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# CBSE Academic Class X Mathematics (Standard) Sample Question Paper 2022-23

Name of the Board : Central Board of Secondary Education (CBSE)
Class : X STD
Document Type : Sample Question Paper
Subject : Mathematics (Standard)
Year : 2022-23

Contents :

## CBSE X Mathematics (Standard) Sample Question Paper

CBSE Students can download the Mathematics (Standard) Application Sample Question Paper for the year 2022-23 from the website of CBSE Academic.

Related / Similar Question Paper : CBSE Academic Class X Social Science Sample Question Paper 2022-23

## CBSE Mathematics (Standard) Question Paper

1 Let a and b be two positive integers such that a = p3q4 and b = p2q3 , where p and q are prime numbers. If HCF(a,b) = pmqn and LCM(a,b) = prqs, then (m+n)(r+s)=
(a) 15
(b) 30
(c) 35
(d) 72

2 Let p be a prime number. The quadratic equation having its roots as factors of p is
(a) x2 –px +p=0
(b) x2–(p+1)x +p=0
(c) x2+(p+1)x +p=0
(d) x2 –px+p+1=0

3 If α and β are the zeros of a polynomial f(x) = px2 – 2x + 3p and α + β = αβ, then p is
(a)-2/3
(b) 2/3
(c) 1/3
(d) -1/3

4 If the system of equations 3x+y =1 and (2k-1)x +(k-1)y =2k+1 is inconsistent, then k =
(a) -1
(b) 0
(c) 1
(d) 2

5 If the vertices of a parallelogram PQRS taken in order are P(3,4), Q(-2,3) and R(-3,-2), then the coordinates of its fourth vertex S are
(a) (-2,-1)
(b) (-2,-3)
(c) (2,-1)
(d) (1,2)

6 ∆ABC~∆PQR. If AM and PN are altitudes of ∆ABC and ∆PQR respectively and AB2: PQ2 = 4 : 9, then AM: PN =
(a) 3:2
(b) 16:81
(c) 4:9
(d) 2:3

7 If x tan 60°cos 60°= sin60°cot 60°, then x =
(a) cos30°
(b) tan30°
(c) sin30°
(d) cot30°

8 If sinθ + cosθ = √2, then tanθ + cot θ =
(a) 1
(b) 2
(c) 3
(d) 4

10 ABCD is a trapezium with AD ∥ BC and AD = 4cm. If the diagonals AC and BD intersect each other at O such that AO/OC = DO/OB =1/2, then BC =
(a) 6cm
(b) 7cm
(c) 8cm
(d) 9cm

11 If two tangents inclined at an angle of 60ᵒ are drawn to a circle of radius 3cm, then the length of each tangent is equal to
(a) 3√3 2 cm
(b) 3cm
(c) 6cm
(d) 3√3cm

12 The area of the circle that can be inscribed in a square of 6cm is
(a) 36π cm2
(b) 18π cm2
(c) 12 π cm2
(d) 9π cm2

13 The sum of the length, breadth and height of a cuboid is 6√3cm and the length of its diagonal is 2√3cm. The total surface area of the cuboid is
(a) 48 cm2
(b) 72 cm2
(c) 96 cm2
(d) 108 cm2

14 If the difference of Mode and Median of a data is 24, then the difference of median and mean is
(a) 8
(b) 12
(c) 24
(d) 36

15 The number of revolutions made by a circular wheel of radius 0.25m in rolling a distance of 11km is
(a) 2800
(b) 4000
(c) 5500
(d) 7000

16 For the following distribution, Class 0-5 5-10 10-15 15-20 20-25 Frequency 10 15 12 20 9 the sum of the lower limits of the median and modal class is
(a) 15
(b) 25
(c) 30
(d) 35

17 Two dice are rolled simultaneously. What is the probability that 6 will come up at least once?
(a)1/6
(b) 7/36
(c) 11/36
(d) 13/36

18 If 5 tanβ =4, then 5 𝑠𝑖𝑛𝛽−2 cos 𝛽 5 sin 𝛽+2 cos 𝛽 =
(a) 1/3
(b) 2/5
(c) 3/5
(d) 6

19 DIRECTION: In the question number 19 and 20, a statement of assertion (A) is followed by a statement of Reason (R). Choose the correct option
Statement A (Assertion): If product of two numbers is 5780 and their HCF is 17, then their LCM is 340
Statement R( Reason) : HCF is always a factor of LCM
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A)
(b) Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A)
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.

20 Statement A (Assertion): If the co-ordinates of the mid-points of the sides AB and AC of ∆ABC are D(3,5) and E(-3,-3) respectively, then BC = 20 units Statement R( Reason) : The line joining the mid points of two sides of a triangle is parallel to the third side and equal to half of it.
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A)
(b) Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A)
(c) Assertion (A) is true but reason(R) is false.
(d) Assertion (A) is false but reason(R) is true.