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Q. Calculate the value of 12 × 8 - 24. (2021)

A. 72
B. 96
C. 48
D. 60

Solution

12 × 8 = 96, then 96 - 24 = 72.

Correct Answer: A — 72

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Q. Calculate the value of 12 × 8 - 4 × 6. (2021)

A. 72
B. 60
C. 48
D. 54

Solution

12 × 8 = 96 and 4 × 6 = 24, so 96 - 24 = 72.

Correct Answer: B — 60

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Q. Calculate the value of 25% of 200. (2015)

A. 50
B. 25
C. 75
D. 100

Solution

25% of 200 = (25/100) × 200 = 50.

Correct Answer: A — 50

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Q. Calculate the value of 5! (5 factorial). (2020)

A. 120
B. 100
C. 60
D. 24

Solution

5! = 5 × 4 × 3 × 2 × 1 = 120.

Correct Answer: A — 120

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Q. Calculate the value of 5! - 4!. (2019)

A. 20
B. 24
C. 120
D. 96

Solution

5! = 120 and 4! = 24, so 120 - 24 = 96.

Correct Answer: D — 96

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Q. Calculate the value of 6^2 - 4^2. (2023) 2023

A. 20
B. 22
C. 24
D. 18

Solution

6^2 = 36 and 4^2 = 16, so 36 - 16 = 20.

Correct Answer: A — 20

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Q. Calculate the value of 8 + 2 × 5. (2015)

A. 18
B. 20
C. 10
D. 16

Solution

According to BODMAS, 2 × 5 = 10, then 8 + 10 = 18.

Correct Answer: D — 16

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Q. Calculate the value of 8 × (2 + 3). (2015)

A. 40
B. 30
C. 50
D. 20

Solution

2 + 3 = 5, then 8 × 5 = 40.

Correct Answer: A — 40

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Q. Calculate the value of 8^2 - 4^2. (2021)

A. 48
B. 60
C. 50
D. 40

Solution

8^2 = 64 and 4^2 = 16, so 64 - 16 = 48.

Correct Answer: A — 48

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Q. Calculate the variance for the following data: 2, 4, 4, 4, 5, 5, 7, 9. (2019)

A. 4
B. 5
C. 6
D. 7

Solution

Mean = 5. Variance = [(2-5)² + (4-5)² + (4-5)² + (4-5)² + (5-5)² + (5-5)² + (7-5)² + (9-5)²] / 8 = 4.

Correct Answer: B — 5

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Q. Calculate the variance for the following data: 3, 7, 7, 19. (2022)

A. 20
B. 25
C. 30
D. 35

Solution

Mean = (3 + 7 + 7 + 19) / 4 = 9. Variance = [(3-9)² + (7-9)² + (7-9)² + (19-9)²] / 4 = 25.

Correct Answer: B — 25

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Q. Calculate the variance for the following data: 5, 7, 9, 11. (2022)

A. 2.5
B. 3.5
C. 4.0
D. 5.0

Solution

Mean = (5 + 7 + 9 + 11) / 4 = 8. Variance = [(5-8)² + (7-8)² + (9-8)² + (11-8)²] / 4 = 3.5.

Correct Answer: B — 3.5

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Q. Calculate the variance of the data set {2, 4, 4, 4, 5, 5, 7, 9}.

A. 4
B. 6
C. 5
D. 3

Solution

Mean = 5, Variance = [(2-5)² + (4-5)² + (4-5)² + (4-5)² + (5-5)² + (5-5)² + (7-5)² + (9-5)²] / 8 = 4.

Correct Answer: B — 6

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Q. Calculate the variance of the data set {4, 8, 6, 5, 3}.

A. 2.5
B. 3.2
C. 1.5
D. 4.0

Solution

Mean = (4+8+6+5+3)/5 = 5.2. Variance = [(4-5.2)² + (8-5.2)² + (6-5.2)² + (5-5.2)² + (3-5.2)²]/5 = 2.5.

Correct Answer: A — 2.5

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Q. Calculate the variance of the following numbers: 1, 2, 3, 4, 5. (2022)

A. 2
B. 1.5
C. 1
D. 0.5

Solution

Mean = (1 + 2 + 3 + 4 + 5) / 5 = 3. Variance = [(1-3)² + (2-3)² + (3-3)² + (4-3)² + (5-3)²] / 5 = 2.

Correct Answer: B — 1.5

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Q. Calculate the vector product of A = (3, 2, 1) and B = (1, 0, 2).

A. (4, 5, -2)
B. (2, 5, -3)
C. (2, -5, 3)
D. (5, -2, 3)

Solution

A × B = |i  j  k|\n|3  2  1|\n|1  0  2| = (4, 5, -2)

Correct Answer: A — (4, 5, -2)

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Q. Calculate the weight of a 10 kg object on the surface of Mars, where the acceleration due to gravity is 3.7 m/s².

A. 37 N
B. 74 N
C. 10 N
D. 100 N

Solution

Weight = mass * gravity = 10 kg * 3.7 m/s² = 37 N

Correct Answer: A — 37 N

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Q. Calculate the weight of a 10 kg object on the surface of the Earth (g = 9.8 m/s²).

A. 98 N
B. 10 N
C. 9.8 N
D. 100 N

Solution

Weight W = m * g = 10 kg * 9.8 m/s² = 98 N.

Correct Answer: A — 98 N

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Q. Calculate the weighted mean of the following data: (10, 2), (20, 3), (30, 5).

A. 20
B. 25
C. 30
D. 35

Solution

Weighted Mean = (10*2 + 20*3 + 30*5) / (2 + 3 + 5) = 220 / 10 = 22.

Correct Answer: B — 25

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Q. Calculate the weighted mean of the following data: (2, 3), (4, 5), (6, 7) where the first number is the weight.

A. 4.5
B. 5
C. 5.5
D. 6

Solution

Weighted mean = (2*3 + 4*5 + 6*7) / (2 + 4 + 6) = (6 + 20 + 42) / 12 = 68 / 12 = 5.67.

Correct Answer: C — 5.5

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Q. Calculate the weighted mean of the numbers 10, 20, and 30 with weights 1, 2, and 3 respectively.

A. 20
B. 25
C. 30
D. 15

Solution

Weighted mean = (10*1 + 20*2 + 30*3) / (1 + 2 + 3) = 140 / 6 = 23.33.

Correct Answer: B — 25

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Q. Calculate the weighted mean of the scores 70, 80, and 90 with weights 1, 2, and 3 respectively.

A. 80
B. 85
C. 90
D. 75

Solution

Weighted mean = (70*1 + 80*2 + 90*3) / (1 + 2 + 3) = 85.

Correct Answer: B — 85

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Q. Calculate ∫ from 0 to 1 of (1 - x^2) dx.

A. 1/3
B. 1/2
C. 2/3
D. 1

Solution

The integral evaluates to [x - x^3/3] from 0 to 1 = (1 - 1/3) = 2/3.

Correct Answer: B — 1/2

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Q. Calculate ∫ from 0 to 1 of (1/x) dx.

A. 0
B. 1
C. ln(1)
D. ln(2)

Solution

The integral evaluates to [ln(x)] from 0 to 1 = ln(1) - ln(0) which diverges.

Correct Answer: C — ln(1)

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Q. Calculate ∫ from 0 to 1 of (2x^2 + 3x + 1) dx.

A. 1
B. 2
C. 3
D. 4

Solution

The integral evaluates to [2x^3/3 + (3/2)x^2 + x] from 0 to 1 = (2/3 + 3/2 + 1) = 3.

Correct Answer: C — 3

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Q. Calculate ∫ from 0 to 1 of (4x^3 - 2x^2 + x) dx.

A. 1/4
B. 1/3
C. 1/2
D. 1

Solution

The integral evaluates to [x^4 - (2/3)x^3 + (1/2)x^2] from 0 to 1 = (1 - 2/3 + 1/2) = 1/6.

Correct Answer: C — 1/2

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Q. Calculate ∫ from 0 to 1 of (4x^3 - 3x^2 + 2x - 1) dx.

A. 0
B. 1
C. 2
D. 3

Solution

The integral evaluates to [x^4 - x^3 + x^2 - x] from 0 to 1 = (1 - 1 + 1 - 1) = 0.

Correct Answer: B — 1

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Q. Calculate ∫ from 0 to 1 of (4x^3 - 4x^2 + 1) dx.

A. 1
B. 2
C. 3
D. 4

Solution

The integral evaluates to [x^4 - (4/3)x^3 + x] from 0 to 1 = 1 - (4/3) + 1 = 2/3.

Correct Answer: A — 1

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Q. Calculate ∫ from 0 to 1 of (6x^2 - 4x + 1) dx.

A. 1
B. 2
C. 3
D. 4

Solution

The integral evaluates to [2x^3 - 2x^2 + x] from 0 to 1 = (2 - 2 + 1) = 1.

Correct Answer: A — 1

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Q. Calculate ∫ from 0 to 1 of (x^2 * e^x) dx.

A. 1/e
B. 2/e
C. 3/e
D. 4/e

Solution

Using integration by parts, the integral evaluates to (2/e - 1/e) = 1/e.

Correct Answer: B — 2/e

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Major Competitive Exams

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