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Maths MCQs Bank

Verified Question Bank for High-Performance Exam Preparation.

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1

The HCF of 96 and 404 by prime factorization method is:

A
4
✅
B
96
C
101
D
24
2

If the product of two numbers is 182 and their HCF is 13, then their LCM is:

A
14
✅
B
26
C
169
D
91
3

A rational number between √2 and √3 is:

A
1.5
✅
B
1.4
C
1.9
D
2.1
4

The decimal expansion of 14587/1250 will terminate after how many decimal places?

A
1
B
2
C
3
D
4
✅
5

If α and β are the zeroes of the quadratic polynomial x² - 5x + k, and α - β = 1, then the value of k is:

A
4
B
6
✅
C
3
D
5
6

A quadratic polynomial whose zeroes are 5 and -2 is:

A
x² - 3x - 10
✅
B
x² + 3x - 10
C
x² - 3x + 10
D
x² + 3x + 10
7

If one zero of the polynomial (a² + 9)x² + 13x + 6a is reciprocal of the other, then the value of 'a' is:

A
1
B
3
✅
C
-3
D
-1
8

For what value of 'k' will the following pair of linear equations have infinitely many solutions? 2x + 3y = 7, (k-1)x + (k+2)y = 3k

A
1
B
7
✅
C
10
D
2
9

The pair of equations y = 0 and y = -7 has:

A
One solution
B
Two solutions
C
Infinitely many solutions
D
No solution
✅
10

The value of 'c' for which the pair of equations cx - y = 2 and 6x - 2y = 3 will have infinitely many solutions is:

A
3
B
-3
C
-12
D
No value
✅
11

If x = a, y = b is the solution of the equations x - y = 2 and x + y = 4, then the values of a and b are, respectively:

A
3 and 1
✅
B
1 and 3
C
-1 and 3
D
-3 and 1
12

The roots of the quadratic equation x² - 0.04 = 0 are:

A
±0.2
✅
B
±0.02
C
±0.4
D
±2
13

The nature of the roots of the quadratic equation 2x² - 4x + 3 = 0 is:

A
Real and equal
B
Real and distinct
C
No real roots
✅
D
Cannot be determined
14

If the quadratic equation 2x² + kx + 3 = 0 has equal roots, then the value of k is:

A
±√6
B
±4
C
±3√2
D
±2√6
✅
15

If one root of the quadratic equation x² - ax + 3 = 0 is 1, then the value of 'a' is:

A
4
✅
B
3
C
-4
D
-3
16

The 10th term of the AP: 2, 7, 12, ... is:

A
47
✅
B
49
C
52
D
57
17

Which term of the AP: 21, 18, 15, ... is -81?

A
34th
B
35th
✅
C
36th
D
37th
18

The sum of the first 10 terms of the AP: 2, 7, 12, ... is:

A
245
✅
B
250
C
255
D
260
19

If 7th term of an AP is 32 and its 13th term is 62, then the AP is:

A
5, 10, 15, ...
B
2, 7, 12, ...
✅
C
2, 5, 8, ...
D
2, 4, 6, ...
20

In ΔABC, DE || BC. If AD/DB = 3/5 and AC = 4.8 cm, then AE is:

A
1.8 cm
✅
B
2.4 cm
C
3.0 cm
D
3.6 cm
21

If the areas of two similar triangles are in the ratio 4:9, then the ratio of their corresponding sides is:

A
2:3
✅
B
4:9
C
16:81
D
√2:√3
22

In an isosceles right-angled triangle, if the hypotenuse is 5√2 cm, then the length of each equal side is:

A
5 cm
✅
B
10 cm
C
5√2 cm
D
2.5 cm
23

A ladder 10 m long reaches a window 8 m above the ground. The distance of the foot of the ladder from the base of the wall is:

A
6 m
✅
B
8 m
C
10 m
D
√164 m
24

The distance of the point (3, 4) from the origin is:

A
3 units
B
4 units
C
5 units
✅
D
7 units
25

The coordinates of the midpoint of the line segment joining P(4, -5) and Q(-2, 9) are:

A
(1, 2)
✅
B
(2, 1)
C
(-1, 2)
D
(1, -2)
26

The ratio in which the y-axis divides the line segment joining the points (5, -6) and (-1, -4) is:

A
1:5
B
5:1
✅
C
1:1
D
2:3
27

The area of a triangle with vertices (2, 3), (-1, 0), (2, -4) is:

A
21/2 sq. units
✅
B
10 sq. units
C
15/2 sq. units
D
12 sq. units
28

If sin A = 3/5, then the value of tan A is:

A
3/4
✅
B
4/3
C
5/3
D
4/5
29

If sin A = cos A, then the value of A is:

A
0°
B
30°
C
45°
✅
D
60°
30

The value of (1 + tan²θ) / (1 + cot²θ) is:

A
sec²θ
B
cot²θ
C
tan²θ
✅
D
sin²θ
31

The angle of elevation of the top of a tower from a point on the ground, which is 30 m away from the foot of the tower, is 30°. The height of the tower is:

A
10√3 m
✅
B
30√3 m
C
10 m
D
30 m
32

If the angle of elevation of a tower from two points at a distance 'a' and 'b' from the base and in the same straight line with it are complementary, then the height of the tower is:

A
√(a/b)
B
√(ab)
✅
C
a/b
D
ab
33

The length of the tangent from a point A at distance 5 cm from the centre of the circle is 4 cm. The radius of the circle is:

A
3 cm
✅
B
4 cm
C
5 cm
D
2.5 cm
34

From an external point P, two tangents PA and PB are drawn to a circle with centre O. If ∠APB = 80°, then ∠POA is:

A
50°
✅
B
60°
C
70°
D
80°
35

If two tangents inclined at an angle of 60° are drawn to a circle of radius 3 cm, then the length of each tangent is:

A
3√3 cm
✅
B
3 cm
C
3/√3 cm
D
6 cm
36

The area of a circle whose circumference is 22 cm is:

A
38.5 cm²
✅
B
77 cm²
C
154 cm²
D
19.25 cm²
37

The perimeter of a sector of a circle with radius 5.7 cm and sector angle 30° is:

A
11.4 cm
B
12 cm
C
12.3 cm
✅
D
13 cm
38

The area of a quadrant of a circle whose circumference is 22 cm is:

A
11 cm²
B
38.5 cm²
C
9.625 cm²
D
19.25 cm²
✅
39

The area of the largest triangle that can be inscribed in a semicircle of radius 'r' is:

A
r²
✅
B
2r²
C
r³/2
D
√2 r²
40

The surface area of a sphere of radius 'r' is:

A
2πr²
B
4πr²
✅
C
(4/3)πr³
D
πr²
41

A metallic sphere of radius 4.2 cm is melted and recast into the shape of a cylinder of radius 6 cm. The height of the cylinder is:

A
2.744 cm
✅
B
2.8 cm
C
2.92 cm
D
3.1 cm
42

The total surface area of a solid hemisphere of radius 'r' is:

A
2πr²
B
3πr²
✅
C
4πr²
D
πr²
43

The ratio of the volumes of two cones with the same base radius is 2:3. If the height of the first cone is 6 cm, then the height of the second cone is:

A
9 cm
✅
B
4 cm
C
12 cm
D
3 cm
44

The mean of the first five natural numbers is:

A
2
B
3
✅
C
4
D
5
45

If the mean of 6, 8, 5, 7, x, 4 is 7, then the value of x is:

A
10
B
12
✅
C
15
D
18
46

For a frequency distribution, mode = 24 and mean = 20. The median is:

A
21
B
22
✅
C
23
D
24
47

A card is drawn from a well-shuffled deck of 52 cards. The probability of getting a red face card is:

A
3/26
✅
B
3/13
C
1/26
D
1/13
48

If the HCF of 65 and 117 is expressible in the form 65m − 117, then the value of m is:

A
2
✅
B
1
C
3
D
4
49

The quadratic equation 2x² − 4x + 3 = 0 has:

A
No real roots
✅
B
Two equal real roots
C
Two distinct real roots
D
One real and one imaginary root
50

The sum of the first 20 terms of the arithmetic progression 3, 7, 11, 15, ... is:

A
820
✅
B
780
C
800
D
840
51

If the lines represented by the equations 2x + 3y = 5 and 4x + 6y = 10 are considered, which of the following is true?

A
The lines are coincident and have infinitely many solutions
✅
B
The lines are parallel and have no solution
C
The lines intersect at exactly one point
D
The lines are perpendicular to each other
52

In triangle ABC, if DE is parallel to BC where D is on AB and E is on AC, AD = 4 cm, DB = 6 cm, and AE = 5 cm, then EC is equal to:

A
7.5 cm
✅
B
6.5 cm
C
8 cm
D
5.5 cm
53

A tangent PQ at point P on a circle of radius 5 cm meets a line through the centre O at point Q such that OQ = 13 cm. The length of PQ is:

A
12 cm
✅
B
10 cm
C
8 cm
D
11 cm
54

The value of (sin 30° + cos 60°) × (sin 60° + cos 30°) is:

A
(1 + √3)/2
✅
B
√3
C
1
D
(√3 + 1)/4
55

The total surface area of a solid hemisphere of radius r is:

A
3πr²
✅
B
2πr²
C
4πr²
D
πr²
56

The mean of the following frequency distribution is: Class intervals: 0–10, 10–20, 20–30, 30–40; Frequencies: 4, 6, 8, 2. The mean is:

A
19
✅
B
20
C
18
D
21
57

A card is drawn at random from a well-shuffled deck of 52 playing cards. The probability of getting a face card (Jack, Queen, or King) is:

A
3/13
✅
B
1/13
C
4/13
D
2/13

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