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English General Knowledge Mathematics

Q. A 1 kg block of metal at 100°C is placed in 2 kg of water at 20°C. If the final temperature is 30°C, what is the specific heat capacity of the metal? (2023)

A. 0.5 J/kg°C
B. 1 J/kg°C
C. 2 J/kg°C
D. 4 J/kg°C

Solution

Using conservation of energy: m1c1(T1 - Tf) = m2c2(Tf - T2), we find c1 = 2 J/kg°C.

Correct Answer: C — 2 J/kg°C

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Q. A 10 kg mass is lifted to a height of 5 m. What is the potential energy gained? (Take g = 10 m/s²)

A. 50 J
B. 100 J
C. 150 J
D. 200 J

Solution

Potential energy PE = mgh = 10 kg * 10 m/s² * 5 m = 500 J.

Correct Answer: B — 100 J

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Q. A 10 kg object is dropped from a height of 5 m. What is its speed just before it hits the ground? (Use g = 9.8 m/s²) (2021)

A. 10 m/s
B. 15 m/s
C. 20 m/s
D. 25 m/s

Solution

Using energy conservation, Potential Energy = Kinetic Energy at the ground. mgh = (1/2)mv². v = sqrt(2gh) = sqrt(2 × 9.8 m/s² × 5 m) ≈ 10 m/s.

Correct Answer: B — 15 m/s

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Q. A 10 kg object is lifted to a height of 5 m. What is the potential energy gained? (Take g = 9.8 m/s²) (2021)

A. 490 J
B. 980 J
C. 390 J
D. 590 J

Solution

Potential Energy (PE) = mgh = 10 kg × 9.8 m/s² × 5 m = 490 J.

Correct Answer: B — 980 J

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Q. A 10 kg object is lifted to a height of 5 m. What is the potential energy gained? (Take g = 10 m/s²)

A. 50 J
B. 100 J
C. 150 J
D. 200 J

Solution

Potential energy PE = mgh = 10 kg * 10 m/s² * 5 m = 500 J.

Correct Answer: D — 200 J

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Q. A 10 kg object is lifted to a height of 5 m. What is the potential energy gained by the object? (Take g = 10 m/s²)

A. 50 J
B. 100 J
C. 150 J
D. 200 J

Solution

Potential energy PE = mgh = 10 kg × 10 m/s² × 5 m = 500 J.

Correct Answer: B — 100 J

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Q. A 10 kg object is lifted to a height of 5 m. What is the work done against gravity? (Take g = 10 m/s²)

A. 50 J
B. 100 J
C. 150 J
D. 200 J

Solution

Work done W = mgh = 10 kg × 10 m/s² × 5 m = 500 J.

Correct Answer: B — 100 J

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Q. A 10 kg object is moving with a speed of 2 m/s. What is its momentum?

A. 20 kg·m/s
B. 10 kg·m/s
C. 5 kg·m/s
D. 15 kg·m/s

Solution

Momentum (p) = mass × velocity = 10 kg × 2 m/s = 20 kg·m/s.

Correct Answer: A — 20 kg·m/s

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Q. A 10 kg object is moving with a speed of 5 m/s. What is its momentum? (2022)

A. 50 kg m/s
B. 10 kg m/s
C. 25 kg m/s
D. 15 kg m/s

Solution

Momentum = mass × velocity = 10 kg × 5 m/s = 50 kg m/s.

Correct Answer: A — 50 kg m/s

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Q. A 10 kg object is moving with a velocity of 5 m/s. What is its kinetic energy?

A. 125 J
B. 50 J
C. 100 J
D. 75 J

Solution

Kinetic energy KE = (1/2)mv² = (1/2)(10)(5²) = 125 J.

Correct Answer: A — 125 J

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Q. A 100 g piece of metal at 150°C is placed in 200 g of water at 25°C. What is the final temperature of the system assuming no heat loss? (2019)

A. 30°C
B. 40°C
C. 50°C
D. 60°C

Solution

Using the principle of conservation of energy, we can calculate the final temperature to be 50°C.

Correct Answer: C — 50°C

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Q. A 15-meter tall tree casts a shadow of 10 meters. What is the angle of elevation of the sun? (2019)

A. 30 degrees
B. 45 degrees
C. 60 degrees
D. 75 degrees

Solution

tan(θ) = height/shadow = 15/10 = 1.5, θ = tan⁻¹(1.5) ≈ 56.31 degrees, which is closest to 60 degrees.

Correct Answer: C — 60 degrees

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Q. A 2 kg object is dropped from a height of 10 m. What is its speed just before it hits the ground? (Use g = 9.8 m/s²) (2021)

A. 14 m/s
B. 20 m/s
C. 10 m/s
D. 15 m/s

Solution

Using energy conservation, PE = KE: mgh = 0.5mv². Solving gives v = √(2gh) = √(2 × 9.8 m/s² × 10 m) = 14 m/s.

Correct Answer: A — 14 m/s

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Q. A 2 kg object is heated from 20°C to 80°C. If the specific heat capacity is 0.5 J/g°C, how much heat is absorbed? (2019)

A. 60 kJ
B. 80 kJ
C. 100 kJ
D. 120 kJ

Solution

Heat absorbed (Q) = mcΔT = (2000 g)(0.5 J/g°C)(60°C) = 60,000 J = 60 kJ.

Correct Answer: B — 80 kJ

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Q. A 2 kg piece of copper (specific heat = 0.385 J/g°C) is heated from 25°C to 75°C. How much heat is absorbed? (2022)

A. 2000 J
B. 3000 J
C. 4000 J
D. 5000 J

Solution

Q = mcΔT = 2000 g * 0.385 J/g°C * (75°C - 25°C) = 38500 J.

Correct Answer: B — 3000 J

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Q. A 2 kg piece of iron at 150°C is placed in 1 kg of water at 20°C. What will be the final temperature of the system? (Specific heat of iron = 0.45 J/g°C, water = 4.18 J/g°C) (2023)

A. 25°C
B. 30°C
C. 35°C
D. 40°C

Solution

Using heat transfer equations, we find the final temperature to be approximately 35°C.

Correct Answer: C — 35°C

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Q. A 5 kg block of metal is heated from 20°C to 100°C. If the specific heat capacity of the metal is 0.5 J/g°C, how much heat is required? (2023)

A. 2000 J
B. 2500 J
C. 3000 J
D. 3500 J

Solution

Heat (Q) = m * c * ΔT = 5000 g * 0.5 J/g°C * (100°C - 20°C) = 5000 * 0.5 * 80 = 200000 J = 2000 J.

Correct Answer: C — 3000 J

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Q. A 5 kg object is dropped from a height of 10 m. What is its potential energy at the top? (Take g = 9.8 m/s²) (2020)

A. 49 J
B. 98 J
C. 39 J
D. 59 J

Solution

Potential Energy (PE) = mgh = 5 kg × 9.8 m/s² × 10 m = 490 J.

Correct Answer: B — 98 J

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Q. A 5 kg object is dropped from a height of 10 m. What is its speed just before it hits the ground? (Use g = 9.8 m/s²) (2021)

A. 14 m/s
B. 20 m/s
C. 10 m/s
D. 15 m/s

Solution

Using energy conservation, Potential Energy = Kinetic Energy. mgh = 1/2 mv². v = √(2gh) = √(2 × 9.8 m/s² × 10 m) = 14 m/s.

Correct Answer: A — 14 m/s

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Q. A 5 kg object is dropped from a height of 20 m. What is its velocity just before it hits the ground? (Take g = 10 m/s²)

A. 10 m/s
B. 20 m/s
C. 15 m/s
D. 25 m/s

Solution

Using the formula v² = u² + 2gh, where u = 0, we have v = √(0 + 2*10*20) = √400 = 20 m/s.

Correct Answer: B — 20 m/s

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Q. A 5 kg object is lifted to a height of 10 m. What is the potential energy gained by the object? (Take g = 10 m/s²)

A. 50 J
B. 100 J
C. 150 J
D. 200 J

Solution

Potential energy PE = mgh = 5 kg * 10 m/s² * 10 m = 500 J.

Correct Answer: B — 100 J

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Q. A 50 kg object is moving with a velocity of 10 m/s. What is its kinetic energy? (2022)

A. 2500 J
B. 500 J
C. 1000 J
D. 2000 J

Solution

Kinetic energy KE = (1/2)mv² = (1/2)(50)(10²) = 2500 J.

Correct Answer: A — 2500 J

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Q. A bag contains 4 white and 6 black balls. If one ball is drawn at random, what is the probability that it is not black?

A. 2/5
B. 1/5
C. 1/2
D. 4/10

Solution

Total balls = 4 + 6 = 10. Probability of not drawing a black ball = Number of white balls / Total balls = 4/10 = 2/5.

Correct Answer: A — 2/5

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Q. A bag contains 4 white balls and 6 black balls. If one ball is drawn at random, what is the probability that it is not black?

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

Solution

Total balls = 4 + 6 = 10. Probability of not drawing a black ball = Number of white balls / Total balls = 4/10 = 2/5.

Correct Answer: C — 4/5

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Q. A bag contains 4 white balls and 6 black balls. If one ball is drawn at random, what is the probability that it is black?

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

Solution

The total number of balls is 4 + 6 = 10. The number of black balls is 6. Therefore, the probability of drawing a black ball is 6/10 = 3/5.

Correct Answer: B — 3/5

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Q. A bag contains 4 white, 3 black, and 5 red balls. If one ball is drawn at random, what is the probability that it is not black?

A. 1/4
B. 3/4
C. 5/12
D. 2/3

Solution

Total balls = 4 + 3 + 5 = 12. Non-black balls = 4 + 5 = 9. Probability = Non-black balls / Total balls = 9/12 = 3/4.

Correct Answer: B — 3/4

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Q. A bag contains 4 white, 5 black, and 6 red balls. If one ball is drawn at random, what is the probability that it is not black?

A. 1/3
B. 2/3
C. 5/11
D. 7/11

Solution

Total balls = 4 + 5 + 6 = 15. Non-black balls = 4 + 6 = 10. Probability = Non-black balls / Total balls = 10/15 = 2/3.

Correct Answer: D — 7/11

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Q. A bag contains 5 red balls and 3 blue balls. What is the probability of drawing a red ball? (2022)

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

Solution

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

Correct Answer: B — 5/8

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Q. A balanced diet consists of 50% carbohydrates, 30% proteins, and 20% fats. If a person consumes 2400 calories, how many calories are from carbohydrates?

A. 1000 calories
B. 1200 calories
C. 1400 calories
D. 1600 calories

Solution

50% of 2400 calories = 0.50 * 2400 = 1200 calories.

Correct Answer: B — 1200 calories

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Q. A balanced diet should consist of what percentage of carbohydrates, proteins, and fats respectively? (2021)

A. 50%, 30%, 20%
B. 60%, 25%, 15%
C. 40%, 40%, 20%
D. 70%, 20%, 10%

Solution

A balanced diet typically consists of 60% carbohydrates, 25% proteins, and 15% fats.

Correct Answer: B — 60%, 25%, 15%

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