CBSE CLASS 10 MATHEMATICS QUESTIONS AND ANSWERS

CBSE CLASS 10 MATHEMATICS QUESTIONS AND ANSWERS (Hayagrivaa Academy of Mathematics)

ANSWERS ARE GIVEN IN YELLOW

1. Find the sum of the exponents of prime factors of 1764.

1764 = 2^2 x 3^2 x 7^2

Sum of the exponents= 2+2+2=6

2. Sum of the zeroes of the quadratic polynomial 3x^2-kx+6 is 3, then find the value of k.

Sum of the zeroes = k/3 = 3 (given)

Therefore k = 9

3. If a regular hexagon is inscribed in a circle of radius r, what will be its perimeter?

A regular hexagon consists of 6 equilateral triangles. Here it is inscribed in a circle of radius r which is equal to its side.

So, perimeter will be 6r

4. Find the sum of the first 16 terms of the AP 10,6,2,.....

a=10
d=6-10=-4
S₁₆= (16/2)(20-60) = 8x - 40 = -320

5. What will be the solution of y=0 and y=5?

Both are parallel lines. So there can be no solution.

6. If sinx- cosx=0, then find the value of sin^4x + cos^4x

Given sinx-cosx = 0
(sinx-cosx)^2= 0
sin^2x + cos^2x - 2sinxcosx = 0
1 = 2sinx cosx
sinxcosx = 1/2
sin^4x + cos^4x =
(Sin^2x + cos^2x)^2 - 2sin^2x cos^2x
= 1 - 2(1/4)
1-(1/2)
= 1/2

7. In an AP, if a=2.4, d=0 and n=50, then find aₙ

Since d=0, aₙ will be 2.4 (the value of a itself)

8. If m, n are the zeroes of the polynomial 2x^2-4x+5, then find the value of m^2+n^2

m+n = -(-4)/2 = 2
mn = 5/2
m^2+n^2 = (m+n)^2-2mn
= 4 - 2(5/2)
= 4-5 = -1

9. Find the nature of roots of 3x^2+4√3x+4

Discriminant

b^2-4ac = (4√3)^2 - 4(3)(4)
= 48-48 = 0
The given equation has two equal real roots.

10. If tan(2x+25)=1, then find the value of x

tan(2x+25) = 1 = tan45
2x+25= 45
2x = 20
x=10

11. Find the ratio of volumes of two cones with same radii

(1/3)πr^2 h₁ : (1/3)πr^2h₂
Cancelling the other terms, we get
h₁ : h₂

12. The median of a set of 9 distinct observation is 20.5. If each of the largest 4 observation of the set is increased by 2, then how will the median value change?

The median will be the 5 th observation.
Out of 9 observation, the last four terms are increased which will have no impact on the value of the median.
Therefore the median remains the same.

13. Two concentric circles are of radii 10 cm and 8 cm. Find the length of the chord of the larger circle which touches the smaller circle.

Theorems used:
The tangent AB (smaller circle) is perpendicular at the point of contact M.
The perpendicular drawn from the centre of the circle to the chord AB (larger) bisects the chord.








The length of the chord is 12 cm

14. If the angle of depression of an object from a 75 m high tower is 30°, then what will be the distance of the object from the tower?

Let AB be the height of the tower and BC be the distance of the object from the tower.

The distance of the object from the tower is 75√3 m.

15. A race track is in the form of a ring whose inner and outer circumference are 437 m and 503 m respectively. Find the area of the track

Let r and R be the radii of the inner and outer rings (circular) respectively.