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Q. A cone has a base radius of 3 m and a height of 4 m. What is the surface area of the cone?

A. 15π
B. 18π
C. 21π
D. 24π

Solution

The surface area of a cone is given by SA = πr(r + l), where l is the slant height. Here, l = √(3² + 4²) = 5, so SA = π(3)(3 + 5) = 24π.

Correct Answer: C — 21π

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Q. A cone has a base radius of 4 cm and a height of 9 cm. What is its volume?

A. 12π
B. 36π
C. 48π
D. 72π

Solution

The volume of a cone is given by V = (1/3)πr²h. Here, r = 4 and h = 9, so V = (1/3)π(4)²(9) = 48π.

Correct Answer: B — 36π

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Q. A cone has a base radius of 5 cm and a height of 12 cm. What is its surface area?

A. 50π cm²
B. 65π cm²
C. 70π cm²
D. 80π cm²

Solution

The surface area of a cone is given by SA = πr(r + l), where l is the slant height. Here, l = √(5² + 12²) = 13, so SA = π(5)(5 + 13) = 90π cm².

Correct Answer: B — 65π cm²

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Q. A cone has a radius of 4 cm and a height of 9 cm. What is its volume? (Use π = 3.14) (2023)

A. 50.24 cm³
B. 113.04 cm³
C. 150.72 cm³
D. 226.08 cm³

Solution

Volume = (1/3)πr²h = (1/3) * 3.14 * (4)² * 9 = 113.04 cm³.

Correct Answer: B — 113.04 cm³

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Q. A conical pendulum consists of a mass attached to a string that swings in a horizontal circle. If the angle of the string with the vertical is θ, what is the expression for the tension in the string?

A. mg/cos(θ)
B. mg/sin(θ)
C. mg/tan(θ)
D. mg

Solution

Tension T = mg/cos(θ) to balance the vertical component of weight.

Correct Answer: A — mg/cos(θ)

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Q. A conical pendulum consists of a mass m attached to a string of length L, swinging in a horizontal circle. What is the expression for the tension in the string?

A. T = mg
B. T = mg/cos(θ)
C. T = mg/sin(θ)
D. T = m(v²/r)

Solution

In a conical pendulum, T = mg/cos(θ) where θ is the angle with the vertical.

Correct Answer: B — T = mg/cos(θ)

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Q. A conical pendulum swings in a horizontal circle. If the angle of the string with the vertical is θ, what is the expression for the tension in the string?

A. T = mg
B. T = mg/cos(θ)
C. T = mg/sin(θ)
D. T = mg tan(θ)

Solution

The vertical component of tension balances the weight: T cos(θ) = mg, thus T = mg/cos(θ).

Correct Answer: B — T = mg/cos(θ)

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Q. A conical pendulum swings in a horizontal circle. If the angle of the string with the vertical is θ, what is the relationship between the tension and the gravitational force acting on the pendulum bob?

A. T = mg
B. T = mg cos(θ)
C. T = mg sin(θ)
D. T = mg tan(θ)

Solution

The vertical component of tension balances the weight: T cos(θ) = mg.

Correct Answer: B — T = mg cos(θ)

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Q. A conical pendulum swings in a horizontal circle. If the angle of the string with the vertical is θ, what is the relationship between the tension in the string and the gravitational force?

A. T = mg
B. T = mg/cos(θ)
C. T = mg/sin(θ)
D. T = mg/tan(θ)

Solution

Tension T provides the centripetal force and balances the weight, T = mg/cos(θ).

Correct Answer: B — T = mg/cos(θ)

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Q. A conical pendulum swings in a horizontal circle. If the angle of the string with the vertical is θ, what is the relationship between the tension in the string and the gravitational force acting on the pendulum bob?

A. T = mg
B. T = mg cos(θ)
C. T = mg sin(θ)
D. T = mg tan(θ)

Solution

Tension provides the vertical component to balance the weight: T cos(θ) = mg.

Correct Answer: B — T = mg cos(θ)

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Q. A conical pendulum swings in a horizontal circle. If the angle of the string with the vertical increases, what happens to the tension in the string?

A. Increases
B. Decreases
C. Remains the same
D. Becomes zero

Solution

As the angle increases, the vertical component of tension must increase to balance the weight.

Correct Answer: A — Increases

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Q. A conical pendulum swings with a constant speed. If the angle of the string with the vertical is θ, what is the expression for the tension in the string?

A. mg/cos(θ)
B. mg/sin(θ)
C. mg/tan(θ)
D. mg

Solution

Tension T = mg/cos(θ) to balance the vertical component of weight.

Correct Answer: A — mg/cos(θ)

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Q. A container has 30 liters of a mixture of water and alcohol in the ratio 2:1. How much alcohol is in the container?

A. 5 liters
B. 10 liters
C. 15 liters
D. 20 liters

Solution

Total parts = 2 + 1 = 3. Volume of alcohol = (1/3) * 30 = 10 liters.

Correct Answer: B — 10 liters

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Q. A container has 60 liters of a mixture of milk and water in the ratio 5:1. How much water is in the mixture?

A. 10 liters
B. 12 liters
C. 15 liters
D. 8 liters

Solution

The total parts = 5 + 1 = 6. Water = (1/6) * 60 = 10 liters.

Correct Answer: B — 12 liters

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Q. A container has a mixture of milk and water in the ratio 5:3. If 4 liters of water is added, what will be the new ratio of milk to water?

A. 5:7
B. 5:6
C. 5:8
D. 5:9

Solution

Initial water = 3 parts. After adding 4 liters, new water = 3 + 4 = 7 parts. Ratio = 5:7.

Correct Answer: B — 5:6

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Q. A convex lens has a focal length of 15 cm. What is the power of the lens?

A. +6.67 D
B. +7.5 D
C. +10 D
D. +15 D

Solution

Power (P) = 1/f (in meters). f = 0.15 m, so P = 1/0.15 = +6.67 D.

Correct Answer: B — +7.5 D

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Q. A convex lens has a focal length of 20 cm. If an object is placed 60 cm from the lens, what is the distance of the image from the lens?

A. 15 cm
B. 30 cm
C. 45 cm
D. 60 cm

Solution

Using the lens formula 1/f = 1/v - 1/u, we find v = 30 cm.

Correct Answer: C — 45 cm

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Q. A convex lens has a focal length of 20 cm. If an object is placed 60 cm from the lens, what is the position of the image?

A. 15 cm
B. 20 cm
C. 30 cm
D. 40 cm

Solution

Using the lens formula, 1/f = 1/v - 1/u, we find v = 30 cm.

Correct Answer: D — 40 cm

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Q. A convex lens has a focal length of 20 cm. If an object is placed at a distance of 30 cm from the lens, what is the distance of the image from the lens?

A. 60 cm
B. 15 cm
C. 30 cm
D. 10 cm

Solution

Using the lens formula 1/f = 1/v - 1/u, we find v = 60 cm.

Correct Answer: A — 60 cm

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Q. A convex lens has a focal length of 20 cm. If an object is placed at a distance of 40 cm from the lens, what is the distance of the image from the lens?

A. 20 cm
B. 40 cm
C. 60 cm
D. 80 cm

Solution

Using the lens formula 1/f = 1/v - 1/u, where f = 20 cm and u = -40 cm, we find v = 20 cm. The image is formed at 20 cm on the opposite side.

Correct Answer: A — 20 cm

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Q. A convex lens has a focal length of 20 cm. If an object is placed at a distance of 60 cm from the lens, what is the distance of the image from the lens?

A. 15 cm
B. 30 cm
C. 45 cm
D. 60 cm

Solution

Using the lens formula 1/f = 1/v - 1/u, we find v = 30 cm.

Correct Answer: C — 45 cm

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Q. A convex lens has a focal length of 20 cm. What is the power of the lens?

A. -5 D
B. 5 D
C. 20 D
D. 0.05 D

Solution

Power (P) = 1/f (in meters). f = 20 cm = 0.2 m, so P = 1/0.2 = 5 D.

Correct Answer: B — 5 D

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Q. A convex lens has a focal length of 25 cm. What is the power of the lens? (2021)

A. +2 D
B. +4 D
C. +6 D
D. +8 D

Solution

Power (P) = 1/f (in meters). Thus, P = 1/0.25 = +4 D.

Correct Answer: B — +4 D

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Q. A convoy of military trucks travels 240 km in 4 hours. What is the average speed of the convoy? (2023)

A. 50 km/h
B. 60 km/h
C. 70 km/h
D. 80 km/h

Solution

Average Speed = Total Distance / Total Time = 240 km / 4 h = 60 km/h

Correct Answer: B — 60 km/h

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Q. A convoy of trucks travels 240 km in 4 hours. What is the average speed of the convoy? (2023)

A. 50 km/h
B. 60 km/h
C. 70 km/h
D. 80 km/h

Solution

Average Speed = Total Distance / Total Time = 240 km / 4 h = 60 km/h

Correct Answer: B — 60 km/h

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Q. A convoy of trucks travels 300 km at an average speed of 75 km/h. How long does the journey take? (2021)

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

Solution

Time = Distance / Speed = 300 km / 75 km/h = 4 hours.

Correct Answer: B — 3 hours

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Q. A copper wire has a resistivity of 1.68 x 10^-8 Ω·m. What is the resistance of a 100 m long wire with a cross-sectional area of 1 mm²?

A. 1.68 Ω
B. 0.168 Ω
C. 0.0168 Ω
D. 16.8 Ω

Solution

Resistance (R) = ρ * (L / A) = 1.68 x 10^-8 * (100 / 1 x 10^-6) = 1.68 Ω.

Correct Answer: A — 1.68 Ω

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Q. A country aims to reduce its carbon emissions by 20% over 5 years. If the current emissions are 1,000 tons, what will be the target emissions after 5 years?

A. 800 tons
B. 900 tons
C. 700 tons
D. 600 tons

Solution

Target emissions = 1,000 * (1 - 0.20) = 1,000 * 0.80 = 800 tons.

Correct Answer: A — 800 tons

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Q. A country celebrates its independence every 15th August. If the first celebration was in 1947, how many celebrations will occur by 2022? (2022)

A. 75
B. 76
C. 74
D. 73

Solution

From 1947 to 2022 = 2022 - 1947 = 75 years. Celebrations = 75 + 1 = 76.

Correct Answer: B — 76

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Q. A country has a budget of $1.5 billion for international aid. If it allocates 40% of this budget to education, how much is allocated to education?

A. $600 million
B. $700 million
C. $800 million
D. $900 million

Solution

Amount allocated to education = 40% of $1.5 billion = 0.4 * 1.5 billion = $600 million.

Correct Answer: A — $600 million

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Major Competitive Exams

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