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Q. A student has a 70% chance of passing an exam. What is the probability that the student fails the exam?

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

Solution

The probability of failing the exam is 1 - 0.7 = 0.3.

Correct Answer: A — 0.3

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Q. A student has scores of 60, 70, and 80 in three tests. If he wants an average of 75 after the fourth test, what score does he need?

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

Solution

Let the fourth score be x. (60 + 70 + 80 + x) / 4 = 75 => 210 + x = 300 => x = 90.

Correct Answer: A — 90

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Q. A student is selected at random from a class of 40 students, where 25 are boys and 15 are girls. What is the probability that the student is a girl given that the student is not a boy?

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

Solution

The total number of students that are not boys is 15 (girls). The probability of selecting a girl given that the student is not a boy is 15/15 = 1.

Correct Answer: C — 2/3

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Q. A student is selected at random from a class of 40 students, where 25 are boys and 15 are girls. What is the probability that the student is a boy given that the student is not a girl?

A. 1/2
B. 3/4
C. 5/8
D. 2/5

Solution

If the student is not a girl, they must be a boy. Therefore, P(Boy | Not Girl) = 1.

Correct Answer: B — 3/4

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Q. A student is selected at random from a group of 40 students, where 25 are studying Mathematics and 15 are studying Physics. What is the probability that the student is studying Mathematics given that they are not studying Physics?

A. 5/8
B. 3/8
C. 1/2
D. 1/3

Solution

If the student is not studying Physics, they must be studying Mathematics. Therefore, P(Math | Not Physics) = 1.

Correct Answer: A — 5/8

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Q. A student is selected at random from a group of 40 students, where 25 are studying Mathematics and 15 are studying Physics. What is the probability that the student is studying Physics given that the student is not studying Mathematics?

A. 0
B. 1/3
C. 3/8
D. 1/2

Solution

If the student is not studying Mathematics, they must be studying Physics. Therefore, the probability is 1.

Correct Answer: B — 1/3

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Q. A student is selected at random from a group of students who study Mathematics and Physics. If 70% study Mathematics and 40% study both subjects, what is the probability that a student studies Physics given that they study Mathematics?

A. 0.4
B. 0.3
C. 0.5
D. 0.6

Solution

Using the formula P(Physics|Mathematics) = P(Physics and Mathematics) / P(Mathematics) = 0.4 / 0.7 = 0.571.

Correct Answer: A — 0.4

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Q. A student is selected from a class of 40 students, where 25 are girls and 15 are boys. What is the probability that the student is a girl given that the student is not a boy?

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

Solution

If the student is not a boy, they must be a girl. Therefore, the probability is 1.

Correct Answer: A — 1

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Q. A student measures a length as 30.2 m, but the actual length is 30 m. What is the error in measurement?

A. 0.2 m
B. 0.1 m
C. 0.3 m
D. 0.5 m

Solution

Error = Measured value - True value = 30.2 m - 30 m = 0.2 m.

Correct Answer: A — 0.2 m

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Q. A student measures the length of a rod as 15.3 cm. If the true length is 15 cm, what is the error in measurement?

A. 0.3 cm
B. 0.2 cm
C. 0.1 cm
D. 0.5 cm

Solution

Error in measurement = Measured value - True value = 15.3 - 15 = 0.3 cm.

Correct Answer: A — 0.3 cm

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Q. A student measures the length of a rod as 150 cm with a possible error of 2 cm. What is the range of the true length?

A. 148 cm to 152 cm
B. 149 cm to 151 cm
C. 150 cm to 152 cm
D. 150 cm to 154 cm

Solution

True length can vary from 150 - 2 to 150 + 2, which is 148 cm to 152 cm.

Correct Answer: A — 148 cm to 152 cm

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Q. A student measures the length of a rod multiple times and records the values: 10.1 cm, 10.2 cm, 10.0 cm, 10.3 cm. What is the average length of the rod?

A. 10.0 cm
B. 10.1 cm
C. 10.2 cm
D. 10.3 cm

Solution

Average length = (10.1 + 10.2 + 10.0 + 10.3) / 4 = 10.15 cm.

Correct Answer: B — 10.1 cm

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Q. A student measures the length of a rod multiple times and records values of 10.1 cm, 10.2 cm, and 10.0 cm. What is the average length of the rod?

A. 10.0 cm
B. 10.1 cm
C. 10.2 cm
D. 10.3 cm

Solution

Average length = (10.1 + 10.2 + 10.0) / 3 = 10.1 cm.

Correct Answer: B — 10.1 cm

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Q. A student measures the length of a table as 1.20 m with an uncertainty of 0.02 m. What is the total length if he measures 3 tables?

A. 3.60 m
B. 3.58 m
C. 3.62 m
D. 3.64 m

Solution

Total length = 3 * 1.20 m = 3.60 m. The uncertainty for 3 tables = 3 * 0.02 m = 0.06 m.

Correct Answer: A — 3.60 m

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Q. A student measures the mass of an object as 200 g with an uncertainty of ±2 g. What is the relative uncertainty?

A. 1%
B. 0.5%
C. 2%
D. 0.1%

Solution

Relative uncertainty = (Uncertainty / Measured value) * 100 = (2 / 200) * 100 = 1%.

Correct Answer: B — 0.5%

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Q. A student measures the speed of a car as 60 km/h with an uncertainty of ±2 km/h. What is the percentage error in the speed measurement?

A. 3.33%
B. 2.0%
C. 1.5%
D. 4.0%

Solution

Percentage error = (Uncertainty / Measured value) * 100 = (2 / 60) * 100 = 3.33%.

Correct Answer: A — 3.33%

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Q. A student measures the speed of a car as 60 km/h with an uncertainty of ±2 km/h. What is the percentage uncertainty?

A. 3.33%
B. 2.5%
C. 4.0%
D. 5.0%

Solution

Percentage uncertainty = (Uncertainty / Measured value) * 100 = (2 / 60) * 100 = 3.33%.

Correct Answer: A — 3.33%

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Q. A student measures the speed of a car as 60.0 km/h with an uncertainty of ±2.0 km/h. What is the percentage uncertainty in the speed measurement?

A. 3.33%
B. 2.0%
C. 1.67%
D. 5.0%

Solution

Percentage uncertainty = (absolute uncertainty / measured value) * 100 = (2.0 / 60.0) * 100 = 3.33%.

Correct Answer: A — 3.33%

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Q. A student measures the temperature of water as 25°C with an uncertainty of ±0.5°C. What is the minimum temperature?

A. 24.5°C
B. 25.0°C
C. 25.5°C
D. 26.0°C

Solution

Minimum temperature = Measured value - Uncertainty = 25.0 - 0.5 = 24.5°C.

Correct Answer: A — 24.5°C

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Q. A student measures the time period of a pendulum as 2.0 s with an uncertainty of ±0.1 s. What is the absolute error in the time period?

A. 0.1 s
B. 0.05 s
C. 0.2 s
D. 0.01 s

Solution

The absolute error is given directly as ±0.1 s.

Correct Answer: A — 0.1 s

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Q. A student measures the time period of a pendulum as 2.0 s with an uncertainty of ±0.1 s. What is the percentage uncertainty in the time period?

A. 5%
B. 10%
C. 2.5%
D. 1%

Solution

Percentage uncertainty = (Uncertainty / Measured value) * 100 = (0.1 / 2.0) * 100 = 5%.

Correct Answer: C — 2.5%

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Q. A student measures the time period of a pendulum as 2.0 s with an uncertainty of ±0.1 s. What is the fractional error in the time period?

A. 0.05
B. 0.1
C. 0.02
D. 0.1

Solution

Fractional error = (absolute error / measured value) = 0.1 / 2.0 = 0.05.

Correct Answer: A — 0.05

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Q. A student measures the width of a table as 1.2 m with a possible error of 0.02 m. What is the range of the true width?

A. 1.18 m to 1.22 m
B. 1.20 m to 1.22 m
C. 1.20 m to 1.24 m
D. 1.18 m to 1.20 m

Solution

True width = Measured value ± Absolute error = 1.2 ± 0.02 gives the range 1.18 m to 1.22 m.

Correct Answer: A — 1.18 m to 1.22 m

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Q. A student must score at least 60% to pass an exam. If the exam is out of 250 marks, what is the minimum score required to pass? (2019)

A. 140
B. 150
C. 160
D. 170

Solution

Minimum Score = (60 / 100) * 250 = 150.

Correct Answer: B — 150

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Q. A student must score at least 60% to pass. If the total marks are 250, what is the minimum score required? (2019)

A. 120
B. 130
C. 140
D. 150

Solution

Minimum Score = 60% of 250 = (60/100) * 250 = 150.

Correct Answer: C — 140

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Q. A student needs to score at least 60% to pass an exam. If the exam is out of 150 marks, what is the minimum score required to pass? (2023)

A. 90
B. 80
C. 70
D. 60

Solution

Minimum score to pass = 60% of 150 = 0.6 * 150 = 90.

Correct Answer: A — 90

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Q. A student needs to score at least 60% to pass an exam. If the exam is out of 200 marks, what is the minimum score required to pass?

A. 100
B. 120
C. 140
D. 160

Solution

Minimum score to pass = 60% of 200 = 0.60 * 200 = 120.

Correct Answer: B — 120

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Q. A student needs to score at least 75% to qualify for a scholarship. If the total marks are 400, what is the minimum score required? (2022)

A. 250
B. 300
C. 350
D. 375

Solution

Minimum Score = (75 / 100) * 400 = 300.

Correct Answer: B — 300

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Q. A student needs to score at least 75% to qualify for an award. If the total marks are 200, what is the minimum score required? (2022)

A. 140
B. 150
C. 160
D. 170

Solution

Minimum Score = 75% of 200 = (75/100) * 200 = 150.

Correct Answer: B — 150

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Q. A student needs to score at least 80% in an exam of 500 marks to get a scholarship. What is the minimum score required? (2023)

A. 350
B. 400
C. 450
D. 500

Solution

Minimum Score = (80 / 100) * 500 = 400.

Correct Answer: B — 400

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Major Competitive Exams

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