be a and common difference be ‘d’.
Now, S₆ = 42
⇒ \(\frac{6}{2}\)(2a + 5d) = 42
2a + 5d = 14
Also, \(\frac{a_{11}}{a_{33}}\) = \(\frac{1}{3}\)
⇒ \(\frac{a+10 d}{a+32 d}\) = \(\frac{1}{3}\)
⇒ 3a + 30 d = a + 32 d
⇒ 2a = 2d
⇒ a = d
Put a = d in equation (i), we get 2a + 5 = 14
a = 2
∴ First term of an AP = 2

Question 5.
Consider the following distribution:

(A) Calculate the frequency of the class 30-40.
(B) Calculate the class mark of the class (2)
Answer:

(A) So, frequency of the class 30-40 is 3.
(B) Class mark of the class 10-25
= \(\frac{10+25}{2}\) = \(\frac{35}{2}\) = 17.5

Related Theory:
Class mark can be calculated by dividing the sum of upper and lower limits by 2.

Question 6.
In the given figure, ∠APB = 90°. Then what is the length of OP?

In the figure, PQ and RS are the common tangents to two circle intersecting at O. prove that PQ = RS. (2)

Answer:
In the given figure, OA = r. AP and PB are tangents to the circle.
Then tangent is perpendicular to the radius at the point of contact.
∴ ∠OAP = 90°
And ∠APB = 90°
∴ ∠APO = 45°
(Since OP bisects ∠APB)
∴ In ∆APO
sin 45° = \(\frac{\mathrm{OA}}{\mathrm{OP}}\)
\(\frac{1}{\sqrt{2}}\) = \(\frac{r}{\mathrm{OP}}\)
⇒ OP = √2r units

Related Theory:
For the trigonometric ratio sine of an angle is equal to the \(\frac{Perpendicular}{\text { Hypotenuse }}\)
Or
Given: RQ and RS are common tangents to 2 circles intersecting at 0.
To Proof: PQ = RS
Since, tangents from an external point to a circle are equal.
∴ OP = OR …… (i)
And OS = OQ …(ii)
⇒ PQ = OP + OQ
= OR + OS
[From (i) and (ii)] = RS
Hence, proved.

Section – B (12 marks)

Question 7.
Poonam saved a portion of the pocket money. In first week, she saves ₹ 5 and then increased her weekly savings by ₹ 1.75 each week. In which week, will her weekly saving be ₹ 20.75? (3)
Answer:
Suppose amount of weekly savings will be ₹ 20.75 in the nth week. Clearly, amount of weekly savings form an AP with first term, a = 5, common difference, d = 1.75
∵ nth term = 20.75
a + (n – 1) × 1.75 = 20.75
5 + (n – 1) × 1.75 = 20.75
⇒ (n – 1) × 1.75 = 20.75 – 5
⇒ (n – 1) × 1.75 = 15.75
(n – 1) = \(\frac{15.75}{1.75}\)
(n – 1) = 9
⇒ n = 10
Hence, Poonam’s weekly saving will be ₹ 20.75 in 10 week.

Question 8.
A vertical tower stands on a horizontal plane is surmounted by a vertical flag staff of height ‘h’. At a point on the ground, the angles of elevations at the bottom and the tops of the flag staff are a and p respectively. Prove
that the height of the tower is \(\frac{h \tan \alpha}{\tan \beta-\tan \alpha}\)
OR
The figure shows two different positions P and Q of a helicopter flying horizontally at a uniform speed of 72 km/hr.

It is found that it takes the helicopter 10 min. to fly from P to Q. The angles of elevation of P and Q from point A on the ground are 45° and 60° respectively.
Find :
(A) The distance PQ.
(B) The distance AQ
(C) The height of the helicopter above the ground. (3)
Answer:
In the figure, AB and BC represent the tower and flagstaff respectively.

In ∆OAB,

OR
(A) As the helicopter is flying at the speed of 72 km/sec, So in 10 min it will fly
\(\left(\frac{72}{60} \times 10\right)\)km = 12 km

(B) Let, the height of the helicopter from the ground be ‘h’ km.
Then,
\(\frac{h}{\mathrm{AM}}\) = tan 60° and \(\frac{h}{\mathrm{AM}}\) = tan 45°
\(\frac{h}{\mathrm{AM}}\) = √3 and \(\frac{h}{\mathrm{AN}}\) = 1

h = √3 AM and h = AN
∴ √3 AM = AN
Since, AN – AM = MN = PQ = 12 cm
√3 AM = AM + 12
⇒ AM (√3 – 1) = 12
AM = \(\frac{12}{\sqrt{3}-1} \times \frac{\sqrt{3}+1}{\sqrt{3}+1}\)
= \(\frac{12(\sqrt{3}+1)}{2}\)
= 16.4 km
Now in ∆AMQ
\(\frac{A M}{A Q}\) = cos 60°
= \(\frac{1}{2}\)
⇒ AQ = 2 AM
⇒ AQ = 2 × 16.4
= 32.8 km

(C) From above, we have h = AN
= AM + 12
= 16.4 + 12
= 28.4 km

Related Theory:
Do the necessary constructions in the given figure to get the answer.

Question 9.
In the given figure, AB and CB are common tangents to the two circles of radii a and b(a > b). Prove that AB = CD (3)

Answer:
Given: Two circles of different radii such that radii of circle with centre O is a and with centre O’ is b

Construction: Join AD and BC
To Prove: AB = CD
Proof: The tangent drawn form an external point to a circle are equal in length.
If A is external point for circle having centre O’
then, AB = AD …(i)
If C is external point for circle having centre O’
then BC = CD …(ii)
Now, B is external point for circle having centre O
then, AB = BC ,..(iii)
So, from (i) (ii) and (iii), we get
AB = BC = CD
So, AB = CD
Hence proved.

Caution:
Here, circles are at a distance from each other and radii are also not equal So, use the property of tangents to get the answer.

Question 10.
What are the roots of quadratic equation 5x² – 6x – 2 = 0, by completing the square method? (3 )
Answer:
Given quadratic equation:
5x² – 6x – 2 =0 …(i)
On multiplying eq. (i) by 5, we get
25x² – 30x – 10 = 0
⇒ (5x)² – 2 × 5x × 3 – 10 = 0
On adding and subtracting 32 we get,
⇒ (5x)² – 2 × 5x × 3 + 3² – 10 – 3² = 0
⇒ (5x – 3)² – 10 – 9 = 0
[∵ (a – b)² = a² – 2ab + b²]
⇒ (5x – 3)² = 19
On taking square root on both sides, we get
⇒ (5x – 3) = ± √19
5x = 3 ± √19
On taking positive sign, we get .
x = \(\frac{3+\sqrt{19}}{5}\)
On taking negative sign we get
x = \(\frac{3-\sqrt{19}}{5}\)
Hence, \(\frac{3+\sqrt{19}}{5}\) and \(\frac{3-\sqrt{19}}{5}\) are the roots of the quadratic equations.

Related Theory:
Completing the square method is used for converting a quadratic expression of the form ax² + bx + c to the form a(x – h)² + k.

Section – C (16 marks)

Question 11.
Draw a circle of radius 5 cm. Draw two tangents to a circle, which are perpendicular to each other.
OR
Draw a circle of radius 2 cm. From a point 6 cm away from its centre, construct the pair of tangents to the circle Measure the lengths of tangents. (4)
Answer:

Steps of construction:

1. Draw a circle of radius 5 cm with centre O
2. Take, point A on the circle and join OA.
3. Draw perpendicular to OA at A
4. Draw OB, making an angle of 90° with OA.
5. Draw perpendicular to OB at point B. Let these perpendicular intersect at C.
   Hence, CA and CB are the required tangents inclined at an angle of 90°

Related Theory:
Here, quadrilateral OBCA formed is a cyclic quadrilateral. Therefore, for forming tangents inclined at 90°. The angle between the radii in the circle should also be 90°
OR

Steps of construction:

1. Draw a circle of radius 2 cm, with centre O.
2. Mark a point P at a distance of 6 cm from the centre of the circle.
3. Draw a perpendicular bisector of Line OP at P
4. From P as centre and OP’ as radius draw a circle intersecting the previous circle at M and N.
5. Join MP and NP
   MP and NP are the required tangents.

Related Theory:
Here, we apply 2 properties of circles for construction. As, tangent is perpendicular the radius and angle in a semicircle is a right angle.

Question 12.
If the median of the following distribution is 58 and sum of all the frequencies is 140. What is the value of x and y? (4)

Answer:
Given, distribution is:

And, 105 + x + y = 140
⇒ x + y = 35 (i)
Here, Median = 58
Then, median class is 55-65,
l = 55,
\(\frac{N}{2}\) = \(\frac{140}{2}\) = 70
Then, c.f. = 43 + x
Median = l + \(\left(\frac{\frac{N}{2}-c . f}{f}\right)\) × h
⇒ 58 = 55 + \(\left(\frac{70-43-x}{40}\right)\) × 10
⇒ BD = 100 m.
⇒ 3 = \(\frac{27-x}{4}\)
⇒ 12 = 27 – x
⇒ x = 27 – 12 = 15
∴ y = 35 – 15 = 20
Hence, value of x and y are 15 and 20.

Question 13.
Case Study—1
Light house is a pilLar type structure in the sea, used to give directions to ships. These are often built on the island, arts cell on cliffs. Lighthouse on water surface act as a navigational aid to the mariners and send warning to boats and ships for dangers. Traditionally, light house have been bacons of navigation for mariners for centuries, but in 21st century lighthouse are going through a major transformation as tourist destination also. India has 189 lighthouses dotting its vast coast line. A man is standing on the top of the light house.

He observes that two boats P and Q are approaching to light house from opposite direction.
He finds that angle of depression of boat P is 45° and angle of depression of boat Q is 30°.

(A) What is the distance of the boat which is nearer to the light house, at a moment? (2)
Answer:
Here, the boat at C is nearer to light house as it has lesser angle of depression i.e., angle of elevation.
∴ In ∆ACD
tan 45° = \(\frac{A D}{B D}\)
1 = \(\frac{100}{B D}\)
⇒ BD = 100 m.

(B) What is the distance between the two boats? (2)
Answer:
Distance between the 2 boats = BC
i.e., BC = BD + CD
∴ In ∆ADB, tan 30° = \(\frac{A D}{B D}\)
⇒ \(\frac{1}{\sqrt{3}}\) = \(\frac{100}{B D}\)
⇒ BD = 10o√3 m
∴ Distance between boats
= CD + BD
= 100 + 100 √3
= 100 (1 + √3) m.

Question 14.
Case Study—2
Devashish’s mother bought him a ball. He being very intellectual and always interested in finding new things, Devashish try to evaluate the radius of the ball foil calculating its volume and surface area. He tried to do it by compress seace, etc. But he was not successful. So, he saw a video on you tube, regarding the practical use of volume and surface area. Devashish decided to conduct an experiment to find the radius r of a sphere. For this he took a cylindrical container with radius, R = 7 cm and height 10 cm. He filled the container almost half by water as shown in the figure. Now he dropped the ball whose radius is to be measured in the container. After dropping the ball, the water level in the container raised by 3.4 cm.

(A) What is the approximate radius of the spherical ball dropped in the container? (2)
Answer:
5 cm

Explanation: Here, height of water raised by 3.40 cm by dropping the sphere.
The radius of container, R = 7 cm
Then, volume of the height raised = Volume of sphere
πR²h = \(\frac{4}{3}\)πr³
⇒ 7 × 7 × 3.4 = \(\frac{4}{3}\) × r³
⇒ r³ = \(\frac{7 \times 7 \times 3 \times 3.4}{4}\)
≈ 125
⇒ r = 5 cm
Hence, the radius of sphere is 5 cm.

(B) If this spherical ball is cut into two hemispherical shapes, then what is surface area of two hemispheres combined ? (2 )
Answer:
Radius of sphere = 5 cm
∴ Radius of each hemisphere = 5 cm
Surface area of one hemisphere = 2πr² + πr² = 3πr²
∴ Surface area of 2 hemisphere = 2 × 3πr²
= 6πr²
= 6 × \(\frac{22}{7}\) × 5 × 5
= 471.43 cm³

The post CBSE Sample Papers for Class 10 Maths Basic Term 2 Set 4 with Solutions appeared first on Learn CBSE.

Students can access the CBSE Sample Papers for Class 10 English with Solutions and marking scheme Term 2 Set 7 will help students in understanding the difficulty level of the exam.

CBSE Sample Papers for Class 10 English Term 2 Set 7 for Practice

Time Allowed: 2 Hours
Maximum Marks: 40

General Instructions:

• The Question Paper contains THREE sections—READING, WRITING & GRAMMAR and LITERATURE.
• Attempt questions based on specific instructions for each part.

Section – A
Reading [10 Marks]

Question 1.
Read the passage given below.
Research has shown that the human mind can process words at the rate of about 500 per minute, whereas a speaker speaks at the rate of about 150 words a minute. The difference between the two is 350, which is quite large.
So, a speaker must make every effort to retain the attention of the audience and the listener should also be careful not to let his/her mind
5. wander. Good communication calls for good listening skills.

Listening starts with hearing but goes beyond that. Hearing, in other words, is necessary but not sufficient for Listening. Listening involves hearing with attention. Listening is a process that calls for attention and concentration.
While listening, one should be observant. In other words, listening has to do with the ears as well as with the mind.
10. It calls for participation and involvement.
It is quite often a dialogue rather than a monologue. It is necessary to make it abundantly clear that one is interested in knowing what the other person has to say.

Good Listening is an art that can be cultivated.
A good listener knows the art of getting much more than what the speaker is trying to convey. He/she knows how to prompt, persuade but IS. not to cut-off or interrupt what the other person has to say. At times, the speaker may or may not be coherent, articulate and well-organised in his/her thoughts and expressions. He/she may have it in mind, yet fail to marshal the right words while communicating thoughts. Nevertheless, a good listener puts him/her at ease, helps him/her articulate his/her thoughts. For Listening to be effective, it is also necessary that barriers to listening are removed. Such 20. barriers can be both physical and psychological. Physical barriers generally relate to hindrances to proper hearing, whereas psychological barriers are more fundamental and relate to the interpretation and evaluation of the speaker and the message.

Based on your understanding of the passage, answer ANY FIVE questions out of the six given below. (1 × 5)
(A) What does the author mean when he says, “barriers to listening are removed”? (1)
(B) Mention any two characteristics of the writer as inferred from the statement, ‘Good listening is an art that can be cultivated’. (1)
(C) Rewrite the following sentence by replacing the underlined phrase with a word that means the same from lines 10-15.
His mind was as well developed and maintained as his bodily powers; he wrote well, and his observations are generally acute and accurate; he was brave, kindly and generous. (1)
(D) List one quality of a good listener that makes the listening truly effective. (1)
(E) Why does the author say that “it is quite often a dialogue rather than a monologue? (1)
(F) How does the writer differentiate between listening and hearing? (1)

Question 2.
Read the following excerpt from a case study titled ‘Stress and Covid -19.’
A new study has found that peo pie who experienced increased stress, anxiety and depression at the start of the pandemic. were at greater risk of getting Covid-19.

20. A professor says: “The significance of the work is in that it turns the debate regarding the mental health aspects of the pandemic on its head. Our data show that increased stress, anxiety and depression are not only consequences of living with the pandemic, but may also be factors that increase our risk of getting SARS-CoV-2 too. Further work is now needed to determine whether and how public health policy should change to accommodate the fact that the most distressed people in our communities appear to be at greatest risk of Covid-19 infection.”

25. Another professor of Cognitive Behavioural (Psychotherapy from King’s College) London said: “Previous work has shown a clear relationship between distress and the development of viral infections indicating a vulnerability.
30. Our study found that distress was associated with self-reported Covid-19 infection and the next step is to investigate whether this association is found in those with confirmed infection.”

On the basis of your understanding of the passage, answer ANY FIVE questions out of the six given below. (1 × 5)
(A) Why does the professor from King’s College London, say, ‘Previous work has shown a clear relationship between distress and the development of viral infections indicating a vulnerability? (1)
(B) Comment on the significance of the need to address the psychological issues with reference to lines 10-20. (1)
(C) Justify the finding that during the Covid-19 pandemic, there has been a well-documented deterioration in psychological well-being and increased social isolation. (1)
(D) Why does the narrator feel public health policy should change to accommodate the fact ‘‘that the most distressed people in our communities appear to be at greatest risk of Covid-19 infection.” (1)
(E) People who experienced increased stress, anxiety and depression at the start of the pandemic, were at greater risk of getting Covid-19. How does evidence from the table support the statement? (1)
(F) What purpose does the data in the passage seem to solve? (1)

Section – B
Writing And Grammar (10 marks)

Question 3.
Attempt ANY ONE from (A) and (B)
(A) You came across the given concept chart while searching for something on Google. You are compelled to think of the impact, that social media is leaving on young minds. Write a paragraph in about 120 words suggesting ways to deal with the problem.

Write a paragraph in not more than 120 words, analysing the given information. (5)
(B) You are the Secretary of an NGO. You have come across the following adverstisement of M/s Arora Woollen Mills.

You have decided to distribute blankets among homeless. Write a letter to place an order with M/s. Arora Woollen Mills stating your exact requirement. (5)

Question 4.
The following paragraph has not been edited. There is one error In each Line. Identify the error and write its correction against the correct b[ank number. Remember to underLine the correction. The first one has been done for you. (1 × 3)

Genetics played a key role to keep your hair healthy, But the weather, pollution, or your approach to hair care are all critical to maintained your crowning glory. A well-rounded dieting is an important factor in hair and scalp health.

Question 5.
Read the conversation and complete the passage that follows.
Simi: I do wish to get good marks in my final exams. How cari I do that?
Mother: You must devote some of your daiLy time to study at home.
Simi: Youre right mom. I am going to make a timetable to follow now.
Simi told her mother that she (a) …………. final exams and askded how she could do that. Mother replied that she must devote some of her daily time to study at home. At this, Simi replied that her mother (b) …………….. (1 + 1)

Section -C
Literature (20 marks)

Question 6.
Answer ANY SIX questions in 30-40 words each. (2 × 6)
(A) What is the significance of a baker in the Goan village, especially in celebrations? (2)
(B) Justify how Tale of the Custard the Dragon’ by Ogden Nash is funny as well as serious. (2)
(C) ‘Possessions can possess you’. Comment on the aptness of the statement with regard to the story, ‘The Necklace’. (2)
(D) Explain the reason behind Valli’s change of mood while going and coming back in the bus. (2)
(E) Which two issues as stated in the story ‘Bholi’ our society is yet to get rid of, in spite of all the advancements? (2)
(F) Briefly state the poetic aspect of the poem ‘Amanda’. (2)
(G) What does the poet Walt Whitman suggest by saying that ‘they do not sweat and whine about their condition’ in the poem ‘Animals’? (2)

Question 7.
Answer ANY TWO of the following in about 120 words each. (4 × 2)
(A) Examine and highlight the theme of the story ‘Madam Rides the Bus’. (4)
(B) Develop a conversation between the young lawyer and one of his associates regarding his experience of getting be fooled by Lutkins in the story ‘The Hack Driver’. (4)
(C) Evaluate ‘The sermon at Benares’ as an important life lesson. (4)

The post CBSE Sample Papers for Class 10 English Term 2 Set 7 for Practice appeared first on Learn CBSE.

Students can access the CBSE Sample Papers for Class 10 Maths Basic with Solutions and marking scheme Term 2 Set 4 will help students in understanding the difficulty level of the exam.

CBSE Sample Papers for Class 10 Maths BasicTerm 2 Set 4 with Solutions

Time allowed: 2 hours
Maximum Marks: 40

General Instructions:

• The question paper consists of 14 questions divided into 3 sections A, B, C.
• Section A comprises of 6 questions of 2 marks each. Internal choice has been provided in two questions.
• Section B comprises of 4 questions of 3 marks each. Internal choice has been provided in one questions.
• Section C comprises of 4 questions of 4 marks each. An internal choice has been provided in one questions. It contains two case study based questions.

Section – A (12 Marks)

Question 1.
If for the quadratic equation 2x² + kx – 6 = 0, 2 is one of its root, then find the value of k. Also, find the value of the other root.
OR
The sum of squares of three consecutive positive integers are 50. Then what are the three integers? (2)
Answer:
Since, x = 2 is a root of the equation. 2x² + kx – 6 = 0
∴ 2 × 2² + k × 2 – 6 = 0
⇒ 8 + 2k – 6 = 0
⇒ k = – 1
Put k = – 1 in the equation.
2x² + kx – 6 = 0
We get
2x² – x – 6 = 0
⇒ 2x² – 4x + 3x – 6 = 0
⇒ 2x(x – 2) + 3(x – 2) = 0
⇒ x = 2, \(\frac{-3}{2}\)

Caution:
First, find the value of k, to formulate the equation. Then, find the roots of the quadratic equation
OR
Consider three consecutive integer as x, x + 1 and x + 2.
A.T.Q x² + (x + 1)² + (x + 2)² = 50
⇒ x² + x² + 1 + 2x + x² + 4 + 4x = 50
⇒ 3x² + 6x – 45 =0
⇒ 3(x² + 2x – 15) = 0
⇒ x² + 2x – 15 = 0
⇒ x² + 5x – 3x – 15 = 0
⇒ x(x + 5) – 3(x + 5) =0
⇒ x = 3, – 5
x ≠ – 5 (rejected)
Hence, integers are 3, 4, 5.

Question 2.
The surface area of a sphere and a cube are equal. Then, find the ratio of their volumes. (2)
Answer:
Let, surface area of sphere be x cm²
⇒ 4πr² = x
⇒ r = \(\sqrt{\frac{x}{4 \neq}}\) cm,
where, r is the radius of the sphere Also, surface area of cube be x cm²
⇒ 6 × side² = x
⇒ side = \(\sqrt{\frac{x}{6}}\) cm

Caution:
Apply the exponents property in the end to solve the question and get the answer.

Question 3.
The daily minimum steps climbed by a man during a week were as under.

What are the mean of the steps? (2)
Answer:
Number of steps climbed in a week:
35, 30, 27, 32, 23, 28
Mean = \(\frac{\text { Sum of observations(Steps) }}{\text { Total no. of observations }}\)
= \(\frac{35+30+27+32+23+28}{6}\)
= \(\frac{175}{6}\)
= 29.17

Question 4.
The sum of first 6 terms of on AP. is 42. The ratio of its 11th term is 1: 3. CaLcuLate the first term of an AP. (2)
Answer:
Let the first term of the AP be a and common difference be ‘d’.
Now, S₆ = 42
⇒ \(\frac{6}{2}\)(2a + 5d) = 42
2a + 5d = 14
Also, \(\frac{a_{11}}{a_{33}}\) = \(\frac{1}{3}\)
⇒ \(\frac{a+10 d}{a+32 d}\) = \(\frac{1}{3}\)
⇒ 3a + 30 d = a + 32 d
⇒ 2a = 2d
⇒ a = d
Put a = d in equation (i), we get 2a + 5 = 14
a = 2
∴ First term of an AP = 2

Question 5.
Consider the following distribution:

(A) Calculate the frequency of the class 30-40.
(B) Calculate the class mark of the class (2)
Answer:

(A) So, frequency of the class 30-40 is 3.
(B) Class mark of the class 10-25
= \(\frac{10+25}{2}\) = \(\frac{35}{2}\) = 17.5

Related Theory:
Class mark can be calculated by dividing the sum of upper and lower limits by 2.

Question 6.
In the given figure, ∠APB = 90°. Then what is the length of OP?

In the figure, PQ and RS are the common tangents to two circle intersecting at O. prove that PQ = RS. (2)

Answer:
In the given figure, OA = r. AP and PB are tangents to the circle.
Then tangent is perpendicular to the radius at the point of contact.
∴ ∠OAP = 90°
And ∠APB = 90°
∴ ∠APO = 45°
(Since OP bisects ∠APB)
∴ In ∆APO
sin 45° = \(\frac{\mathrm{OA}}{\mathrm{OP}}\)
\(\frac{1}{\sqrt{2}}\) = \(\frac{r}{\mathrm{OP}}\)
⇒ OP = √2r units

Related Theory:
For the trigonometric ratio sine of an angle is equal to the \(\frac{Perpendicular}{\text { Hypotenuse }}\)
Or
Given: RQ and RS are common tangents to 2 circles intersecting at 0.
To Proof: PQ = RS
Since, tangents from an external point to a circle are equal.
∴ OP = OR …… (i)
And OS = OQ …(ii)
⇒ PQ = OP + OQ
= OR + OS
[From (i) and (ii)] = RS
Hence, proved.

Section – B (12 marks)

Question 7.
Poonam saved a portion of the pocket money. In first week, she saves ₹ 5 and then increased her weekly savings by ₹ 1.75 each week. In which week, will her weekly saving be ₹ 20.75? (3)
Answer:
Suppose amount of weekly savings will be ₹ 20.75 in the nth week. Clearly, amount of weekly savings form an AP with first term, a = 5, common difference, d = 1.75
∵ nth term = 20.75
a + (n – 1) × 1.75 = 20.75
5 + (n – 1) × 1.75 = 20.75
⇒ (n – 1) × 1.75 = 20.75 – 5
⇒ (n – 1) × 1.75 = 15.75
(n – 1) = \(\frac{15.75}{1.75}\)
(n – 1) = 9
⇒ n = 10
Hence, Poonam’s weekly saving will be ₹ 20.75 in 10 week.

Question 8.
A vertical tower stands on a horizontal plane is surmounted by a vertical flag staff of height ‘h’. At a point on the ground, the angles of elevations at the bottom and the tops of the flag staff are a and p respectively. Prove
that the height of the tower is \(\frac{h \tan \alpha}{\tan \beta-\tan \alpha}\)
OR
The figure shows two different positions P and Q of a helicopter flying horizontally at a uniform speed of 72 km/hr.

It is found that it takes the helicopter 10 min. to fly from P to Q. The angles of elevation of P and Q from point A on the ground are 45° and 60° respectively.
Find :
(A) The distance PQ.
(B) The distance AQ
(C) The height of the helicopter above the ground. (3)
Answer:
In the figure, AB and BC represent the tower and flagstaff respectively.

In ∆OAB,

OR
(A) As the helicopter is flying at the speed of 72 km/sec, So in 10 min it will fly
\(\left(\frac{72}{60} \times 10\right)\)km = 12 km

(B) Let, the height of the helicopter from the ground be ‘h’ km.
Then,
\(\frac{h}{\mathrm{AM}}\) = tan 60° and \(\frac{h}{\mathrm{AM}}\) = tan 45°
\(\frac{h}{\mathrm{AM}}\) = √3 and \(\frac{h}{\mathrm{AN}}\) = 1

h = √3 AM and h = AN
∴ √3 AM = AN
Since, AN – AM = MN = PQ = 12 cm
√3 AM = AM + 12
⇒ AM (√3 – 1) = 12
AM = \(\frac{12}{\sqrt{3}-1} \times \frac{\sqrt{3}+1}{\sqrt{3}+1}\)
= \(\frac{12(\sqrt{3}+1)}{2}\)
= 16.4 km
Now in ∆AMQ
\(\frac{A M}{A Q}\) = cos 60°
= \(\frac{1}{2}\)
⇒ AQ = 2 AM
⇒ AQ = 2 × 16.4
= 32.8 km

(C) From above, we have h = AN
= AM + 12
= 16.4 + 12
= 28.4 km

Related Theory:
Do the necessary constructions in the given figure to get the answer.

Question 9.
In the given figure, AB and CB are common tangents to the two circles of radii a and b(a > b). Prove that AB = CD (3)

Answer:
Given: Two circles of different radii such that radii of circle with centre O is a and with centre O’ is b

Construction: Join AD and BC
To Prove: AB = CD
Proof: The tangent drawn form an external point to a circle are equal in length.
If A is external point for circle having centre O’
then, AB = AD …(i)
If C is external point for circle having centre O’
then BC = CD …(ii)
Now, B is external point for circle having centre O
then, AB = BC ,..(iii)
So, from (i) (ii) and (iii), we get
AB = BC = CD
So, AB = CD
Hence proved.

Caution:
Here, circles are at a distance from each other and radii are also not equal So, use the property of tangents to get the answer.

Question 10.
What are the roots of quadratic equation 5x² – 6x – 2 = 0, by completing the square method? (3 )
Answer:
Given quadratic equation:
5x² – 6x – 2 =0 …(i)
On multiplying eq. (i) by 5, we get
25x² – 30x – 10 = 0
⇒ (5x)² – 2 × 5x × 3 – 10 = 0
On adding and subtracting 32 we get,
⇒ (5x)² – 2 × 5x × 3 + 3² – 10 – 3² = 0
⇒ (5x – 3)² – 10 – 9 = 0
[∵ (a – b)² = a² – 2ab + b²]
⇒ (5x – 3)² = 19
On taking square root on both sides, we get
⇒ (5x – 3) = ± √19
5x = 3 ± √19
On taking positive sign, we get .
x = \(\frac{3+\sqrt{19}}{5}\)
On taking negative sign we get
x = \(\frac{3-\sqrt{19}}{5}\)
Hence, \(\frac{3+\sqrt{19}}{5}\) and \(\frac{3-\sqrt{19}}{5}\) are the roots of the quadratic equations.

Related Theory:
Completing the square method is used for converting a quadratic expression of the form ax² + bx + c to the form a(x – h)² + k.

Section – C (16 marks)

Question 11.
Draw a circle of radius 5 cm. Draw two tangents to a circle, which are perpendicular to each other.
OR
Draw a circle of radius 2 cm. From a point 6 cm away from its centre, construct the pair of tangents to the circle Measure the lengths of tangents. (4)
Answer:

Steps of construction:

1. Draw a circle of radius 5 cm with centre O
2. Take, point A on the circle and join OA.
3. Draw perpendicular to OA at A
4. Draw OB, making an angle of 90° with OA.
5. Draw perpendicular to OB at point B. Let these perpendicular intersect at C.
   Hence, CA and CB are the required tangents inclined at an angle of 90°

Related Theory:
Here, quadrilateral OBCA formed is a cyclic quadrilateral. Therefore, for forming tangents inclined at 90°. The angle between the radii in the circle should also be 90°
OR

Steps of construction:

1. Draw a circle of radius 2 cm, with centre O.
2. Mark a point P at a distance of 6 cm from the centre of the circle.
3. Draw a perpendicular bisector of Line OP at P
4. From P as centre and OP’ as radius draw a circle intersecting the previous circle at M and N.
5. Join MP and NP
   MP and NP are the required tangents.

Related Theory:
Here, we apply 2 properties of circles for construction. As, tangent is perpendicular the radius and angle in a semicircle is a right angle.

Question 12.
If the median of the following distribution is 58 and sum of all the frequencies is 140. What is the value of x and y? (4)

Answer:
Given, distribution is:

And, 105 + x + y = 140
⇒ x + y = 35 (i)
Here, Median = 58
Then, median class is 55-65,
l = 55,
\(\frac{N}{2}\) = \(\frac{140}{2}\) = 70
Then, c.f. = 43 + x
Median = l + \(\left(\frac{\frac{N}{2}-c . f}{f}\right)\) × h
⇒ 58 = 55 + \(\left(\frac{70-43-x}{40}\right)\) × 10
⇒ BD = 100 m.
⇒ 3 = \(\frac{27-x}{4}\)
⇒ 12 = 27 – x
⇒ x = 27 – 12 = 15
∴ y = 35 – 15 = 20
Hence, value of x and y are 15 and 20.

Question 13.
Case Study—1
Light house is a pilLar type structure in the sea, used to give directions to ships. These are often built on the island, arts cell on cliffs. Lighthouse on water surface act as a navigational aid to the mariners and send warning to boats and ships for dangers. Traditionally, light house have been bacons of navigation for mariners for centuries, but in 21st century lighthouse are going through a major transformation as tourist destination also. India has 189 lighthouses dotting its vast coast line. A man is standing on the top of the light house.

He observes that two boats P and Q are approaching to light house from opposite direction.
He finds that angle of depression of boat P is 45° and angle of depression of boat Q is 30°.

(A) What is the distance of the boat which is nearer to the light house, at a moment? (2)
Answer:
Here, the boat at C is nearer to light house as it has lesser angle of depression i.e., angle of elevation.
∴ In ∆ACD
tan 45° = \(\frac{A D}{B D}\)
1 = \(\frac{100}{B D}\)
⇒ BD = 100 m.

(B) What is the distance between the two boats? (2)
Answer:
Distance between the 2 boats = BC
i.e., BC = BD + CD
∴ In ∆ADB, tan 30° = \(\frac{A D}{B D}\)
⇒ \(\frac{1}{\sqrt{3}}\) = \(\frac{100}{B D}\)
⇒ BD = 10o√3 m
∴ Distance between boats
= CD + BD
= 100 + 100 √3
= 100 (1 + √3) m.

Question 14.
Case Study—2
Devashish’s mother bought him a ball. He being very intellectual and always interested in finding new things, Devashish try to evaluate the radius of the ball foil calculating its volume and surface area. He tried to do it by compress seace, etc. But he was not successful. So, he saw a video on you tube, regarding the practical use of volume and surface area. Devashish decided to conduct an experiment to find the radius r of a sphere. For this he took a cylindrical container with radius, R = 7 cm and height 10 cm. He filled the container almost half by water as shown in the figure. Now he dropped the ball whose radius is to be measured in the container. After dropping the ball, the water level in the container raised by 3.4 cm.

(A) What is the approximate radius of the spherical ball dropped in the container? (2)
Answer:
5 cm

Explanation: Here, height of water raised by 3.40 cm by dropping the sphere.
The radius of container, R = 7 cm
Then, volume of the height raised = Volume of sphere
πR²h = \(\frac{4}{3}\)πr³
⇒ 7 × 7 × 3.4 = \(\frac{4}{3}\) × r³
⇒ r³ = \(\frac{7 \times 7 \times 3 \times 3.4}{4}\)
≈ 125
⇒ r = 5 cm
Hence, the radius of sphere is 5 cm.

(B) If this spherical ball is cut into two hemispherical shapes, then what is surface area of two hemispheres combined ? (2 )
Answer:
Radius of sphere = 5 cm
∴ Radius of each hemisphere = 5 cm
Surface area of one hemisphere = 2πr² + πr² = 3πr²
∴ Surface area of 2 hemisphere = 2 × 3πr²
= 6πr²
= 6 × \(\frac{22}{7}\) × 5 × 5
= 471.43 cm³

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