Major Competitive Exams

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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 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 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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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 probability of event A is 0.2 and the probability of event B is 0.5, what is the probability of either A or B occurring if A and B are independent?

A. 0.7
B. 0.6
C. 0.5
D. 0.4

Solution

The probability of either A or B occurring is P(A) + P(B) - P(A and B) = 0.2 + 0.5 - (0.2 * 0.5) = 0.7.

Correct Answer: A — 0.7

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Q. If the probability of event A is 0.4 and event B is 0.5, what is the probability of both events occurring if they are independent?

A. 0.2
B. 0.4
C. 0.5
D. 0.6

Solution

P(A and B) = P(A) * P(B) = 0.4 * 0.5 = 0.2.

Correct Answer: A — 0.2

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Q. If the probability of event A is 0.4 and the probability of event B is 0.5, what is the probability of both A and B occurring if they are independent?

A. 0.2
B. 0.4
C. 0.5
D. 0.9

Solution

For independent events, P(A and B) = P(A) * P(B) = 0.4 * 0.5 = 0.2.

Correct Answer: A — 0.2

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Q. If the probability of event C is 0.2 and the probability of event D is 0.3, what is the probability of either C or D occurring if they are mutually exclusive?

A. 0.5
B. 0.6
C. 0.3
D. 0.2

Solution

For mutually exclusive events, P(C or D) = P(C) + P(D) = 0.2 + 0.3 = 0.5.

Correct Answer: B — 0.6

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Q. If the probability of rain tomorrow is 0.7, what is the probability that it will not rain?

A. 0.3
B. 0.5
C. 0.7
D. 0.9

Solution

The probability that it will not rain is 1 - 0.7 = 0.3.

Correct Answer: A — 0.3

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Q. If the product of two consecutive integers is 72, which of the following pairs could represent these integers?

A. 8 and 9
B. 6 and 7
C. 5 and 6
D. 9 and 10

Solution

6 and 7 are consecutive integers whose product is 42, not 72.

Correct Answer: B — 6 and 7

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Q. If the product of two consecutive integers is 72, which of the following pairs could represent those integers?

A. 8 and 9
B. 6 and 7
C. 5 and 6
D. 4 and 5

Solution

The product of 6 and 7 is 42, while 8 and 9 gives 72. Therefore, the correct pair is 8 and 9.

Correct Answer: B — 6 and 7

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Q. If the product of two numbers is 144 and one of the numbers is 12, what is the other number? (2023)

A. 12
B. 10
C. 8
D. 6

Solution

The other number can be found by dividing the product by the known number: 144 / 12 = 12.

Correct Answer: D — 6

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Q. If the product of two numbers is 48 and one of the numbers is 6, what can be inferred about the other number?

A. It is 8.
B. It is 12.
C. It is 6.
D. It is 4.

Solution

If the product is 48 and one number is 6, then the other number must be 48 ÷ 6 = 8.

Correct Answer: A — It is 8.

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Major Competitive Exams

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