NDA Exam Preparation Resources | Soulshift Education

NDA

English General Knowledge Mathematics

Q. If the Parliament is in session for 120 days in a year and the Lok Sabha meets for 75% of those days, how many days does the Lok Sabha meet?

A. 90
B. 80
C. 75
D. 100

Solution

Days Lok Sabha meets = 75% of 120 = 0.75 * 120 = 90.

Correct Answer: A — 90

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Q. If the Parliament is in session for 90 days in a year and the Lok Sabha meets for 60% of those days, how many days does the Lok Sabha meet?

A. 54
B. 60
C. 66
D. 72

Solution

Days Lok Sabha meets = 60% of 90 = 0.60 * 90 = 54 days.

Correct Answer: A — 54

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Q. If the Parliament meets for 120 days in a year and the Lok Sabha meets for 75% of those days, how many days does the Lok Sabha meet?

A. 90
B. 80
C. 75
D. 100

Solution

75% of 120 = 0.75 * 120 = 90 days.

Correct Answer: A — 90

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Q. If the perimeter of a rectangle is 20 cm and the length is 6 cm, what is the width?

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

Solution

Perimeter P = 2(length + width). So, 20 = 2(6 + width). Solving gives width = 4 cm.

Correct Answer: B — 5 cm

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Q. If the perimeter of a rectangle is 30 cm and the length is 10 cm, what is the width?

A. 5 cm
B. 10 cm
C. 7.5 cm
D. 15 cm

Solution

Perimeter P = 2(length + width). So, 30 = 2(10 + width). Dividing by 2 gives 15 = 10 + width. Thus, width = 15 - 10 = 5 cm.

Correct Answer: A — 5 cm

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Q. If the perimeter of a rectangle is 50 cm and the length is 15 cm, what is the width? (2020)

A. 10 cm
B. 12.5 cm
C. 15 cm
D. 20 cm

Solution

Perimeter = 2(length + width). So, 50 = 2(15 + width). Solving gives width = 10 cm.

Correct Answer: B — 12.5 cm

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Q. If the perimeter of a square is 36 cm, what is the length of one side? (2023)

A. 9 cm
B. 12 cm
C. 6 cm
D. 15 cm

Solution

The perimeter of a square is given by 4 times the length of one side. Therefore, if the perimeter is 36 cm, the length of one side is 36 cm / 4 = 9 cm.

Correct Answer: B — 12 cm

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Q. If the perimeter of a square is 64 cm, what is the length of one side? (2023)

A. 12 cm
B. 14 cm
C. 16 cm
D. 18 cm

Solution

Perimeter of a square = 4 × side. Therefore, 4 × side = 64 cm, giving side = 64/4 = 16 cm.

Correct Answer: C — 16 cm

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Q. If the perimeter of a triangle is 30 cm and the lengths of two sides are 10 cm and 12 cm, what is the length of the third side? (2020)

A. 8 cm
B. 10 cm
C. 12 cm
D. 14 cm

Solution

Let the third side be x. Then, 10 + 12 + x = 30, so x = 30 - 22 = 8 cm.

Correct Answer: A — 8 cm

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Q. If the perimeter of triangle DEF is 36 cm and the lengths of sides DE and EF are 10 cm and 12 cm respectively, what is the length of side DF? (2020)

A. 10 cm
B. 12 cm
C. 14 cm
D. 16 cm

Solution

Perimeter = DE + EF + DF. Therefore, DF = 36 - (10 + 12) = 14 cm.

Correct Answer: C — 14 cm

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Q. If the pH of a river is measured to be 7.5, what type of water is it considered? (2020)

A. Acidic
B. Neutral
C. Alkaline
D. Distilled

Solution

A pH greater than 7 is considered alkaline.

Correct Answer: C — Alkaline

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Q. If the pH of a river water is 8, what type of soil is likely to be found in the surrounding area?

A. Acidic soil
B. Neutral soil
C. Alkaline soil
D. Saline soil

Solution

A pH of 8 indicates alkaline soil.

Correct Answer: C — Alkaline soil

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Q. If the pH of a solution is 11, what is the concentration of hydroxide ions [OH-] in the solution?

A. 1 x 10^-3 M
B. 1 x 10^-11 M
C. 1 x 10^-2 M
D. 1 x 10^-14 M

Solution

pOH = 14 - pH = 3, [OH-] = 10^-3 M.

Correct Answer: C — 1 x 10^-2 M

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Q. If the point (x, y) lies on the line 3x - 4y = 12, what is the value of y when x = 4? (2023)

A. 0
B. 3
C. 4
D. 2

Solution

Substituting x = 4 gives 3(4) - 4y = 12 => 12 - 4y = 12 => y = 0.

Correct Answer: D — 2

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Q. If the point (x, y) lies on the line 4x - 5y = 20, what is the value of y when x = 0?

A. 4
B. 5
C. 0
D. -4

Solution

Substituting x = 0: 4(0) - 5y = 20 => -5y = 20 => y = -4.

Correct Answer: B — 5

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Q. If the polynomial equation x^3 - 6x^2 + 11x - 6 = 0 has roots a, b, and c, what is the value of a + b + c? (2021)

A. 6
B. 11
C. 3
D. 0

Solution

By Vieta's formulas, the sum of the roots (a + b + c) of the polynomial x^3 - 6x^2 + 11x - 6 is equal to the coefficient of x^2 with the opposite sign, which is 6.

Correct Answer: A — 6

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Q. If the population of a city increases by 10% every year, what will be the population after 2 years if the current population is 1000? (2021)

A. 1210
B. 1100
C. 1020
D. 1200

Solution

Population after 1 year = 1000 * 1.10 = 1100. Population after 2 years = 1100 * 1.10 = 1210.

Correct Answer: A — 1210

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Q. If the population of a city is 1 million and it grows at a rate of 2% per year, what will be the population after one year? (2023)

A. 1.02 million
B. 1.05 million
C. 1.1 million
D. 1.1 million

Solution

Population after one year = Current Population * (1 + Growth Rate) = 1 million * (1 + 0.02) = 1 million * 1.02 = 1.02 million.

Correct Answer: A — 1.02 million

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Q. If the population of a country increases by 5% every year, what will be the population after 2 years if the current population is 100,000?

A. 110,250
B. 105,000
C. 120,000
D. 102,500

Solution

Population after 2 years = 100,000 * (1 + 0.05)^2 = 100,000 * 1.1025 = 110,250.

Correct Answer: A — 110,250

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Q. If the population of a town increases by 10% every year, what will be the population after 2 years if the current population is 1000? (2021)

A. 1210
B. 1100
C. 1020
D. 1200

Solution

Population after 1 year = 1000 * 1.10 = 1100. Population after 2 years = 1100 * 1.10 = 1210.

Correct Answer: A — 1210

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Q. If the position vector of point P is given by r = 2i + 3j + 4k, what is the distance from the origin to point P?

A. 5
B. 6
C. 7
D. 8

Solution

Distance = |r| = √(2^2 + 3^2 + 4^2) = √(4 + 9 + 16) = √29.

Correct Answer: B — 6

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Q. If the position vector of point P is given by r = 2i + 3j + 4k, what is the x-component of r?

A. 2
B. 3
C. 4
D. 5

Solution

The x-component of r is 2.

Correct Answer: A — 2

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Q. If the position vector of point P is given by r = 2i + 3j + 4k, what is the x-coordinate of point P? (2020)

A. 2
B. 3
C. 4
D. 5

Solution

The x-coordinate of point P is the coefficient of i in the position vector, which is 2.

Correct Answer: A — 2

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Q. If the position vector of point P is given by r = 3i + 4j, what is the distance of point P from the origin?

A. 5
B. 7
C. 4
D. 3

Solution

Distance = |r| = √(3^2 + 4^2) = √(9 + 16) = √25 = 5.

Correct Answer: A — 5

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Q. If the price of a shirt is $40 after a 20% discount, what was the original price?

A. $50
B. $60
C. $70
D. $80

Solution

Let the original price be x. Then, x - 0.2x = 40, which gives 0.8x = 40. Thus, x = 40 / 0.8 = $50.

Correct Answer: A — $50

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Q. If the probability of an event A is 0.4, what is the probability of the event not occurring? (2021)

A. 0.4
B. 0.6
C. 0.8
D. 0.2

Solution

Probability of not A = 1 - P(A) = 1 - 0.4 = 0.6.

Correct Answer: B — 0.6

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Q. If the probability of an event is 0.25, what are the odds in favor of the event?

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

Solution

Odds in favor = probability of event / (1 - probability of event) = 0.25 / 0.75 = 1:3.

Correct Answer: A — 1:3

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Q. If the probability of an event occurring is 0.3, what is the probability of it not occurring? (2023)

A. 0.3
B. 0.7
C. 0.5
D. 0.1

Solution

Probability of not occurring = 1 - P(event) = 1 - 0.3 = 0.7.

Correct Answer: B — 0.7

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Q. If the quadratic equation ax^2 + bx + c = 0 has roots p and q, what is the value of p + q? (2020)

A. -b/a
B. b/a
C. c/a
D. -c/a

Solution

By Vieta's formulas, the sum of the roots p + q = -b/a.

Correct Answer: A — -b/a

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Q. If the quadratic equation x^2 + 2x + 1 = 0 is solved, what are the roots? (2022)

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

Solution

The equation can be factored as (x + 1)(x + 1) = 0, giving the root -1 with multiplicity 2.

Correct Answer: A — -1

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