Defence Exams
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
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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 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
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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 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
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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 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
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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 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
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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 ball is dropped from a height of 80 m. How long will it take to reach the ground? (Take g = 10 m/s²) (2021)
A.
4 s
B.
5 s
C.
6 s
D.
8 s
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Solution
Using the formula h = (1/2)gt², we have 80 = (1/2)(10)t². Solving gives t² = 16, so t = 4 s.
Correct Answer: B — 5 s
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Q. A basketball player has a free throw success rate of 75%. If he takes 20 free throws, how many successful throws can be expected? (2019)
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Solution
Expected successful throws = 75% of 20 = 0.75 * 20 = 15.
Correct Answer: A — 15
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Q. A beam of light passes from air into a medium with a refractive index of 1.5. If the angle of incidence is 30 degrees, what is the angle of refraction? (2022)
A.
19.1 degrees
B.
20 degrees
C.
25 degrees
D.
30 degrees
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Solution
Using Snell's law, n1 * sin(i) = n2 * sin(r). Thus, sin(r) = (1 * sin(30)) / 1.5 = 0.333, giving r ≈ 19.1 degrees.
Correct Answer: A — 19.1 degrees
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Q. A bill is passed in the Lok Sabha with a majority of 55%. If there are 545 members, how many members voted in favor of the bill?
A.
300
B.
275
C.
250
D.
200
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Solution
Members voting in favor = 55% of 545 = 0.55 * 545 = 299.75, rounded to 300.
Correct Answer: B — 275
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Q. A bill is passed in the Lok Sabha with a majority of 60%. If there are 545 members in the Lok Sabha, how many members voted in favor of the bill?
A.
327
B.
330
C.
300
D.
350
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Solution
Members voting in favor = 60% of 545 = 0.6 * 545 = 327.
Correct Answer: A — 327
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Q. A block of mass 5 kg is placed on a frictionless surface and is pushed with a force of 20 N. What is the acceleration of the block?
A.
2 m/s²
B.
4 m/s²
C.
5 m/s²
D.
10 m/s²
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Solution
Using Newton's second law, F = ma, we have a = F/m = 20 N / 5 kg = 4 m/s².
Correct Answer: B — 4 m/s²
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Q. A body is thrown vertically upwards with a speed of 20 m/s. What is the maximum height reached by the body? (Take g = 10 m/s²)
A.
20 m
B.
40 m
C.
30 m
D.
50 m
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Solution
Using the formula h = (u²)/(2g), where u = 20 m/s and g = 10 m/s², we get h = (20²)/(2*10) = 400/20 = 20 m.
Correct Answer: B — 40 m
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Q. A box contains 3 red, 5 blue, and 2 green balls. If one ball is drawn at random, what is the probability that it is blue?
A.
1/10
B.
1/5
C.
1/2
D.
1/3
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Solution
Total balls = 3 + 5 + 2 = 10. Probability of drawing a blue ball = Number of blue balls / Total balls = 5/10 = 1/2.
Correct Answer: B — 1/5
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Q. A box contains 5 red balls and 3 blue balls. What is the probability of drawing a red ball? (2021)
A.
3/8
B.
5/8
C.
1/2
D.
1/3
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Solution
Total balls = 5 + 3 = 8. Probability of red = 5/8.
Correct Answer: B — 5/8
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Q. A bus travels from city A to city B, a distance of 120 km, at a speed of 60 km/h. How long does it take to reach city B? (2023)
A.
1 hour
B.
1.5 hours
C.
2 hours
D.
2.5 hours
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Solution
Time = Distance / Speed = 120 km / 60 km/h = 2 hours.
Correct Answer: C — 2 hours
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Q. A capacitor of capacitance 10 microfarads is charged to a voltage of 5 volts. What is the charge stored in the capacitor?
A.
50 microcoulombs
B.
5 microcoulombs
C.
0.5 microcoulombs
D.
100 microcoulombs
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Solution
Charge (Q) is given by Q = C * V. Thus, Q = 10 µF * 5 V = 50 µC.
Correct Answer: A — 50 microcoulombs
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Q. A capacitor stores 5 microfarads of charge at a voltage of 10 volts. What is the energy stored in the capacitor?
A.
0.25 mJ
B.
0.5 mJ
C.
0.75 mJ
D.
1 mJ
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Solution
The energy stored in a capacitor is given by the formula E = 0.5 * C * V^2. Here, E = 0.5 * 5 * 10^-6 F * (10 V)^2 = 0.5 * 5 * 10^-6 * 100 = 0.25 mJ.
Correct Answer: B — 0.5 mJ
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Q. A car travels 100 km in 2 hours and then 50 km in 1 hour. What is the total average speed of the car? (2019)
A.
50 km/h
B.
60 km/h
C.
70 km/h
D.
80 km/h
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Solution
Total distance = 100 + 50 = 150 km. Total time = 2 + 1 = 3 hours. Average speed = Total distance / Total time = 150/3 = 50 km/h.
Correct Answer: B — 60 km/h
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Q. A car travels 150 km in 2 hours and then 100 km in 1 hour. What is the average speed of the car for the entire trip? (2020)
A.
75 km/h
B.
80 km/h
C.
85 km/h
D.
90 km/h
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Solution
Total distance = 150 + 100 = 250 km. Total time = 2 + 1 = 3 hours. Average speed = Total distance / Total time = 250 km / 3 hours = 83.33 km/h, which rounds to 80 km/h.
Correct Answer: B — 80 km/h
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Q. A car travels at a speed of 60 km/h. How far will it travel in 2.5 hours? (2021)
A.
120 km
B.
150 km
C.
180 km
D.
200 km
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Solution
Distance = Speed × Time = 60 km/h × 2.5 h = 150 km
Correct Answer: B — 150 km
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Q. A certain city has a population of 200,000. If the population decreases by 10% every year, what will be the population after 3 years?
A.
162,000
B.
150,000
C.
170,000
D.
180,000
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Solution
Population after 3 years = 200,000 * (1 - 0.10)^3 = 200,000 * 0.729 = 145,800.
Correct Answer: A — 162,000
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Q. A certain disease affects 1 in every 200 people. If a random sample of 1000 people is taken, how many are expected to be affected? (2019)
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Solution
Expected affected = (1/200) × 1000 = 5 people.
Correct Answer: A — 5
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Q. A certain disease has a 10% chance of being transmitted from an infected person to a healthy person. If there are 50 infected individuals, what is the expected number of transmissions if each interacts with one healthy person? (2023)
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Solution
Expected transmissions = 10% of 50 = 0.1 * 50 = 5 transmissions.
Correct Answer: B — 5
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Q. A certain disease has a basic reproduction number (R0) of 3. If one infected person enters a population of 1000, how many people could potentially be infected after one generation? (2021)
A.
300
B.
600
C.
900
D.
1200
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Solution
If R0 = 3, then 1 infected person can infect 3 others. Therefore, potential infections = 3 * 1 = 3 people.
Correct Answer: A — 300
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Q. A certain disease has a mortality rate of 10%. If 500 people are infected, how many are expected to survive? (2019)
A.
450
B.
400
C.
500
D.
350
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Solution
Expected survivors = Total infected - (Mortality rate × Total infected) = 500 - (0.10 × 500) = 500 - 50 = 450.
Correct Answer: A — 450
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Q. A chord of a circle is 8 cm long and is 3 cm away from the center. What is the radius of the circle? (2021)
A.
5 cm
B.
7 cm
C.
10 cm
D.
9 cm
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Solution
Using Pythagoras theorem, r² = (3)² + (4)² = 9 + 16 = 25. Thus, r = 5 cm.
Correct Answer: B — 7 cm
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Q. A circle has a circumference of 31.4 cm. What is its radius? (2021)
A.
5 cm
B.
10 cm
C.
15 cm
D.
20 cm
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Solution
Circumference = 2πr. Thus, r = Circumference/(2π) = 31.4/(2π) = 5 cm.
Correct Answer: A — 5 cm
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Q. A class of 30 students has an average score of 75. If one student scores 90, what will be the new average? (2022)
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Solution
Total score = 75 * 30 = 2250. New total = 2250 - 75 + 90 = 2265. New average = 2265 / 30 = 75.5.
Correct Answer: B — 77
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Q. A coin is tossed three times. What is the probability of getting at least one head?
A.
1/8
B.
1/2
C.
7/8
D.
3/8
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Solution
Probability of getting no heads (all tails) = (1/2)^3 = 1/8. Therefore, probability of at least one head = 1 - 1/8 = 7/8.
Correct Answer: C — 7/8
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Q. A concave mirror has a focal length of 20 cm. What is the radius of curvature of the mirror? (2021)
A.
10 cm
B.
20 cm
C.
30 cm
D.
40 cm
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Solution
The radius of curvature (R) is twice the focal length (f). Therefore, R = 2f = 2 * 20 cm = 40 cm.
Correct Answer: B — 20 cm
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