CBSE CLASS 10 MATHEMATICS QUESTIONS AND ANSWERS PART 4

CBSE CLASS 10 MATHEMATICS QUESTIONS AND ANSWERS PART 4

ANSWERS ARE GIVEN IN YELLOW

1. What is the maximum number of zeroes of a cubic polynomial?

The maximum number of zeroes of a cubic polynomial is 3.

2. Find k if the pair of linear equations 2kx + 5y = 7, 6x-5y = 11 has a unique solution.

2k/6 ≠ 5/-5
k ≠ -3

3. What are the linear factors of the quadratic equation x²+kx+1 =0?

Discriminant should be greater than or equal to zero.
k²-4≥ 0
(k+2)(k-2)≥ 0
k+2 ≥ 0 and k-2 ≥ 0
So k≤-2 , k≥2

4. A chord of a circle of radius 10 cm subtends a right angle at the centre. Find the length of the chord.

Since angle at the centre is 90°, a right angled triangle is formed by the chord and two radii. Let us use Pythagoras theorem
Length of the chord = √(10² +10²)
= √(2x100) = 10√2 cm

5. If the area of a semi-circular field is 15400 sq.m, find the perimeter of the field.

Area of a semi-circular field= πr²/2
πr² = 15400 x 2
r² = 15400 x 2 x 7/22
r² = 700 x 7 x 2
r = 70√2 m
Perimeter of the semi-circular field is
πr + d
= (22/7) (70√2) + 2(70√2)
= 220√2 + 140√2
= 360√2 m

6. If x-2y+k =0 is a median of the triangle whose vertices are at points A(-1,3), B(0,4), C (-5,2) then find k

The coordinates of the centroid G of △ABC lies on the median.
Coordinates of G are
((-1+0-5)/3, (3+4+2)/3 )
(-2, 3)
Substituting this in the median equation, we get
-2-6+k=0
k=8

7. If △ABC is right angled at C, then what is the value of cos(A+B)?

A+B+C = 180° (Angle sum property of a triangle)
Given C =90°
So, A+B = 180-90 = 90°
Therefore cos(A+B) = cos90 = 0

8. Find the ratio of lateral surface areas of two cylinders with equal height.

Let R and r be the radii of the two cylinders with equal height h
Ratio of lateral surface areas of the two cylinders will be
2πRh: 2πrh
R:r

9. Which central tendency is used for finding the popular size of readymade garments?

Mode

10. If 2-√3 is a root of the quadratic polynomial, then what will be the other root?

The other root will be 2+√3.
Irrational roots always occur in pairs.

11. √3 sinx - cosx = 0, 0°<x<90°, find the value of x

√3 sinx - cosx = 0
√3 sinx = cosx
sinx/cosx = 1/√3
tanx= 1/√3
x = 30°

12. Find the value of x, if the mode of the following data is 20.

15, 20, 25, 18, 13, 15, 25, 15, 18, 17, 20, 25, 20, x, 18
First of all, let us write the data in the ascending order so that we don't miss any value.
13,15,15,15,17,18,18,18,20,20,20,x, 25,25,25
Since the mode is the highest occurring value, the value of x should be 20.

13. The mean and median of 100 observation are 50 and 52. The value of the largest observation is 100. It was later found to be 110. Find the true mean and median.

Total observation= mean x number of observation
= 50 x 100 = 5000
New total will be
5000-100+110 = 5010
New mean =5010/100 = 50.1
Median will be the same 52 as the change in the largest observation will have no impact on the value of median.

14. If the perimeter of a circle is equal to that of a square, then what is the ratio of their areas?

Perimeter(circumference) of a circle of radius r = 2πr
Perimeter of a square of side a = 4a
Given 2πr = 4a
which gives r= 2a/π
Area of a circle=πr²
Area of a square of side a=a²
Ratio of areas of circle and square is
π(2a/π)² : a²
π(4a²/π²) : a²

Simplifying, we get
4/π : 1
4x(7/22) : 1
(14/11) : 1
14:11

15. The nth term of an AP whose sum to n terms is Sₙ, is given by aₙ = Sₙ - Sₙ₋₁ . Is this correct?

Yes. This is correct.

a = a₁ = S₁ (only one term)
a₂ = S₂ - S₁ (total of 2 terms)
a₃ = S₃ - S₂ (total of 3 terms)