Modern India: Essential Study Resources for Competitive Exams

Modern India

Q. A box contains 3 red balls and 2 blue balls. What is the probability of picking a red ball? (2023)

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

Solution

Probability = Number of favorable outcomes / Total outcomes = 3/(3+2) = 3/5 = 0.6.

Correct Answer: A — 0.6

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Q. A box contains 3 red balls and 5 blue balls. If one ball is drawn at random, what is the probability that it is red? (2019)

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

Solution

Total balls = 3 + 5 = 8. Probability of red = 3/8.

Correct Answer: A — 3/8

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Q. A box contains 3 red balls and 5 blue balls. What is the probability of drawing a red ball? (2019)

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

Solution

Total balls = 3 + 5 = 8. Probability of red ball = 3/8.

Correct Answer: A — 3/8

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Q. A box contains 3 red, 5 blue, and 2 green balls. What is the probability of drawing a blue ball? (2021)

A. 1/2
B. 5/10
C. 1/5
D. 1/3

Solution

Total balls = 3 + 5 + 2 = 10. Probability of blue = Number of blue balls / Total balls = 5/10 = 1/2.

Correct Answer: A — 1/2

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Q. A car covers a distance of 150 km in 3 hours. What is the speed of the car in km/h? (2022)

A. 45 km/h
B. 50 km/h
C. 55 km/h
D. 60 km/h

Solution

Speed = Distance / Time = 150 km / 3 h = 50 km/h.

Correct Answer: B — 50 km/h

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Q. A car covers a distance of 240 km in 3 hours. What is its average speed? (2021)

A. 80 km/h
B. 70 km/h
C. 60 km/h
D. 90 km/h

Solution

Average Speed = Total Distance / Total Time = 240 km / 3 h = 80 km/h.

Correct Answer: A — 80 km/h

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Q. A car travels 60 km in 1 hour and 30 minutes. What is the average speed of the car in km/h? (2019)

A. 40
B. 50
C. 45
D. 60

Solution

Time taken = 1.5 hours. Average speed = Distance / Time = 60 km / 1.5 h = 40 km/h.

Correct Answer: C — 45

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Q. A car travels 60 km in 1 hour and then 90 km in 1.5 hours. What is the average speed of the car for the entire journey?

A. 70 km/h
B. 75 km/h
C. 80 km/h
D. 85 km/h

Solution

Total distance = 60 + 90 = 150 km. Total time = 1 + 1.5 = 2.5 hours. Average speed = Total distance / Total time = 150 / 2.5 = 60 km/h.

Correct Answer: B — 75 km/h

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Q. A car travels 60 km in 1 hour. How far will it travel in 2.5 hours at the same speed? (2022)

A. 150 km
B. 120 km
C. 180 km
D. 100 km

Solution

Distance = Speed * Time = 60 km/h * 2.5 h = 150 km.

Correct Answer: A — 150 km

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Q. A man invests Rs. 5000 at a rate of 5% per annum compounded annually. What will be the amount after 3 years? (2020)

A. Rs. 5750
B. Rs. 6300
C. Rs. 5000
D. Rs. 5798.75

Solution

Amount = P(1 + r)^n = 5000(1 + 0.05)^3 = 5000(1.157625) = 5798.75.

Correct Answer: D — Rs. 5798.75

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Q. A man invests Rs. 5000 at an interest rate of 5% per annum. How much interest will he earn in 3 years? (2020)

A. 750
B. 500
C. 1500
D. 1000

Solution

Simple Interest = Principal * Rate * Time = 5000 * 0.05 * 3 = 750.

Correct Answer: A — 750

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Q. A man spends 40% of his income on necessities and 25% on savings. If he has $200 left, what is his total income? (2020)

A. $500
B. $600
C. $400
D. $300

Solution

Let total income = x. Then, 0.35x = 200. Therefore, x = 200 / 0.35 = $600.

Correct Answer: B — $600

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Q. A rectangle has a length of 10 cm and a width of 5 cm. What is its area? (2022)

A. 50 cm²
B. 60 cm²
C. 40 cm²
D. 30 cm²

Solution

Area = Length * Width = 10 cm * 5 cm = 50 cm².

Correct Answer: A — 50 cm²

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Q. A rectangle has a length of 10 cm and a width of 5 cm. What is the area of the rectangle? (2022)

A. 50 cm²
B. 25 cm²
C. 15 cm²
D. 30 cm²

Solution

Area = Length × Width = 10 cm × 5 cm = 50 cm².

Correct Answer: A — 50 cm²

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Q. A shopkeeper sells a shirt for $300 after giving a discount of 20%. What was the original price of the shirt? (2020)

A. $360
B. $400
C. $320
D. $300

Solution

Let the original price be x. Then, x - 0.20x = 300. Therefore, 0.80x = 300, x = 300 / 0.80 = $400.

Correct Answer: B — $400

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Q. A shopkeeper sells a shirt for Rs. 800 after giving a discount of 20%. What was the original price of the shirt? (2020)

A. Rs. 1000
B. Rs. 900
C. Rs. 800
D. Rs. 750

Solution

Let the original price be x. Then, x - 0.20x = 800 => 0.80x = 800 => x = 1000.

Correct Answer: A — Rs. 1000

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Q. A shopkeeper sells a shirt for Rs. 800 after giving a discount of 20%. What was the marked price of the shirt? (2020)

A. Rs. 1000
B. Rs. 900
C. Rs. 800
D. Rs. 750

Solution

Let marked price = x. Then, 0.8x = 800 => x = 800/0.8 = 1000.

Correct Answer: A — Rs. 1000

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Q. A shopkeeper sells an article for Rs. 800, making a profit of 20%. What was the cost price of the article? (2020)

A. Rs. 600
B. Rs. 640
C. Rs. 500
D. Rs. 700

Solution

Let CP = x. Then, 800 = x + 0.20x = 1.20x. Therefore, x = 800 / 1.20 = 666.67.

Correct Answer: A — Rs. 600

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Q. A train travels at a speed of 80 km/h. How long will it take to cover a distance of 240 km?

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

Solution

Time = Distance / Speed = 240 km / 80 km/h = 3 hours.

Correct Answer: B — 3 hours

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Q. A train travels at a speed of 90 km/h. How far will it travel in 2.5 hours? (2019)

A. 200 km
B. 225 km
C. 250 km
D. 300 km

Solution

Distance = Speed * Time = 90 km/h * 2.5 h = 225 km.

Correct Answer: B — 225 km

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Q. A train travels at a speed of 90 km/h. How long will it take to cover 270 km? (2020)

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

Solution

Time = Distance / Speed = 270 km / 90 km/h = 3 hours.

Correct Answer: B — 3 hours

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Q. A train travels at a speed of 90 km/h. How long will it take to cover a distance of 270 km? (2021)

A. 2.5 hours
B. 3 hours
C. 3.5 hours
D. 4 hours

Solution

Time = Distance / Speed = 270 km / 90 km/h = 3 hours.

Correct Answer: B — 3 hours

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Q. If 3x + 2 = 11, what is the value of x? (2023)

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

Solution

3x + 2 = 11 => 3x = 9 => x = 3.

Correct Answer: A — 2

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Q. If a book costs Rs. 150 and is on a 20% discount, what is the sale price? (2023)

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

Solution

Discount = 20% of 150 = 150 * 20 / 100 = 30. Sale price = 150 - 30 = 120.

Correct Answer: A — 120

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Q. If a book costs Rs. 150 and is on sale for 20% off, what is the sale price? (2022)

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

Solution

Discount = 20% of 150 = 30. Sale price = 150 - 30 = 120.

Correct Answer: A — 120

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Q. If a book costs Rs. 250 and is on sale for 20% off, what is the sale price? (2023)

A. 200
B. 220
C. 180
D. 250

Solution

Discount = 20% of 250 = 50. Sale price = 250 - 50 = 200.

Correct Answer: A — 200

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Q. If a car travels 60 km in 1 hour, how far will it travel in 2.5 hours at the same speed? (2019)

A. 150 km
B. 120 km
C. 180 km
D. 100 km

Solution

Distance = Speed × Time = 60 km/h × 2.5 h = 150 km.

Correct Answer: A — 150 km

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Q. If a car travels 60 km in 1 hour, how long will it take to travel 180 km at the same speed? (2019)

A. 2 hours
B. 3 hours
C. 4 hours
D. 1.5 hours

Solution

Time = Distance/Speed = 180 km / 60 km/h = 3 hours.

Correct Answer: B — 3 hours

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Q. If a rectangle has a length of 10 cm and a width of 5 cm, what is the area of the rectangle? (2022)

A. 50 cm²
B. 55 cm²
C. 60 cm²
D. 65 cm²

Solution

Area = length × width = 10 cm × 5 cm = 50 cm².

Correct Answer: A — 50 cm²

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Q. If a triangle has sides of lengths 3 cm, 4 cm, and 5 cm, what is its area? (2021)

A. 6 cm²
B. 12 cm²
C. 8 cm²
D. 10 cm²

Solution

Area = 1/2 × base × height = 1/2 × 3 cm × 4 cm = 6 cm².

Correct Answer: A — 6 cm²

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Modern India

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