CBSE Class 10 Mathematics Sample Paper Set 12

SECTION A

Q1. The sum of exponents of prime factors in the prime factorisation of 196 is
A) 3
B) 4
C) 5
D) 2

Q2. If two positive integers A and B can be expressed as A = xy³ and B = x⁴y²z; x, y being prime numbers then HCF (A, B) is
A) x𝑦²
B) 𝑥⁴𝑦²z
C) 𝑥⁴𝑦³
D) 𝑥⁴𝑦3z

Q3. In the following question, a statement of assertion (A) is followed by a statement of reason (R).
(A) HCF (23, 53) is 1.
(R) If p and q are prime then HCF (p, q) = 1
Now mark the correct choice as:
(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 reasons (R) is false.
(d) Assertion (A) is false but reasons (R) is true.

Q4. If sum of the zeroes of the quadratic polynomial k𝑥²+2x+3k is equal to the product of its zeroes , then the value of k is:
A) 1/3
B) -1/3
C) 2/3
D) -2/3

Q5. For what value of ‘k’ will the following pairs of linear equations are inconsistent 3x+4y=1 and (2k-1) x+(k-1) y = 2k+1
A) K=1
B) k=2
C) k=3
D) k=4

Q6. Which of the following equations has 2 as a root?
A) 𝑥²-4x+5=0
B) 𝑥²+3x-12=0
C) 2𝑥²-7x+6=0
D) 3𝑥²-6x-2=0

Q7. The ratio in which the X -axis divides the line segment joining A( 2,-3) and B(5,6) is :
A) 2:3
B) 3:5
C) 1:2
D) 2:1

Q8. Distance between the pairs of points: (a, b) and (-a,-b) is:
A) 2√𝑎² + 𝑏²
B) √𝑎² + 𝑏²
C) 0
D) √2𝑎² + 2𝑏²

Q9. In the following question, a statement of assertion (A) is followed by a statement of reason (R).
Assertion:- The points A (-2, 1), B (1, 0) and C (4, – 1) are collinear.
Reason:- Three points A, B and C are collinear in same straight line, if AB + BC = AC.

Now choose the correct option among following:
(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 reasons (R) is false.
(D) Assertion (A) is false but reasons (R) is true.

Q10. If cos A= 4/5, then the value of tan A is
A) 3/5
B) 3/4
C) 4/3
D) 5/3

Q11. If ΔABC is right angled at C , then the value ofcos (A +B) is:
A) 0
B) 1
C) 1/2

Q12. If sinα=1/2 and cosβ=1/2, then the value of (α+β) is:
A) 0⁰
B) 30⁰
C) 60⁰
D) 900

Q13. It is given that, Δ ABC ~Δ 𝐸DF such that AB = 5 cm, AC=7cm, DF=15cm and DE= 12 cm.then the length of EF is:
A) 17 cm
B) 16.8 cm
C) 6.25 cm
D) 24 cm

Q14. Two chords AB and CD of a circle intersect at E such that AE = 2 .4cm, BE = 3. 2cm and CE = 1. 6cm. The length of DE is:
A) 1.6 cm
B) 3.2 cm
C) 4.8 cm
D) 6.4 cm

Q15. In a circle of radius 14 cm, an arc subtends an angle of 450at the centre , then the area of the sector is:
A) 71 𝑐𝑚²
B) 76 𝑐𝑚²
C) 77 𝑐𝑚²
D) 154 𝑐𝑚2

Q16. If the circumference of a circle increases from 4 π to 8 π , then its area is :
A) Halved
B) doubled
C) tripled
D) quadrupled

Q17. The base radii of a cone and a cylinder are equal. If their curved surface areas are also equal, then the ratio of the slant height of the cone to the height of the cylinder is:
A) 2:1
B) 1:2
C) 1: 3
D) 3:1

Q18. The median and mode respectively of a frequency distribution are 26 and 29, Then its mean is:
A) 27.5
B) 24.5
C) 28.4
D) 25.8

Q19. For finding the popular size of readymade garments, which central tendency is used?
A) Mean
B) Median
C) Mode
D) Both mean and mode

Q20. Which of the following cannot be the probability of an event?
A) 1/3
B) 0.1
C) 3%
D) 17/16

SECTION B

Q21. A fraction becomes 1/3 when 2 is subtracted from the numerator and it becomes ½ when 1 is subtracted from the denominator. Find the fraction.

Q22. Evaluate 𝑠𝑖𝑛²60²-2tan45⁰-𝑐𝑜𝑠230⁰.

OR

If Sin(A+B) =√3/2 And tan(A-B)=1/√3; 00<A+B≤900; A>B, Find A and B.

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