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Aditya Birla Scholarship 2019 | Dates, Eligibility, Rewards, Selection and Application Process 

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Aditya Birla Scholarship 2019: Aditya Birla Scholarship is an initiative of the Aditya Birla Group. This scholarship offered to meritorious students from the renowned institutes of India every year. Institutes like IITs, IIMs, BITs, and XLRI with the aim of encouraging them to pursue their academic and co-curricular excellence and leadership abilities. Aditya Birla Group has already been released the online applications for the Aditya Birla Scholarship 2019-20.

This scholarship covers academic as well as hostel fees for the entire course duration. If they maintain a good academic report throughout their course duration. So, eligible candidates can apply for this scholarship on or before July 13, 2019. Candidates can apply online for this scholarship on the official website of Aditya Birla Group. Read the complete article to get all the information about the Aditya Birla Scholarship.

Aditya Birla Scholarship 2019-20

Aditya Birla Scholarship can be applied through online mode only. This scholarship offered to only the students from IITs/IIMs/BITs/XLRI institutes all over India. This scholarship introduced in 1999 to provide opportunities for outstanding students to learn through networking with the country’s first global conglomerate.

This Scholarship is named in honor of the late Mr. Aditya Vikram Birla. This scholarship helps to make future leaders in accordance with the goal of pursuing Mr. Birla’s ideals. This scholarship achieved through nurturing outstanding academic excellence and humane leadership values. This has been implemented in partnership with IITs, IIMs, XLRI, BITS, and law campuses.

Aditya Birla Group believes in nurturing a culture of innovation and experimentation. The Group working in 5000 villages reaching out to 7.5 million people every year. This helps them to know the academic and extra-academic opportunities under this scheme. Aditya Birla Group invites scholars to work with them if they are eligible for it. But, it is not mandatory to join the Group after the completion of their course.

Aditya Birla Scholarship Overview

ParticularsDetails
Conducting BodyAditya Birla Group
Scholarship NameAditya Birla Scholarship
Scholarship TypePost-Matric Scholarship
Application ModeOnline
Applicable StateAll Over India
Academic Year2019-20
Purpose of ScholarshipOffered to IITs, IIMs, BITs, and XLRI institute students to pursue their academic and co-curricular excellence and make the leadership abilities
Application Deadline13th July 2019
Websitewww.adityabirla.com/home

Aditya Birla Group Scholarships

Aditya Birla Scholarship Important Dates

EventsImportant Dates
Last Date of Scholarship Application SubmissionJuly 13, 2019
Intimation to Selected CandidatesThird Week of August 2019
Interview to Selected CandidatesThird Week of September 2019

Aditya Birla Scholarship Eligibility Criteria

Students from the below-listed institutes are eligible to apply:

  • B.Tech. in IITs – Delhi, Chennai, Mumbai, Kharagpur, Kanpur, Roorkee, Guwahati.
  • XLRI – Jamshedpur.
  • IIMs – Bangalore, Kolkata, Ahmedabad, Indore, Lucknow, Shilong, Kozhikode.
  • BITs Campuses.
  • National Law School of India University – Bangalore.
  • NALSAR University of Law – Hyderabad.
  • National Law University – Jodhpur.
  • National Law University – Gujarat.
  • National University of Juridical Sciences – Kolkata.
  • The first top 20 students of the entrance exam conducted for admission are eligible to apply through the Dean of the respective Institutes.

Aditya Birla Scholarship Rewards

Aditya Birla Scholarship covers a large portion of academic and hostel fees for the IITs/ BITs stream students. However, it covers some portion of the tuition fee for the management and law stream students. Refer to the table below to know the Aditya Birla Scholarship Rewards.

InstitutesAmount per Annum
IITs/BITs (Pilani)Rs. 1,00,000
LAWRs. 1,80,000 or Actual Fees, whichever is lower
IIMs/XLRIRs. 1,75,000

Aditya Birla Scholarship Selection Process

Refer to the below-listed selection process for the Aditya Birla Scholarship.

  • 160 students from the IITs/ BITS (Pilani), 180 students from the IIMs/ XLRI, and 100 students from law campuses will be evaluated as per the information mentioned in the application form.
  • Students will be evaluated to select for the next round based on their overall achievements on both sides of academic and co-curricular excellence.
  • Then, the panel will review the essays written by these students to select them for the final round.
  • The selected students will be invited for an interview which will be held in Mumbai. In this interview, the best 16 students each from Engineering and Management and 8 from Law will be determined.
  • These selected students will be named ‘Aditya Birla Scholars’. Shortlisted students will be provided with travel reimbursement, accommodation, and a token allowance.
  • A well-known panel of luminaries and academicians will conduct the interviews.
  • Shortlisted students must bring all the supporting documents such as photocopies of mark sheets, certificates, etc.
  • Aditya Birla Scholars will be awarded the scholarship amount. This is administered by the Deans or Directors of the institutes.
  • The scholarship amount will be given through cheques directly to their office.
  • The scholarships are valid in continued performance for the course. As the scholarship, the result is declared only in September. So, the institute will refund the amount which has already been paid by the students.
  • The Scholars performance will be monitored thoroughly for the renewal of the scholarship every year.

Aditya Birla Scholarship Application Process

Refer to the below points to apply for the Aditya Birla Scholarship.

  • Go to the official website of Aditya Birla Group @ http://www.adityabirlascholars.net/
  • Select the link related to scholarship on the homepage.
  • Then, read all the prescribed instructions to fill the Aditya Birla Scholarship Form.
  • Download the Aditya Birla Scholarship Application Form.
  • After this, fill the correct and necessary information in the application form.
  • Attach all the supporting documents along with the form.
  • Submit it along with the supporting documents to the Dean of your institution.

Documents Required for Aditya Birla Scholarship

Attach the below-listed supporting documents to apply for the Aditya Birla Scholarship.

  • Photocopies of the previous examination certificates and mark sheets
  • Photocopy of the first page of bank passbook in the name of the student
  • Photocopy of student’s Aadhar card

Aditya Birla Scholarship Renewal

The performance assessment will be done every year until the course completion for the renewal process. The Scholars will be assessed on qualitative and quantitative parameters to judge their excellence on the academic and leadership side. This will help in determining the renewal of the scholarship and the honor of continuing as the ‘Aditya Birla Scholar’. Refer to the below-listed criteria for the renewal of the scholarship:

  • The scholar must belong to the top 25% of the students batch to meet the scholastic standards.
  • The work done by the Scholar during the course of the program will be assessed.
  • At least 60% of the assignments of the Scholar must have a rating of 7 on a 9 point scale.
  • Scholars participate in at least 2 forums of campus will be determined.
  • The Scholars learnings will be determined by giving a 250-word essay on ‘Being an Aditya Birla Scholar – experience sharing’ to the Scholar.
  • The above data for the performance measurement should be submitted by the Scholar and verified by the Dean at the institute.
  • The evaluation will be performed based on the overall performance in all areas.

Aditya Birla Scholarship Contact Details

In case of any help or queries related to Aditya Birla Scholarship, students may contact using the below details

Address:
Aditya Birla Center,
‘C’ Wing, 1st Floor, S.K. Ahire Marg Worli,
Mumbai- 30
Phone Number: 91-22-66525000 / 24995000

FAQ’s on Aditya Birla Scholarship

Question 1.
What is the Aditya Birla Scholarship?

Answer:
Aditya Birla Scholarship is an initiative of the Aditya Birla Group. This scholarship offered to meritorious students from the renowned institutes of India every year. Institutes like IITs, IIMs, BITs, and XLRI with the aim of encouraging them to pursue their academic and co-curricular excellence and leadership abilities.

Question 2.
What is the result declaration date of the Aditya Birla Scholarship?

Answer:
The result of the Aditya Birla Scholarship will be declared in September.

Question 3.
What is the last date to apply for the Aditya Birla Scholarship?

Answer:
The last date to apply for the Aditya Birla Scholarship is 13th July 2019.

Question 4.
Is Aditya Birla Scholarship available for all State candidates?

Answer:
Yes, the Aditya Birla Scholarship is available all over India.

Question 5.
What are the rewards provided under the Aditya Birla Scholarship?

Answer:
Aditya Birla Scholarship covers a large portion of academic and hostel fees for the IITs/ BITs stream students. However, it covers some portion of the tuition fee for the management and law stream students. If they maintain a good academic report throughout their course duration.

Hope this article will help you to get more information about the Aditya Birla Scholarship. If you have queries related to Aditya Birla Scholarship, then leave it in the comment box.

You can also find more Scholarship Articles for 12th passed, 10th passed Students and many more.

The post Aditya Birla Scholarship 2019 | Dates, Eligibility, Rewards, Selection and Application Process  appeared first on Learn CBSE.


CBSE Sample Papers for Class 10 Maths

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Download CBSE Sample papers for Class 10 Maths and Marking Scheme PDF 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 – 2020, 2019, 2018, 2017, 2016.

https://www.instamojo.com/phaniraju/cbse-sample-papers-for-class-10/

CBSE Sample Question Paper for Class 10 Maths @ cbse.nic.in

Year of ExaminationMaths Sample Question PaperAnswers/ Marking Scheme
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Solved CBSE Sample Papers for Class 10 Maths 2019

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CBSE Previous Year Question Papers Class 10 Maths With Solutions

CBSE Previous Year Question Papers class 10 Maths

CBSE Class 10 Maths Question Paper 2018 CBSE Class 10 Maths Question Paper 2017
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CBSE Topper Answer Sheet Class 10 Maths

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CBSE Class 10 Previous Year Question Paper Maths 2018

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CBSE Previous Year Question Paper Class 10 Maths 2017

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CBSE Previous Year Question Paper Class 10 Maths 2016

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CBSE Previous Year Question Papers Class 10 Maths 2015

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CBSE Previous Year Question Papers Class 10 Maths 2014

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CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2

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CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2

Time Allowed: 3 hours
Maximum Marks: 80

General Instructions:

  • All questions are compulsory.
  • This question paper consists of 30 questions divided into four sections- A, B, C and D.
  • Section A contains 6 questions of 1 mark each, Section B contains 6 questions of 2 marks each, Section C contains 10 questions of 3 marks each and Section D contains 8 questions of 4 marks each.
  • There is no overall choice. However, an internal choice has been provided in two questions of 1 mark each, two questions of 2 marks each, four questions of 3 marks each and three questions of 4 marks each. You have to attempt only one of the alternative in all such questions.
  • Use of calculators is not permitted.

CBSE Sample Papers Class 10 Maths

CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set I

Section – A

Question 1.
What is the common difference of an A.P. in which a21 – a7 = 84 ? [1]
Solution:
Given, a21 – a7 = 84
⇒ (a + 20d) – (a + 6d) = 84
⇒ a + 20d – a – 6d = 84
⇒ 20d – 6d = 84
⇒ 14d = 84
Hence common difference = 6

Question 2.
If the angle between two tangents drawn from an external point P to a circle of radius a and centre O, is 60°, then find the length of OP. [1]
Solution:
Given, ∠APB = 60°
∠APO = 30°
CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set I Q2
In right angle ΔOAP,
\frac { OP }{ OA } = cosec 30°
\frac { OP }{ a } = 2
⇒ OP = 2a

Question 3.
If a tower 30 m high, casts a shadow 10√3 m long on the ground, then what is the angle of elevation of the sun? [1]
Solution:
In ΔABC,
tan θ = \frac { AB }{ BC }
CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set I Q3
⇒ tan θ = \frac { 30 }{ 10\surd 3 } = √3
⇒ tan θ = tan 60°
⇒ θ = 60°
Hence angle of elevation is 60°.

Question 4.
The probability of selecting a rotten apple randomly from a heap of 900 apples is 0-18. What is the number of rotten apples in the heap? [1]
Solution:
Total apples = 900
P(E) = 0.18
CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set I Q4
No. of rotten apples = 900 × 0.18 = 162

Section – B

Question 5.
Find the value of p, for which one root of the quadratic equation px2 – 14x + 8 = 0 is 6 times the other. [2]
Solution:
Given equation is px2 – 14x + 8 = 0
Let one root = α
then other root = 6α
CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set I Q5
CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set I Q5.1

Question 6.
Which term of the progression 20, 19\frac { 1 }{ 4 }, 18\frac { 1 }{ 2 }, 17\frac { 3 }{ 4 }, … is the first negative term ? [2]
Solution:
Given, A.P. is 20, 19\frac { 1 }{ 4 }, 18\frac { 1 }{ 2 }, 17\frac { 3 }{ 4 }, …..
CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set I Q6

Question 7.
Prove that the tangents drawn at the endpoints of a chord of a circle make equal angles with the chord. [2]
Solution:
Given, a circle of radius OA and centred at O with chord AB and tangents PQ & RS are drawn from point A and B respectively.
CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set I Q7
Draw OM ⊥ AB, and join OA and OB.
In ∆OAM and ∆OMB,
OA = OB (Radii)
OM = OM (Common)
∠OMA = ∠OMB (Each 90°)
∆OAM = ∆OMB (By R.H.S. Congurency)
∠OAM = ∠OBM (C.PC.T.)
Also, ∠OAP = ∠OBR = 90° (Line joining point of contact of tangent to centre is perpendicular on it)
On addition,
∠OAM + ∠OAP = ∠OBM + ∠OBR
⇒ ∠PAB = ∠RBA
⇒ ∠PAQ – ∠PAB = ∠RBS – ∠RBA
⇒ ∠QAB = ∠SBA
Hence Proved

Question 8.
A circle touches all the four sides of a quadrilateral ABCD. Prove that AB + CD = BC + DA [2]
Solution:
Given, a quad. ABCD and a circle touch its all four sides at P, Q, R, and S respectively.
CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set I Q8
To prove: AB + CD = BC + DA
Now, L.H.S. = AB + CD
= AP + PB + CR + RD
= AS + BQ + CQ + DS (Tangents from same external point are always equal)
= (AS + SD) + (BQ + QC)
= AD + BC
= R.H.S.
Hence Proved.

Question 9.
A line intersects the y-axis and x-axis at the points P and Q respectively. If (2, -5) is the mid-point of PQ, then find the coordinates of P and Q. [2]
Solution:
Let co-ordinate of P (0, y)
Co-ordinate of Q (x, 0)
CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set I Q9

Question 10.
If the distances of P(x, y), from A(5, 1) and B(-1, 5) are equal, then prove that 3x = 2y. [2]
Solution:
Given, PA = PB
CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set I Q10
⇒ x2 + 25 – 10x + y2 + 1 – 2y = x2 + 1 + 2x + y2 + 25 – 10y
⇒ -10x – 2y = 2x – 10y
⇒ -10x – 2x = -10y + 2y
⇒ 12x = 8y
⇒ 3x = 2y
Hence Proved.

Section – C

Question 11.
If ad ≠ bc, then prove that the equation (a2 + b2) x2 + 2 (ac + bd) x + (c2 + d2) = 0 has no real roots. [3]
Solution:
Given, ad ≠ bc
(a2 + b2) x2 + 2(ac + bd)x + (c2 + d2) = 0
D = b2 – 4ac
= [2(ac + bd)]2 – 4 (a2 + b2) (c2 + d2)]
= 4[a2c2 + b2d2 + 2abcd] – 4(a2c2 + a2d2 + b2c2 + b2d2)
= 4[a2c2 + b2d2 + 2abcd – a2c2 – a2d2 – b2c2 – b2d2]
= 4[-a2d2 – b2c2 + 2abcd]
= -4[a2d2 + b2c2 – 2abcd]
= -4[ad – bc]2
D is negative
Hence given equation has no real roots.
Hence Proved.

Question 12.
The first term of an A.E is 5, the last term is 45 and the sum of all its terms is 400. Find the number of terms and the common difference of the A.P. [3]
Solution:
Given, a = 5, an = 45, Sn = 400
We have, Sn = \frac { n }{ 2 } [a + an]
⇒ 400 = \frac { n }{ 2 } [5 + 45]
⇒ 400 = \frac { n }{ 2 } [50]
⇒ 25n = 400
⇒ n = 16
Now, an = a + (n – 1) d
⇒ 45 = 5 + (16 – 1)d
⇒ 45 – 5 = 15d
⇒ 15d = 40
⇒ d = \frac { 8 }{ 3 }
So n = 16 and d = \frac { 8 }{ 3 }

Question 13.
On a straight line passing through the foot of a tower, two points C and D are at distances of 4 m and 16 m from the foot respectively. If the angles of elevation from C and D of the top of the tower are complementary, then find the height of the tower. [3]
Solution:
Let height AB of tower = h m.
CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set I Q13
CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set I Q13.1

Question 14.
A bag contains 15 white and some black balls. If the probability of drawing a black ball from the bag is thrice that of drawing a white ball, find the number of black balls in the bag. [3]
Solution:
Given, no. of white balls = 15
Let no. of black balls = x
Total balls = (15 + x)
According to the question,
P(Blackball) = 3 × P(White ball)
\frac { x }{ 15+x } = 3 × \frac { 15 }{ 15+x }
⇒ x = 45
No. of black balls in bag = 45

Question 15.
In what ratio does the point (\frac { 24 }{ 11 }, y) the line segment joining the points P(2, -2) and Q(3, 7) ? Also, find the value of y. [3]
CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set I Q15
Solution:
Let point R divides PQ in the ratio k : 1
CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set I Q15.1
CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set I Q15.2

Question 16.
Three semicircles each of diameter 3 cm, a circle of diameter 4.5 cm and a semi-circle of radius 4.5 cm are drawn in the given figure. Find the area of the shaded region. [3]
CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set I Q16
Solution:
Given, radius of large semi-circle = 4.5 cm
CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set I Q16.1
CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set I Q16.2
CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set I Q16.3

Question 17.
In the given figure, two concentric circles with centre O have radii 21 cm and 42 cm. If ∠AOB = 60°, find the area of the shaded region. [Use π = \frac { 22 }{ 7 }]
CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set I Q17
Solution:
Angle for shaded region = 360° - 60° = 300°
Area of shaded region
CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set I Q17.1

Question 18.
Water in a canal, 5-4 m wide and 1.8 m deep, is flowing with a speed of 25 km/hour. How much area can it irrigate in 40 minutes, if 10 cm of standing water is required for irrigation ? [3]
Solution:
Width of canal = 5.4 m
Depth of canal = 1.8 m
Length of water in canal for 1 hr = 25 km = 25000 m
Volume of water flown out from canal in 1 hr = l × b × h = 5.4 × 1.8 × 25000 = 243000 m3
Volume of water for 40 min = 243000 × \frac { 40 }{ 60 } = 162000 m3
Area to be irrigated with 10 cm standing water in field = \frac { Volume }{ Height }
= \frac { 162000\times 100 }{ 10 } m2
= 1620000 m2
= 162 hectare

Question 19.
The slant height of a frustum of a cone is 4 cm and the perimeters of its circular ends are 18 cm and 6 cm. Find the curved surface area of the frustum. [3]
Solution:
Slant height of frustum 'l' = 4 cm
Perimeter of upper top = 18 cm
CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set I Q19

Question 20.
The dimensions of a solid iron cuboid are 4.4 m × 2.6 m × 1.0 m. It is melted and recast into hollow cylindrical pipe of 30 cm inner radius and thickness 5 cm. Find the length of the pipe. [3]
Solution:
Inner radius of pipe 'r' = 30 cm
The thickness of pipe = 5 cm
Outer radius 'R' = 30 + 5 = 35 cm
Now, Volume of hollow pipe = Volume of Cuboid
CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set I Q20

Section - D

Question 21.
Solve for x:
CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set I Q21
Solution:
CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set I Q21.1

Question 22.
Two taps running together can fill a tank in 3\frac { 1 }{ 13 } hours. If one tap takes 3 hours more than the other to fill the tank, then how much time will each tap take to fill the tank ? [4]
Solution:
Let tank fill by one tap = x hrs
other tap = (x + 3) hrs
Together they fill by 3\frac { 1 }{ 13 } = \frac { 40 }{ 13 } hrs
CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set I Q22
Either x - 5 = 0 or 13x + 24 = 0
x = 5, x = -24/13 (Rejected)
One tap fill the tank in 5 hrs
So other tap fill the tank in 5 + 3 = 8 hrs

Question 23.
If the ratio of the sum of the first n terms of two A.P.S is (7n + 1) : (4n + 27), then find the ratio of their 9th terms. [4]
Solution:
Ratio of the sum of first n terms of two A.P.s are
CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set I Q23
Hence ratio of 9th terms of two A.P.s is 24 : 19

Question 24.
Prove that the lengths of two tangents drawn from an external point to a circle are equal. [4]
Solution:
Given, a circle with centre O and external point P. |
Two tangents PA and PB are drawn.
CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set I Q24
To Prove: PA = PB
Construction: Join radius OA and OB also join O to P.
Proof: In ∆OAP and ∆OBP,
OA = OB (Radii)
∠A = ∠B (Each 90°)
OP = OP (Common)
∆AOP = ∆BOP (RHS cong.)
PA = PB [By C.PC.T.]
Hence Proved.

Question 25.
In the given figure, XY and XY are two parallel tangents to a circle with centre O and another tangent AB with a point of contact C, is intersecting XY at A and X'Y' at B. Prove that ∠AOB = 90°. [4]
CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set I Q25
Solution:
Given, XX' & YY' are parallel.
Tangent AB is another tangent which touches the circle at C.
CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set I Q25.1
To prove: ∠AOB = 90°
Construction: Join OC.
Proof: In ∆OPA and ∆OCA,
OP = OC (Radii)
∠OPA = ∠OCA (Radius ⊥ Tangent)
OA = OA (Common)
∆OPA = ∆OCA (CPCT)
∠1 = ∠2 ...(i)
Similarly, ∆OQB = ∆OCB
∠3 = ∠4 ...(ii)
Also, POQ is a diameter of circle
∠POQ = 180° (Straight angle)
∠1 + ∠2 + ∠3 + ∠4 = 180°
From eq. (i) and (ii),
∠2 + ∠2 + ∠3 + ∠3 = 180°
⇒ 2(∠2 + ∠3) = 180°
⇒ ∠2 + ∠3 = 90°
Hence, ∠AOB = 90°
Hence Proved.

Question 26.
Construct a triangle ABC with side BC = 7 cm, ∠B = 45°, ∠A = 105°. Then construct another triangle whose sides are \frac { 3 }{ 4 } times the corresponding sides of the ∆ABC. [4]
Solution:
BC = 7 cm, ∠B = 45°, ∠A = 105°
∠C = 180 ° - (∠B + ∠A) = 180° - (45° + 105°) = 180° - 150° = 30°
CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set I Q26
Steps of construction:

  1. Draw a line segment BC = 7 cm.
  2. Draw an angle 45° at B and 30° at C. They intersect at A.
  3. Draw an acute angle at B.
  4. Divide angle ray in 4 equal parts as B1, B2, B3 and B4.
  5. Join B4 to C.
  6. From By draw a line parallel to B4C intersecting BC at C'.
  7. Draw another line parallel to CA from C' intersecting AB ray at A.
    Hence, ∆A'BC' is required triangle such that ∆A'BC' ~ ∆ABC with A'B = \frac { 3 }{ 4 } AB.

Question 27.
An aeroplane is flying at a height of 300 m above the ground. Flying at this height, the angles of depression from the aeroplane of two points on both banks of a river in opposite directions are 45° and 60° respectively. Find the width of the river. [Use √3 = 1.732] [4]
Solution:
Let aeroplane is at A, 300 m high from a river. C and D are opposite banks of river.
CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set I Q27

Question 28.
If the points A(k + 1, 2k), B(3k, 2k + 3) and C(5k - 1, 5k) are collinear, then find the value of k. [4]
Solution:
Since A(k + 1, 2k), B(3k, 2k + 3) and C(5k - 1, 5k) are collinear points, so area of triangle = 0.
CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set I Q28
CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set I Q28.1

Question 29.
Two different dice are thrown together. Find the probability that the numbers obtained have
(i) even sum, and
(ii) even product. [4]
Solution:
When two different dice are thrown together
Total outcomes = 6 × 6 = 36
(i) For even sum: Favourable outcomes are
(1, 1), (1, 3), (1, 5), (2, 2), (2, 4), (2, 6),
(3, 1), (3, 3), (3, 5), (4, 2), (4, 4), (4, 6),
(5, 1), (5, 3), (5, 5), (6, 2), (6, 4), (6, 6)
No. of favourable outcomes = 18
CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set I Q29
(ii) For even product: Favourable outcomes are
(1, 2), (1, 4), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),
(3, 2), (3, 4), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6),
(5, 2), (5, 4), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6).
No. of favourable outcomes = 27
CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set I Q29.1

Question 30.
In the given figure, ABCD is a rectangle of dimensions 21 cm × 14 cm. A semicircle is drawn with BC as diameter. Find the area and the perimeter of the shaded region in the figure. [4]
CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set I Q30
Solution:
Area of Shaded region = Area of a rectangle - Area of a semi-circle
CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set I Q30.1

Question 31.
In a rain-water harvesting system, the rainwater from a roof of 22 m × 20 m drains into a cylindrical tank having a diameter of base 2 m and height 35 m. If the tank is full, find the rainfall in cm. Write your views on water conservation. [4]
Solution:
Volume of water collected in system = Volume of a cylindrical tank
CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set I Q31

CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set II

Note: Except for the following questions, all the remaining questions have been asked in previous sets.

Section - B

Question 10.
Which term of the A.P. 8, 14, 20, 26,... will be 72 more than its 41st term? [2]
Solution:
A.P. is 8, 14, 20, 26,....
a = 8, d = 14 - 8 = 6
Let an = a41 + 72
a + (n - 1)d = a + 40d + 72
⇒ (n - 1) 6 = 40 × 6 + 72 = 240 + 72 = 312
⇒ n - 1 = 52
⇒ n = 52 + 1 = 53rd term

Section - C

Question 18.
From a solid right circular cylinder of height 24 cm and radius 0.7 cm, a right circular cone of the same height and same radius is cut out. Find the total surface area of the remaining solid. [3]
Solution:
Given,
Height of cylinder 'h' = 2.4 cm,
Radius of base 'r' = 0.7 cm
CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set II Q18
CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set II Q18.1

Question 19.
If the 10th term of an A.E is 52 and the 17th term is 20 more than the 13th term, find the A.P. [3]
Solution:
Given, a10 = 52;
a17 = a13 + 20
⇒ a + 16d = a + 12d + 20
⇒ 16d = 12d + 20
⇒ 4d = 20
⇒ d = 5
Also, a + 9d = 52
⇒ a + 9 × 5 = 52
⇒ a + 45 = 52
⇒ a = 7
Therefore A.E = 7, 12, 17, 22, 27,....

Question 20.
If the roots of the equation (c2 - ab) x2 - 2(a2 - bc) x + b2 - ac = 0 in x are equal, then show that either a = 0 or a3 + b3 + c3 = 3abc. [3]
Solution:
CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set II Q20

Section - D

Question 28.
Solve for x:
CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set II Q28
Solution:
CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set II Q28.1
CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set II Q28.2

Question 29.
A train covers a distance of 300 km at a uniform speed. If the speed of the train is increased by 5 km/hour, it takes 2 hours less on the journey. Find the original speed of the train. [4]
Solution:
Let original speed of train = x km/hr
Increased speed of train = (x + 5) km/hr
Distance = 300 km
According to the question,
CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set II Q29

Question 30.
A man observes a car from the top of a tower, which is moving towards the tower with a uniform speed. If the angle of depression of the car changes from 30° to 45° in 12 minutes, find the time taken by the car now to reach the tower. [4]
Solution:
Let AB is a tower, the car is at point D at 30° and goes to C at 45° in 12 minutes.
CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set II Q30
CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set II Q30.1

Question 31.
In the given figure, ΔABC is a right-angled triangle in which ∠A is 90°. Semi-circles are drawn on AB, AC and BC as diameters. Find the area of the shaded region. [4]
CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set II Q31
Solution:
In right ΔBAC, by Pythagoras theorem,
CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set II Q31.1
CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set II Q31.2

CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set III

Note: Except for the following questions, all the remaining questions have been asked in previous sets.

Section - B

Question 10.
For what value of n, are the terms of two A.Ps 63, 65, 67,.... and 3, 10, 17,.... equal ? [2]
Solution:
1st A.P. is 63, 65, 67,...
a = 63, d = 65 - 63 = 2
an = a + (n - 1 )d = 63 + (n - 1) 2 = 63 + 2n - 2 = 61 + 2n
2nd A.E is 3, 10, 17,...
a = 3, d = 10 - 3 = 7
an = a + (n - 1 )d = 3 + (n - 1) 7 = 3 + 7n - 7 = 7n - 4
According to question,
61 + 2n = 7n - 4
⇒ 61 + 4 = 7n - 2n
⇒ 65 = 5n
⇒ n = 13
Hence, 13th term of both A.P. is equal.

Section - C

Question 18.
A toy is in the form of a cone of radius 3-5 cm mounted on a hemisphere of the same radius on its circular face. The total height of the toy is 15*5 cm. Find the total surface area of the toy. [3]
Solution:
Given, radius of base 'r' = 3.5 cm
Total height of toy = 15.5 cm
Height of cone 'h' = 15.5 - 3.5 = 12 cm
CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set III Q18
CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set III Q18.1

Question 19.
How many terms of an A.E 9, 17, 25,... must be taken to give a sum of 636? [3]
Solution: A.P. is 9, 17, 25,....,
Sn = 636
a = 9, d = 17 - 9 = 8
CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set III Q19

Question 20.
If the roots of the equation (a2 + b2) x2 - 2 (ac + bd) x + (c2 + d2) = 0 are equal, prove that \frac { a }{ b } = \frac { c }{ d } [3]
Solution:
CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set III Q20

Section - D

Question 28.
Solve for x:
CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set III Q28
Solution:
CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set III Q28.1

Question 29.
A takes 6 days less than B to do a work. If both A and B working together can do it in 4 days, how many days will B take to finish it? [4]
Solution:
Let B can finish a work in x days
so, A can finish work in (x - 6) days
Together they finish work in 4 days
Now,
CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set III Q29
⇒ 4 (2x - 6) = x2 - 6x
⇒ 8x - 24 = x2 - 6x
⇒ x2 - 14x + 24 = 0
⇒ x2 - 12x - 2x + 24 = 0
⇒ x(x - 12) - 2(x - 12) = 0
⇒ (x - 12) (x - 2) = 0
Either x - 12 = 0 or x - 2 = 0
x = 12 or x = 2 (Rejected)
B can finish work in 12 days
A can finish work in 6 days.

Question 30.
From the top of a tower, 100 m high, a man observes two cars on the opposite sides of the tower and in a same straight line with its base, with angles of depression 30° and 45°. Find the distance between cars.
[Take √3 = 1.732] [4]
Solution:
Let AB is a tower.
Cars are at point C and D respectively
CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set III Q30
Distance between two cars = x + y = 173.2 + 100 = 273.2 m

Question 31.
In the given figure, O is the centre of the circle with AC = 24 cm, AB = 7 cm and ∠BOD = 90°. Find the area of the shaded region. [4]
CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set III Q31
Solution:
Given, C (O, OB) with AC = 24 cm AB = 7 cm and ∠BOD = 90°
CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set III Q31.1
∠CAB = 90° (Angle in semi-circle)
Using pythagoras theorem in ∆CAB,
BC2 = AC2 + AB2 = (24)2 + (7)2 = 576 + 49 = 625
⇒ BC = 25 cm
Radius of circle = OB = OD = OC = \frac { 25 }{ 2 } cm
Area of shaded region = Area of semi-circle with diamieter BC - Area of ∆CAB + Area of sector BOD
CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set III Q31.2

CBSE Previous Year Question Papers CBSE Previous Year Question Papers Class 10 Maths

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Solved CBSE Sample Papers for Class 10 Maths Set 3

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Download Solved CBSE Sample Papers for Class 10 Maths Set 3 2019 PDF to understand the pattern of questions asks in the board exam. Know about the important topics and questions to be prepared for CBSE Class 10 Maths board exam and Score More marks. Here we have given Maths Sample Paper for Class 10 Solved Set 3.

Board – Central Board of Secondary Education, cbse.nic.in
Subject – CBSE Class 10 Mathematics
Year of Examination – 2019.

You can also Download NCERT Solutions for Class 10 Maths to help you to revise complete Syllabus and score more marks in your examinations.

Solved CBSE Sample Papers for Class 10 Maths Set 3

Solved CBSE Sample Papers for Class 10 Maths Paper 3 1
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CBSE Previous Year Question Papers Class 10 Maths 2018

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CBSE Previous Year Question Papers Class 10 Maths 2018

Time Allowed: 3 hours
Maximum Marks: 80

General Instructions:

  • All questions are compulsory.
  • This question paper consists of 30 questions divided into four sections- A, B, C and D.
  • Section A contains 6 questions of 1 mark each, Section B contains 6 questions of 2 marks each, Section C contains 10 questions of 3 marks each and Section D contains 8 questions of 4 marks each.
  • There is no overall choice. However, an internal choice has been provided in two questions of 1 mark each, two questions of 2 marks each, four questions of 3 marks each and three questions of 4 marks each. You have to attempt only one of the alternative in all such questions.
  • Use of calculators is not permitted.

CBSE Sample Papers Class 10 Maths

CBSE Previous Year Question Papers Class 10 Maths 2018 Set I

Section – A

Question 1.
If x = 3 is one root of the quadratic equation x2 – 2kx – 6 = 0, then find the value of k. [1]
Solution:
Given quadratic equation is, x2 – 2kx – 6 = 0
x = 3 is a root of above equation, then
(3)2 – 2k (3) – 6 = 0
⇒ 9 – 6k – 6 = 0
⇒ 3 – 6k = 0
⇒ 3 = 6k
⇒ k = \frac { 3 }{ 6 } = \frac { 1 }{ 2 }
⇒ k = \frac { 1 }{ 2 }

Question 2.
What is the HCF of the smallest prime number and the smallest composite number? [1]
Solution:
Smallest prime number = 2
Smallest composite number = 4
Prime factorisation of 2 is 1 × 2
Prime factorisation of 4 is 1 × 22
HCF (2, 4) = 2

Question 3.
Find the distance of a point P(x, y) from the origin. [1]
Solution:
The given point is P (x, y).
The origin is O (0, 0)
The distance of point P from the origin,
CBSE Previous Year Question Papers Class 10 Maths 2018 Q3

Question 4.
In an AP if the common difference (d) = -4 and the seventh term (a7) is 4, then find the first term. [1]
Solution:
Given,
d = -4, a7 = 4
a + 6d = 4
⇒ a + 6(-4) = 4
⇒ a – 24 = 4
⇒ a = 4 + 24
⇒ a = 28

Question 5.
What is the value of (cos2 67° – sin2 23°) ? [1]
Solution:
We have, cos2 67° – sin2 23°
= cos2 67° – cos2 (90° – 23°) [∵ sin (90° – θ) = cos θ]
= cos2 67° – cos2 67°
= 0

Question 6.
Given ΔABC ~ ΔPQR, if \frac { AB }{ PQ } = \frac { 1 }{ 3 }, then find \frac { ar\triangle ABC }{ ar\triangle PQR }
Solution:
CBSE Previous Year Question Papers Class 10 Maths 2018 Q6

Section – B

Question 7.
Given that √2 is irrational, prove that (5 + 3√2) is an irrational number. [2]
Solution:
Given, √2 is an irrational number.
Let √2 = m
Suppose, 5 + 3√2 is a rational number.
CBSE Previous Year Question Papers Class 10 Maths 2018 Q7
But \frac { a-5b }{ 3b } is rational number, so m is rational number which contradicts the fact that m = √2 is irrational number.
So, our supposition is wrong.
Hence, 5 + 3√2 is also irrational.
Hence Proved.

Question 8.
In fig. 1, ABCD is a rectangle. Find the values of x and y. [2]
CBSE Previous Year Question Papers Class 10 Maths 2018 Q8
Solution:
Given, ABCD is a rectangle.
AB = CD
⇒ 30 = x + y
or x + y = 30 …(i)
Similarly, AD = BC
⇒ 14 = x – y
or x – y = 14 …(ii)
On adding eq. (i) and (ii), we get
2x = 44
⇒ x = 22
Putting the value of x in eq. (i), we get
22 + y = 30
⇒ y = 30 – 22
⇒ y = 8
So, x = 22, y = 8.

Question 9.
Find the sum of the first 8 multiples of 3. [2]
Solution:
First 8 multiples of 3 are 3, 6, 9,….. up to 8 terms
We can observe that the above series is an AP with
a = 3, d = 6 – 3 = 3, n = 8
Sum of n terms of an A.P is given by,
CBSE Previous Year Question Papers Class 10 Maths 2018 Q9

Question 10.
Find the ratio in which P(4, m) divides the line segment joining the points A(2, 3) and B(6, -3). Hence find m. [2]
CBSE Previous Year Question Papers Class 10 Maths 2018 Q10
Solution:
Let P divides line segment AB in the ratio k : 1
Coordinates of P
CBSE Previous Year Question Papers Class 10 Maths 2018 Q10.1

Question 11.
Two different dice are tossed together. Find the probability:
(i) of getting a doublet.
(ii) of getting a sum 10, of the numbers on the two dice. [2]
Solution:
Total outcomes on tossing two different dice = 36
(i) A: getting a doublet
A = {(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)}
Number of favourable outcomes of A = 6
CBSE Previous Year Question Papers Class 10 Maths 2018 Q11
(ii) B: getting a sum 10.
B = {(4, 6), (5, 5), (6, 4)}
Number of favourable outcomes of B = 3
CBSE Previous Year Question Papers Class 10 Maths 2018 Q11.1

Question 12.
An integer is chosen at random between 1 and 100. Find the probability that it is:
(i) divisible by 8.
(ii) not divisible by 8. [2]
Solution:
The total number are 2, 3, 4, …….. 99
(i) Let E be the event of getting a number divisible by 8.
E = {8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96} = 12
CBSE Previous Year Question Papers Class 10 Maths 2018 Q12
(ii) Let E’ be the event of getting a number not divisible by 8.
Then, P(E’) = 1 – P(E) = 1 – 0.1224 = 0.8756

Section – C

Question 13.
Find HCF and LCM of 404 and 96 and verify that HCF × LCM = Product of the two given numbers. [3]
Solution:
CBSE Previous Year Question Papers Class 10 Maths 2018 Q13
Prime factorization of 404 = 2 × 2 × 101
Prime factorization of 96 = 2 × 2 × 2 × 2 × 2 × 3
HCF = 2 × 2 = 4
And LCM = 2 × 2 × 2 × 2 × 2 × 3 × 101 = 9696
HCF = 4, LCM = 9696
Verification:
HCF × LCM = Product of the two given numbers
4 × 9696 = 404 × 96
38784 = 38784
Hence Verified.

Question 14.
Find all zeroes of the polynomial (2x4 – 9x3 + 5x2 + 3x – 1) if two of its zeroes are (2 + √3) and (2 – √3). [3]
Solution:
Here, p(x) = 2x4 – 9x3 + 5x2 + 3x – 1
And two of its zeroes are (2 + √3) and (2 – √3).
Quadratic polynomial with zeroes is given by,
{x – (2 + √3)}. {x – (2 – √3)}
⇒ (x – 2 – √3) (x – 2 + √3)
⇒ (x – 2)2 – (√3)2
⇒ x2 – 4x + 4 – 3
⇒ x2 – 4x + 1 = g(x) (say)
Now, g(x) will be a factor of p(x) so g(x) will be divisible by p(x)
CBSE Previous Year Question Papers Class 10 Maths 2018 Q14
For other zeroes,
2x2 – x – 1 = 0
2x2 – 2x + x – 1 = 0
or 2x (x – 1) + 1 (x – 1) = 0
(x – 1) (2a + 1) = 0
x – 1 = 0 and 2x + 1 = 0
x = 1, x = \frac { -1 }{ 2 }
Zeroes of p(x) are
1, \frac { -1 }{ 2 }, 2 + √3 and 2 – √3.

Question 15.
If A(-2, 1) and B(a, 0), C(4, b) and D( 1, 2) are the vertices of a parallelogram ABCD, find the values of a and b. Hence find the lengths of its sides. [3]
OR
If A(-5, 7), B(-4, -5), C(-1, -6) and D(4, 5) are the vertices of a quadrilateral, find the area of the quadrilateral ABCD.
Solution:
Given ABCD is a parallelogram.
CBSE Previous Year Question Papers Class 10 Maths 2018 Q15
CBSE Previous Year Question Papers Class 10 Maths 2018 Q15.1
CBSE Previous Year Question Papers Class 10 Maths 2018 Q15.2
CBSE Previous Year Question Papers Class 10 Maths 2018 Q15.3
CBSE Previous Year Question Papers Class 10 Maths 2018 Q15.4

Question 16.
A plane left 30 minutes late than its scheduled time and in order to reach the destination 1500 km away in time, it had to increase its speed by 100 km/h from the usual speed. Find its usual speed. [3]
Solution:
Let the usual speed of plane be x km/h.
Increased speed = (x + 100) km/h.
Distance to cover = 1500 km.
Time taken by plane with usual speed = \frac { 1500 }{ x } hr
Time taken by plane with increased speed = \frac { 1500 }{ 100+x }
According to the question,
CBSE Previous Year Question Papers Class 10 Maths 2018 Q16
x2 + 100x = 300000
x2 + 100x – 300000 = 0
x2 + 600x – 500x – 300000 = 0
x(x + 600) – 500(x + 600) = 0
(x + 600) (x – 500) = 0
Either x + 600 = 0 ⇒ x = -600 (Rejected)
or x – 500 = 0 ⇒ x = 500
Usual speed of plane = 500 km/hr.

Question 17.
Prove that the area of an equilateral triangle described on one side of the square is equal to half the area of the equilateral triangle described on one of its diagonal. [3]
OR
If the area of two similar triangles is equal, prove that they are congruent.
Solution:
Let ABCD be a square with side ‘a’.
CBSE Previous Year Question Papers Class 10 Maths 2018 Q17
CBSE Previous Year Question Papers Class 10 Maths 2018 Q17.1
CBSE Previous Year Question Papers Class 10 Maths 2018 Q17.2

Question 18.
Prove that the lengths of tangents drawn from an external point of a circle are equal. [3]
Solution:
Given: A circle with centre O on which two tangents PM and PN are drawn from an external point P.
CBSE Previous Year Question Papers Class 10 Maths 2018 Q18
To Prove: PM = PN
Construction: Join OM, ON and OP
Proof: Since tangent and radius are perpendicular at point of contact,
∠OMP = ∠ONP = 90°
In ΔPOM and ΔPON,
OM = ON (Radii)
∠OMP = ∠ONP
PO = OP (Common)
ΔOMP = ΔONP (RHS cong.)
PM = PN (C.P.C.T)
Hence Proved.

Question 19.
If 4 tan θ = 3, evaluate \left( \frac { 4sin\theta -cos\theta +1 }{ 4sin\theta +cos\theta -1 } \right)
or
If tan 2A = cot (A – 18°), where 2A is an acute angle, find the value of A.
Solution:
Given, 4 tan θ = 3
⇒ tan θ = \frac { 3 }{ 4 } (= \frac { P }{ B })
CBSE Previous Year Question Papers Class 10 Maths 2018 Q19
CBSE Previous Year Question Papers Class 10 Maths 2018 Q19.1
OR
Given, tan 2A = cot (A – 18°)
⇒ cot (90° – 2A) = cot (A – 18°)
[∵ tan θ = cot (90° – θ)]
⇒ 90° – 2A = A – 18°
⇒ 90° + 18° = A + 2A
⇒ 108° = 3A
⇒ A = 36°

Question 20.
Find the area of the shaded region in Fig. 2, where arcs are drawn with centres A, B, C and D intersect in pairs at mid-points P, Q, R and S of the sides AB, BC, CD and DA respectively of a square ABCD of side 12 cm. [Use π = 3.14] [3]
CBSE Previous Year Question Papers Class 10 Maths 2018 Q20
Solution:
Given, ABCD is a square of side 12 cm.
CBSE Previous Year Question Papers Class 10 Maths 2018 Q20.1
P, Q, R and S are the midpoints of sides AB, BC, CD and AD respectively.
Area of shaded region = Area of square – 4 × Area of quadrant
= a2 – 4 × \frac { 1 }{ 4 } πr2
= (12)2 – 3.14 × (6)2
= 144 – 3.14 × 36
= 144 – 113.04
= 30.96 cm2

Question 21.
A wooden article was made by scooping out a hemisphere form each end of a solid cylinder, as shown in Fig. 3. If the height of the cylinder is 10 cm and its base is of radius 3.5 cm. Find the total surface area of the article. [3]
CBSE Previous Year Question Papers Class 10 Maths 2018 Q21
OR
A heap of rice is in the form of a cone of base diameter 24 m and height 3.5 m. Find the volume of the rice. How much canvas cloth is required to just cover the heap?
Solution:
CBSE Previous Year Question Papers Class 10 Maths 2018 Q21.1
Given, Radius (r) of cylinder = Radius of hemisphere = 3.5 cm.
Total SA of article = CSA of cylinder + 2 × CSA of hemisphere
Height of cylinder, h = 10 cm
TSA = 2πrh + 2 × 2πr2
= 2πrh + 4πr2
= 2πrh (h + 2r)
= 2 × \frac { 22 }{ 7 } × 3.5 (10 + 2 × 3.5)
= 2 × 22 × 0.5 × (10 + 7)
= 2 × 11 × 17
= 374 cm2
OR
Base diameter of cone = 24 m.
Radius r = 12 m
Height of cone, h = 3.5 m
Volume of rice in conical heap = \frac { 1 }{ 3 } πr2h
= \frac { 1 }{ 3 } × \frac { 22 }{ 7 } × 12 × 12 × 3.5 = 528 cm3
CBSE Previous Year Question Papers Class 10 Maths 2018 Q21.2

Question 22.
The table below shows the salaries of 280 persons: [3]
CBSE Previous Year Question Papers Class 10 Maths 2018 Q22
Calculate the median salary of the data.
Solution:
CBSE Previous Year Question Papers Class 10 Maths 2018 Q22.1
\frac { N }{ 2 } = \frac { 280 }{ 2 } = 140
The cumulative frequency just greater than 140 is 182.
Median class is 10 -15.
l = 10, h = 5, N = 280, c.f. = 49 and f = 133
CBSE Previous Year Question Papers Class 10 Maths 2018 Q22.2

Section – D

Question 23.
A motorboat whose speed is 18 km/hr in still water takes 1 hr more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream. [4]
OR
A train travels at a certain average speed for a distance of 63 km and then travels at a distance of 72 km at an average speed of 6 km/hr more than its original speed. If it takes 3 hours to complete the total journey, what is the original average speed?
Solution:
Given, speed of motorboat instil
water = 18 km/hr.
Let speed of stream = x km/hr.
Speed of boat downstream = (18 + x) km/hr.
And speed of boat upstream = (18 – x) km/hr.
Time of the upstream journey = \frac { 24 }{ 18-x }
Time of the downstream journey = \frac { 24 }{ 18+x }
According to the question,
CBSE Previous Year Question Papers Class 10 Maths 2018 Q23
⇒ x2 + 48x – 324 = 0
⇒ x2 + 54x – 6x – 324 = 0
⇒ x(x + 54) – 6(x + 54) = 0
⇒ (x + 54)(x – 6) = 0
Either x + 54 = 0 ⇒ x = -54
Rejected, as speed cannot be negative
or x – 6 = 0 ⇒ x = 6
Thus, the speed of the stream is 6 km/hr.
OR
Let the original average speed of train be x km/hr.
Increased speed of train = (x + 6) km/hr.
Time taken to cover 63 km with average speed = \frac { 63 }{ x } hr.
Time taken to cover 72 km with increased speed = \frac { 72 }{ x+6 }
According to the question,
CBSE Previous Year Question Papers Class 10 Maths 2018 Q23.1
⇒ 135x + 378 = 3(x2 + 6x)
⇒ 135x + 378 = 3x2 + 18x
⇒ 3x2 + 18x – 135x – 378 = 0
⇒ 3x2 – 117x – 378 = 0
⇒ 3(x2 – 39x – 126) = 0
⇒ x2 – 39x – 126 = 0
⇒ x2 – 42x + 3x – 126 – 0
⇒ x(x – 42) + 3(x – 42) = 0
⇒ (x – 42) (x + 3) = 0
Either x – 42 = 0 ⇒ x = 42
or x + 3 = 0 ⇒ x = -3
Rejected (as speed cannot be negative)
Thus, average speed of train is 42 km/hr.

Question 24.
The sum of four consecutive numbers in an AP is 32 and the ratio of the product of the first and the last term to the product of two middle terms is 7:15. Find the numbers. [4]
Solution:
Let the first term of AP be a and d be a common difference.
Let your consecutive term of an AP be a – 3d, a – d, a + d and a + 3d
According to the question,
a – 3d + a – d + a + d + a + 3d = 32
⇒ 4a = 32
⇒ a = 8 …(i)
Also,
(a – 3d) (a + 3d) : (a – d) (a + d) = 7 : 15
CBSE Previous Year Question Papers Class 10 Maths 2018 Q24
For d = 2, four terms of AP are,
a – 3d = 8 – 3 (2) = 2
a – d = 8 – 2 = 6
a + d = 8 + 2 = 10
a + 3d = 8 + 3(2) = 14
For d = -2, four term are
a – 3d = 8 – 3(-2) = 14
a – d = 8 – (-2) = 10
a + d = 8 + (-2) = 6
a + 3d = 8 + 3 (-2) = 2
Thus, the four terms of AP series are 2, 6, 10, 14 or 14, 10, 6, 2.

Question 25.
In an equilateral ∆ABC, D is a point on side BC such that BD = \frac { 1 }{ 3 } BC. Prove that 9(AD)2 = 7(AB)2. [4]
OR
Prove that, in a right triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides.
Solution:
CBSE Previous Year Question Papers Class 10 Maths 2018 Q25
Given, ABC is an equilateral triangle and D is a point on BC such that BD = \frac { 1 }{ 3 } BC.
To prove: 9AD2 = 7AB2
Construction : Draw AE ⊥ BC
Proof: BD = \frac { 1 }{ 3 } BC …(i) (Given)
AE ⊥ BC
We know that perpendicular from a vertex of equilateral triangle to the base divides base in two equal parts.
BE = EC = \frac { 1 }{ 2 } BC …(ii)
In ∆AEB,
AD2 = AE2 + DE2 (Pythagoras theorem)
or AE2 = AD2 – DE2 …(iii)
Similarly, In ∆AEB,
AB2 = AE2 + BE2
CBSE Previous Year Question Papers Class 10 Maths 2018 Q25.1
CBSE Previous Year Question Papers Class 10 Maths 2018 Q25.2
OR
Given: ∆ABC is a right angle triangle, right-angled at A.
CBSE Previous Year Question Papers Class 10 Maths 2018 Q25.3
To prove : BC2 = AB2 + AC2
Construction : Draw AD ⊥ BC.
Proof: In ∆ADB and ∆BAC,
∠B = ∠B (Common)
∠ADB = ∠BAC (Each 90°)
∆ADB ~ ∆BAC (By AA similarity axiom)
\frac { AB }{ BC } = \frac { BD }{ AB } (CPCT)
AB2 = BC × BD
Similarly,
∆ADC ~ ∆CAB
\frac { AC }{ BC } = \frac { DC }{ AC }
AC2 = BC × DC …(ii)
On adding equation (i) and (ii)
AB2 + AC2 = BC × BD + BC × CD = BC (BD + CD) = BC × BC
AB2 + AC2 = BC2
BC2 = AB2 + AC2
Hence Proved.

Question 26.
Draw a triangle ABC with BC = 6 cm, AB = 5 cm and ∠ABC = 60°. Then construct a triangle whose sides are \frac { 3 }{ 4 } of the corresponding sides of the ∆ABC. [4]
Solution:
CBSE Previous Year Question Papers Class 10 Maths 2018 Q26

  1. Draw a line segment BC = 6 cm.
  2. Construct ∠XBC = 60°.
  3. With B as centre and radius equal to 5 cm, draw an arc intersecting XB at A.
  4. Join AC. Thus, ∆ABC is obtained.
  5. Draw an acute angle ∠CBY below of B.
  6. Mark 4-equal parts on BY as B1, B2, B3 and B4
  7. Join B4 to C.
  8. From By draw a line parallel to B4C intersecting BC at C’.
  9. Draw another line parallel to CA from C’, intersecting AB at A’.
  10. ∆A’BC’ is required triangle which is similar to ∆ABC such that BC’ = \frac { 3 }{ 4 } BC.

Question 27.
CBSE Previous Year Question Papers Class 10 Maths 2018 Q27
Solution:
CBSE Previous Year Question Papers Class 10 Maths 2018 Q27.1
CBSE Previous Year Question Papers Class 10 Maths 2018 Q27.2

Question 28.
The diameters of the lower and upper ends of a bucket in the form of a frustum of a cone are 10 cm and 30 cm respectively. If its height is 24 cm, find:
(i) The area of the metal sheet used to make the bucket.
(ii) Why we should avoid the bucket made by ordinary plastic? [Use π = 3.14] [4]
Solution:
Given, Height of frustum, h = 24 cm.
Diameter of lower end = 10 cm
Radius of lower end, r = 5 cm.
Diameter of upper end = 30 cm
Radius of upper end, R = 15 cm.
CBSE Previous Year Question Papers Class 10 Maths 2018 Q28
(i) Area of metal sheet used to make the bucket = CSA of frustum + Area of base
= πl(R + r) + πr2
= π[26 (15 + 5) + (5)2]
= 3.14 (26 × 20 + 25)
= 3.14 (520 + 25)
= 3.14 × 545
= 1711.3 cm2
(ii) We should avoid the bucket made by ordinary plastic because plastic is harmful to the environment and to protect the environment its use should be avoided.

Question 29.
As observed from the top of a 100 m high lighthouse from the sea-level, the angles of depres¬sion of two ships are 30° and 45°. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships. [Use √3 = 1.732] [4]
Solution:
Let AB be the lighthouse and two ships are at C and D.
CBSE Previous Year Question Papers Class 10 Maths 2018 Q29
Distance between two ships = y – x
= 100√3 – 100 [from equation (i) and (ii)]
= 100 (√3 – 1)
= 100(1.732 – 1)
= 100 (0.732)
= 73.2 m

Question 30.
The mean of the following distribution is 18. Find the frequency f of the class 19-21. [4]
CBSE Previous Year Question Papers Class 10 Maths 2018 Q30
OR
The following distribution gave the daily income of 50 workers of a factory:
CBSE Previous Year Question Papers Class 10 Maths 2018 Q30.1
Convert the distribution above to a less than type cumulative frequency distribution and draw its ogive.
Solution:
CBSE Previous Year Question Papers Class 10 Maths 2018 Q30.2
CBSE Previous Year Question Papers Class 10 Maths 2018 Q30.3

CBSE Previous Year Question Papers CBSE Previous Year Question Papers Class 10 Maths

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Solved CBSE Sample Papers for Class 10 Maths Paper 1

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Board – Central Board of Secondary Education, cbse.nic.in
Subject – CBSE Class 10 Mathematics
Year of Examination – 2019.

Solved CBSE Sample Papers for Class 10 Maths Paper 1

Solved CBSE Sample Papers for Class 10 Maths Paper 1 1
Solved CBSE Sample Papers for Class 10 Maths Paper 1 2
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Solved CBSE Sample Papers for Class 10 Maths Set 4

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Board – Central Board of Secondary Education, cbse.nic.in
Subject – CBSE Class 10 Mathematics
Year of Examination – 2019.

You can also Download NCERT Solutions for Class 10 Maths to help you to revise complete Syllabus and score more marks in your examinations.

Solved CBSE Sample Papers for Class 10 Maths Set 4

Solved CBSE Sample Papers for Class 10 Maths Paper 4 1
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Solved CBSE Sample Papers for Class 10 Maths Set 5

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Board – Central Board of Secondary Education, cbse.nic.in
Subject – CBSE Class 10 Mathematics
Year of Examination – 2019.

You can also Download NCERT Solutions for Class 10 Maths to help you to revise complete Syllabus and score more marks in your examinations.

Solved CBSE Sample Papers for Class 10 Maths Set 5

Solved CBSE Sample Papers for Class 10 Maths Paper 5 1
Solved CBSE Sample Papers for Class 10 Maths Paper 5 2
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CBSE Previous Year Question Papers Class 10 Maths 2019 Outside Delhi

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CBSE Previous Year Question Papers Class 10 Maths 2019 Outside Delhi

Time Allowed: 3 hours
Maximum Marks: 80

General Instructions:

  • All questions are compulsory.
  • This question paper consists of 30 questions divided into four sections- A, B, C and D.
  • Section A contains 6 questions of 1 mark each, Section B contains 6 questions of 2 marks each, Section C contains 10 questions of 3 marks each and Section D contains 8 questions of 4 marks each.
  • There is no overall choice. However, an internal choice has been provided in two questions of 1 mark each, two questions of 2 marks each, four questions of 3 marks each and three questions of 4 marks each. You have to attempt only one of the alternative in all such questions.
  • Use of calculators is not permitted.

CBSE Sample Papers Class 10 Maths

CBSE Previous Year Question Papers Class 10 Maths 2019 Outside Delhi Set I

Section – A

Question 1.
If HCF (336, 54) = 6, find LCM (336, 54). [1]
Solution:
Given, HCF (336, 54) = 6
We know,
HCF × LCM = one number × other number
⇒ 6 × LCM = 336 × 54
⇒ LCM = \frac { 336\times 54 }{ 6 } = 336 × 9 = 3024

Question 2.
Find the nature of roots of the quadratic equation 2x2 – 4x + 3 = 0. [1]
Solution:
Given, 2x2 – 4x + 3 = 0
Comparing it with quadratic equation ax2 + bx + c = 0
Here, a = 2, b = -4 and c = 3
D = b2 – 4ac = (-4)2 – 4 × (2)(3) = 16 – 24 = -8 < 0
Hence, D < 0 this shows that roots will be imaginary.

Question 3.
Find the common difference of the Arithmetic Progression (A.P.) [1]
CBSE Previous Year Question Papers Class 10 Maths 2019 (Outside Delhi) Set I Q3
Solution:
CBSE Previous Year Question Papers Class 10 Maths 2019 (Outside Delhi) Set I Q3.1

Question 4.
Evaluate: sin2 60° + 2 tan 45° – cos2 30° [1]
OR
If sin A = \frac { 3 }{ 4 }, calculate sec A.
Solution:
We know,
CBSE Previous Year Question Papers Class 10 Maths 2019 (Outside Delhi) Set I Q4
CBSE Previous Year Question Papers Class 10 Maths 2019 (Outside Delhi) Set I Q4.1

Question 5.
Write the coordinates of a point P on the x-axis which is equidistant from point A(-2, 0) and B(6, 0).
Solution:
Let coordinates of P on x-axis is (x, 0)
Given, A(-2, 0) and B(6, 0)
Here, PA = PB
CBSE Previous Year Question Papers Class 10 Maths 2019 (Outside Delhi) Set I Q5
On squaring both sides, we get
(x + 2)2 = (x – 6)2
⇒ x2 + 4 + 4x = x2 + 36 – 12x
⇒ 4 + 4x = 36 – 12x
⇒ 16x = 32
⇒ x = 2
Co-ordinates of P are (2, 0)

Question 6.
In Figure 1, ABC is an isosceles triangle right angled at C with AC = 4 cm. Find the length of AB. [1]
CBSE Previous Year Question Papers Class 10 Maths 2019 (Outside Delhi) Set I Q6
OR
In Figure 2, DE || BC. Find the length of side AD, given that AE = 1.8 cm, BD = 7.2 cm and CE = 5.4 cm.
CBSE Previous Year Question Papers Class 10 Maths 2019 (Outside Delhi) Set I Q6.1
Solution:
Given, ∠C = 90° and AC = 4 cm, AB = ?
CBSE Previous Year Question Papers Class 10 Maths 2019 (Outside Delhi) Set I Q6.2
∆ABC is an isosceles triangle so, BC = AC = 4 cm
On applying Phythagoras theorem, we have
AB2 = AC2 + BC2
⇒ AB2 = AC2 + AC2 (∵ BC = AC)
⇒ AB2 = 42 + 42 = 16 + 16 = 32
⇒ AB = √32 = 4√2 cm
OR
Given, DE || BC
On applying, Thales theorem, we have
CBSE Previous Year Question Papers Class 10 Maths 2019 (Outside Delhi) Set I Q6.3

Section – B

Question 7.
Write the smallest number which is divisible by both 306 and 657. [2]
Solution:
Smallest number which is divisible by 306 and 657 is,
LCM (657, 306)
657 = 3 × 3 × 73
306 = 3 × 3 × 2 × 17
LCM =3 × 3 × 73 × 2 × 17 = 22338

Question 8.
Find a relation between x and y if the points A(x, y), B(-4, 6) and C(-2, 3) are collinear. [2]
OR
Find the area of a triangle whose vertices are given as (1, -1) (-4, 6) and (-3, -5).
Solution:
Given, A(x, y), B(-4, 6), C(-2, 3)
x1 = x, y1 = y, x2 = -4, y2 = 6, x3 = -2, y3 = 3
If these points are collinear, then area of triangle made by these points is 0.
CBSE Previous Year Question Papers Class 10 Maths 2019 (Outside Delhi) Set I Q8

Question 9.
The probability of selecting a blue marble at random from a jar that contains only blue, black and green marbles is \frac { 1 }{ 5 }. The probability of selecting a black marble at random from the same jar is \frac { 1 }{ 4 }. If the jar contains 11 green marbles, find the total number of marbles in the jar. [2]
Solution:
Let the probability of selecting a blue marble, black marble and green marble are P(x), P(y), P(z) respectively.
P(x) = \frac { 1 }{ 5 }, P(y) = \frac { 1 }{ 4 } (Given)
We know,
P(x) + P(y) + P(z) = 1
CBSE Previous Year Question Papers Class 10 Maths 2019 (Outside Delhi) Set I Q9
CBSE Previous Year Question Papers Class 10 Maths 2019 (Outside Delhi) Set I Q9.1

Question 10.
Find the value(s) of k so that the pair of equations x + 2y = 5 and 3x + ky + 15 = 0 has a unique solution. [2]
Solution:
Given, x + 2y = 5, 3x + ky + 15 = 0
Comparing above equations with
a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0,
We get,
a1 = 1, b1 = 2, c1 = -5
a2 = 3, b2 = k, c2 = 15
Condition for the pair of equations to have unique solution is
CBSE Previous Year Question Papers Class 10 Maths 2019 (Outside Delhi) Set I Q10
k can have any value except 6.

Question 11.
The larger of the two supplementary angles exceeds the smaller by 18°. Find the angles. [2]
OR
Sumit is 3 times as old as his son. Five years later, he shall be two and a half times as old as his son. How old is Sumit at present?
Solution:
Let two angles A and B are supplementary.
A + B = 180° …(i)
Given, A = B + 18°
On putting A = B + 18° in equation (i),
we get B + 18° + B = 180°
⇒ 2B + 18° = 180°
⇒ 2B = 162°
⇒ B = 81°
A = B + 18°
⇒ A = 99°
OR
Let age of Sumit be x years and age of his son be y years.
Then, according to question we have, x = 3y …… (i)
Five years later, x + 5 = 2\frac { 1 }{ 2 }(y + 5) …….. (ii)
On putting x = 3y in equation (ii)
CBSE Previous Year Question Papers Class 10 Maths 2019 (Outside Delhi) Set I Q11

Question 12.
Find the mode of the following frequency distribution:
CBSE Previous Year Question Papers Class 10 Maths 2019 (Outside Delhi) Set I Q12
Solution:
CBSE Previous Year Question Papers Class 10 Maths 2019 (Outside Delhi) Set I Q12.1
Here, the maximum frequency is 50.
So, 35 – 40 will be the modal class.
l = 35, f0 = 34, f1 = 50, f2 = 42 and h = 5
CBSE Previous Year Question Papers Class 10 Maths 2019 (Outside Delhi) Set I Q12.2

Section – C

Question 13.
Prove that 2 + 5√3 is an irrational number, given that √3 is an irrational number. [3]
OR
Using Euclid’s Algorithm, find the HCF of 2048 and 960.
Solution:
Let 2 + 5√3 = r, where, r is rational.
⇒ (2 + 5√3)2 = r2
⇒ 4 + 75 + 20√3 = r2
⇒ 79 + 20√3 = r2
⇒ 20√3 = r2 – 79
⇒ √3 = \frac { { r }^{ 2 }-79 }{ 20 }
Now, \frac { { r }^{ 2 }-79 }{ 20 } is a rational number. So, √3 must also be a rational number.
But √3 is an irrational number (Given).
So, our assumption is wrong.
2 + 5√3 is an irrational number.
Hence Proved.
OR
Step I:
Here 2048 > 960 so, On applying Euclid’s algorithm, we get
2048 = 960 × 2 + 128
Step II:
Because remainder 128 ≠ 0, so, On applying Euclid’s algorithm between 960 and 128, we get
960 = 128 × 7 + 64
Step III:
Again remainder 64 ≠ 0, so
128 = 64 × 2 + 0
Here remainder is 0. So, the process ends here. And the dividend is 64 so, required HCF is 64.

Question 14.
Two right triangles ABC and DBC are drawn on the same hypotenuse BC and on the same side of BC. If AC and BD intersect at P, prove that AP × PC = BP × DP. [3]
OR
Diagonals of a trapezium PQRS intersect each other at the point O, PQ || RS and PQ = 3RS. Find the ratio of the areas of triangles POQ and ROS.
Solution:
Given, ∆ABC, ∆DBC are right-angle triangles, right-angled at A and D, on the same side of BC.
AC & BD intersect at P.
CBSE Previous Year Question Papers Class 10 Maths 2019 (Outside Delhi) Set I Q14
In ∆APB and ∆PDC,
∠A = ∠D = 90°
∠APB = ∠DPC (Vertically opposite)
∆APB ~ ∆PDC (By AA Similarity)
\frac { AP }{ BP } = \frac { PD }{ PC } (by c.s.s.t.)
⇒ AP × PC = BP × PD.
Hence Proved.
OR
Given, PQRS is a trapezium where PQ || RS and diagonals intersect at O and PQ = 3RS
CBSE Previous Year Question Papers Class 10 Maths 2019 (Outside Delhi) Set I Q14.1
In ∆POQ and ∆ROS, we have
∠ROS = ∠POQ (vertically opposite angles)
∠OQP = ∠OSR (alternate angles)
Hence, ∆POQ ~ ∆ROS by AA similarity then,
If two triangles are similar, then ratio of areas is equal to the ratio of square of its corresponding sides. Then,
CBSE Previous Year Question Papers Class 10 Maths 2019 (Outside Delhi) Set I Q14.2

Question 15.
In Figure 3, PQ and RS are two parallel tangents to a circle with centre O and another tangent AB with the point of contact C intersecting PQ at A and RS at B. Prove that ∠AOB = 90°. [3]
CBSE Previous Year Question Papers Class 10 Maths 2019 (Outside Delhi) Set I Q15
Solution:
Given, PQ || RS
To prove: ∠AOB = 90°
CBSE Previous Year Question Papers Class 10 Maths 2019 (Outside Delhi) Set I Q15.1
Construction: Join O and C, D and E
In ∆ODA and ∆OCA
OD = OC (radii of circle)
OA = OA (common)
AD = AC (tangent drawn from the same point)
By SSS congruency
∆ODA = ∆OCA
Then, ∠DOA = ∠AOC …(i)
Similarly, in ∆EOB and ∆BOC, we have
∆EOB = ∆BOC
∠EOB = ∠BOC …(ii)
EOD is a diameter of the circle, therefore it is a straight line.
Hence, ∠DOA + ∠AOC + ∠EOB + ∠BOC = 180°
⇒ 2(∠AOC) + 2(∠BOC) = 180°
⇒ ∠AOC + ∠BOC = 90°
⇒ ∠AOB = 90°.
Hence Proved.

Question 16.
Find the ratio in which the line x – 3y = 0 divides the line segment joining the points (-2, -5) and (6, 3). Find the coordinates of the point of intersection. [3]
Solution:
Let the required ratio be k : 1
By section formula, we have
CBSE Previous Year Question Papers Class 10 Maths 2019 (Outside Delhi) Set I Q16
CBSE Previous Year Question Papers Class 10 Maths 2019 (Outside Delhi) Set I Q16.1
CBSE Previous Year Question Papers Class 10 Maths 2019 (Outside Delhi) Set I Q16.2

Question 17.
Evaluate:
CBSE Previous Year Question Papers Class 10 Maths 2019 (Outside Delhi) Set I Q17
Solution:
CBSE Previous Year Question Papers Class 10 Maths 2019 (Outside Delhi) Set I Q17.1
CBSE Previous Year Question Papers Class 10 Maths 2019 (Outside Delhi) Set I Q17.2

Question 18.
In Figure 4, a square OABC is inscribed in a quadrant OPBQ. If OA = 15 cm, find the area of the shaded region. (Use π = 3.14)
CBSE Previous Year Question Papers Class 10 Maths 2019 (Outside Delhi) Set I Q18
In Figure 5, ABCD is a square with side 2√2 cm and inscribed in a circle. Find the area of the shaded region. (Use π = 3.14)
CBSE Previous Year Question Papers Class 10 Maths 2019 (Outside Delhi) Set I Q18.1
Solution:
Given, OABC is a square with OA = 15 cm
OB = radius = r
CBSE Previous Year Question Papers Class 10 Maths 2019 (Outside Delhi) Set I Q18.2
Let side of square be a then,
a2 + a2 = r2
⇒ 2a2 = r2
⇒  r = √2 a
⇒  r = 15√2 cm (∵ a = 15 cm)
Area of square = Side × Side = 15 × 15 = 225 cm2
CBSE Previous Year Question Papers Class 10 Maths 2019 (Outside Delhi) Set I Q18.3
Area of shaded region = Area of quadrant OPBQ – Area of square
= 353.25 – 225 = 128.25 cm2
OR
Given, ABCD is a square with side 2√2 cm
BD = 2r
CBSE Previous Year Question Papers Class 10 Maths 2019 (Outside Delhi) Set I Q18.4
In ∆BDC,
BD2 = DC2 + BC2
⇒ 4r2 = 2(DC)2 (∵ DC = CB = Side = 2√2 )
⇒ 4r2 = 2 × 2√2 × 2√2
⇒ 4r2 = 8 × 2
⇒ 4r2 = 16
⇒ r2 = 4
⇒ r = 2 cm
Area of square BCDA = Side × Side = DC × BC = 2√2 × 2√2 = 8 cm2
Area of circle = πr2 = 3.14 × 2 × 2 = 12.56 cm2
Area of shaded region = Area of circle – Area of square. = 12.56 – 8 = 4.56 cm2

Question 19.
A solid is in the form of a cylinder with hemispherical ends. The total height of the solid is 20 cm and the diameter of the cylinder is 7 cm. Find the total volume of the solid. (Use π = \frac { 22 }{ 7 }) [3]
Solution:
ABCD is a cylinder and BFC and AED are two hemisphere which has radius (r) = \frac { 7 }{ 2 } cm
CBSE Previous Year Question Papers Class 10 Maths 2019 (Outside Delhi) Set I Q19
CBSE Previous Year Question Papers Class 10 Maths 2019 (Outside Delhi) Set I Q19.1
Total volume of solid = Volume of two hemisphere + Volume of cylinder
= 179.67 + 500.5 = 680.17 cm3

Question 20.
The marks obtained by 100 students in an examination are given below: [3]
CBSE Previous Year Question Papers Class 10 Maths 2019 (Outside Delhi) Set I Q20
Find the mean marks of the students.
Solution:
CBSE Previous Year Question Papers Class 10 Maths 2019 (Outside Delhi) Set I Q20.1

Question 21.
For what value of k, is the polynomial f(x) = 3x4 – 9x3 + x2 + 15x + k completely divisible by 3x2 – 5? [3]
OR
Find the zeroes of the quadratic polynomial 7y2\frac { 11 }{ 3 } y – \frac { 2 }{ 3 } and verify the relationship between the zeroes and the coefficients.
Solution:
Given,
f(x) = 3x4 – 9x3 + x2 + 15x + k
It is completely divisible by 3x2 – 5
CBSE Previous Year Question Papers Class 10 Maths 2019 (Outside Delhi) Set I Q21
CBSE Previous Year Question Papers Class 10 Maths 2019 (Outside Delhi) Set I Q21.1
CBSE Previous Year Question Papers Class 10 Maths 2019 (Outside Delhi) Set I Q21.2

Question 22.
Write all the values of p for which the quadratic equation x2 + px + 16 = 0 has equal roots. Find the roots of the equation so obtained. [3]
Solution:
Given, equation is x2 + px + 16 = 0
This is of the form ax2 + bx + c = 0
where, a = 1, b = p and c = 16
D = b2 – 4ac = p2 – 4 × 1 × 16 = p2 – 64
for equal roots, we have D = 0
p2 – 64 = 0
⇒ p2 = 64
⇒ p = ±8
Putting p = 8 in given equation we have,
x2 + 8x + 16 = 0
⇒ (x + 4)2 = 0
⇒ x + 4 = 0
⇒ x = -4
Now, putting p = -8 in the given equation, we get
x2 – 8x + 16 = 0
⇒ (x – 4)2 = 0
⇒ x = 4
Required roots are -4 and -4 or 4 and 4.

Section – D

Question 23.
If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then prove that the other two sides are divided in the same ratio. [4]
Solution:
Given, A ∆ABC in which DE || BC and DE intersect AB and AC at D and E respectively.
CBSE Previous Year Question Papers Class 10 Maths 2019 (Outside Delhi) Set I Q23
To prove: \frac { AD }{ DB } = \frac { AE }{ EC }
Construction: Join BE and CD
Draw EL ⊥ AB and DM ⊥ AC
Proof: we have
area (∆ADE) = \frac { 1 }{ 2 } × AD × EL
and area (∆DBE) = \frac { 1 }{ 2 } × DB × EL (∵ ∆ = \frac { 1 }{ 2 } × b × h)
CBSE Previous Year Question Papers Class 10 Maths 2019 (Outside Delhi) Set I Q23.1
Now, ∆DBE and ∆ECD, being on same base DE and between the same parallels DE and BC, We have
area (∆DBE) = area (∆ECD) …..(iii)
from equations (i), (ii) and (iii), we have
\frac { AD }{ DB } = \frac { AE }{ EC }
Hence Proved.

Question 24.
Amit, standing on a horizontal plane, finds a bird flying at a distance of 200 m from him at an elevation of 30°. Deepak standing on the roof of a 50 m high building, finds the angle of elevation of the same bird to be 45°. Amit and Deepak are on opposite sides of the bird. Find the distance of the bird from Deepak. [4]
Solution:
Let Amit be at C point and the bird is at A point. Such that ∠ACB = 30°. AB is the height of bird from point B on ground and Deepak is at D point, DE is the building of height 50 m.
CBSE Previous Year Question Papers Class 10 Maths 2019 (Outside Delhi) Set I Q24
CBSE Previous Year Question Papers Class 10 Maths 2019 (Outside Delhi) Set I Q24.1
Hence, the distance of bird from Deepak is 50√2 m.

Question 25.
A solid iron pole consists of a cylinder of height 220 cm and base diameter 24 cm, which is surmounted by another cylinder of height 60 cm and radius 8 cm. Find the mass of the pole, given that 1 cm3 of iron has approximately 8 gm mass. (Use π = 3.14) [4]
Solution:
Let AB be the iron pole of height 220 cm with base radius 12 cm and there is the other cylinder CD of height 60 cm whose base radius is 8 cm.
CBSE Previous Year Question Papers Class 10 Maths 2019 (Outside Delhi) Set I Q25
Volume of AB pole = πr1h1 = 3.14 × 12 × 12 × 220 = 99475.2 cm3
Volume of CD pole = πr2h2 = 3.14 × 8 × 8 × 60 = 12057.6 cm3
Total volume of the poles = 99475.2 + 12057.6 = 111532.8 cm3
It is given that,
Mass of 1 cm3 of iron = 8 gm
Then mass of 111532.8 cm3 of iron = 111532.8 × 8 gm
Then total mass of the pole is = 111532.8 × 8 gm = 892262.4 gm = 892.2624 kg

Question 26.
Construct an equilateral ∆ABC with each side 5 cm. Then construct another triangle whose sides are \frac { 2 }{ 3 } times the corresponding sides. Draw two concentric circles of radii 2 cm and 5 cm. Take a point P on the outer circle and construct a pair of tangents PA and PB to the smaller circle. Measure PA.
Solution:
Steps for construction are as follows:

  1. Draw a line segment BC = 5 cm
  2. At B and C construct ∠CBX = 60° and ∠BCX = 60°
  3. With B as centre and radius 5 cm, draw an arc cutting ray BX at A. On graph paper, we take the scale.
  4. Join AC. Thus an equilateral ∆ABC is obtained.
    CBSE Previous Year Question Papers Class 10 Maths 2019 (Outside Delhi) Set I Q26
  5. Below BC, make an acute angle ∠CBY
  6. Along BY, mark off 3 points B1, B2, B3 Such that BB1, B1B2, B2B3 are equal.
  7. Join B3C
  8. From B2 draw B2D || B3C, meeting BC at D
  9. From D, draw DE || CA, meeting AB at E.
    Then ∆EBD is the required triangle, each of whose sides is \frac { 2 }{ 3 } of the corresponding side of ∆ABC.

Question 27.
Change the following data into ‘less than type’ distribution and draw its ogive:
CBSE Previous Year Question Papers Class 10 Maths 2019 (Outside Delhi) Set I Q27
Solution:
CBSE Previous Year Question Papers Class 10 Maths 2019 (Outside Delhi) Set I Q27.1
CBSE Previous Year Question Papers Class 10 Maths 2019 (Outside Delhi) Set I Q27.2

Question 28.
Prove that:
CBSE Previous Year Question Papers Class 10 Maths 2019 (Outside Delhi) Set I Q28
Solution:
CBSE Previous Year Question Papers Class 10 Maths 2019 (Outside Delhi) Set I Q28.1
CBSE Previous Year Question Papers Class 10 Maths 2019 (Outside Delhi) Set I Q28.2
CBSE Previous Year Question Papers Class 10 Maths 2019 (Outside Delhi) Set I Q28.3
CBSE Previous Year Question Papers Class 10 Maths 2019 (Outside Delhi) Set I Q28.4
CBSE Previous Year Question Papers Class 10 Maths 2019 (Outside Delhi) Set I Q28.5

Question 29.
Which term of the Arithmetic Progression -7, -12, -17, -22,…..will be -82? Is -100 any term of the A.P.? Give a reason for your answer. [4]
OR
How many terms of the Arithmetic Progression 45, 39, 33, …. must be taken so that their sum is 180? Explain the double answer.
Solution:
-7, -12, -17, -22, …….
Here a = -7, d = -12 – (-7) = -12 + 7 = -5
Let Tn = -82
Tn = a + (n – 1) d
⇒ -82 = -7 + (n – 1) (-5)
⇒ -82 = -7 – 5n + 5
⇒ -82 = -2 – 5n
⇒ -82 + 2 = -5n
⇒ -80 = -5n
⇒ n = 16
Therefore, 16th term will be -82.
Let Tn = -100
Again, Tn = a + (n -1) d
⇒ -100 = -7 + (n – 1) (-5)
⇒ -100 = -7 – 5n + 5
⇒ -100 = – 2 – 5n
⇒ -100 + 2 = -5n
⇒ -98 = -5n
⇒ n = \frac { 98 }{ 5 }
But the number of terms can not be in fraction.
So, -100 can not be the term of this A.P.
OR
45, 39, 33, …..
Here a = 45, d = 39 – 45 = -6
Let Sn = 180
\frac { n }{ 2 } [ 2a + (n – 1) d] = 180
\frac { n }{ 2 } [2 × 45 + (n – 1) (-6)] = 180
\frac { n }{ 2 } [90 – 6n + 6] = 180
\frac { n }{ 2 } [96 – 6n] = 180
⇒ n(96 – 6n) = 360
⇒ 96n – 6n2 = 360
⇒ 6n2 – 96n + 360 = 0
On dividing the above equation by 6
⇒ n2 – 16n + 60 = 0
⇒ n2 – 10n – 6n + 60 = 0
⇒ n(n – 10) – 6 (n – 10) = 0
⇒ (n – 10) (n – 6) = 0
⇒ n = 10, 6
Sum of first 10 terms = Sum of first 6 terms = 180
This means that the sum of all terms from 7th to 10th is zero.

Question 30.
In a class test, the sum of Aran’s marks in Hindi and English is 30. Had he got 2 marks more in Hindi and 3 marks less in English, the product of the marks would have been 210. Find his marks in the two subjects. [4]
Solution:
Let Aran marks in Hindi be x and marks in English be y.
Then, according to question, we have
x + y = 30 …(i)
(x + 2)(y – 3) = 210 …(ii)
from equation (i) put x = 30 – y in equation (ii)
(30 – y + 2) (y – 3) = 210
⇒ (32 – y) (y – 3) = 210
⇒ 32y – 96 – y2 + 3y = 210
⇒ y2 – 35y + 306 = 0
⇒ y2 – 18y – 17y + 306 = 0
⇒ y(y – 18) – 17(y – 18) = 0
⇒ (y – 18) (y – 17) = o
⇒ y = 18, 17
Put y = 18 and 17 in equation (i), we get x = 12, 13
Hence his marks in hindi can be 12 and 13 and in english his marks can be 18 and 17.

CBSE Previous Year Question Papers Class 10 Maths 2019 Outside Delhi Set II

Note: Except for the following questions, all the remaining questions have been asked in Set I.

Section – A

Question 6.
Find the 21st term of the A.P. -4\frac { 1 }{ 2 }, -3, -1\frac { 1 }{ 2 }, … [1]
Solution:
CBSE Previous Year Question Papers Class 10 Maths 2019 (Outside Delhi) Set II Q6

Section – B

Question 7.
For what value of k, will the following pair of equations have infinitely many solutions:
2x + 3y = 7 and (k + 2)x – 3(1 – k)y = 5k + 1 [2]
Solution:
Given, The system of equations is
2x + 3y = 7 and (k + 2) x – 3 (1 – k) y = 5k +1
These equations are of the form a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0
where, a1 = 2, b1 = 3, c1 = -7
a2 = (k + 2), b2 = -3(1 – k), c2 = -(5k + 1)
Since, the given system of equations have infinitely many solutions.
CBSE Previous Year Question Papers Class 10 Maths 2019 (Outside Delhi) Set II Q7
Hence, the given system of equations has infinitely many solutions when k = 4.

Section – C

Question 13.
Point A lies on the line segment XY joining X(6, -6) and Y (-4, -1) in such a way that \frac { XA }{ XY } = \frac { 2 }{ 5 }. If Point A also lies on the line 3x + k (y + 1) = 0, find the value of k. [3]
Solution:
Given,
CBSE Previous Year Question Papers Class 10 Maths 2019 (Outside Delhi) Set II Q13
Since, point A(2, -4) lies on line 3x + k (y + 1) = 0.
Therefore it will satisfy the equation.
On putting x = 2 and y = -4 in the equation, we get
3 × 2 + k(-4 + 1) = 0
⇒ 6 – 3k = 0
⇒ 3k = 6
⇒ k = 2

Question 14.
Solve for x: x2 + 5x – (a2 + a – 6) = 0 [3]
Solution:
Taking (a2 + a – 6)
= a2 + 3a – 2a – 6
= a(a + 3) – 2 (a + 3)
= (a + 3) (a – 2)
x2 + 5x – (a + 3) (a – 2) = 0
⇒ x2 + (a + 3)x – (a – 2)x – (a + 3)(a – 2) = 0
⇒  x[x + (a + 3)] – (a – 2) [x + (a + 3)] = 0
⇒ (x – a + 2)(x + a + 3) = 0
Hence, x – a + 2 = 0 and x + a + 3 = 0
x = a – 2 and x = -(a + 3)
Required values of x are (a – 2), -(a + 3)

Question 15.
Find A and B if sin (A + 2B) = \frac { \surd 3 }{ 2 } and cos (A + 4B) = 0, where A and B are acute angles. [3]
Solution:
Given,
sin (A + 2B) = \frac { \surd 3 }{ 2 } and cos (A + 4B) = 0
⇒ sin (A + 2B) = 60° (∵ sin 60° = \frac { \surd 3 }{ 2 })
A + 2B =60 …(i)
cos (A + 4B) = cos 90° (∵ cos 90° = 0)
⇒ A + 4B = 90° …(ii)
On solving equation (i) and (ii), we get
B = 15° and A = 30°

Section – D

Question 23.
Prove that the ratio of the areas of two similar triangles is equal to the ratio of the squares on their corresponding sides.
Solution:
Given, ΔABC ~ ΔDEF
CBSE Previous Year Question Papers Class 10 Maths 2019 (Outside Delhi) Set II Q23
CBSE Previous Year Question Papers Class 10 Maths 2019 (Outside Delhi) Set II Q23.1

Question 24.
Two poles of equal heights are standing opposite to each other on either side of the road which is 80 m wide. From a point P between them on the road, the angle of elevation of the top of a pole is 60° and the angle of depression from the top of the other pole of point P is 30°. Find the heights of the poles and the distance of the point P from the poles. [4]
Solution:
Let AC is the road of 80 m width. P is the point on road AC and height of poles AB and CD is h m.
CBSE Previous Year Question Papers Class 10 Maths 2019 (Outside Delhi) Set II Q24
⇒ h = \frac { 80-x }{ \surd 3 } …… (ii)
Equating the values of h from equation (i) and (ii) we get
⇒ x√3 = \frac { 80-x }{ \surd 3 }
⇒ 3x = 80 – x
⇒ 4x = 80
⇒ x = 20m
On putting x = 20 in equation (i), we get
h = √3 × 20 = 20√3
h = 20√3 m
Thus, height of poles is 20√3 m and point P is at a distance of 20 m from left pole and (80 – 20) i.e., 60 m from right pole.

Question 25.
The total cost of a certain length of a piece of cloth is ₹ 200. If the piece was 5 m longer and each metre of cloth costs ₹ 2 less, the cost of the piece would have remained unchanged. How long is the piece and what is its original rate per metre? [4]
Solution:
Let the original length of the piece of cloth is x m and rate of cloth is ₹ y per metre.
Then according to question, we have
x × y = 200 …(i)
and if length be 5 m longer and each meter of cloth be ₹ 2 less then
(x + 5) (y – 2) = 200
⇒ (x + 5) (y – 2) = 200
⇒ xy – 2x + 5y – 10 = 200 …(ii)
On equating equation (i) and (ii), we have
xy = xy – 2x + 5y – 10
⇒ 2x – 5y = -10 …… (iii)
⇒ y = \frac { 200 }{ x } from equation (i)
⇒ 2x – 5 × \frac { 200 }{ x } = -10
⇒ 2x – \frac { 1000 }{ x } = -10
⇒ 2x2 – 1000 = -10x
⇒ 2x2 + 10x – 1000 = 0
⇒ x2 + 5x – 500 = 0
⇒ x2 + 25x – 20x – 500 = 0
⇒ x(x + 25) – 20 (x + 25) = 0
⇒ (x + 25) (x – 20) = 0
⇒ x = 20 (x ≠ -25 length of cloth can never be negative)
∴ x × y = 200
20 × y = 200
y = 10
Thus, length of the piece of cloth is 20 m and original price per metre is ₹ 10.

CBSE Previous Year Question Papers Class 10 Maths 2019 Outside Delhi Set III

Note: Except for the following questions, all the remaining questions have been asked in previous sets.

Section – B

Question 7.
A die is thrown twice. Find the probability that
(i) 5 will come up at least once. [2]
(ii) 5 will not come up either time.
Solution:
When two dice are thrown simultaneously, all possible outcomes are
(1.1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)
(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)
(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)
(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)
(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)
(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)
Total number of outcomes = 36
Total outcomes where 5 comes up at least once = 11
CBSE Previous Year Question Papers Class 10 Maths 2019 (Outside Delhi) Set III Q7

Section – C

Question 13.
Find the ratio in which the y-axis divides the line segment joining the points (-1, -4) and (5, -6). Also, find the coordinates of the point of intersection. [3]
Solution:
Let the y-axis cut the line joining point A(-1, -4) and point B(5, -6) in the ratio k : 1 at the point P(0, y)
Then, by section formula, we have
CBSE Previous Year Question Papers Class 10 Maths 2019 (Outside Delhi) Set III Q13
CBSE Previous Year Question Papers Class 10 Maths 2019 (Outside Delhi) Set III Q13.1

Question 14.
Find the value of: [3]
CBSE Previous Year Question Papers Class 10 Maths 2019 (Outside Delhi) Set III Q14
Solution:
CBSE Previous Year Question Papers Class 10 Maths 2019 (Outside Delhi) Set III Q14.1
CBSE Previous Year Question Papers Class 10 Maths 2019 (Outside Delhi) Set III Q14.2

Question 15.
Two spheres of same metal weigh 1 kg and 7 kg. The radius of the smaller sphere is 3 cm. The two spheres are melted to form a single big sphere. Find the diameter of the new sphere. [3]
Solution:
Given, a radius of small sphere be r = 3 cm
CBSE Previous Year Question Papers Class 10 Maths 2019 (Outside Delhi) Set III Q15
Both spheres are made by same metal, then their densities will be same.
Let radius of bigger sphere = r’ then,
CBSE Previous Year Question Papers Class 10 Maths 2019 (Outside Delhi) Set III Q15.1
Then according to question, we have,
Volume of bigger sphere + Volume of smaller shpere = Volume of new sphere.
\frac { 4 }{ 3 } (r’)3 + \frac { 4 }{ 3 } (r)3 = \frac { 4 }{ 3 } (R)3
⇒ r’3 + r3 = R3
⇒ 189 + 27 = R3
⇒ 216 = R3
⇒ R = 6
D = 6 × 2 = 12
Radius of new sphere is 6 cm.
So, the diameter is 12 cm.

Section – D

Question 23.
In a triangle, if the square of one side is equal to the sum of the squares of the other two sides, then prove that the angle opposite the first side is a right angle. [4]
Solution:
Given, ∆ABC in which AC2 = AB2 + BC2
CBSE Previous Year Question Papers Class 10 Maths 2019 (Outside Delhi) Set III Q23
To prove: ∠B = 90°
Consturction : Draw a ∆DEF such that
DE = AB, EF = BC and ∠E = 90°.
Proof: In ∆DEF we have ∠E = 90°
So, by Pythagoras theorem, we have
DF2 = DE2 + EF2
⇒ DF2 = AB2 + BC2 …(i)
(∵ DE = AB and EF = BC)
AC2 = AB2 + BC2 …(ii) (Given)
From equation (i) and (ii), we get
AC2 = DF2 ⇒ AC = DF.
Now, in ∆ABC and ∆DEF, we have
AB = DE, BC = EF and AC = DF.
∆ABC = ∆DEF.
Hence, ∠B = ∠E = 90°.
Hence Proved.

Question 24.
From a point P on the ground, the angle of elevation of the top of a tower is 30° and that of the top of the flag-staff fixed on the top of the tower is 45°. If the length of the flag-staff is 5 m, find the height of the tower. (Use √3 = 1.732) [4]
Solution:
Let AB be the tower and BC be the flag-staff.
CBSE Previous Year Question Papers Class 10 Maths 2019 (Outside Delhi) Set III Q24
Let P be a point on the ground such that
∠APB = 30° and ∠APC = 45°, BC = 5 m
Let AB = h m and PA = x metres
From right ∆PAB, we have
CBSE Previous Year Question Papers Class 10 Maths 2019 (Outside Delhi) Set III Q24.1
CBSE Previous Year Question Papers Class 10 Maths 2019 (Outside Delhi) Set III Q24.2
Hence, the height of the tower is 6.83 m

Question 25.
A right cylindrical container of radius 6 cm and height 15 cm is full of ice-cream, which has to be distributed to 10 children in equal cones having a hemispherical shape on the top. If the height of the conical portion is four times its base radius, find the radius of the ice-cream cone. [4]
Solution:
Let R and H be the radius and height of the cylinder.
Given, R = 6 cm, H = 15 cm.
Volume of ice-cream in the cylinder = πR2H = π × 36 × 15 = 540π cm3
Let the radius of cone be r cm
Height of the cone (h) = 4r
Radius of hemispherical portion = r cm.
Volume of ice-cream in cone = Volume of cone + Volume of the hemisphere
CBSE Previous Year Question Papers Class 10 Maths 2019 (Outside Delhi) Set III Q25
Number of ice cream cones distributed to the children = 10
⇒ 10 × Volume of ice-cream in each cone = Volume of ice-cream in cylindrical container
⇒ 10 × 2πr3 = 540π
⇒ 20r3 = 540
⇒ r3 = 27
⇒ r = 3
Thus, the radius of the ice-cream cone is 3 cm.

CBSE Previous Year Question Papers CBSE Previous Year Question Papers Class 10 Maths

The post CBSE Previous Year Question Papers Class 10 Maths 2019 Outside Delhi appeared first on Learn CBSE.

Solved CBSE Sample Papers for Class 10 Maths Set 6

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Download Solved CBSE Sample Papers for Class 10 Maths Set 6 2019 PDF to understand the pattern of questions asks in the board exam. Know about the important topics and questions to be prepared for CBSE Class 10 Maths board exam and Score More marks. Here we have given Maths Sample Paper for Class 10 Solved Set 6.

Board – Central Board of Secondary Education, cbse.nic.in
Subject – CBSE Class 10 Mathematics
Year of Examination – 2019.

You can also Download NCERT Solutions for Class 10 Maths to help you to revise complete Syllabus and score more marks in your examinations.

Solved CBSE Sample Papers for Class 10 Maths Set 6

Solved CBSE Sample Papers for Class 10 Maths Paper 6 1
Solved CBSE Sample Papers for Class 10 Maths Paper 6 2
Solved CBSE Sample Papers for Class 10 Maths Paper 6 3
CBSE Sample Papers for Class 10 Maths Solved paper 6 4
CBSE Sample Papers for Class 10 Maths Solved paper 6 5
CBSE Sample Papers for Class 10 Maths Solved paper 6 6
CBSE Sample Papers for Class 10 Maths Set 6 7
CBSE Sample Papers for Class 10 Maths Set 6 8
CBSE Sample Papers for Class 10 Maths Set 6 9
Sample Papers for Class 10 Maths Solved paper 6 10
Sample Papers for Class 10 Maths Solved paper 6 11
Sample Papers for Class 10 Maths Solved paper 6 12
Maths Sample Papers for Class 10 Set 6 13
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CBSE Previous Year Question Papers Class 10 Maths 2019 Delhi

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CBSE Previous Year Question Papers Class 10 Maths 2019 Delhi

Time Allowed: 3 hours
Maximum Marks: 80

General Instructions:

  • All questions are compulsory.
  • This question paper consists of 30 questions divided into four sections- A, B, C and D.
  • Section A contains 6 questions of 1 mark each, Section B contains 6 questions of 2 marks each, Section C contains 10 questions of 3 marks each and Section D contains 8 questions of 4 marks each.
  • There is no overall choice. However, an internal choice has been provided in two questions of 1 mark each, two questions of 2 marks each, four questions of 3 marks each and three questions of 4 marks each. You have to attempt only one of the alternative in all such questions.
  • Use of calculators is not permitted.

CBSE Sample Papers Class 10 Maths

CBSE Previous Year Question Papers Class 10 Maths 2019 Delhi Set I

Section – A

Question 1.
Find the coordinates of a point A, where AB is diameter of a circle whose centre is (2, -3) and B is the point (1, 4). [1]
Solution:
Let the co-ordinates of point A be (x, y) and point O (2, -3) be point the centre, then
By mid-point formula,
CBSE Previous Year Question Papers Class 10 Maths 2019 Delhi Set I Q1
The co-ordinates of point A are (3, -10)

Question 2.
For what values of k, the roots of the equation x2 + 4x + k = 0 are real? [1]
OR
Find the value of k for which the roots of the equation 3x2 – 10x + k = 0 are reciprocal of each other.
Solution:
The given equation is x2 + 4x + k = 0
On comparing the given equation with ax2 + bx + c = 0, we get
a = 1, b = 4 and c = k
For real roots, D ≥ 0
or b2 – 4ac ≥ 0
or 16 – 4k ≥ 0
or k ≤ 4
For k ≤ 4, equation x2 + 4x + k will have real roots.
OR
The given equation is 3x2 – 10x + k = 0
On comparing it with ax2 + bx + c = 0, we get
a = 3, b = -10, c = k
Let the roots of the equation are α and \frac { 1 }{ \alpha }
Product of the roots = \frac { c }{ a }
α . \frac { 1 }{ \alpha } = \frac { k }{ 3 }
or k = 3

Question 3.
Find A if tan 2A = cot (A – 24°) [1]
OR
Find the value of (sin2 33° + sin2 57°)
Solution:
Given, tan 2A = cot (A – 24°)
or cot (90° – 2A) = cot (A – 24°) [∵ tan θ = cot (90° – θ)]
or 90° – 2A = A – 24°
or 3A = 90° + 24°
or 3A = 114°
A = 38°
OR
sin2 33° + sin2 57°
= sin2 33° + cos2 (90° – 57°)
= sin2 33° + cos2 33°
= 1 [∴ sin2 θ + cos2 θ = 1]

Question 4.
Flow many two digits numbers are divisible by 3? [1]
Solution:
The two-digit numbers divisible by 3 are 12, 15, 18, ……… 99
This is an A.P. in which a = 12, d = 3, an = 99
an = a + (n – 1) d
99 = 12 + (n – 1) × 3
87 = (n – 1) × 3
or n – 1 = 29
or n = 30
So, there are 30 two-digit numbers divisible by 3.

Question 5.
In Fig., DE || BC, AD = 1 cm and BD = 2 cm. what is the ratio of the ar (ΔABC) to the ar (ΔADE) ? [1]
CBSE Previous Year Question Papers Class 10 Maths 2019 Delhi Set I Q5
Solution:
Given, AD = 1 cm, BD = 2 cm
AB = 1 + 2 = 3 cm
Also, DE || BC (Given)
∠ADE = ∠ABC …(i) (corresponding angles)
In ΔABC and ΔADE
∠A = ∠A (common)
∠ABC = ∠ADE [by equation (i)]
ΔABC ~ ΔADE (by AA rule)
Now,
CBSE Previous Year Question Papers Class 10 Maths 2019 Delhi Set I Q5.1

Question 6.
Find a rational number between √2 and √3. [1]
Solution:
As √2 = 1.414 ….
√3 = 1.732…..
So, a rational number between √2 and √3 is 1.5 or we can take any number between 1.414 and 1.732

Section – B

Question 7.
Find the HCF of 1260 and 7344 using Euclid’s algorithm. [2]
OR
Show that every positive odd integer is of the form (4q + 1) or (4q + 3), where q is some integer.
Solution:
Two numbers are 1260 and 7344
Since 7344 > 1260, we apply the Euclid division lemma to 7344 and 1260, we get
7344 = 1260 × 5 + 1044
Also, 1260 = 1044 × 1 + 216
1044 = 216 × 4 + 180
216 = 180 × 1 + 36
180 = 36 × 5 + 0
Now, remainder is 0, hence our procedure stops here.
H.C.F. of 7344 and 1260 is 36.
OR
Let ‘a’ be any positive odd integer.
We apply the division algorithm with a and b = 4
a = bq + r, where 0 ≤ r < b
or a = 4q + r,
the possible remainders are 0, 1, 2, 3
Then when r = 0, ⇒ a = 4q
r = 1, ⇒ a = 4q + 1
r = 2, ⇒ a = 4q + 2
and when r = 3, ⇒ a = 4q + 3
Since a is odd, a cannot be 4q or 4q + 2
(Since both are divisible by 2)
Therefore, any odd integer is of the form 4q + 1 or 4q + 3.
Hence Proved.

Question 8.
Which term of the A.P. 3, 15, 27, 39, …… will be 120 more than its 21st term? [2]
OR
If Sn, the sum of first tt terms of an A.P. is given by Sn = 3n2 – 4n, find the nth term.
Solution:
The given A.P. is 3, 15, 27, 39,…
Here a = 3, d = 12
a21 = a + 20d = 3 + 20 × 12 = 3 + 240 = 243
Now, an = a21 + 120 = 243 + 120 = 363
an =a + (n – 1) d
363 = 3 + (n – 1) × 12
or 360 = (n – 1) × 12
or n – 1 = 30
n = 31
Hence, the term which is 120 more than its 21st term will be its 31st term.
OR
Given, Sn = 3n2 – 4n
We know that
an = Sn – Sn-1
= 3n2 – 4n – [3 (n – 1)2 – 4 (n – 1)]
= 3n2 – 4n – [3 (n2 – 2n + 1) – 4n + 4]
= 3n2 – 4n – (3n2 – 6n + 3 – 4n + 4)
= 3n2 – 4n – 3n2 + 10n – 7
= 6n – 7
So, nth term will be 6n – 7

Question 9.
Find the ratio in which the segment joining the points (1, -3) and (4, 5) is divided by x-axis? Also, find the coordinates of this point on the x-axis. [2]
Solution:
Let the given points be A (1, -3) and B (4, -5) and the line-segment joining by these points is divided by the x-axis, so the co-ordinate of the point of intersection will be P(x, 0)
CBSE Previous Year Question Papers Class 10 Maths 2019 Delhi Set I Q9
CBSE Previous Year Question Papers Class 10 Maths 2019 Delhi Set I Q9.1

Question 10.
A game consists of tossing a coin 3 times and noting the outcome each time. If getting the same result in all the tosses is a success, find the probability of losing the game. [2]
Solution:
When a coin is tossed three times, the set of all possible outcomes is given by,
S = {HHH, HHT, HTH, HTT, TTT, TTH, THT, THH}
Same result on all tosses = HHH, TTT
CBSE Previous Year Question Papers Class 10 Maths 2019 Delhi Set I Q10

Question 11.
A die is thrown once. Find the probability of getting a number which
(i) is a prime number
(ii) lies between 2 and 6. [2]
Solution:
In throwing a die Total possible outcomes = 6
i.e., S = {1, 2, 3, 4, 5, 6}
Prime numbers 2, 3, 5
CBSE Previous Year Question Papers Class 10 Maths 2019 Delhi Set I Q11
Numbers between 2 and 6 are 3, 4, 5
P (Numbers between 2 and 6) = \frac { 3 }{ 6 } = \frac { 1 }{ 2 }

Question 12.
Find c if the system of equations cx + 3y + (3 – c) = 0, 12x + cy – c = 0 has infinitely many solutions? [2]
Solution:
The given equations are
cx + 3y + (3 – c) = 0
and 12x + cy – c = 0
On comparing with equation a1x + b1y + c1 = 0
and equation a2x + b2y + c2 = 0, we get
a1 = c, b1 = 3, c1 = 3 – c
and a2 = 12, b2 = c, c2 = -c
For infinitely many solutions
CBSE Previous Year Question Papers Class 10 Maths 2019 Delhi Set I Q12

Section – C

Question 13.
Prove that √2 is an irrational number. [3]
Solution:
Let √2 is a rational number.
So, √2 = \frac { a }{ b } where a and b are co-prime integers and b ≠ 0
or √2 b = a
Squaring on both sides, we get
2b2 = a2
Therefore, 2 divdies a2
or 2 divides a (from theorem)
Let a = 2c, for some integer c
From equation (i)
2b2 = (2c)2
or 2b2 = 4c2
or b2 = 2c2
It means that 2 divides b2 and so 2 divides b
Therefore a and b have at least 2 as a common factor.
But this contradicts the fact that a and b are co-prime.
This contradiction is due to our wrong assumption that √2 is rational.
So, we conclude that √2 is irrational.
Hence Proved.

Question 14.
Find the value of k such that the polynomial x2 – (k + 6)x + 2(2k – 1) has sum of its zeros equal to half to their product. [3]
Solution:
The given quadratic polynomial is x2 – (k + 6) x + 2(2k – 1)
Comparing with ax2 + bx + c, we get a = 1, b = -(k + 6) and c = 2(2k + 1)
Let the zeroes of the polynomial be α and β
we know that
CBSE Previous Year Question Papers Class 10 Maths 2019 Delhi Set I Q14
According to question
Sum of zeroes = \frac { 1 }{ 2 } of their product
α + β = \frac { 1 }{ 2 } αβ
or k + 6 =\frac { 1 }{ 2 } × 2(2k – 1) [using equations (i) & (ii)]
or k + 6 = 2k – 1
k = 7

Question 15.
A father’s age is three times the sum of the ages of his two children. After 5 years his age will be two times the sum of their ages. Find the present age of the father. [3]
OR
A fraction becomes \frac { 1 }{ 3 } when 2 is subtracted from the numerator and it becomes \frac { 1 }{ 2 } when 1 is subtracted from the denominator. Find the fraction.
Solution:
Let the present age of father be x years and sum of ages of his two children be y years
According to question
x = 3y …(i)
After 5 years
Father’s age = (x + 5) years
Sum of ages of two children = (y + 5 + 5) years = (y + 10) years
In 2nd case
According to question
x + 5 = 2 (y + 10)
or x + 5 = 2y + 20
or x – 2y = 15
or 3y – 2y = 15 (Using equations (i))
y = 15
Now from equation (i)
x = 3y (Put y = 15)
or x = 3 × 15
x = 45
So, Present age of father = 45 years.
OR
Let the fraction be \frac { x }{ y }
According to question \frac { x-2 }{ y } = \frac { 1 }{ 3 }
or 3(x – 2) = y
or 3x – y = 6 …(i)
again, According to question
\frac { x }{ y-1 } = \frac { 1 }{ 2 }
or 2x = y – 1
or 2x – y = -1 …(ii)
On solving equation (i) and (ii), we get
x = 7, y = 15
The required fraction is \frac { 7 }{ 15 }

Question 16.
Find the point on y-axis which is equidistant from the points (5, -2) and (-3, 2). [3]
OR
The line segment joining the points A(2, 1) and B(5, -8) is trisected at the points P and Q such that P is nearer to A. If P also lies on the line given by 2x – y + k = 0, find the value of k.
Solution:
We know that a point on the y-axis is of the form (0, y).
So, let the point P(0, y) be equidistant from A (5, -2) and B (-3, 2)
Then AP = BP
or AP2 = BP2
or (5 – 0)2 + (-2 – y)2 = (-3 – 0)2 + (2 – y)2
or 25 + 4 + y2 + 4y = 9 + 4 + y2 – 4y
8y = -16
y = -2
So, the required point is (0, -2)
OR
The line segment AB is trisected at the points P and Q and P is nearest to A
So, P divides AB in the ratio 1 : 2
CBSE Previous Year Question Papers Class 10 Maths 2019 Delhi Set I Q16
P lies on the line 2x – y + k = 0
It will satisfy the equation.
On putting x = 3 and y = -2 in the given equation, we get
2(3) – (-2) + k = 0
6 + 2 + k = 0
k = -8
Hence, k = -8

Question 17.
Prove that (sin θ + cosec θ )2 + (cos θ + sec θ)2 = 7 + tan2 θ + cot2 θ. [3]
OR
Prove that (1 + cot A – cosec A) (1 + tan A + sec A) = 2.
Solution:
L.H.S. = (sin θ + cosec θ)2 + (cos θ + sec θ)2
= sin2 θ + cosec2 θ + 2. sin θ. cosec θ + cos2 θ + sec2 θ + 2 cos θ sec θ.
(∵ (a + b)2 = a2 + b2 + 2ab)
CBSE Previous Year Question Papers Class 10 Maths 2019 Delhi Set I Q17
CBSE Previous Year Question Papers Class 10 Maths 2019 Delhi Set I Q17.1

Question 18.
In Fig. PQ is a chord of length 8 cm of a circle of radius 5 cm and centre O. The tangents at P and Q intersect at point T. Find the length of TP. [3]
CBSE Previous Year Question Papers Class 10 Maths 2019 Delhi Set I Q18
Solution:
Join OT, let it intersect PQ at the point R
Now, ΔTPQ is an isosceles triangle and TO is the angle bisector of ∠PTQ.
So, OT ⊥ PQ and therefore, OT bisects PQ
PR = RQ = 4 cm
CBSE Previous Year Question Papers Class 10 Maths 2019 Delhi Set I Q18.1

Question 19.
In Fig. ∠ACB = 90° and CD ⊥ AB, prove that CD2 = BD × AD. [3]
CBSE Previous Year Question Papers Class 10 Maths 2019 Delhi Set I Q19
OR
If P and Q are the points on side CA and CB respectively of ΔABC, right-angled at C, prove that (AQ2 + BP2) = (AB2 + PQ2).
Solution:
Given, A ΔACB in which ∠ACB = 90° and CD ⊥ AB
To prove : CD2 = BD × AD
Proof: In ΔADC and ΔACB
∠A = ∠A (common)
∠ADC = ∠ACB (90° each)
ΔADC ~ ΔACB (By AA rule)…(i)
Similarly,
ΔCDB ~ ΔACB (By AA rule)…(ii)
From equation (i) and (ii)
ΔADC ~ ΔCDB
\frac { AD }{ CD } = \frac { CD }{ DB }
(by the definition of similarity of triangles)
or CD2 = AD . BD
or CD2 = BD × AD
Hence Proved.
OR
Given, ABC is a right-angled triangle in which ∠C = 90°
CBSE Previous Year Question Papers Class 10 Maths 2019 Delhi Set I Q19.1
To prove : AQ2 + BP2 = AB2 + PQ2
Construction: Join AQ, PB and PQ
Proof: In ΔAQC, ∠C = 90°
AQ2 = AC2 + CQ2 …(i) (Using Pythagoras theorem)
In ΔPBC, ∠C = 90°
BP2 = BC2 + CP2 …(ii) (Using Pythagoras theorem)
Adding equation (i) and (ii)
AQ2 + BP2 = AC2 + CQ2 + BC2 + CP2 = AC2 + BC2 + CQ2 + CP2
or AQ2 + BP2 = AB2 + PQ2
Hence Proved.

Question 20.
Find the area of the shaded region in Fig. if ABCD is a rectangle with sides 8 cm and 6 cm and D is the centre of the circle. [3]
[Take π = 3.14]
CBSE Previous Year Question Papers Class 10 Maths 2019 Delhi Set I Q20
Solution:
Given, ABCD is a rectangle with sides AB = 8 cm and BC = 6 cm
In ΔABC
AC2 = 82 + 62 (By Pythagoras Theorem)
⇒ AC2 = 64 + 36
⇒ AC2 = 100
⇒ AC = 10 cm
The diagonal of the rectangle will be the diameter of the circle
radius of the circle = \frac { 10 }{ 2 } = 5 cm
Area of shaded portion = Area of circle – Area of Rectangle
= πr2 – l × b
= 3.14 × 5 × 5 – 8 × 6
= 78.50 – 48
= 30.50 cm2
Hence, Area of shaded portion = 30.5 cm2

Question 21.
Water in a canal, 6 m wide and 1.5 m deep, is flowing with a speed of 10 km/hour. How much area will it irrigate in 30 minutes, if 8 cm standing water is needed? [3]
Solution:
Let b be the width and h be the depth of the canal
b = 6 m and h = 1.5 m
Water is flowing with a speed = 10 km/h = 10,000 m/h
Length of water flowing in 1 hr = 10,000 m
Length (l) of water flowing in \frac { 1 }{ 2 } hr = 5,000 m
Volume of water flowing in 30 min. = l × b × h = 5000 × 6 × 1.5 m3
Let the area irrigated in 30 min (\frac { 1 }{ 2 } hr) be x m2
Volume of water required for irrigation = Volume of water flowing in 30 min.
x × \frac { 8 }{ 100 } = 5000 × 6 × 1.5
x = 562500 m2 = 56.25 hectares. (∵ 1 hactare = 104 m2)
Hence, the canal will irrigate 56.25 hectares in 30 min.

Question 22.
Find the mode of the following frequency distribution. [3]
CBSE Previous Year Question Papers Class 10 Maths 2019 Delhi Set I Q22
Solution:
The given frequency distribution table is
CBSE Previous Year Question Papers Class 10 Maths 2019 Delhi Set I Q22.1
Here, the maximum class frequency is 16
Modal class = 30-40
lower limit (l) of modal class = 30
Class size (h) =10
Frequency (f1) of the modal class = 16
Frequency (f0) of preceding class = 10
Frequency (f2) of succeeding class = 12
CBSE Previous Year Question Papers Class 10 Maths 2019 Delhi Set I Q22.2

Section – D

Question 23.
Two water taps together can fill a tank in 1\frac { 7 }{ 8 } hours. The tap with longer diameter takes 2 hours less than the tap with a smaller one to fill the tank separately. Find the time in which each tap can fill the tank separately. [4]
OR
A boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours, it can go 40 km upstream and 55 km downstream. Determine the speed of the stream and that of the boat in still water.
Solution:
Let the tap A with longer diameter take x hours and the tap B with smaller diameter take (x + 2) hours to fill the tank.
Portion of tank filled by the tap A in 1 hr. = \frac { 1 }{ x }
and Portion of tank filled by the tap B in 1 hr. = \frac { 1 }{ x+2 }
Portion of the tank filled by both taps in 1 hr. = \frac { 1 }{ x } + \frac { 1 }{ x+2 } = \frac { x+2+x }{ x(x+2) }
Time taken by both taps to fill the tank = 1\frac { 7 }{ 8 } hrs = \frac { 15 }{ 8 } hrs
Portion of the tank filled by both in 1 hr. = \frac { 8 }{ 15 }
According to question,
\frac { 2x+2 }{ x(x+2) } = \frac { 8 }{ 15 }
\frac { 2(x+1) }{ x(x+2) } = \frac { 8 }{ 15 }
⇒ 15x + 15 = 4x2 + 8x
⇒ 4x2 – 7x – 15 = 0
⇒ 4x2 – 12x + 5x – 15 = 0
⇒ 4x (x – 3) + 5 (x – 3 ) = 0
⇒ (4x + 5)(x – 3) =0
⇒ 4x + 5 = 0 or x – 3 = 0
⇒ x = \frac { -5 }{ 4 } Since, time can not be negative hence, neglegted this value is; x = 3
Hence, the time taken with longer diameter tap = 3 hours
and the time taken with smaller diameter tap = 5 hours.
OR
Let the speed of the boat in still water be x km/h and the speed of the stream be y km/h
Then the speed of the boat downstream = (x + y) km/h
and the speed of the boat upstream = (x – y) km/h
We know that,
CBSE Previous Year Question Papers Class 10 Maths 2019 Delhi Set I Q23
CBSE Previous Year Question Papers Class 10 Maths 2019 Delhi Set I Q23.1
On solving, we get x = 8 and y = 3
Hence, the speed of the boat in still water = 8 km/h
and the speed of the stream = 3 km/h

Question 24.
If the sum of first four terms of an A.P. is 40 and that of first 14 terms is 280. Find the sum of its first n terms. [4]
Solution:
Given, S4 = 40 and S14 = 280
If a be the first term and d be the common difference of an A.P.
CBSE Previous Year Question Papers Class 10 Maths 2019 Delhi Set I Q24
CBSE Previous Year Question Papers Class 10 Maths 2019 Delhi Set I Q24.1

Question 25.
CBSE Previous Year Question Papers Class 10 Maths 2019 Delhi Set I Q25
Solution:
CBSE Previous Year Question Papers Class 10 Maths 2019 Delhi Set I Q25.1

Question 26.
A man in a boat rowing away from a lighthouse 100 m high takes 2 minutes to change the angle of elevation of the top of the lighthouse from 60° to 30°. Find the speed of the boat in metres per minute. [Use √3 = 1.732] [4]
Solution:
Let AB be the lighthouse C and D be the two positions of the boat, such that,
CD = x m and BC = y m
CBSE Previous Year Question Papers Class 10 Maths 2019 Delhi Set I Q26
CBSE Previous Year Question Papers Class 10 Maths 2019 Delhi Set I Q26.1

Question 27.
Construct a ∆ABC in which CA = 6 cm, AB = 5 cm and ∠BAC = 45°. Then construct a triangle whose sides are \frac { 3 }{ 5 } of the corresponding sides of ∆ABC. [4]
Solution:
Steps of Construction are as follows:

  1. Draw AB = 5 cm
  2. At the point, A draw ∠BAX = 45°
  3. From AX cut off AC = 6 cm
  4. Join BC, ∆ABC is formed with given data.
  5. Draw AY making an acute angle with AB as shown in the figure.
    CBSE Previous Year Question Papers Class 10 Maths 2019 Delhi Set I Q27
  6. Draw 5 arcs P1, P2, P3, P4, and P5 with equal intervals.
  7. Join BP5.
  8. Draw P3B’ || P5B meeting AB at B’.
  9. From B’, draw B’C’ || BC meeting AC at C’
    ∆AB’C’ ~ ∆ABC
    Hence ∆AB’C’ is the required triangle.

Question 28.
A bucket open at the top is in the form of a frustum of a cone with a capacity of 12308.8 cm3. The radii of the top and bottom of circular ends of the bucket are 20 cm and 12 cm respectively. Find the height of the bucket and also the area of the metal sheet used in making it. (Use π = 3.14) [4]
Solution:
Let r and R be the radii of the top and the bottom circular ends of the bucket respectively.
Let h be the height of the bucket.
R = 20 cm and r = 12 cm
Capacity of the bucket = 12308.8 cm3
Volume of bucket (frustum)
CBSE Previous Year Question Papers Class 10 Maths 2019 Delhi Set I Q28
Thus, the height of the bucket is 15 cm.
The area of the metal sheet used in making the bucket = CSA of bucket + area of the circular bottom
CBSE Previous Year Question Papers Class 10 Maths 2019 Delhi Set I Q28.1
Area of metal sheet used = π[(R + r)l + r2]
= 3.14 [(20 + 12) × 17 + 122]
= 3.14 [32 × 17 + 144]
= 3.14 [544 + 144]
= 3.14 × 688
= 2160.32 cm2

Question 29.
Prove that in a right-angle triangle, the square of the hypotenuse is equal the sum of squares of the other two sides. [4]
Solution:
Given, A ΔABC right angled at B.
To prove : AC2 = AB2 + BC2
CBSE Previous Year Question Papers Class 10 Maths 2019 Delhi Set I Q29
Construction : Draw BD ⊥ AC
Proof: In ΔADB and ΔABC
∠A = ∠A (common)
∠ADB = ∠ABC (90° each)
ΔADB ~ ΔABC (By AA rule)
So, \frac { AD }{ AB } = \frac { AB }{ AC } (sides are proportional)
or AB2 = AD.AC …(i)
Also, In ΔBDC and ΔABC
∠C = ∠C (common)
∠BDC = ∠ABC (90° each)
ΔBDC ~ ΔABC
So, \frac { CD }{ BC } = \frac { BC }{ AC }
or BC2 = CD.AC …(ii)
Adding equation (i) and (ii), we get
AB2 + BC2 = AD.AC + CD.AC
= AC (AD + CD)
= AC × AC
= AC2
or AC2 = AB2 + BC2
Hence Proved.

Question 30.
If the median of the following frequency distribution is 32.5. Find the values of f1 and f2. [4]
CBSE Previous Year Question Papers Class 10 Maths 2019 Delhi Set I Q30
OR
The marks obtained by 100 students of a class in an examination are given below.
CBSE Previous Year Question Papers Class 10 Maths 2019 Delhi Set I Q30.1
Draw ‘a less than’ type cumulative frequency curves (ogive). Hence find the median.
Solution:
Median = 32.5
CBSE Previous Year Question Papers Class 10 Maths 2019 Delhi Set I Q30.2
CBSE Previous Year Question Papers Class 10 Maths 2019 Delhi Set I Q30.3
CBSE Previous Year Question Papers Class 10 Maths 2019 Delhi Set I Q30.4
CBSE Previous Year Question Papers Class 10 Maths 2019 Delhi Set I Q30.5
To draw a less than ogive, we mark the upper-class limits of the class intervals on the x-axis and their c.f. on the y-axis by taking a convenient scale.
Here, n = 100 ⇒ \frac { n }{ 2 } = 50
To get median from graph From 50, we draw a perpendicular to the curve then from that point draw again perpendicular to x-axis.
The point where this perpendicular meet on the x-axis will be the median.
Median = 29
CBSE Previous Year Question Papers Class 10 Maths 2019 Delhi Set I Q30.6

CBSE Previous Year Question Papers Class 10 Maths 2019 Delhi Set II

Note: Except for the following questions, all the remaining questions have been asked in previous sets.

Section – A

Question 1.
Find the coordinates of a point A, where AB is a diameter of the circle with centre (-2, 2) and B is the point with coordinates (3, 4). [1]
Solution:
By mid-point formula
\frac { x+3 }{ 2 } = -2
x = -4 – 3 = -7
CBSE Previous Year Question Papers Class 10 Maths 2019 Delhi Set II Q1
and \frac { y+4 }{ 2 } = 2
⇒ y = 0
Co-ordinates of point A are (-7, 0).

Section – B

Question 7.
Find the value of k for which the following pair of linear equations have infinitely many solutions. [2]
2x + 3y = 7, (k + 1)x + (2k – 1)y = 4k + 1
Solution:
Given,
2x + 3y = 7 and (k + 1) x + (2k – 1)y = 4k + 1
On comparing above equations with
a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0, we get
a1 = 2, b1 = 3, c1 = -7
a2 = k + 1, b2 = 2k – 1, c2 = -(4k + 1)
For infinitely many solutions
CBSE Previous Year Question Papers Class 10 Maths 2019 Delhi Set II Q7
⇒ 2(2k – 1) = 3 (k + 1)
⇒ 4k – 2 = 3k + 3
⇒ k = 5
or 3 (4k + 1) = 7(2k – 1)
⇒ k = 5
Hence, k = 5.

Section – C

Question 13.
The arithmetic mean of the following frequency distribution is 53. Find the value of k. [3]
CBSE Previous Year Question Papers Class 10 Maths 2019 Delhi Set II Q13
Solution:
Given, Median = 53
CBSE Previous Year Question Papers Class 10 Maths 2019 Delhi Set II Q13.1

Question 14.
Find the area of the segment shown in Fig. if radius of the circle is 21 cm and ∠AOB = 120° (π = \frac { 22 }{ 7 }) [3]
Solution:
Given, Radius of the circle = 21 cm and ∠AOB = 120°
CBSE Previous Year Question Papers Class 10 Maths 2019 Delhi Set II Q14
CBSE Previous Year Question Papers Class 10 Maths 2019 Delhi Set II Q14.1

Question 16.
In Fig. a circle is inscribed in a ∆ABC having sides BC = 8 cm, AB = 10 cm and AC = 12 cm. Find the lengths BL, CM and AN. [3]
Solution:
A circle is inscribed in a ∆ABC
AB = 10 cm, BC = 8 cm and AC = 12 cm
Let AN = AM = z
BN = BL = x
CL = CM = y
(Tangents drawn from an exterior points are equal in length.)
Perimeter of ∆ = AB + BC + CA = 10 + 8 + 12 = 30
or x + z + x + y + y + z = 30
2 (x + y + z) = 30
x + y + z = 15 …(i)
Also, AB = 10 cm
or x + z = 10 …(ii)
and AC = 12
or y + z = 12 …(iii)
and BC = 8 cm
x + y = 8 …(iv)
From equation (i) and (ii), y = 5 cm
From equation (i) and (iii), x = 3 cm
From equation (i) and (iv), z = 7 cm
So, BL = 3 cm, CM = 5 cm, AN = 7 cm.

Section – D

Question 23.
CBSE Previous Year Question Papers Class 10 Maths 2019 Delhi Set II Q23
Solution:
CBSE Previous Year Question Papers Class 10 Maths 2019 Delhi Set II Q23.1

Question 24.
The first term of an A.P. is 3, the last term is 83 and the sum of all its terms is 903. Find the number of terms and the common difference of the A.P. [4]
Solution:
Given, a = 3, an = 83 = l
Sn = 903
an = a + (n – 1)d
83 = 3 + (n – 1)d
(n – 1)d = 80 …(i)
Also, Sn = \frac { n }{ 2 } (a + l)
⇒ 903 = \frac { n }{ 2 } (3 + 83)
⇒ 1806 = n × 86
⇒ n = 21
From Equation(i)
(21 – 1)d = 80
d = 4
Hence, No. of terms are 21 and common difference is 4 of given A.P.

Question 25.
Construct a triangle ABC with side BC = 6 cm, ∠B = 45°, ∠A = 105°. Then construct another triangle whose sides are \frac { 3 }{ 4 } times the corresponding sides of the ∆ABC. [4]
Solution:
Steps of construction:
1. Draw a ∆ABC in which BC = 6 cm, ∠B = 45° and ∠C = 30°
[∵ ∠A = 105°, (given)
and ∠A + ∠B + ∠C = 180°
105° + 45° + ∠C = 180°
∠C = 180° – 150°
∠C = 30°]
CBSE Previous Year Question Papers Class 10 Maths 2019 Delhi Set II Q25
2. Draw a ray BX and mark 4 arcs of an equal radius on it.
3. Join P4C, From P3, draw P3C’ || P4C which meets BC at C’.
4. From C’ draw C’A || CA, which meets AB at A’
∆A’BC’ ~ ∆ABC and ∆A’BC’ is the required triangle.

CBSE Previous Year Question Papers Class 10 Maths 2019 Delhi Set III

Note: Except for the following questions, all the remaining questions have been asked in previous sets.

Section – A

Question 1.
Two positive integers a and b can be written as a = x3y2 and b = xy3. x, y are prime numbers. Find LCM (a, b). [1]
Solution:
Given, a = x3y2 and b = xy3
L.C.M (a, b) = Product of the greatest power of each prime factors = x3y3

Section – B

Question 7.
Find, how many two-digit natural numbers are divisible by 7. [2]
OR
If the sum of first n terms of an A.P. is n2, then find its 10th term.
Solution:
Two digit numbers which are divisible by 7 are 14, 21, 28,…. 98
It is an A.P., such that a = 14, an = 98; d = 21 – 14 = 7
an = a + (n – 1)d
98 = 14 + (n – 1) × 7
84 = (n – 1) × 7
or n – 1 = 12
n = 13
Hence, there are 13 two digit numbers, divisible by 7.
OR
Given, Sn = n2, Sn-1 = (n – 1)2
an = Sn – Sn-1
= n2 – (n – 1)2
= n2 – [n2 – 2n + 1]
= n2 – n2 + 2n – 1
an = 2n – 1
Put n = 10, a10 = 2 × 10 – 1 = 19
Hence 10th term = 19

Section – C

Question 13.
Find all zeroes of the polynomial 3x3 + 10x2 – 9x – 4 if one of its zero is 1. [3]
Solution:
Given, P(x) = 3x3 + 10x2 – 9x – 4
x = 1 is a zero of P(x)
(x – 1) is a factor of P(x)
To find other zeroes, we divide P(x) by (x – 1)
CBSE Previous Year Question Papers Class 10 Maths 2019 Delhi Set III Q13
P(x) = (x – 1) (3x2 + 13x + 4)
= (x – 1)(3x2 + 12x + x + 4)
= (x – 1) {3x (x + 4) + 1 (x + 4)}
= (x – 1)(x + 4)(3x + 1)
other zeroes are x + 4 = 0 ⇒ x = -4,
and 3x + 1 = 0 ⇒ x = \frac { -1 }{ 3 }
other zeroes are x = -4 and x = \frac { -1 }{ 3 }

Question 15.
Prove that \frac { 2+\surd 3 }{ 5 } is an irrational number, given that √3 is an irrational number. [3]
Solution:
Let \frac { 2+\surd 3 }{ 5 } is a rational number
CBSE Previous Year Question Papers Class 10 Maths 2019 Delhi Set III Q15
In R.H.S., a, b, 2 and 5 are integers.
R.H.S. is a rational number but L.H.S. = √3,
which is given that √3 is irrational.
So, it is a contradiction.
Hence, \frac { 2+\surd 3 }{ 5 } is an irrational number.

Section – D

Question 23.
If sec θ = x + \frac { 1 }{ 4x } , x ≠ 0, find (sec θ + tan θ). [4]
Solution:
CBSE Previous Year Question Papers Class 10 Maths 2019 Delhi Set III Q23
CBSE Previous Year Question Papers Class 10 Maths 2019 Delhi Set III Q23.1

Question 24.
Prove that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. [4]
Solution:
Given, Two triangles ΔABC and ΔPQR are similar to each other.
CBSE Previous Year Question Papers Class 10 Maths 2019 Delhi Set III Q24
CBSE Previous Year Question Papers Class 10 Maths 2019 Delhi Set III Q24.1
CBSE Previous Year Question Papers Class 10 Maths 2019 Delhi Set III Q24.2

Question 25.
The following distribution gives the daily income of 50 workers of a factory.
CBSE Previous Year Question Papers Class 10 Maths 2019 Delhi Set III Q25
Convert the distribution above to a ‘less than type’ cumulative frequency distribution and draw its ogive. [4]
OR
The table below shows the daily expenditure on the food of 25 households in a locality. Find the mean daily expenditure of food.
CBSE Previous Year Question Papers Class 10 Maths 2019 Delhi Set III Q25.1
Solution:
CBSE Previous Year Question Papers Class 10 Maths 2019 Delhi Set III Q25.2
CBSE Previous Year Question Papers Class 10 Maths 2019 Delhi Set III Q25.3

CBSE Previous Year Question Papers CBSE Previous Year Question Papers Class 10 Maths

The post CBSE Previous Year Question Papers Class 10 Maths 2019 Delhi appeared first on Learn CBSE.

CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 7

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CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 7

                                                                   Section A

1.Rohan’s mother is 26 years older than him. The product of their ages (in years) after 3 years from now will be 360. We would like to find Rohan’s present age.
Represent above situation in the form of quadratic equation.

2.The first and last terms of an AP are 1 and 11 respectively. If the sum of its terms is 36, find the number of terms.

Download Formula Book for Class 10 Maths and Science CBSE Sample Papers for Class 10 Maths

3.Find the ratio in which the y-axis divides the line segment joining the points (5, – 6) and (-1, -4).

4.An arc of a circle is of length 5n cm and the sector it bounds has an area of 20tt cm2. Find the radius of the circle.

                                                             Section B

CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 7-39

6.The sum of four numbers in an AP is 0 and their product is 9. Find the numbers.

7.In figure, two circles touch each other at the point C. Prove that the common tangent to the circles at C, bisects the common tangent at P and Q.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 7-33

8.Two dice are thrown simultaneously. Find the probability that the sum of the two numbers appearing on the top is more than 8.

9.In the given figure, find the area of the shaded region, where AC = 13 cm, AB = 12 cm, O is centre of the circle and triangle ABC = triangle DAB = 90°.(Use pi =3.14)
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 7-34

10.The diameter of a spherical cannonball is 42 cm. It is melted and recast into a right circular mould, the base of which is 28 cm in diameter. Find the height of the cone

                                                                      Section C
11.For what value of k, are the roots of the quadratic equation (k – 4)x2 + (k – 4) x + 4 = 0 equal?

12.Solve for x :(x-2/x-4)+(x-6/x-8) = 6 2/3, (x not equal to 4,8)

13.Find the sum of all multiples of 7 lying between 103 and 999.

14.Draw a circle of radius 5 cm. From a point, 12 cm away from its centre, construct the pair of tangents to the circle and measure their lengths.

15.Three coins are tossed together. Find the probability of:
(i) getting at most one tail.
(ii) getting at least one tail.

16.Cards marked with numbers 5 to 100 are placed in a box and mixed thoroughly. One card is drawn from this box. Find the probability that the number on the card is:
(i) a perfect square.
(ii) a multiple of 7.
(iii) a prime number less than 25.

17.Determine the ratio in which the point C(p, -3) divides the join of A(-6, 3) and B(2, -9). Also find the value of p.

18.The line segment PQ joining the points P(2, -4) and Q(5, 2) is trisected at the points R(3, a) and S(b, 0). Find the values of a and b.

19.A steel wire when bent in the form of a square encloses an area of 196 sq. cm. If the same wire is bent into the form of a circle, find the area of the circle. (Use pi = 22/7)

20.A hemispherical bowl of internal diameter 60 cm contains some liquid. This liquid is to be filled into cylindrical shaped bottles each of diameter 10 cm and height 12 cm. Find the number of bottles necessary to empty the bowl.

                                                                   Section D
21.Two pipes running together can fill a cistern in 6 minutes. If one pipe takes 5 minutes more than the other to fill the cistern, find the time in which each pipe would fill the cistern.

22. Sahil repays the total loan of Rs 2,36,000 by paying every month starting with the first instalment of Rs 2000. He increases the instalment Rs 200 every month.
(a)What amount would he pay as the last instalment of loan?
(b)On 5th of every month the amount of instalment is directly transferred from his bank account. Therefore, Sahil ensures sufficient funds in his bank account before 5th of every month. What values are depicted by Sahil in this act?

23.In figure, OP is equal to diameter of the circle. Prove that triangle APB is an equilateral triangle.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 7-36

24.PAQ is a tangent to the circle with centre O at a point A as shown in figure. If OBA = 35°, find the value of angle BAQ and angle ACB.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 7-37

CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 7-38

CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 7-40

27.A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle of 30° with the ground. The distance between the foot of the tree to the point where to top touches the ground is 8 m. Find the height of the tree.

28.If the points A(l, -2), B(2, 3), C(-3, 2) and D(-4, -3) are the vertices of parallelogram ABCD, then taking AB as the base, find the height of the parallelogram.

29.The short and long hands of a clock are 4 cm and 6 cm long respectively. Find the sum of the distances travelled by their tips in two days (48 hours). [Take pi = 22/7]

30.A cylindrical vessel with internal diameter 10 cm and height 10.5 cm is full of water. A solid cone of base diameter 7 cm and height 6 cm is completely immersed in water. Find the volume of
(i water displaced out of the cylindrical vessel.
(ii) water left in the cylindrical vessel. [Take pi = 22/7]

31.The diameter of a roller 120 cm long is 84 cm. If it takes 500 complete revolutions to level a playground, determine the cost of levelling it at the rate of 30 paise per square metre.

Answers

                                                                     Section A

1.Rohan’s mother is 26 years older than him. The product of their ages (in years) after 3 years from now will be 360. We would like to find Rohan’s present age.
Represent above situation in the form of quadratic equation.
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 7-1

2.The first and last terms of an AP are 1 and 11 respectively. If the sum of its terms is 36, find the number of terms.
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 7-2

3.Find the ratio in which the y-axis divides the line segment joining the points (5, – 6) and (-1, -4).
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 7-3

4.An arc of a circle is of length 5n cm and the sector it bounds has an area of 20tt cm2. Find the radius of the circle.
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 7-4

                                                                 Section B

CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 7-39
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 7-5

6.The sum of four numbers in an AP is 0 and their product is 9. Find the numbers.
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 7-6

7.In figure, two circles touch each other at the point C. Prove that the common tangent to the circles at C, bisects the common tangent at P and Q.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 7-33
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 7-32

8.Two dice are thrown simultaneously. Find the probability that the sum of the two numbers appearing on the top is more than 8.
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 7-8

9.In the given figure, find the area of the shaded region, where AC = 13 cm, AB = 12 cm, O is centre of the circle and triangle ABC = triangle DAB = 90°.(Use pi =3.14)
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 7-34
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 7-9

10.The diameter of a spherical cannonball is 42 cm. It is melted and recast into a right circular mould, the base of which is 28 cm in diameter. Find the height of the cone
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 7-10

                                                                      Section C
11.For what value of k, are the roots of the quadratic equation (k – 4)X2 + (k – 4) x + 4 = 0 equal?
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 7-11

12.Solve for x :(x-2/x-4)+(x-6/x-8) = 6 2/3, (x not equal to 4,8)
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 7-12

13.Find the sum of all multiples of 7 lying between 103 and 999.
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 7-13

14.Draw a circle of radius 5 cm. From a point, 12 cm away from its centre, construct the pair of tangents to the circle and measure their lengths.
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 7-14

15.Three coins are tossed together. Find the probability of:
(i) getting at most one tail.
(ii) getting at least one tail.
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 7-15

16.Cards marked with numbers 5 to 100 are placed in a box and mixed thoroughly. One card is drawn from this box. Find the probability that the number on the card is:
(i) a perfect square.
(ii) a multiple of 7.
(iii) a prime number less than 25.
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 7-16

17.Determine the ratio in which the point C(p, -3) divides the join of A(-6, 3) and B(2, -9). Also find the value of p.
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 7-17

18.The line segment PQ joining the points P(2, -4) and Q(5, 2) is trisected at the points R(3, a) and S(b, 0). Find the values of a and b.
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 7-18

19.A steel wire when bent in the form of a square encloses an area of 196 sq. cm. If the same wire is bent into the form of a circle, find the area of the circle. (Use pi = 22/7)
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 7-19

20.A hemispherical bowl of internal diameter 60 cm contains some liquid. This liquid is to be filled into cylindrical shaped bottles each of diameter 10 cm and height 12 cm. Find the number of bottles necessary to empty the bowl.
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 7-20
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 7-20.a

                                                                      Section D
21.Two pipes running together can fill a cistern in 6 minutes. If one pipe takes 5 minutes more than the other to fill the cistern, find the time in which each pipe would fill the cistern.
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 7-21.

22.  Sahil repays the total loan of Rs 2,36,000 by paying every month starting with the first instalment of Rs 2000. He increases the instalment Rs 200 every month.
(a)What amount would he pay as the last instalment of loan?
(b)On 5th of every month the amount of instalment is directly transferred from his bank account. Therefore, Sahil ensures sufficient funds in his bank account before 5th of every month. What values are depicted by Sahil in this act?
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 7-22

23.In figure, OP is equal to diameter of the circle. Prove that triangle APB is an equilateral triangle.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 7-36
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 7-23

24.PAQ is a tangent to the circle with centre O at a point A as shown in figure. If OBA = 35°, find the value of angle BAQ and angle ACB.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 7-37
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 7-24

CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 7-38
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 7-25
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 7-25.a

CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 7-40
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 7-26

27.A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle of 30° with the ground. The distance between the foot of the tree to the point where to top touches the ground is 8 m. Find the height of the tree.
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 7-27

28.If the points A(l, -2), B(2, 3), C(-3, 2) and D(-4, -3) are the vertices of parallelogram ABCD, then taking AB as the base, find the height of the parallelogram.
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 7-q-1jpg_Page1

29.The short and long hands of a clock are 4 cm and 6 cm long respectively. Find the sum of the distances travelled by their tips in two days (48 hours). [Take pi = 22/7]
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 7-29

30.A cylindrical vessel with internal diameter 10 cm and height 10.5 cm is full of water. A solid cone of base diameter 7 cm and height 6 cm is completely immersed in water. Find the volume of
(i water displaced out of the cylindrical vessel.
(ii) water left in the cylindrical vessel. [Take pi = 22/7]
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 7-30
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 7-30.a

31.The diameter of a roller 120 cm long is 84 cm. If it takes 500 complete revolutions to level a playground, determine the cost of levelling it at the rate of 30 paise per square metre
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 7-31

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CBSE Previous Year Question Papers Class 10 Maths SA2 Outside Delhi – 2012

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CBSE Previous Year Question Papers Class 10 Maths SA2 Outside Delhi – 2012

Time allowed: 3 hours                                                                                           Maximum marks: 90

GENERAL INSTRUCTIONS:

  1. All questions are compulsory.
  2. The Question Taper consists of 31 questions divided into four Sections A, B. C. and D.
  3. Section A contains 4 questions of 1 mark each. Section B contains 6 questions of 2 marks each, Section C contains 10 questions of 3 marks each and Section D contains 11 questions of 4 marks each.
  4.  Use of calculators is not permitted.

SET I

SECTION A
Questions number 1 to 4 carry 1 mark each.
Question.1 In Figure 1, AP, AQ and BC are tangents to the circle. If AB = 5 cm, AC = 6 cm and BC = 4 cm, then calculate the length of AP (in cm).
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2012-62
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2012-1

CBSE Sample Papers Class 10 Maths

Question.2 The circumference of a circle is 22 cm. Calculate the area of its quadrant (in cm2).
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2012-2

Question.3 A solid right circular cone is cut into two parts at the middle of its height by a plane parallel to its base. Find the ratio of the volume of the smaller cone to the whole cone.
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2012-3

Question.4. Find the distance of the point (-3, 4) from the .Y-axis.
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2012-4

SECTION B
Questions number 5 to 10 carry 2 marks each.
Question.5 The 7th term of an A.P. is 20 and its 13th term is 32. Find the A.P.
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2012-5
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2012-6

Question.6 PQRS is a diameter of a circle of radius 6 cm. The equal lengths PQ, QR and RS are drawn on PQ and QS as diameters, as shown in Fig. 2. Find the perimeter of the shaded region.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2012-63
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2012-7

Question.7 Find the value of for which the roots of the equation px(x-2)+6 = 0 are equal
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2012-8

Question.8 How many two-digits number are divisible by 3?
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2012-9

Question.9 In figure 3, a right triangle ABC, circumscribes a circle of radius r if AB and BC are of lenths 8cm and 6cm respectively, find the value of r
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2012-70
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2012-10

Question.10 Prove that the tangents drawn at the ends of a diameter of a circle of parallel
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2012-11

SECTION C
Question.11 In figure 4, ABCD is a square of side 4 cm. A quadrant of a circle of radius 1 cm is drawn at each vertex of the square and a circle of diameter 2 cm is also drawn. Find the area of shaded region. (Use π = 3.14)
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2012-65
Or
From a rectangular sheet of paper ABCD with AB = 40 cm and AD = 28 cm, a semi-circular
portion with BC as diameteris cut off. Find the area of remining paper (use π = 22/7)
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2012-12
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2012-13

Question.12 A solid sphere of radius 10.5 cm is melted and recast into smeller solid cones, each of radius 3.5 cm and hight 3 cm. Find the number of cones so formed. (Use π = 22/7)
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2012-14

Question.13 Find the value of k, if the point P(2, 4) is equidistant from the points A(5, k) and B(k, 7).
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2012-15

Question.14 A card is drawn at random from a well-shuffled pack of 52 cards. Find the probability of getting
(i) a red king. (ii) a queen or a jack.
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2012-16

Question.15 Solve the following quadratic equation for x: x2 – 4ax – b2 + 4a2 = 0
Or
If the sum of two natural numbers is 8 and their product is 15, find the numbers.
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2012-17
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2012-18

Question.16Find the sum of all multiples of 7 lying between 500 and 900.
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2012-19

Question.17 Draw a triangle ABC with BC = 7 cm, ∠B = 45° and ∠C = 60°. Then construct another
triangle, whose sides are 3/5 times the corresponding sides of ΔABC.
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2012-20

Question.18 In Figure 5, a circle is inscribed in a triangle PQR with PQ = 10 cm, QR = 8 cm and PR = 12 cm. Find the lengths of QM, RN and PL.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2012-66
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2012-21

Question.19 In Figure 6, O is the centre of the circle with AC = 24 cm, AB = 7 cm and ∠BOD = 90°. Find the area of the shaded region. (Use π = 3.14)
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2012-67
Or
In Figure 7, find the area of the shaded region, if ABCD is a square of side 14 cm and APD and BPC are semicircles.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2012-68
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2012-22
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2012-23

Question.20 An icecream seller sells his icecreams in two ways:
(A) In a cone of r = 5 cm, h- 8 cm
(B) In a cup in shape of cylinder with r = 5 cm, h = 8 cm He charges the same price for both but prefers to sell his icecream in a cone.
(a) Find the volume of the cone and the cup.
(b) Which out of the two has more capacity?
(c) By choosing a cone, which value is not being followed by the icecream seller?
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2012-69
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2012-24

SECTION D
Questions number 21 to 31 carry 4 marks each.
Question.21 The angles of depression of the top and bottom of a tower as seen from the top of a 60 √3 m high cliff are 45° and 60° respectively. Find the height of the tower.
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2012-25

Question.22 Find the coordinates of a point P, which lies on the line segment joining the points A(-2, -2)
and B(2, -4) such that AP = 3/7 AB.
Or
Find the area of the quadrilateral ABCD whose vertices are A(-3, -1), B(-2, -4), C(4, -1) and D(3, 4).
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2012-26
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2012-27
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2012-28

Question. 23 If the points A(x, y), B(3, 6) and C(-3, 4) are collinear, show that x – 3y + 15 = 0.
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2012-29

Question.24 All kings, queens and aces are removed from a pack of 52 cards. The remaining cards are well shuffled and then a card is drawn from it. Find the probability that the drawn card is (i) a black face card. (ii) a red card.
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2012-30
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2012-31

Question.25 The numerator of a fraction is 3 less than its denominator. If 1 is added to the denominator, the fraction is decreased by . Find the fraction.
Or
In a flight of 2800 km, an aircraft was slowed down due to bad weather. Its average speed is reduced by 100 km/h and time increased by 30 minutes. Find the original duration of the flight.
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2012-32
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2012-33
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2012-34

Question.26 Find the common difference of an A.P. whose first term is 5 and the sum of its first four terms is half the sum of the next four terms.
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2012-35

Question.27 Prove that the length of tangents drawn from an external point to a circle are equal.
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2012-36

Question.28 A hemispherical tank, full of water, is emptied by a pipe at the rate of y litres per sec.
How much time will it take to empty half the tank if the diameter of the base of the tank is 3 m?
Or
A drinking glass is in the shape of the frustum of a cone of height 14 cm. The diameters of
its two circular ends are 4 cm and 2 cm. Find the capacity of the glass. [Use π = 22/7 ]
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2012-37
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2012-38

Question.29 A military tent of height 8.25 m is in the form of a right circular cylinder of base diameter 30 m and height 5.5 m surmounted by a right circular cone of same base radius. Find the length of the canvas used in making the tent, if the breadth of the canvas is 1.5 m.
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2012-39
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2012-40

Question.30 The angles of elevation and depression of the top and bottom of a light-house from the top of a 60 m high building are 30° and 60° respectively. Find
(i) the difference between the heights of the light-house and the building.
(ii)the distance between the light-house and tire building.
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2012-41

Question.31 If the centroid of ΔABC, in which A (a, b), B(F, c), C(c, a) is at the origin, then calculate the value of (a3 + b3 + c3).
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2012-42

SET II

Note: Except for the following questions, all the remaining questions have been asked in Set-I.
Question.13 Find the value of k for which the roots of the equation kx (3x – 4) + 4 = 0, are equal.
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2012-43
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2012-44

Question.14 How many three-digit numbers are divisible by 11?
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2012-45

Question.21 A box contains 70 cards numbered from 1 to 70. If one card is drawn at random from the box, find the probability that it bears
(i) a perfect square number. (ii) a number divisible by 2 and 3.
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2012-46

Question.22 Find the value of k, for which the points A(6, -1), B(k, -6) and C(0, -7) are collinear.
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2012-47

Question.23 Draw a right triangle in which the sides (other than hypotenuse) are of lengths 8 cm and 6
cm. Then construct another triangle whose sides are 3/4 times the corresponding sides of the given triangle.
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2012-48

Question.24 Find the sum of all multiples of 8 lying between 201 and 950.
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2012-49

Question.29 If the sum of the first 7 terms of an A.P. is 119 and that of the first 17 terms is 714, find the sum of its first n terms.
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2012-50
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2012-51

Question.30 Prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact.
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2012-52

SET III

Note: Except for the following questions, all the remaining questions have been asked in Set-I and Set-11.
Question.13 Find the value of m for which the roots of the equation
mx (6x + 10) + 25 = 0, are equal.
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2012-53

Question.14 Flow many three-digit numbers are divisible by 12?
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2012-54

Question.21 Find the sum of all multiples of 9 lying between 400 and 800.
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2012-55

Question.22 Find the value of p, if the points A(l, 2), B(3, p) and C(5, -4) are collinear.
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2012-56
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2012-57

Question.23 Red kings and black aces are removed from a pack of 52 cards. The remaining cards are well shuffled and then a card is drawn from it. Find the probability that the drawn card is
(i) a black face card. (ii) a red card.
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2012-58

Question.24 Draw a triangle with sides 5 cm, 6 cm and 7 cm. Then construct another triangle whose
sides are 2/3 times the corresponding sides of the first triangle.
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2012-59
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2012-60

Question.30 A sum of Rs 1,600 is to be used to give ten cash prizes to students of a school for their overall academic performance. If each prize is Rs 20 less than its preceding prize, find the value of each of the prizes.
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2012-61

CBSE Previous Year Question Papers CBSE Previous Year Question Papers Class 10 Maths

The post CBSE Previous Year Question Papers Class 10 Maths SA2 Outside Delhi – 2012 appeared first on Learn CBSE.

CBSE Previous Year Question Papers Class 10 Maths SA2 Delhi – 2013

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CBSE Previous Year Question Papers Class 10 Maths SA2 Delhi – 2013

Time allowed: 3 hours                                                                                           Maximum marks: 90

GENERAL INSTRUCTIONS:

  1. All questions are compulsory.
  2. The Question Taper consists of 31 questions divided into four Sections A, B. C. and D.
  3. Section A contains 4 questions of 1 mark each. Section B contains 6 questions of 2 marks each, Section C contains 10 questions of 3 marks each and Section D contains 11 questions of 4 marks each.
  4.  Use of calculators is not permitted.

SET I

Questions number 1 to 4 carry 1 mark each.
Question.1 Find the common difference of the Ap
cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2013-66
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2013-1

CBSE Sample Papers Class 10 Maths

Question.2 In Fig.1, Calculate the area of triangle ABC (in sq.units).
cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2013-58
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2013-2

SECTION A
Question.3 In Fig. 2, PA and PB are two tangents drawn from an external point P to a circle with centre C and radius 4 cm. If PA PB, then find the length of each tangent.
cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2013-59
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2013-3

Question.4 If the difference between the circumference and the radius of a circle is 37 cm, then using
π= 22/7, calculate the circumference (in cm) of the circle.
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2013-4

SECTION B
Questions number 5 to 20 carry 2 marks each.
Question.5 Solve the following quadratic equation for x:
cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2013-67
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2013-5

Question.6 How many three-digit natural numbers are divisible by 7?
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2013-6

Question.7 In Fig. 3, a circle inscribed in triangle ABC touches its sides AB, BC and AC at points D, E and F respectively. If AB = 12 cm, BC = 8 cm and AC = 10 cm, then find the lengths of AD, BE and CF.
cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2013-60
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2013-7

Question.8 Prove that the parallelogram circumscribing a circle is a rhombus.
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2013-8

Question.9 A card is drawn at random from a well shuffled pack of 52 playing cards. Find the probability that the drawn card is neither a king nor a queen.
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2013-9

Question.10 Two circular pieces of equal radii and maximum area, touching each other are cut out from a rectangular card board of dimensions 14 cm x 7 cm. Find the area of the remaining card
board. [Use π = 22/7 ]
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2013-10

SECTION C
Questions number 11 to 20 carry 3 marks each.
Question.11 For what value of k, are the roots of the quadratic equation kx(x – 2) + 6 =0 equal?
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2013-11

Question.12 Find the number of terms of the AP18,151/2, 13,…., -491/2 and find the sum of all its terms.
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2013-12

Question.13 Construct a triangle with sides 5 cm, 4 cm and 6 cm. Then construct another triangle whose
sides are 2/3 times the corresponding sides of first triangle.
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2013-13
cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2013-14

Question.14 The horizontal distance between two poles is 15 m. The angle of depression of the top of first pole as seen from the top of second pole is 30°. If the height of the second pole is 24 m, find the height of the first pole. [Use √3 = 1.732]
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2013-15

Question.15 Prove that the points (7,10), (-2,5) and (3, -4) are the vertices of an isosceles right triangle.
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2013-16
cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2013-17

Question.16 Find the ratio in which the y-axis divides the line segment joining the points (-4, -6) and (10,12). Also find the coordinates of the point of division.
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2013-18

Question.17 In Fig. 4, AB and CD are two diameters of a circle with centre O, which are perpendicular to each other. QB is the diameter of the smaller
circle. If QA = 7 cm, find the area of the shaded region. [Useπ= 22/7]
cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2013-61
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2013-19

Question.18 A vessel is in the form of a hemispherical bowl surmounted by a hollow cylinder of same diameter. The diameter of the hemispherical bowl is 14 cm and the total height of the vessel is 13 cm. Find the total (inner) suface area of the vessel. [Use π = 22/7 ]
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2013-20

Question.19 A wooden toy was made by scooping out a hemisphere of same radius from each end of a solid cylinder. If the height of the cylinder is 10 cm, and its base is of radius 3.5 cm, find the volume of wood in the toy. [Use π = 22/7 ]
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2013-21

Question.20 In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre.
Find: (i) the length of the arc (ii) area of the sector formed by the arc. [Use π = 22/7 ]
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2013-22

SECTION D
Questions number 21 to 31 carry 4 marks each.
Question.21 Solve the following for x:
cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2013-68
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2013-23

Question.22 Sum of the areas of two squares is 400  cm2. If the difference of their perimeters is 16 cm, find the sides of the two squares.
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2013-24

Question.23 If the sum of first 7 terms of an A.P. is 49 and that of first 17 terms is 289, find the sum of its first n terms.
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2013-25

Question.24 Prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact.
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2013-26

Question.25 In Fig. 5, l and m are two parallel tangents to a circle with centre O, touching the circle at A and B respectively. .Another tangent at C intersects the line / at D and m at E. Prove that ∠DOE = 90°.
cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2013-62
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2013-27
cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2013-28

Question.26 The angle of elevation of the top of a building from the foot of the 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 60 m high, find the height of the building.
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2013-29

Question.27 A group consists of 12 persons, of which 3 are extremely patient, other 6 are extremely honest and rest are extremely kind. A person from the group is selected at random. Assuming that each person is equally likely to be selected, find the probability of selecting a person who is
(i) extremely patient
(ii) extremely kind or honest.
Which of the above values you prefer more?
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2013-30

Question.28 The three vertices of a parallelogram ABCD are A(3, -4), B(-l, -3) and C(-6, 2). Find the coordinates of vertex D and find the area of ABCD.
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2013-31
cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2013-32

Question.29 Water is flowing through a cylindrical pipe, of internal diameter 2 cm, into a cylindrical tank of base radius 40 cm, at the rate of 0.4 m/s. Determine the rise in level of water in the tank in half an hour.
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2013-33

Question.30 A bucket open at the top, and made up of a metal sheet is in the form of a frustum of a cone. The depth of the bucket is 26 Cm and the diameters of its upper and lower circular ends are 30 cm and 10 cm respectively. Find the cost of metal sheet used in it at the rate of Rs 10 per 100 cm2. [Use π = 3.14]
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2013-34
cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2013-35

Question.31 In Fig. 6, ABC is a right-angled triangle right angled at A.
Semicircles are drawn on AB, AC and BC as diametres. Find the area of the shaded region.
cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2013-63
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2013-36
cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2013-37

SET II

Note: Except for the following questions, all the remaining questions have been asked in Set-1,
Question.4 Find the common difference of the A.P.
cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2013-69
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2013-38

Question.10 A die is tossed once. Find the probability of getting an even number or a multiple of 3.
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2013-39

Question.17 Prove that the points A(0, -1), B(-2, 3), C(6, 7) and D(8, 3) are the vertices of a rectangle ABCD?
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2013-40

Question.18 Draw a triangle PQR in which QR = 6 cm, PQ = 5 cm and ∠PQR = 60°. Then construct an-
other triangle whose sides are 3/5 times the corresponding sides of ΔPQR?
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2013-64
cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2013-41

Question.19 The «th term of an A.P. is given by (-4n + 15). Find the sum of first 20 terms of this A.P.
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2013-65
cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2013-42

Question.20 For what value of k, the roots of the quadratic equation kx(x – 2√5) + 10 = 0, are equal?
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2013-43

Question.28 Find the value of x for which the points (x, -1), (2,1) and (4, 5) are collinear.
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2013-44

Question.29 From a point P on the ground, the angle of elevation of the top of a 10m tall building is 30°. A flagstaff is fixed at the top of the building and the angle of elevation of the top of the flagstaff from P is 45°. Find the length of the flagstaff and the distance of the building from the point P. (Take √3 = 1.73)
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2013-45

Question.30 The 24th term of an AP is twice its 10th term. Show that its 72nd term is 4 times its 15th term.
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2013-46
cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2013-47

SET III

Note: Except for the following questions, all the remaining questions have been asked in Set-I and Set-II.
Question.4 Find the common difference of the A.P.
cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2013-70
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2013-48

Question.10 A card is drawn at random from a well shuffled pack of 52 playing cards. Find the probability that the drawn card is neither a jack nor an ace.
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2013-49

Question.17 For what values of k, the roots of the quadratic equation (k + 4)x2 + (k + 1)x + 1 = 0 are equal?
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2013-50

Question.18 The sum of first n terms of an AP is 3n2 + 4n . Find the 25th term of this AP.
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2013-51

Question.19 Construct a tangent to a circle of radius 4cm from a point on the concentric circle of radius 6 cm.
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2013-52

Question.20 Show that the points (-2, 3), (8, 3) and (o, 7) are the vertices of a right triangle.
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2013-53

Question.28 Find the number of terms of the A.P. -12, -9, -6,……,21. If 1 is added to each term of this
A.P., then find the sum of all terms of the A.P. thus obtained.
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2013-54
cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2013-55

Question.29 Two poles of equal heights are standing opposite each other on either side of the road, which is 80 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 60° and 30° respectively. Find the height of the poles and the distances of the point from the poles.
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2013-56

Question.30 If the area of triangle ABC formed by A(x, y), B(1, 2) and C(2,1) is 6 square units, then prove that x + y = 15 or x + y = -9.
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2013-57

CBSE Previous Year Question Papers CBSE Previous Year Question Papers Class 10 Maths

The post CBSE Previous Year Question Papers Class 10 Maths SA2 Delhi – 2013 appeared first on Learn CBSE.

CBSE Previous Year Question Papers Class 10 Maths SA2 Outside Delhi – 2014

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CBSE Previous Year Question Papers Class 10 Maths SA2 Outside Delhi – 2014

Time allowed: 3 hours                                                                                           Maximum marks: 90

GENERAL INSTRUCTIONS:

  1. All questions are compulsory.
  2. The Question Taper consists of 31 questions divided into four Sections A, B. C. and D.
  3. Section A contains 4 questions of 1 mark each. Section B contains 6 questions of 2 marks each, Section C contains 10 questions of 3 marks each and Section D contains 11 questions of 4 marks each.
  4.  Use of calculators is not permitted.

SET I

SECTION A
Questions number 1 to 4 carry 1 mark each.
Question.1 In a right triangle ABC, right-angled at B, BC = 12 cm and AB = 5 cm. Calculate the radius of the circle inscribed in the triangle (in cm).
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2014-1
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2014-2

CBSE Sample Papers Class 10 Maths

Question.2 In a family of 3 children calculate the probability of having at least one boy.
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2014-3

Question.3 ABCD is a rectangle whose three vertices are B(4, 0), C(4, 3) and D(0, 3). Calculate the length of one of its diagonals.
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2014-4

Question.4 A chord of a circle of radius 10 cm subtends a right angle at its centre. Calculate the length of the chord (in cm).
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2014-5

SECTION B
Questions number 5 to 10 carry 2 marks each.
Question.5 Find the values of p for which the quadratic equation 4x2 + px + 3 = 0 has equal roots.
Solution.

Question.6 Find the number of natural numbers between 101 and 999 which are divisible by both 2 and 5.
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2014-6

Question.7 In Figure 1, common tangents AB and CD to the two circles with centres O1 and O2 intersect at E. Prove that AB = CD.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2014-65
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2014-7

Question.8 The incircle of an isosceles triangle ABC, in which AB = AC, touches the sides BC, CA and AB at D, E and F respectively. Prove that BD = DC.
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2014-8
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2014-9

Question.9 Two different dice are tossed together. Find the probability
(i) that the number on each die is even.
(ii) that the sum of numbers appearing on the two dice is 5.
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2014-10

Question.10 If the total surface area of a solid hemisphere is 462 cm2, find its volume. [Take π=22/7]
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2014-12

SECTION C
Questions number 11 to 20 carry 3 marks each.
Question.11 Solve for
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2014-70
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2014-13

Question.12 The sum of the 5th and the 9th terms of an AP is 30. If its 25th term is three times its 8th term, find the AP.
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2014-14
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2014-15

Question.13 Construct a triangle with sides 5 cm, 5.5 cm and 6.5 cm. Now construct another triangle,
whose sides are 3/5 times the corresponding sides of the given triangle.
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2014-16

Question.14 The angle of elevation of an aeroplane from a point on the ground is 60°. After a flight of 30 seconds the angle of elevation becomes 30°. If the aeroplane is flying at a constant height of 3000 √3 m, find the speed of the aeroplane.
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2014-17

Question.15 If the point P(k – 1, 2) is equidistant from the points A(3, k) and B(k, 5), find the values of k.
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2014-18
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2014-19

Question.16. Find the ratio in which the line segment joining the points A(3, -3) and B(-2, 7) is divided by x-axis. Also find the coordinates of the point of division.
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2014-20

Question.17 In Figure 2, two concentric circles with centre O, have radii 21 cm and 42 cm. If ∠AOB = 60°, find the area of the shaded region. [Use π = 22/7 ]
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2014-66
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2014-21
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2014-22

Question.18 The largest possible sphere is carved out of a wooden solid cube of side 7 cm. Find the
volume of the wood left. [Use π = 22/7 ]
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2014-23

Question.19 Water in a canal, 6 m wide and 1.5 m deep, is flowing at a speed of 4 km/h. How much area will it irrigate in 10 minutes, if 8 cm of standing water is needed for irrigation?
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2014-24

Question.20 In Figure 3, ABCD is a trapezium of area 24.5 sq. cm. In it, AD || BC, ∠DAB = 90°, AD = 10 cm and BC = 4 cm. If ABE is a quadrant of a circle, find the area of
the shaded region. [Take π = 22/7 ]
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2014-67
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2014-25
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2014-26

SECTION D
Questions number 21 to 31 carry 4 marks each.
Question.21 Solve for x:
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2014-71
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2014-27

Question.22 In a school, students decided to plant trees in and around the school to reduce air pollution. It was decided that the number of trees, that each section of each class will plant,
will be double of the class in which they are studying. If there are 1 to 12 classes in the school and each class has two Sections, find how many trees were planted by the students. Which value is shown in this question?
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2014-28

Question.23 The angle of elevation of the top of a tower at a distance of 120 m from a point A on the ground is 45°. If the angle of elevation of the top of a flagstaff fixed at the top of the tower, at A is 60°, then find the height of the flagstaff. [Use √3 = 1.73]
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2014-29
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2014-30

Question.24 Red queens and black jacks are removed from a pack of 52 playing cards. A card is drawn at random from the remaining cards, after reshuffling them. Find the probability that the drawn card is
(i) a king (ii) of red colour (iii) a face card (iv) a queen
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2014-31

Question.25 If A(-3, 5), B(-2, -7), C(l, -8) and D(6, 3) are the vertices of a quadrilateral ABCD, find its area.
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2014-32

Question.26 A motorboat whose speed in still water is 18 km/h, takes 1 hour more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream.
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2014-33
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2014-34

Question.27 In Figure 4, PQ is a chord of length 16 cm, of a circle of radius 10 cm. The tangents at P and Q intersect at a point T. Find the length of TP.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2014-68
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2014-35
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2014-36

Question.28 Prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2014-37

Question.29  150 spherical marbles, each of diameter 1.4 cm, are dropped in a cylindrical vessel of diameter 7 cm containing some water, which are completely immersed in water. Find the rise in the level of water in the vessel.
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2014-38

Question.30 A container open at the top, is in the form of a frustum of a cone of height 24 cm with radii of its lower and upper circular ends as 8 cm and 20 cm respectively. Find the cost of milk which can completely fill the container at the rate of Rs 21 per litre. [Use π = 22/7]
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2014-39

Question.31 A tent consists of a frustum of a cone, surmounted by a cone. If the diameter of the upper and lower circular ends of the frustum be 14 m and 26 m respectively, the height of the frustum be 8 m and the slant height of the surmounted conical portion be 12 m, find the area of canvas required to make the tent. (Assume that the radii of the upper circular end of the frustum and the base of surmounted conical portion are equal).
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2014-40
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2014-41

SET II

Note: Except for the following questions, all the remaining questions have been asked in Set-I.
Question.10 Find the values of k for which the quadratic equation 9x2 – 3kx + k = 0 has equal roots.
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2014-42

Question.18 The sum of the 2nd and the 7th terms of an AP is 30. If its 15th term is 1 less than twice its 8th term, find the AP.
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2014-43

Question.19 Draw a line segment AB of length 8 cm. Taking A as centre, draw a circle of radius 4 cm and taking B as centre, draw another circle of radius 3 cm. Construct tangents to each circle from the centre of the other circle.
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2014-44
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2014-45

Question.20 Prove that the diagonals of a rectangle ABCD, with vertices A(2, -1), B(5, -1), C(5, 6) and D(2, 6), are equal and bisect each other.
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2014-46

Question.27
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2014-72
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2014-47
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2014-48

Question.28 All the red face cards are removed from a pack of 52 playing cards. A card is drawn at random from the remaining cards, after reshuffling them. Find the probability that the drawn card is
(i) of red colour (ii) a queen (iii) an ace (iv) a face card
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2014-49

Question.29 A(4, -6), B(3, -2) and C(5, 2) are the vertices of a ΔABC and AD is its median. Prove that the median AD divides ΔABC into two triangles of equal areas.
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2014-50

Question.30 Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2014-51

SET III

Note: Except for the following questions, all the remaining questions have been asked in Set-I and Set-11.
Question.10 Find the value of p so that the quadratic equation px (x – 3) + 9 = 0 has equal roots.
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2014-52

Question.18 The sum of the first seven terms of an AP is 182. If its 4th and the 17th terms are in the ratio 1 : 5, find the AP.
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2014-53
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2014-54

Question.19 From the top of a 60 m high building, the angles of depression of the top and the bottom of a tower are 45° and 60° respectively. Find the height of the tower. [Take √3 = 1.73]
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2014-55

Question.20 Find a point P on the y-axis which is equidistant from the points A(4, 8) and B(-6, 6). Also find the distance AP.
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2014-56
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2014-57

Question.27
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2014-73
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2014-58

Question.28 Five cards—the ten, jack, queen, king and ace of diamonds, are well shuffled with their faces downwards. One card is then picked up at random.
(a) What is the probability that the drawn card is the queen?
(b) If the queen is drawn and put aside, and a second card is drawn, find the probability
that the second card is (i) an ace (ii) a queen.
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2014-59

Question.29 If A(4, 2), B(7, 6) and C(l, 4) are the vertices of a ΔABC and AD is its median, prove that the median AD divides ΔABC into two triangles of equal areas.
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2014-60
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2014-61

Question.30 In Figure 4, a triangle ABC is drawn to circumscribe a circle of radius 4 cm, such that the segments BD and DC are of lengths 8 cm and 6 cm respectively. Find the sides AB and AC.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2014-69
Solution.
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2014-62
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2014-63
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2014-64

CBSE Previous Year Question Papers CBSE Previous Year Question Papers Class 10 Maths

The post CBSE Previous Year Question Papers Class 10 Maths SA2 Outside Delhi – 2014 appeared first on Learn CBSE.


CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 8

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CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 8

Section A

1. Without determining the roots, comment upon the nature of the roots of the following quadratic equation:

7x2 – 6x + 1 = 0
cbse-sample-papers-for-class-10-sa2-maths-solved-2016-set-8-2

Download Formula Book for Class 10 Maths and Science CBSE Sample Papers for Class 10 Maths

3. In the given figure, if O is the centre of a circle. AB is a chord and the tangent AC at A makes an angle of 65° with AB, then find Angle AOB.
cbse-sample-papers-for-class-10-sa2-maths-solved-2016-set-8-3

4.A letter of English alphabet is chosen at random. Find the probability that the letter is a consonant.

Section B

5. Reciprocal of a number when subtracted from the number equals to -24/5 . Find the number.

6.6th term of the Arithmetic Progression is zero. Prove that 21st term is triple of 11th term.

7. In the given figure, PT is a tangent to the circle with centre O. If QR = 6 cm, PR = 8 cm and

Triangle PRQ ~ Triangle TPO, OT/ PT
cbse-sample-papers-for-class-10-sa2-maths-solved-2016-set-8-7

8. Prove that the line segment joining the points of contact of two parallel tangents to a circle is a diameter of the circle.

9. If (x, y) is equidistant from (7, -2) and (3, 1) express x in terms of y.

10. The length of line segment joining the points A(2, -3) and B(10, y) is 10 units. If A and B are in same quadrant, find the value of y.

Section C

11. Find the values of p so that the quadratic equation: x2 – 2p(3x – 7) – 2x + 21 = 0 has equal roots.

12. The sum of three numbers in AP is 3 and their product is -35. Find the numbers.

13. An aeroplane when flying at a height of 6 km from the ground passes vertically above another plane at an instant when the angle of elevation of the two planes from the same point on the ground are 60° and 30° respectively. Find the vertical distance between the two aeroplanes at that instant.

14. The inner circumference of a circular track is  880 m  and the track is 28    m wide. Calculate the cost of   levelling the track at the rate of 50 paise per square  metre.  Also find the cost of fencing the outer circle at  the rate of Rs 10 per metre. (Take, pie= 22/7) .

15. The interior of a building is in the form of a right circular cylinder of radius 7 m and height 6 m surmounted
by a right circular cone of the same radius and of   vertical angle 60°.    Find the cost of painting the building
from inside at the rate of Rs 30 per m2 . (Take, pie = 22/7)

16.An iron pillar has some part in the form of a right circular cylinder and the remaining in the form of a right circular cone. The radius of the base of each cone and cylinder is 16 cm. The cylindrical part is 480 cm high and the conical part is 72 cm high. Find the weight of the pillar if 1 cubic cm of iron weigh 7.5 g.

17. Find the number of bricks, each measuring 25 cm x 12.5 cm x 7.5 cm required to construct a wall 12 m long
10 m high and 0.5 m thick, while the cement and sand mixture occupies 1/20  of the volume of the wall.

18. The internal radii of the ends of a bucket full of milk and of internal height 32 cm are 28 cm and 14 cm. If this milk is poured into a hemispherical vessel, the vessel is completely filled. Find the internal diameter of the hemispherical vessel.

19.If the points A(l, -2), B(2, 3), C(x, 2) and D(-4, -3) form a parallelogram, find the value of x and height of parallelogram taking BC as base.

20.A bag contains 20 red balls and x blue balls. If one ball is drawn from the bag, what is the probability that it is
(i)  red? (ii) blue?
If the Probability of drawing red balls is 1/3 the probability of drawing blue balls determine the value of x.

Section D

cbse-sample-papers-for-class-10-sa2-maths-solved-2016-set-8-21

22. A housewife used to spend Rs. 120 per month on the purchase of wheat at the prevailing price. When the price rose by Rs 2 per kg she found that for the same amount she could purchase 2 kg less. Find the new price per kg of the wheat.

23. Malini gets pocket money from her father everyday. Out of the pocket money, she saves Rs 3 on first day and on each succeeding day she increases her saving by 50 paise. At the end of every month, Malini purchases some books, pens and notebooks from the amount that she saved and distribute these items to needy students in her school.
(i) Find the amount saved by Malini on 10th day.
(ii) Find the total amount saved by Malini in 30 days.
(iii) What values are depicted by the act of Malini?

24.A boy standing on a horizontal plane finds a kite flying at a distance of 100 m from him at an elevation of 30°. A girl standing on the roof of 20 m high building finds the angle of elevation of the same kite to be 45°. Both the boys and girls are on opposite side of the kite. Find the distance of the kite from the girl.

25.Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.

26.In the given figure, PT is a tangent and PAB is a secant to a circle with centre O. ON is perpendicular to chord AB. Prove that:
(0 PA • PB = PN2 – AN2 (ii) PN2 – AN2 = OP2 – OT2

cbse-sample-papers-for-class-10-sa2-maths-solved-2016-set-8-26

27.Draw two concentric circles of radius 3 cm and 6 cm. Taking a point on the outer circle, construct the pair of tangents to the other circle.

28.In each corner of a triangular field a horse is tethered with a rope of length 7 m. Sides of the triangle are 60 m, 80 m and 100 m.
(i) Find the area of the field over which horses can graze.
(ii) Area of the field which can not be grazed by the horses.

29.A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank in his field, which is 10 m in diameter and 2 m deep. If water flows through the pipe at the rate of 6 km/h, in how much time will the tank be filled?

30.If two opposite vertices of a square are (5, 4) and (1, -6) then find the coordinates of its remaining two vertices.

31.Two dice are thrown together. Find the probability that the product of the numbers on the top of two dice is
(i) prime number, (ii) perfect square, (iii) multiple of 4, (iv) more than 36.

The post CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 8 appeared first on Learn CBSE.

CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 11

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CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 11

                                                                Section A

1.Find the value of p which will make the product of 2p – 5 and p – 4 equal in value to p + 8.

2.Which term of the AP 21, 18, 15, … , is zero?

Download Formula Book for Class 10 Maths and Science CBSE Sample Papers for Class 10 Maths

3.Find a relation between x and y such that the point (x, y) is equidistant from the points (7, 1) and (3, 5).

4.If the circumference of a circle exceeds the diameter by pi units, then find the diameter of the circle.

                                                              Section B

CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 11-33

6.Which term of the sequence 25, 22, 19, … is the first negative term?

7.The incircle of an isosceles triangle ABC, with AB = AC, touches the sides AB, BC and CA at D, E and F respectively. Prove that E bisects BC.

8.Find the probability of getting 53 Mondays in a leap year.

CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 11-34

10.A solid cube is cut into eight cubes of equal volumes. Find the ratio of the total surface area of the given cube and that of one small cube.

CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 11-35

                                                                          Section C

12.The cost price of an article is Rs x and is sold at a profit of (x + 20)%. Find the cost price of the article, if its selling price is Rs (1.4x – 48).

13.Find the sum of all the three-digit numbers each of which leaves a remainder 3, when divided by 7.
14.Construct an isosceles triangle whose base is 6 cm and altitude 5 cm and then another triangle whose sides are 4/3 times the corresponding sides of the isosceles triangle.

15.All jacks, queens, kings and aces are removed from a pack of 52 cards. The remaining cards are well shuffled and then a card is drawn from it. Find the probability that the drawn card is
(i) red face card (ii) a card of spade.

16.A child’s game has 12 triangles of which 4 are blue and rest are green. 8 rectangles of which 5 are green and rest are blue, 10 rhombus of which 7 are blue and rest are green. One piece is lost at random. Find the probability that it is
(i) a rectangle
(it) a triangle of green colour
(iii)a rhombus of blue colour.

17.If P(5, -7), Q(4, 7) and R(6, -3) are the vertices of triangle PQR, M is mid point of QR and A is a point on PM joined PA/PM = 2, find the coordinates of A.

18.If (a, 0), (0, b) and (3, 2) are collinear, show that 2a + 3b – ab = 0

CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 11-36

20.A cone of height 48 cm has a curved surface area of 2200 cm2. Find its volume.[use pi=22/7]

                                                                            Section D
21. Solve for x :(2x/x – 3 )+( 1/ 2x + 3) +(3x + 9/(x – 3) (2x + 3))=0 x not equal to 3,-3/2

22.Along a road lies an odd number of stones placed at intervals of 20 metres. These stones have to be assembled around the middle stone. A person can carry only one stone at a time. A man started the job with one of the end stones by carrying them in succession. In carrying all the stones he covered a distance of 6 km. Find the number of stones.

23.If a hexagon ABCDEF circumscribes a circle, prove that AB + CD + EF = BC + DE + FA.

24.QR is a tangent at Q. PR || AQ where AQ is a chord through A and P is a centre, the end point of the diameter AB. Prove that BR is tangent at B.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 11-37

25.In figure tangents PQ and PR are drawn to a circle such that RPQ = 30°. A chord RS is drawn parallel to the tangent PQ. Find triangle RQS.
[Hint : Draw a line through Q perpendicular to QP.]
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 11-38

26.At the foot of a mountain, the elevation of its summit is 45°. After ascending 1000 m towards the mountain up a slope of 30° inclination, the elevation is found to be 60°. Find the height of the mountain.

27.The lower window of a house is at a height of 2 m above the ground and its upper window is 4 m vertically above the lower window. At certian instant the angles of elevation of a balloon from these windows are observed to be 60° and 30° respectively. Find the height of the balloon above the ground.

28.Coordinates of houses of Sonu and Labhoo are (7, 3) and (4, 3) respectively. The coordinates of their school are (2, 2). If both leave their house at the same time in the morning and also reach school in time then (a) who travel faster and (b) which value is depicted in the question?

29.From a thin metallic piece, in the shape of a trapezium ABCD in which AB || CD and ZBCD = 90°, a quarter circle BFEC is removed (See figure). Given AB = BC = 3.5 cm and DE = 2 cm, calculate the area of the remaining(shaded) part of the metal sheet. [Use pi = 22/7]
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 11-39

30.The barrel of a fountain-pen, cylindrical in shape, is 7 cm long and 5 mm in diameter. A full barrel of ink in the pen is used up on writing 330 words on an average. How many words would use up a bottle of ink containing one fifth of a litre?

31.The height of a cone is 30 cm. A small cone is cut off at the top by a plane parallel to the base. If its volume be 1/27 of the volume of the given cone at what height above the base is the section made?

Answers

                                                                Section A

1.Find the value of p which will make the product of 2p – 5 and p – 4 equal in value to p + 8.
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 11-1

2.Which term of the AP 21, 18, 15, … , is zero?
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 11-2

3.Find a relation between x and y such that the point (x, y) is equidistant from the points (7, 1) and (3, 5).
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 11-3
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 11-3.a

4.If the circumference of a circle exceeds the diameter by pi units, then find the diameter of the circle.
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 11-4

                                                              Section B

CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 11-33
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 11-5

6.Which term of the sequence 25, 22, 19, … is the first negative term?
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 11-6

7.The incircle of an isosceles triangle ABC, with AB = AC, touches the sides AB, BC and CA at D, E and F respectively. Prove that E bisects BC.
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 11-7jpg_Page1

8.Find the probability of getting 53 Mondays in a leap year.
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 11-8

CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 11-34
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 11-9

10.A solid cube is cut into eight cubes of equal volumes. Find the ratio of the total surface area of the given cube and that of one small cube.
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 11-10

CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 11-35
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 11-32

                                                                          Section C

12.The cost price of an article is Rs x and is sold at a profit of (x + 20)%. Find the cost price of the article, if its selling price is Rs (1.4x – 48).
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 11-12
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 11-12.a

13.Find the sum of all the three-digit numbers each of which leaves a remainder 3, when divided by 7.
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 11-13

14.Construct an isosceles triangle whose base is 6 cm and altitude 5 cm and then another triangle whose sides are 4/3 times the corresponding sides of the isosceles triangle.
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 11-14

15.All jacks, queens, kings and aces are removed from a pack of 52 cards. The remaining cards are well shuffled and then a card is drawn from it. Find the probability that the drawn card is
(i) red face card (ii) a card of spade.
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 11-15

16.A child’s game has 12 triangles of which 4 are blue and rest are green. 8 rectangles of which 5 are green and rest are blue, 10 rhombus of which 7 are blue and rest are green. One piece is lost at random. Find the probability that it is
(i) a rectangle
(it) a triangle of green colour
(iii)a rhombus of blue colour.
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 11-16

17.If P(5, -7), Q(4, 7) and R(6, -3) are the vertices of triangle PQR, M is mid point of QR and A is a point on PM joined PA/PM = 2, find the coordinates of A.
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 11-17

18.If (a, 0), (0, b) and (3, 2) are collinear, show that 2a + 3b – ab = 0
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 11-18

CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 11-36
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 11-19
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 11-19.a

20.A cone of height 48 cm has a curved surface area of 2200 cm2. Find its volume.[use pi=22/7]
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 11-q-2jpg_Page1

                                                                            Section D
21. Solve for x :((2x/x) – 3 )+( (1/ 2x) + 3) +((3x + 9)/(x – 3) (2x + 3))=0 x not equal to 3,-3/2
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 11-21

22.Along a road lies an odd number of stones placed at intervals of 20 metres. These stones have to be assembled around the middle stone. A person can carry only one stone at a time. A man started the job with one of the end stones by carrying them in succession. In carrying all the stones he covered a distance of 6 km. Find the number of stones.
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 11-22.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 11-22.a

23.If a hexagon ABCDEF circumscribes a circle, prove that AB + CD + EF = BC + DE + FA.
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 11-23

24.QR is a tangent at Q. PR || AQ where AQ is a chord through A and P is a centre, the end point of the diameter AB. Prove that BR is tangent at B.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 11-37
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 11-24

25.In figure tangents PQ and PR are drawn to a circle such that RPQ = 30°. A chord RS is drawn parallel to the tangent PQ. Find triangle RQS.
[Hint : Draw a line through Q perpendicular to QP.]
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 11-38
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 11-25

26.At the foot of a mountain, the elevation of its summit is 45°. After ascending 1000 m towards the mountain up a slope of 30° inclination, the elevation is found to be 60°. Find the height of the mountain.
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 11-26
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 11-26.a
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 11-26.b

27.The lower window of a house is at a height of 2 m above the ground and its upper window is 4 m vertically above the lower window. At certian instant the angles of elevation of a balloon from these windows are observed to be 60° and 30° respectively. Find the height of the balloon above the ground.
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 11-27
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 11-27.a

28.Coordinates of houses of Sonu and Labhoo are (7, 3) and (4, 3) respectively. The coordinates of their school are (2, 2). If both leave their house at the same time in the morning and also reach school in time then (a) who travel faster and (b) which value is depicted in the question?
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 11-28

29.From a thin metallic piece, in the shape of a trapezium ABCD in which AB || CD and ZBCD = 90°, a quarter circle BFEC is removed (See figure). Given AB = BC = 3.5 cm and DE = 2 cm, calculate the area of the remaining(shaded) part of the metal sheet. [Use pi = 22/7]
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 11-39
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 11-29
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 11-29.a

30.The barrel of a fountain-pen, cylindrical in shape, is 7 cm long and 5 mm in diameter. A full barrel of ink in the pen is used up on writing 330 words on an average. How many words would use up a bottle of ink containing one fifth of a litre?
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 11-30

31.The height of a cone is 30 cm. A small cone is cut off at the top by a plane parallel to the base. If its volume be 1/27 of the volume of the given cone at what height above the base is the section made?
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 11-31

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CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 12

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CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 12

                                                                 Section A

CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 12-1

2.Find the length of the shadow of a tree 18 m long when the Sun’s angle of elevation is 45°.

Download Formula Book for Class 10 Maths and Science CBSE Sample Papers for Class 10 Maths

3.If two tangents inclined at an angle of 120° are drawn to a circle of radius 5 cm, then find the length of each tangent.

4.A pair of die is thrown. Find the probability of getting sum of numbers which is perfect square and divisible by 5.

                                                           Section B

5.Solve for x: a/x-a+b/x-b——— -2; x not equal to a.b

6.Which term of the AP: 125, 121, 117, … is 1st negative term?

7.In the given figure, PQR is the tangent to a circle at Q whose centre is O. AB is a chord parallel to PR and BOR = 60°. Find triangle AQB.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 12-2

8.In the given figure, AC is diameter of the circle with centre O. PAQ is the tangent to the circle at A. If AB || CD and ZBAQ = 65°, find triangle DCA.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 12-3

9.Find a relation between x and y if area of the triangle formed by the points (x, y), (1, 2) and (7,0) is 5 sq units.

10.If the point P(2, 1) lies on the line segment joining the points A(4,2) and B(8,4) then find AP/AB

CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 12-4

                                                            Section C
12.The sum of fourth and the ninth terms of an AP is 46 and their product is 465. Find the sum of first 10 terms of this AP.

13.The angle of elevation of the top of a building from the foot of the 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.

14.In figure ABC is a right angled triangle right angled at A. Semicircles are drawn on AB, AC and BC as diameters. If AB = 6 cm, AC = 8 cm, find the area of the shaded region.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 12-5

15.A wooden toy rocket is in the shape of a cone mounted on a cylinder, as shown in figure. The height of the entire rocket is 52 cm while the height of the conical part is 12 cm. The base of the conical portion has a diameter of 10 cm, while the base diameter of the cylindrical portion is 6 cm. If the conical portion is to be painted, red and the cylindrical portion green, find the area of the rocket painted with each of these colours. (Take, pi = 3.14)
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 12-6

16.A building is in the form of a cylinder surmounted by a hemispherical dome. The base diameter of the dome is equal to 2/3 of the total height of the building. Find the surface area of the building, if it contains 2816/21 of air.

17.Solid sphere of diameter 12 cm are dropped into a cylindrical vessel containing some water and are fully submerged. If the diameter of the vessel is 36 cm and the water rises by 80 cm, find the number of solid spheres dropped in the water.

18.The height of a cone is 60 cm. A small cone is cut off at the top by a plane parallel to the base. If its volume is 1/27 of the volume of the given cone, at what height above the base is the section made?

19.ABCD is a rectangle formed by the points A(-l, -1), B(-l, 4), C(5, 4) and D(5, -1). P, Q, R and S are the mid-points of AB, BC, CD and AD respectively. Is the quadrilateral PQRS is a square or rhombus? Justify your answer.

20.What is the probability that an year will have 53 Tuesdays?

                                                                Section D
21.A swimming pool is filled with three pipes with uniform flow of water. The first two pipes operating simultaneously fill the pool in the same time during which the pool is filled by the third pipe alone. The second pipe fills the pool 5 hrs faster than the third pipe and 4 hrs slower than the third pipe. Find the time required by each pipe to fill the pool separately.

22.If the roots of the quadratic equation: p(q – r)x2 + q(r – p)x + r(p – q) = 0 are equal, show that:1/p+ 1/r = 2/q

23.A contractor employed 150 workers to finish a piece of work in a certain fixed number of days. On the first day, all 150 workers worked. He dropped four workers on the second day, four more workers were dropped on the third day and so on. In this way work got finished in 8 more days. Find the number of days in which work was to be completed originally.

CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 12-7

25.The tangent at any point of a circle is perpendicular to the radius through point of contact. Prove it.

26. A contractor was awarded to construct a vertical pillar at a horizontal distance of 200 m from a fixed point. It was decided that angle of elevation of the top of the complete pillar from that point to be 60°. Contractor
finished the job by making a pillar such that the angle of elevation of its top was 45°.
(i) Find the height of the pillar to be increased as per the terms of contract.
(ii) Contractor demands full payment for this work
(a) Is he justified?
(b) Which ‘value’ is he lacking?

27.Draw a right triangle ABC in which AB = 5 cm, BC = 7 cm, B = 90°. Through B, draw BD perpendicular AC. Then draw a circle passing through B, C and D. Construct a pair of tangents to this circle from A.

28.Water is pumped from a sump (an underground tank) to an overhead tank in the shape of cylinder. Sump is in the shape of a cuboid of dimensions 4mx3mx2m. The overhead tank has radius 60 cm and height 80 cm. Find the height of water left in the sump after the overhead tank has been completely filled with water from the sump (assume sump was completely filled before water was pumped to overhead tank). Also compare the capacity of tank with that of sump. (Take pi = 3.14)

29.The area of an equilateral AABC is 17320.5 cm2. With each vertex of the triangle as centre, a circle is drawn with radius equal to half the length of side of the triangle. Find the area of the triangle which is uncommon with circles. (Take pi = 3.14, root 3= 1.73205)

30.Find the coordinates of the point equidistant from three given points A(5, 1), B(-3, -7) and (7, -1).

31.At a fete, cards bearing numbers 1 to 1000, one number on one card are put in a box. Each player select one card at random and that card is not replaced. If the selected card has a perfect square greater than 500, the player wins a prize. What is the probability that: (0 the first player wins a prize? (//) second player wins a prize, if the first has won?

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CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 13

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CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 13

                                                                             SECTION A

1.The sum of the ages of two friends is 20. Four years ago, the product of their ages in years was 48. Is it possible to determine their present ages?

CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 13-1.pdf

Download Formula Book for Class 10 Maths and Science CBSE Sample Papers for Class 10 Maths

3. In the given figure, AB, AC and AD are tangents to the circles with centre O and O’. If AD = 10 cm, find AB
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 13-2

4.The probability of getting a defective pen from a lot of 500 pens is 1/25 Find the number of defective pensin the lot.

                                                             SECTION B
5.For what value of k, given equation has real and equal roots: (k – l)x2 – 2(k – l)x +1 = 0?

6.In the given figure, there are two concentric circles with centre O and of radii 5 cm and 3 cm. From an external point P, tangents PA and PB are drawn to these circles. If AP = 12 cm, find the length of BP
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 13-3

7.Which term of the Arithmetic Progression 3, 10, 17,… will be 84 more than its 13th term?

8.Prove that tangents drawn at the ends of a diameter of a circle are parallel.

9.Find the value of k, if the distance between the points (2, k) and (4, 3) is 8.

10.Find the coordinates of a point P which lies on the line segment joining the points A (-2, 0) and B(0, 8)such that AP = 1/4 AB.

                                                                  SECTION C

CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 13-4

12.A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle 30° with it. The distance between the foot of the tree to the point where the top touches the ground is 8 m. Find the height of the tree.

13.On the first day of the strike of doctors in a hospital, the attendance at its OPD was 1040 patients. As the strike continues, the attendance declined by 80 patients every day. Find from which day of the strike the OPD would have no patient.

14.A juice seller serves his customers using a glass as shown in figure. The inner diameter of the cylindrical glass is 5 cm, but the bottom of the glass has a hemispherical raised portion which reduces the capacity of the glass. If the height of the glass is 10 cm, find the apparent capacity of the glass and its actual capacity. (Use n = 3.14)
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 13-5

CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 13-6

16.A solid is in the form of a right circular cone mounted on a hemisphere. The radius of the hemisphere is 4.2 cm and height of the cone is 8 cm. The solid is placed in a cylindrical tub full of water in such a way that whole solid is submerged in the water. If the radius of the cylinder is 10 cm and its height is 19.6 cm, find the volume of water left in the cylindrical tub. (Use pi =22/7)

17.An equilateral triangle has two vertices at the points (3, 4) and (- 2, 3). Find the coordinates of the third vertex.

18.A hemispherical bowl of internal radius of 30 cm contains a liquid. The liquid is to be filled into cylindrical shaped bottles of diameter 10 cm and height 12 cm. How many bottles are necessary to empty the bowl, if 10% of the liquid is wasted during the process of filling the bottles?

19.The diameter of internal and external surfaces of a hollow spherical vessel are 6 cm and 10 cm respectively.If it is melted and recast into a solid cylinder of height 2~ cm, find the diameter of the cylinder.

20.In the given figure, the shape of the top of a table in a restaurant is that of a sector of a circle with centre O and BOD = 90°, if BO = OD = 60 cm find :
(i)the area of the top of the table
(ii)the perimeter of the table top. (Take pi =3.14)
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 13-7

                                                                  SECTION D

21.Students of class ‘X’ collected Rs 9000. They wanted to divide it equally among a certain number of students residing in slum areas. When they started distributing the amount, 20 more students from nearby slum also joined. Now each student got Rs 160 less.
(a)Find the original number of students living in the slum.
(b)Which value is depicted by students of class X?

22.A spiral is made up of successive semicircles, with centres alternately at A and B, starting with centre at A, of radii 0.5 cm, 1.0 cm, 1.5 cm, 2.0 cm, … . What is the total length of such a spiral made up of thirteen consecutive semicircle?(taken pi=22/7)
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 13-8

23.O is the centre of a circle. PA and PB are tangents to the circle from a point P. Prove that (i) PAOB is a cyclic quadrilateral (ii) PO is the bisector of angle APB (iii) angle OAB = angle OPA.

24.QR is a tangent at Q. PR || AQ, where AQ is a chord through A and P is the centre of the circle with the end point of the diameter AB. Prove that BR is tangent at B.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 13-9

25.Cards numbered 2, 3, 4, 26 are put in a box and mixed thoroughly. One person draws a card from the box. Find the probability that number on the card is (i) even (ii) prime (iii) a perfect square (iv) divisible by 2 or 5.

26.The angle of elevation of a cloud from a point 200 m above a lake is 30° and the angle of depression of its reflection in the lake is 60°. Find the height of the cloud above the lake.

27.Draw a right triangle in which the sides (other than hypotenuse) are of lengths 6 cm and 8 cm. Then construct another triangle whose sides are 4/3 times the corresponding sides of the given triangle.

28.A(6, 1), B(8, 2) and C(9, 4) are three vertices of a parallelogram ABCD. If E is the mid-point of DC, find the area of triangle ADE.

CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 13-10

30.A tent is in the shape of a cylinder surmounted by a conical top. If the height and diameter of the cylindrical part are 2.1 m and 4 m respectively and the slant height of the top is 2.8 m, find the area of the canvas used for making the tent. Find the cost of the canvas of the tent at the rate of Rs 500 per m2. Also, find the volume of air enclosed in the tent.

31.The area of an equilateral triangle is 17320.5 cm2. With each vertex of the triangle as centre, a circle is described with radius equal to half the length of the side of the triangle. Find the area of the triangle not included in the circle.

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CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 9

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CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 9

                                                               Section A

1.If 2 is a root of the equation x2 + bx + 12 = 0 and the equation has equal roots, find the value of b.

CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 9-33

CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 9-34

Download Formula Book for Class 10 Maths and Science CBSE Sample Papers for Class 10 Maths

4.If the perimeter and the area of a circle are numerically equal, then find the radius of the circle.

                                                                 Section B

5.If sin a and cos a are the roots of the equation ax2 + bx + c = 0, then prove that a2 + 2ac = b2.

6.Determine k so that 3k – 3, 2k2 – 5k + 7 and Ak + 2 are the three consecutive terms of an AP.

7.In figure, two tangents PA and PB are drawn to a circle with centre O from an external point P. Prove that triangle APB = 2 triangle OAB.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 9-36

8.Ace, Jack and queen of diamonds are removed from a deck of 52 playing cards. One card is selected from the reamaining cards. Find the probability of getting a card of diamond.

9.In given figure, PQR is a triangle right angled at P, with PQ = 21 cm and PR = 42 cm with the vertices P, Q and R as centres, arcs are drawn each of radius 10 cm. Find the area of the shaded region. (Use pi = 3.14)
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 9-37

10.A cone and a sphere have equal radii and equal volume. What is the ratio of the diameter of the sphere to the height of the cone?
  Section C
11.At t minutes past 2 p.m. the time needed by the minutes hand of a clock to show 3 p.m. was found to be 3 minutes less than t2/4 minutes. Find t.

12.Solve for x :6X2 – 6(a + b)x + (4/3 a2+10/3ab+4/3 b2)= 0

13.The sum of n terms of an AP whose first term is 6 and common difference is 40 is equal to the sum of 2n terms of another AP whose first term is 40 and common difference is 6. Find n.

14.Draw a pair of tangents to a circle of radius 4 cm which are inclined to each other at an angle of 45°.

15.Cards bearing numbers 1, 4, 7, 10,….58 are kept in a bag. A card is drawn at random from the bag. Find
the probability of getting a card bearing
(i)a prime number less than 18.
(ii)a number divisible by 4.

16.Six cards – ace, jack, queen, king, ten and nine of spade are well shuffled with their face downwards. One card is then picked up at random.
(i) What is the probability that the card is an ace?
(ii) If the ace is drawn and put aside, what is the probability that the second card picked up is
(a) a jack,(b) an ace.
.
17.If P is a point lying on the line segment QR, joining Q(-l, -1) and R(4, -1) such that PQ = 3/7 QR, then find the coordinates of P.

18.For what value of k, (k > 0) the area of triangle with vertices (k, 1), (3k, 1) and (2, 4) is 6 sq. units.

19.A bucket is raised from a well by means of a rope which is wound round a wheel of diameter 154 cm. If bucket ascends in 2 minutes 56 seconds with a uniform speed of 2.2 m/s, then calculate the number of
complete revolutions the wheel makes in raising the bucket. (Use pi = 22/7)

20.A solid cone of base radius 30 cm is cut into two parts through the mid-point of its height by a plane parallel to its base. Find the ratio of the volumes of the two parts of the cone.

                                                                 Section D
21.A man bought a certain number of toys for Rs 180; he kept one for his own use and sold the rest for one rupee each more than he gave for them, besides getting his own toy for nothing he made a profit of Rs 10. Find the number of toys.

22.A ladder has rungs 50 cm apart. The rungs decrease uniformly in length from 90 cm at the bottom to 50 cm at the top. If top and bottom rungs are 5 m apart, what is the length of the wood required for the rungs?

23.ABC is a right-angled triangle, right angled at A. A circle is inscribed in it. The lengths of two sides containing the right angle are 24 cm and 10 cm. Find the radius of the incircle.

24.In figure the common tangent, AB and CD to two circles with centres O and O’ intersect at E.Prove that the points O, E and O’ are collinear.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 9-38

25.In the given figure, the diameters of two wheels have measures 4 cm and 2 cm. Determine the lengths of the belts AD and BC that pass around the wheels if it is given that belts cross each other at right angles.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 9-39

26.A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car at an angle of depression of 30°, which is approaching the foot of the tower with a uniform speed, 6 seconds later the angle of depression of the car is found to be 60°. Find the time taken by the car to reach the foot of the tower from this point.

27. A fire in a building B is reported on telephone to two fire stations P and Q, 20 km apart from each other on a straight road. P observes that the fire is at an angle of 60° to the road and Q observes that it is at an angle of 45° to the road. ‘
(a) Which station should send its team and how much will this team have to travel?
(b) What according to you, are the values displayed by the teams at fire stations P and Q?

28.The opposite angular points of a square are (2, 0) and (5, 1). Find the remaining points.

29.In the given figure, three circles of radius 2 cm touch one another externally. These circles are circumscribed by a circle of radius R cm. Find the value of R and the area of the shaded region.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 9-40

30.The area of the base of a cone is 770 cm2 and the curved surface area is 814 cm2. Find the volume of the cone.

31.An agricultural field is in the form of a rectangle of length 20 m and width 14 m. A pit 6 m long, 3 m wide and 2.5 m deep is dug in the corner of the field and the earth taken out of the pit is spread uniformly over the remaining area of the field. Find the extent to which the level of the field has been raised.

Answers

                                                                Section A

1.If 2 is a root of the equation x2 + bx + 12 = 0 and the equation has equal roots, find the value of b.
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 9-1

CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 9-33
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 9-2

CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 9-34
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 9-3

4.If the perimeter and the area of a circle are numerically equal, then find the radius of the circle.
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 9-4

                                                                 Section B

5.If sin a and cos a are the roots of the equation ax2 + bx + c = 0, then prove that a2 + 2ac = b2.
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 9-5

6.Determine k so that 3k – 3, 2k2 – 5k + 7 and Ak + 2 are the three consecutive terms of an AP.
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 9-6

7.In figure, two tangents PA and PB are drawn to a circle with centre O from an external point P. Prove that triangle APB = 2 triangle OAB.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 9-36
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 9-7

8.Ace, Jack and queen of diamonds are removed from a deck of 52 playing cards. One card is selected from the reamaining cards. Find the probability of getting a card of diamond.
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 9-8

9.In given figure, PQR is a triangle right angled at P, with PQ = 21 cm and PR = 42 cm with the vertices P, Q and R as centres, arcs are drawn each of radius 10 cm. Find the area of the shaded region. (Use pi = 3.14)
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 9-37
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 9-32

10.A cone and a sphere have equal radii and equal volume. What is the ratio of the diameter of the sphere to the height of the cone?
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 9-10
                                                                              Section C
11.At t minutes past 2 p.m. the time needed by the minutes hand of a clock to show 3 p.m. was found to be 3 minutes less than t2/4 minutes. Find t.
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 9-11

12.Solve for x :6X2 – 6(a + b)x + ((4/3) a2+(10/3)ab+(4/3) b2)= 0
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 9-12

13.The sum of n terms of an AP whose first term is 6 and common difference is 40 is equal to the sum of 2n terms of another AP whose first term is 40 and common difference is 6. Find n.
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 9-13

14.Draw a pair of tangents to a circle of radius 4 cm which are inclined to each other at an angle of 45°.
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 9-14

15.Cards bearing numbers 1, 4, 7, 10,….58 are kept in a bag. A card is drawn at random from the bag. Find
the probability of getting a card bearing
(i)a prime number less than 18.
(ii)a number divisible by 4.
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 9-15
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 9-15.a

16.Six cards – ace, jack, queen, king, ten and nine of spade are well shuffled with their face downwards. One card is then picked up at random.
(i) What is the probability that the card is an ace?
(ii) If the ace is drawn and put aside, what is the probability that the second card picked up is
(a) a jack,(b) an ace.
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 9-16

17.If P is a point lying on the line segment QR, joining Q(-l, -1) and R(4, -1) such that PQ = 3/7 QR, then find the coordinates of P.
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 9-17

18.For what value of k, (k > 0) the area of triangle with vertices (k, 1), (3k, 1) and (2, 4) is 6 sq. units.
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 9-18

19.A bucket is raised from a well by means of a rope which is wound round a wheel of diameter 154 cm. If bucket ascends in 2 minutes 56 seconds with a uniform speed of 2.2 m/s, then calculate the number of complete revolutions the wheel makes in raising the bucket. (Use pi = 22/7)
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 9-19

20.A solid cone of base radius 30 cm is cut into two parts through the mid-point of its height by a plane parallel to its base. Find the ratio of the volumes of the two parts of the cone.
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 9-20

                                                                 Section D
21.A man bought a certain number of toys for Rs 180; he kept one for his own use and sold the rest for one rupee each more than he gave for them, besides getting his own toy for nothing he made a profit of Rs 10. Find the number of toys.
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 9-21
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 9-45

22.A ladder has rungs 50 cm apart. The rungs decrease uniformly in length from 90 cm at the bottom to 50 cm at the top. If top and bottom rungs are 5 m apart, what is the length of the wood required for the rungs?
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 9-22

23.ABC is a right-angled triangle, right angled at A. A circle is inscribed in it. The lengths of two sides containing the right angle are 24 cm and 10 cm. Find the radius of the in circle.
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 9-23

24.In figure the common tangent, AB and CD to two circles with centres O and O’ intersect at E.Prove that the points O, E and O’ are collinear.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 9-38
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 9-24

25.In the given figure, the diameters of two wheels have measures 4 cm and 2 cm. Determine the lengths of the belts AD and BC that pass around the wheels if it is given that belts cross each other at right angles.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 9-39
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 9-25

26.A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car at an angle of depression of 30°, which is approaching the foot of the tower with a uniform speed, 6 seconds later the angle of depression of the car is found to be 60°. Find the time taken by the car to reach the foot of the tower from this point.
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 9-26

27. A fire in a building B is reported on telephone to two fire stations P and Q, 20 km apart from each other on a straight road. P observes that the fire is at an angle of 60° to the road and Q observes that it is at an angle of 45° to the road. ‘
(a) Which station should send its team and how much will this team have to travel?
(b) What according to you, are the values displayed by the teams at fire stations P and Q?
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 9-27
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 9-27.a

28.The opposite angular points of a square are (2, 0) and (5, 1). Find the remaining points.
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 9-28
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 9-28.a

29.In the given figure, three circles of radius 2 cm touch one another externally. These circles are circumscribed by a circle of radius R cm. Find the value of R and the area of the shaded region.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 9-40
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 9-29
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 9-29.a
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 9-29.b

30.The area of the base of a cone is 770 cm2 and the curved surface area is 814 cm2. Find the volume of the cone.
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 9-30
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 9-30.a

31.An agricultural field is in the form of a rectangle of length 20 m and width 14 m. A pit 6 m long, 3 m wide and 2.5 m deep is dug in the corner of the field and the earth taken out of the pit is spread uniformly over the remaining area of the field. Find the extent to which the level of the field has been raised.
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 9-31

The post CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 9 appeared first on Learn CBSE.

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