Major Competitive Exams

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Q. If the power factor of an AC circuit is 0.8, what is the angle between the current and voltage? (2021)

A. 36.87°
B. 53.13°
C. 60°
D. 45°

Solution

The angle θ can be found using cos(θ) = power factor. Thus, θ = cos⁻¹(0.8) ≈ 36.87°.

Correct Answer: B — 53.13°

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Q. If the pressure of a gas is increased while keeping the temperature constant, what happens to its volume? (2020)

A. It increases
B. It decreases
C. It remains the same
D. It becomes zero

Solution

According to Boyle's Law, P * V = constant at constant temperature, so if P increases, V must decrease.

Correct Answer: B — It decreases

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Q. If the price of a book is increased by 10% and the new price is $22, what was the original price?

A. $20
B. $18
C. $19
D. $21

Solution

Let the original price be x. The new price after a 10% increase is x + 0.1x = 1.1x. Setting this equal to $22 gives us 1.1x = 22, so x = 22/1.1 = 20. Therefore, the original price was $20.

Correct Answer: A — $20

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Q. If the price of a book is increased by 10% and then decreased by 10%, what is the net change in price?

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

Solution

Let the original price be $100. After a 10% increase, the price becomes $110. After a 10% decrease, the price becomes $110 - $11 = $99. The net change is -1%, so the answer is 0%.

Correct Answer: A — 0%

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Q. If the price of a book is increased by 20% and the new price is $24, what was the original price?

A. $18
B. $20
C. $22
D. $25

Solution

Let the original price be x. Then, x + 0.2x = 24, or 1.2x = 24. Thus, x = 24 / 1.2 = 20.

Correct Answer: B — $20

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Q. If the price of a book is increased by 20% and then decreased by 20%, what is the net change in price?

A. 0%
B. 4%
C. 5%
D. 6%

Solution

Let the original price be Rs. 100. After a 20% increase, price = 120. After a 20% decrease, price = 120 - 24 = 96. Net change = (96 - 100)/100 * 100 = -4%.

Correct Answer: B — 4%

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Q. If the price of a book is increased by 20% and then decreased by 20%, what is the net change in the price?

A. 0%
B. 4%
C. 5%
D. 6%

Solution

Let the original price be $100. After a 20% increase, the price becomes $120. After a 20% decrease, the price becomes $120 - 0.20 × 120 = $96. The net change is (96 - 100)/100 × 100 = -4%.

Correct Answer: C — 5%

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Q. If the price of a commodity increases from $20 to $25, what is the percentage increase in price?

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

Solution

Percentage increase = ((25 - 20) / 20) * 100 = 25%

Correct Answer: A — 20%

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Q. If the price of a commodity increases from $50 to $60, what is the percentage increase in price?

A. 10%
B. 20%
C. 15%
D. 25%

Solution

Percentage increase = ((60 - 50) / 50) * 100 = 20%

Correct Answer: B — 20%

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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 price of a shirt is increased by 20% and the new price is $60, what was the original price?

A. $40
B. $50
C. $45
D. $55

Solution

Let the original price be x. Then, x + 0.2x = 60, which gives x = 60/1.2 = $50.

Correct Answer: A — $40

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Q. If the price of a shirt is increased by 20% and then decreased by 20%, what is the net change in the price?

A. 0%
B. 4%
C. 5%
D. 6%

Solution

Let the original price be 100. After a 20% increase, price = 120. After a 20% decrease, price = 120 - 24 = 96. Net change = (96 - 100)/100 * 100% = -4%.

Correct Answer: B — 4%

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Q. If the price of a shirt is increased by 20% and then decreased by 20%, what is the net change in the price of the shirt?

A. 0%
B. 4%
C. 8%
D. 10%

Solution

Let the original price be 100. After a 20% increase, the price is 120. After a 20% decrease, the price is 96. Net change = (96-100)/100 * 100% = -4%.

Correct Answer: B — 4%

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Q. If the price of a shirt is increased by 25% and then decreased by 20%, what is the final price if the original price was $40?

A. $36
B. $38
C. $40
D. $42

Solution

New price after increase = 40 + 25% of 40 = 50; New price after decrease = 50 - 20% of 50 = 40.

Correct Answer: B — $38

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Q. If the price of a stock increases from $50 to $75, what is the return on investment (ROI) as a percentage?

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

Solution

ROI = ((Final price - Initial price) / Initial price) * 100 = ((75 - 50) / 50) * 100 = 50%

Correct Answer: D — 100%

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Q. If the principal amount is $2000 and the total amount after 3 years at a certain rate of simple interest is $2400, what is the rate of interest? (2000)

A. 5%
B. 6.67%
C. 10%
D. 12%

Solution

The interest earned is $400. Using SI = PRT, we have 400 = 2000 * R * 3. Solving for R gives R = 6.67%.

Correct Answer: B — 6.67%

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Q. If the principal is $2000 and the rate of interest is 4% per annum, what will be the total amount after 5 years at simple interest? (2000)

A. $2400
B. $2500
C. $2600
D. $2700

Solution

Using A = P + SI, where SI = P * r * t / 100, we have SI = 2000 * 4 * 5 / 100 = $400. Thus, A = 2000 + 400 = $2400.

Correct Answer: A — $2400

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Q. If the principal is $800 and the rate of interest is 4% per annum, what will be the total amount after 3 years at simple interest?

A. $840
B. $850
C. $860
D. $870

Solution

Using the simple interest formula, Total Amount = Principal + SI = 800 + (800 * 4 * 3) / 100 = $840.

Correct Answer: A — $840

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Q. If the principal is $800 and the rate of interest is 6% per annum, what will be the total amount after 4 years at simple interest?

A. $960
B. $1040
C. $800
D. $840

Solution

Total amount = Principal + SI = 800 + (800 * 6/100 * 4) = $1040.

Correct Answer: B — $1040

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Q. If the principal is Rs. 5000 and the rate of interest is 12% per annum, what will be the total amount after 3 years under simple interest?

A. Rs. 5600
B. Rs. 5800
C. Rs. 6000
D. Rs. 6200

Solution

Simple Interest = P * r * t = 5000 * 0.12 * 3 = 1800. Total Amount = Principal + Interest = 5000 + 1800 = 6800.

Correct Answer: B — Rs. 5800

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Q. If the principal quantum number n = 4 and the azimuthal quantum number l = 2, what is the maximum number of electrons in this subshell?

A. 8
B. 10
C. 14
D. 16

Solution

The maximum number of electrons in a subshell is given by 2(2l + 1). For l = 2, it is 2(2*2 + 1) = 10.

Correct Answer: C — 14

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Q. If the principal quantum number n = 4, what are the possible values of l?

A. 0, 1, 2, 3
B. 1, 2, 3, 4
C. 0, 1, 2, 3, 4
D. 0, 1, 2

Solution

For n=4, l can take values 0, 1, 2, or 3.

Correct Answer: A — 0, 1, 2, 3

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Q. If the principal quantum number n = 4, what are the possible values of the azimuthal quantum number l?

A. 0, 1, 2, 3
B. 1, 2, 3, 4
C. 0, 1, 2, 3, 4
D. 0, 1, 2

Solution

For n=4, l can take values from 0 to n-1, which are 0, 1, 2, and 3.

Correct Answer: A — 0, 1, 2, 3

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Q. If the probability of a student passing an exam is 0.75, what is the probability that the student fails?

A. 0.25
B. 0.5
C. 0.75
D. 0.1

Solution

The probability of failing is 1 - P(passing) = 1 - 0.75 = 0.25.

Correct Answer: A — 0.25

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Q. If the probability of an event A is 0.3, what is the probability of the event not occurring?

A. 0.7
B. 0.3
C. 0.5
D. 0.2

Solution

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

Correct Answer: A — 0.7

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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 A is 0.7, what is the probability of the event not occurring?

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

Solution

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

Correct Answer: A — 0.3

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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 is 0.7, what is the probability of its complement?

A. 0.3
B. 0.7
C. 1
D. 0.5

Solution

Probability of complement = 1 - P(event) = 1 - 0.7 = 0.3.

Correct Answer: A — 0.3

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Q. If the probability of an event is 0.7, what is the probability of the event not occurring?

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

Solution

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

Correct Answer: A — 0.3

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Major Competitive Exams

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