CBSE Class 10 Mathematics Basic 2024 Sample Paper Solved

SECTION A

1. If two positive integers a and b are written as a = x³y³ and b = xy³; x, y are prime numbers, then HCF (a,b) is:
a) xy
b) xy²
c) x³y³
d) x²y²
Answer : B

2. The LCM of smallest two-digit composite number and smallest composite number is:
a) 12
b) 4
c) 20
d) 44
Answer : C

3. If x = 3 is one of the roots of the quadratic equation x² – 2kx – 6 = 0, then the value of k is
a) 1/2
b) 1/4 
c) 3
d) 2
Answer : A

4. The pair of equations y = 0 and y = -7 has:
a) One solution
b) Two solutions
c) Infinitely many solutions
d) No solution
Answer : D

5. Value(s) of k for which the quadratic equation 2x² – kx + k = 0 has equal roots is :
a) 0 only
b) 4
c) 8 only
d) 0,8
Answer : D

6. The distance of the point(3,5) from x-axis(in units) is:
a) 3
b) - 3
c) 5
d) -5
Answer : C

7. If in Δ ABC and Δ PQR, we have 𝐴𝐵/𝑄𝑅 = 𝐵𝐶/𝑃𝑅 = 𝐶𝐴/𝑃𝑄/then:
a) ΔPQR ~ΔCAB
b) ΔPQR ~ΔABC
c) ΔCBA ~ΔPQR
d) ΔBCA ~ΔPQR
Answer : A

8. Which of the following is NOT a similarity criterion?
a) AA
b) SAS
c) AAA
d) RHS
Answer : D

9. In figure, if TP and TQ are the two tangents to a circle with centre O so that ∠POQ = 110°, then ∠PTQ is equal to
(a) 60°
(b) 70°
(c) 80°
(d) 90°
Answer : B

10. If cos A = 4/5 then the value of tan A is:
a) 3/5
b) 3/4
c) 4/3
d) 1/8
Answer : B

11. If the height of the tower is equal to the length of its shadow, then the angle of elevation of the sun is _____
a) 30°
b) 45°
c) 60°
d) 90°
Answer : B

12. 1 – cos² A is equal to
a) sin² A
b) tan²A
c) 1 – sin²A
d) sec²A
Answer : A

13. The radius of a circle is same as the side of a square. Their perimeters are in the ratio
a) 1 : 1
b) 2 : 𝜋
c) 𝜋 : 2
d) √𝜋 : 2
Answer : C

14. The area of the circle is 154cm². The radius of the circle is
a) 7cm
b) 14cm
c) 3.5cm
d) 17.5cm
Answer : A

15. When a die is thrown, the probability of getting an even number less than 4 is
a) 1/4
b) 0
c) 1/2
d) 1/6
Answer : D

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