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# CBSE Academic Class X Mathematics (Basic) 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 (Basic)
Year : 2022-23

Contents :

## CBSE X Mathematics (Basic) Sample Question Paper

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

Related / Similar Question Paper : CBSE Academic Class X Computer Application Sample Question Paper 2022-23

## CBSE Mathematics (Basic) Question Paper

1 If two positive integers p and q can be expressed as p = ab2 and q = a3b; a, b being prime numbers, then LCM (p, q) is
(a) ab
(b) a2b2
(c) a3b2
(d) a3b3

2 What is the greatest possible speed at which a man can walk 52 km and 91 km in an exact number of hours?
(a) 17 km/hours
(b) 7 km/hours
(c) 13 km/hours
(d) 26 km/hours

3 If one zero of the quadratic polynomial x2 + 3x + k is 2, then the value of k is
(a) 10
(b) -10
(c) 5
(d) –5

4 Graphically, the pair of equations given by 6x – 3y + 10 = 0 2x – y + 9 = 0 represents two lines which are
(a) intersecting at exactly one point.
(b) parallel.
(c) coincident.
(d) intersecting at exactly two points.

5 If the quadratic equation x2 + 4x + k = 0 has real and equal roots, then
(a) k < 4
(b) k > 4
(c) k = 4
(d) k ≥ 4

6 The perimeter of a triangle with vertices (0, 4), (0, 0) and (3, 0) is
(a) 5 units
(b) 12 units
(c) 11 units
(d) (7 + √5) units

7 If in triangles ABC and DEF, AB DE = BC FD , then they will be similar, when
(a) B = E
(b) A = D
(c) B = D
(d) A = F

8 In which ratio the y-axis divides the line segment joining the points (5, – 6) and (–1, – 4)?.
(a) 1 : 5
(b) 5 : 1
(c) 1 : 1
(d) 1 : 2

9 In the figure, if PA and PB are tangents to the circle with centre O such that ∠APB = 50°, then ∠OAB is equal to
(a) 25°
(b) 30°
(c) 40°
(d) 50°

10 If sin A = 12, then the value of sec A is :
(a) 2√3
(b) 1√3
(c) √3
(d) 1

11 √3 cos2A + √3 sin2A is equal to
(a) 1
(b) 1√3
(c) √3
(d) 0

12 The value of cos1° . cos2° . cos3° . cos4°. . . . . . . . . . . .. cos90° is
(a) 1
(b) 0
(c) – 1
(d) 2

13 If the perimeter of a circle is equal to that of a square, then the ratio of their areas is
(a) 22 : 7
(b) 14 : 11
(c) 7 : 22
(d) 11: 14

14 If the radii of two circles are in the ratio of 4 : 3, then their areas are in the ratio of :
(a) 4 : 3
(b) 8 : 3
(c) 16 : 9
(d) 9 : 16

15 The total surface area of a solid hemisphere of radius 7 cm is :
(a) 447π cm2
(b) 239π cm2
(c) 174π cm2
(d) 147π cm2

19 Assertion: If HCF of 510 and 92 is 2, then the LCM of 510 & 92 is 32460 Reason: as HCF(a,b) x LCM(a,b) = a x b
(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 but 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

26 Prove that √5 is an irrational number. 3

27 Find the zeroes of the quadratic polynomial 6×2 – 3 – 7x and verify the relationship between the zeroes and the coefficients.

28 A shopkeeper gives books on rent for reading. She takes a fixed charge for the first two days, and an additional charge for each day thereafter. Latika paid Rs 22 for a book kept for six days, while Anand paid Rs 16 for the book kept for four days. Find the fixed charges and the charge for each extra day.
[OR] Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars?