Q. A group of students reported the number of hours they studied last week: 2, 3, 2, 4, 5, 2, 3. What is the mode?
Solution
The mode is 2, as it appears four times in the data set.
Correct Answer: A — 2
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Q. A group of students reported the number of languages they speak: 1, 1, 2, 2, 3, 3, 3, 4. What is the mode?
Solution
The mode is 3, as it appears 3 times, which is more than any other number.
Correct Answer: C — 3
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Q. A group of students scored the following marks in a test: 45, 50, 50, 55, 60, 50, 70. What is the mode of the scores?
Solution
The mode is 50, which appears 3 times in the scores.
Correct Answer: B — 50
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Q. A health scheme has a total budget of ₹3,00,000. If 25% is spent on awareness programs, how much is spent on these programs?
-
A.
₹50,000
-
B.
₹75,000
-
C.
₹1,00,000
-
D.
₹1,25,000
Solution
Amount spent on awareness programs = 25% of ₹3,00,000 = 0.25 * 3,00,000 = ₹75,000.
Correct Answer: B — ₹75,000
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Q. A height is measured as 180 cm with an error of 1 cm. What is the upper limit of the measurement?
-
A.
181 cm
-
B.
179 cm
-
C.
180 cm
-
D.
182 cm
Solution
Upper limit = Measured value + Error = 180 + 1 = 181 cm
Correct Answer: A — 181 cm
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Q. A helicopter ascends at a rate of 300 meters per minute. How high will it be after 10 minutes? (2021)
-
A.
2000 m
-
B.
2500 m
-
C.
3000 m
-
D.
3500 m
Solution
Height = Rate × Time = 300 m/min × 10 min = 3000 m
Correct Answer: C — 3000 m
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Q. A helicopter can ascend at a rate of 300 meters per minute. How long will it take to reach a height of 1500 meters? (2021)
-
A.
3 minutes
-
B.
4 minutes
-
C.
5 minutes
-
D.
6 minutes
Solution
Time = Height / Rate = 1500 m / 300 m/min = 5 minutes
Correct Answer: C — 5 minutes
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Q. A helicopter can lift a maximum weight of 1500 kg. If each soldier weighs 75 kg, how many soldiers can it carry at maximum? (2021)
Solution
Maximum Soldiers = Maximum Weight / Weight per Soldier = 1500 kg / 75 kg = 20
Correct Answer: B — 20
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Q. A helicopter flies at a speed of 150 km/h. How far can it travel in 3 hours? (2021)
-
A.
300 km
-
B.
400 km
-
C.
450 km
-
D.
500 km
Solution
Distance = Speed × Time = 150 km/h × 3 h = 450 km
Correct Answer: C — 450 km
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Q. A helicopter flies at a speed of 240 km/h. How far can it travel in 45 minutes? (2023)
-
A.
180 km
-
B.
120 km
-
C.
90 km
-
D.
60 km
Solution
Distance = Speed * Time = 240 km/h * (45/60) h = 180 km.
Correct Answer: A — 180 km
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Q. A hemisphere has a radius of 3 cm. What is its volume?
-
A.
18π cm³
-
B.
27π cm³
-
C.
36π cm³
-
D.
9π cm³
Solution
Volume of a hemisphere = (2/3)πr³ = (2/3)π(3)³ = (2/3)π(27) = 18π cm³.
Correct Answer: A — 18π cm³
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Q. A hollow cylinder with charge density λ is placed along the z-axis. What is the electric field at a point outside the cylinder?
-
A.
λ/(2πε₀r)
-
B.
λ/(4πε₀r²)
-
C.
Zero
-
D.
λ/(ε₀r)
Solution
For a hollow cylinder, the electric field at a point outside is E = λ/(2πε₀r) using Gauss's law.
Correct Answer: A — λ/(2πε₀r)
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Q. A hollow sphere has a charge +Q distributed uniformly on its surface. What is the electric field at a point inside the sphere?
-
A.
Q/(4πε₀r²)
-
B.
0
-
C.
Q/(4πε₀R²)
-
D.
Q/(4πε₀R)
Solution
The electric field inside a hollow charged sphere is zero due to symmetry.
Correct Answer: B — 0
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Q. A hollow sphere has a charge Q distributed uniformly over its surface. What is the electric field inside the sphere?
-
A.
Q/(4πε₀R²)
-
B.
0
-
C.
Q/(4πε₀)
-
D.
Q/(4πε₀R)
Solution
Inside a hollow charged sphere, the electric field is zero due to symmetry.
Correct Answer: B — 0
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Q. A hollow sphere has a charge Q uniformly distributed on its surface. What is the electric field inside the sphere?
-
A.
Q/4πε₀R²
-
B.
0
-
C.
Q/ε₀
-
D.
Q/4πε₀
Solution
The electric field inside a hollow charged sphere is zero due to symmetry.
Correct Answer: B — 0
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Q. A hollow sphere rolls down a slope of height h. What fraction of its potential energy is converted into translational kinetic energy at the bottom?
-
A.
1/3
-
B.
1/2
-
C.
2/3
-
D.
1
Solution
For a hollow sphere, I = (2/3)mr^2. Using energy conservation, the translational kinetic energy is 2/3 of the potential energy at the top.
Correct Answer: C — 2/3
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Q. A hollow sphere rolls down an incline. If it starts from rest, what fraction of its total energy is translational at the bottom?
-
A.
1/3
-
B.
2/3
-
C.
1/2
-
D.
1/4
Solution
For a hollow sphere, the translational kinetic energy at the bottom is 2/3 of the total energy, hence the fraction is 2/3.
Correct Answer: B — 2/3
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Q. A hollow sphere rolls down an incline. If its mass is m and radius is R, what is its moment of inertia?
-
A.
(2/5)mR^2
-
B.
(1/2)mR^2
-
C.
(2/3)mR^2
-
D.
(3/5)mR^2
Solution
The moment of inertia of a hollow sphere about its center is I = (2/3)mR^2.
Correct Answer: C — (2/3)mR^2
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Q. A hollow sphere with charge Q has a radius R. What is the electric field at a point inside the sphere?
-
A.
Q/(4πε₀R²)
-
B.
0
-
C.
Q/(4πε₀R)
-
D.
Q/(2πε₀R²)
Solution
Inside a hollow charged sphere, the electric field is zero due to symmetry, as per Gauss's law.
Correct Answer: B — 0
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Q. A hollow spherical conductor carries a charge Q. What is the electric field inside the cavity?
-
A.
Q/(4πε₀r²)
-
B.
0
-
C.
Q/(4πε₀R²)
-
D.
Q/(4πε₀R)
Solution
Inside the cavity of a hollow conductor, the electric field is zero due to the shielding effect of the conductor.
Correct Answer: B — 0
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Q. A is older than B but younger than C. D is younger than A. Who is the oldest?
Solution
C is the oldest as A is younger than C.
Correct Answer: C — C
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Q. A is the brother of B. C is the sister of A. D is the mother of B. How is C related to D?
-
A.
Daughter
-
B.
Son
-
C.
Niece
-
D.
Sister
Solution
C is the daughter of D as C is the sister of A and A is the brother of B, making them all siblings.
Correct Answer: A — Daughter
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Q. A is the father of B. C is the mother of B. D is the brother of C. How is D related to A?
-
A.
Brother-in-law
-
B.
Father
-
C.
Uncle
-
D.
Cousin
Solution
D is the brother-in-law of A as C (D's sister) is married to A.
Correct Answer: A — Brother-in-law
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Q. A is the grandfather of B. C is the father of B. How is A related to C?
-
A.
Son
-
B.
Father
-
C.
Grandfather
-
D.
Uncle
Solution
A is the father of C as A is the grandfather of B.
Correct Answer: B — Father
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Q. A is twice as old as B. If B is 10 years old now, how old will A be in 5 years? (2023)
Solution
If B is 10, A is 20. In 5 years, A will be 25.
Correct Answer: B — 25
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Q. A jacket is sold for $120 after a discount of 20%. What was the original price of the jacket?
-
A.
$100
-
B.
$140
-
C.
$150
-
D.
$160
Solution
Let the original price be x. Then, x - 0.20x = 120. Solving gives x = 120/0.80 = $150.
Correct Answer: D — $160
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Q. A jar contains 10 candies, 4 of which are chocolate. What is the probability of selecting a chocolate candy?
-
A.
2/5
-
B.
1/2
-
C.
4/10
-
D.
3/10
Solution
Probability of chocolate candy = 4/10 = 2/5.
Correct Answer: B — 1/2
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Q. A jar contains 4 green, 5 yellow, and 1 red marble. What is the probability of picking a yellow marble? (2019)
-
A.
1/10
-
B.
1/5
-
C.
1/2
-
D.
5/10
Solution
Total marbles = 4 + 5 + 1 = 10. Probability of yellow = 5/10 = 1/2.
Correct Answer: D — 5/10
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Q. A jar contains 4 red, 5 green, and 6 blue marbles. If one marble is drawn at random, what is the probability that it is either red or green?
-
A.
4/15
-
B.
3/5
-
C.
9/15
-
D.
1/3
Solution
Total marbles = 4 + 5 + 6 = 15. Probability of red or green = (4 + 5)/15 = 9/15 = 3/5.
Correct Answer: B — 3/5
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Q. A jar contains 4 red, 5 green, and 6 blue marbles. If one marble is drawn at random, what is the probability that it is not blue?
-
A.
1/3
-
B.
2/3
-
C.
1/2
-
D.
5/11
Solution
Total marbles = 4 + 5 + 6 = 15. Non-blue marbles = 4 + 5 = 9. Probability = 9/15 = 3/5.
Correct Answer: B — 2/3
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