Class 10 CBSE Maths Board Paper 2024

Maximum Marks: 80

Time Allowed: Three hours

(Candidates are allowed additional 15 minutes for only reading the paper.
They must NOT start writing during this time).

This paper is divided into four sections – A, B, C and D.

Answer all questions.

Section A consists of one question having sub-parts of one mark each.

Section B consists of seven questions of two marks each.

Section C consists of nine questions of three marks each, and

Section D consists of three questions of five marks each

. Internal choices have been provided in two questions each in Section B, Section C and Section D.

The intended marks for questions are given in brackets [ ].

All working, including rough work, should be done on the same sheet as and adjacent to the rest of the answer.

Answers to sub parts of the same question must be given in one place only.

A list of useful physical constants is given at the end of this paper.

A simple scientific calculator without a programmable memory may be used for calculations.

Class 10 CBSE Maths Board Paper 2024

Section-A This section comprises multiple choice questions (MCQs) of 1 mark each

Question 1

If the sum of zeroes of the polynomial p(x) = 2x2 - k√2x + 1 is √2, then value of k is : (a) √2 (b) 2 (c) 2√2 (d) 1/2

Solution

Question 2

If the probability of a player winning a game is 0.79, then the probability of his losing the same game is : (a) 1.79 (b) 0.31 (c) 0.21% (d) 0.21

Solution

Question 3

If the roots of equation ax2 + bx + c = 0, a ≠ 0 are real and equal, then which of the following relation is true ? (a) a = b2/c (b) b2 = ac (c) ac = b2/4 (d) c = b2/a

Solution

Question 4

In an A.P., if the first term a = 7, nth term an = 84 and the sum of first n terms sn = 2093/2 then n is equal to : (a) 22 (b) 24 (c) 23 (d) 26

Solution

Question 5

If two positive integers p and q can be expressed as p = 18 a2b4 and q =20 a3b2, where a and b are prime numbers, then LCM (p, q) is (a) 2a2b2 (b) 180a2b2 (c) 12a2b2 (d) 180a3b4

Solution

Question 6

AD is a median of ▵ABC with vertices A(5,-6), B(6, 4) and C(0, 0) Length AD is equal to (a) √68 units (b) 2√15 units (c) √101 units (d) 10 units

Solution

Question 7

If sec θ - tan θ = m, then the value of sec θ + tan θ is (a) 1-(1/m) (b) m2-1 (c) 1/m (d) -m

Solution

Question 8

From the data 1, 4, 7, 9, 16, 21, 25, if all the even numbers are removed, then the probability of getting at random a prime number from the remaining is : (a) 2/5 (b) 1/5 (c) 1/7 (d) 2/7

Solution

Question 9

For some data x1, x2, ... xn with respective frequencies f1,f2,...fn the value of (a) nx (b) 1 (c) ∑fi (d) 0

Solution

Question 10

The zeroes of a polynomial x2 + px + q are twice the zeroes of the polynomial 4x2 - 5x - 6. The value of p is : (a) -5/2 (b) 5/2 (c) -5 (d) 10

Solution

Question 11

If the distance between the points (3, - 5) and (x,-5) is 15 units, then the values of x are : (a) 12,-18 (b) -12,18 (c) 18,5 (d) -9,-12

Solution

Question 12

If cos(α+ β) = 0, then value of cos((α + β)/2) is equal to : (a) 1/√2 (b) 1/2 (c) 0 (d) √2

Solution

Question 13

A solid sphere is cut into two hemispheres. The ratio of the surface areas of sphere to that of two hemispheres taken together, is : (a) 1:1 (b) 1:4 (c) 2:3 (d) 3:2

Solution

Question 14

The middle most observation of every data arranged in order is called : (a) mode (b) median (c) mean (d) deviation

Solution

Question 15

The volume of the largest right circular cone that can be carved out from a solid cube of edge 2 cm is : (a) 4π/3 cu cm (b) 5π/3 cu cm (c) 8π/3 cu cm (d) 2π/3 cu cm

Solution

Question 16

Two dice are rolled together, The probabilities of getting sum of numbers on the two dice as 2,3 or 5 is (a) 7/36 (b) 11/36 (c) 5/36 (d) 4/9

Solution

Question 17

The centre of a circle is at (2, 0). If one end of a diameter is at (6, 0), then the other end is at : (a) (0,0) (b) (4,0) (c) (-2,0) (d) (-6,0)

Solution

Question 18

In the given figure, graphs of two linear equations are shown. The pair of these linear equations is : (a) consistent with unique solution, (b) consistent with infinitely many-r solutions. (c) inconsistent. (d) inconsistent but can be made consistent by extending these lines,

Solution

Question 19

Assertion (A) : The tangents drawn at the end points of a diameter of a circle, are parallel. Reason (R): Diameter of a circle is the longest chord.

Solution

Question 20

Assertion (A) : If the graph of a polynomial touches x-axis at only one point, then the polynomial cannot be a quadratic polynomial. Reason (R): A polynomial of degree n(n >1) can have at most n zeroes.

Solution

Section-B This section comprises very short answer (VSA) type questions of 2 marks each.

Question 21

Solve the following System of linear, equations 7x-2y = 5 and 8x + 7y = 15 verify your answer.

Solution

Question 22

In pack of 52 playing cards one card is lost. From the remaining cards, a card is drawn at random. Find the probability that the drawn card is queen of heart, if the lost card is a black card.

Solution

Question 23

(A) Evaluate 2√2 cos 45o sin 30o + 2√3 cos 30o OR (B) If A= 60° and B = 30°, verify that sin(A+B) = sinA cosB + cosA sinB

Solution

Question 24

In the given figure. ABCD is a quadilateral Diagonal BD bisects ∠B and ∠D both. Prove that (i) ▵ABD ~ ▵CBD (ii) AB=BC

Solution

Question 25

(A) Prove that 5 - 2√3 is an irrational number. It is given that √3 is an irrational number. OR (B) Show that the number 5 x 11 x 17 + 3 x 11 is a composite number.

Solution

Section-C This section comprises short answer (SA) type questions of 3 marks each.

Question 26

Section-A

This section comprises multiple choice questions (MCQs) of 1 mark each

If the sum of zeroes of the polynomial p(x) = 2x² - k√2x + 1 is √2, then value of k is :
(a) √2
(b) 2
(c) 2√2
(d) 1/2

If the probability of a player winning a game is 0.79, then the probability of his losing the same game is :
(a) 1.79
(b) 0.31
(c) 0.21%
(d) 0.21

If the roots of equation ax² + bx + c = 0, a ≠ 0 are real and equal, then which of the following relation is true ?
(a) a = b²/c
(b) b² = ac
(c) ac = b²/4
(d) c = b²/a

In an A.P., if the first term a = 7, nth term a_n = 84 and the sum of first n terms s_n = 2093/2 then n is equal to :
(a) 22
(b) 24
(c) 23
(d) 26

If two positive integers p and q can be expressed as p = 18 a²b⁴ and q =20 a³b², where a and b are prime numbers, then LCM (p, q) is
(a) 2a²b²
(b) 180a²b²
(c) 12a²b²
(d) 180a³b⁴

AD is a median of ▵ABC with vertices A(5,-6), B(6, 4) and C(0, 0)
Length AD is equal to
(a) √68 units
(b) 2√15 units
(c) √101 units
(d) 10 units

If sec θ - tan θ = m, then the value of sec θ + tan θ is
(a) 1-(1/m)
(b) m²-1
(c) 1/m
(d) -m

From the data 1, 4, 7, 9, 16, 21, 25, if all the even numbers are removed, then the probability of getting at random a prime number from the remaining is :
(a) 2/5
(b) 1/5
(c) 1/7
(d) 2/7

For some data x₁, x₂, ... x_n with respective frequencies f₁,f₂,...f_n the value of
(a) nx
(b) 1
(c) ∑f_i
(d) 0

The zeroes of a polynomial x² + px + q are twice the zeroes of the polynomial 4x² - 5x - 6. The value of p is :
(a) -5/2
(b) 5/2
(c) -5
(d) 10

If the distance between the points (3, - 5) and (x,-5) is 15 units, then the values of x are :
(a) 12,-18
(b) -12,18
(c) 18,5
(d) -9,-12

If cos(α+ β) = 0, then value of cos((α + β)/2) is equal to :
(a) 1/√2
(b) 1/2
(c) 0
(d) √2

A solid sphere is cut into two hemispheres. The ratio of the surface areas of sphere to that of two hemispheres taken together, is :
(a) 1:1
(b) 1:4
(c) 2:3
(d) 3:2

The middle most observation of every data arranged in order is called :
(a) mode
(b) median
(c) mean
(d) deviation

The volume of the largest right circular cone that can be carved out from a solid cube of edge 2 cm is :
(a) 4π/3 cu cm
(b) 5π/3 cu cm
(c) 8π/3 cu cm
(d) 2π/3 cu cm

Two dice are rolled together, The probabilities of getting sum of numbers on the two dice as 2,3 or 5 is
(a) 7/36
(b) 11/36
(c) 5/36
(d) 4/9

The centre of a circle is at (2, 0). If one end of a diameter is at (6, 0), then the other end is at :
(a) (0,0)
(b) (4,0)
(c) (-2,0)
(d) (-6,0)

In the given figure, graphs of two linear equations are shown. The pair of these linear equations is :

(a) consistent with unique solution,
(b) consistent with infinitely many-r solutions.
(c) inconsistent.
(d) inconsistent but can be made consistent by extending these lines,

Assertion (A) : The tangents drawn at the end points of a diameter of a circle, are parallel.
Reason (R): Diameter of a circle is the longest chord.

Assertion (A) : If the graph of a polynomial touches x-axis at only one point, then the polynomial cannot be a quadratic polynomial.
Reason (R): A polynomial of degree n(n >1) can have at most n zeroes.

Section-B

This section comprises very short answer (VSA) type questions of 2 marks each.

Solve the following System of linear, equations
7x-2y = 5 and 8x + 7y = 15 verify your answer.

(A) Evaluate 2√2 cos 45^o sin 30^o + 2√3 cos 30^o
OR
(B) If A= 60° and B = 30°, verify that sin(A+B) = sinA cosB + cosA sinB

In the given figure. ABCD is a quadilateral Diagonal BD bisects ∠B and ∠D both. Prove that
(i) ▵ABD ~ ▵CBD
(ii) AB=BC

(A) Prove that 5 - 2√3 is an irrational number. It is given that √3 is an irrational number.
OR
(B) Show that the number 5 x 11 x 17 + 3 x 11 is a composite number.

Section-C

This section comprises short answer (SA) type questions of 3 marks each.

The difference between the outer and inner radii of a hollow right circular cylinder of length 14 cm is 1 cm. If the volume of the metal used in making the cylinder is 176 cm³, find the outer and inner radii of the cylinder.

Section-D

This section comprises long answer (LA) type questions of 5 marks eac h.

An arc of a circle of radius 21 cm subtends an angle of 60° at the centre. Find :
(i) the length of the arc.
(ii) the area of the minor segment of the circle made by the corresponding chord.

Section-E

This section comprises 3 case study based questions of 4 marks each.