CBSE Class 10 Mathematics Standard Sample Paper 2023

SECTION A

Section A consists of 20 questions of 1 mark each.
MARKS

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

Answer : C

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

Answer : B

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

Answer : B

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

Answer : D

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)

Answer : C

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

Answer : D

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

Answer : B

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

Answer : B

9 In the given figure, DE ∥ BC, AE = a units, EC =b units, DE =x units and BC = y units. Which of the following is true? 

Answer : C

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

Answer : C