Q. A car travels at 90 km/h and a truck at 60 km/h in opposite directions. What is the relative speed of the car with respect to the truck?
A.
30 km/h
B.
60 km/h
C.
150 km/h
D.
90 km/h
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Solution
Relative speed = Speed of car + Speed of truck = 90 km/h + 60 km/h = 150 km/h.
Correct Answer: C — 150 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 car travels at a speed of 80 km/h and a bike travels at 60 km/h. If they start from the same point and travel in the same direction, how far apart will they be after 1 hour?
A.
20 km
B.
10 km
C.
30 km
D.
40 km
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Solution
Relative speed = 80 - 60 = 20 km/h. Distance apart after 1 hour = 20 km.
Correct Answer: A — 20 km
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Q. A car travels at a speed of 80 km/h and a truck travels at 60 km/h in the same direction. How far apart will they be after 2 hours if they start together?
A.
20 km
B.
40 km
C.
60 km
D.
80 km
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Solution
Relative speed = 80 - 60 = 20 km/h. Distance = speed * time = 20 * 2 = 40 km.
Correct Answer: B — 40 km
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Q. A car's speed is measured as 60 km/h with a possible error of 2 km/h. What is the minimum speed?
A.
58 km/h
B.
60 km/h
C.
62 km/h
D.
55 km/h
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Solution
Minimum speed = Measured speed - Error = 60 - 2 = 58 km/h.
Correct Answer: A — 58 km/h
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Q. A car's speed is measured as 60 km/h with a relative error of 5%. What is the absolute error?
A.
3 km/h
B.
2 km/h
C.
4 km/h
D.
5 km/h
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Solution
Absolute error = Relative error * Measured value = 0.05 * 60 = 3 km/h.
Correct Answer: A — 3 km/h
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Q. A card is drawn from a standard deck of 52 cards. What is the probability of drawing a heart?
A.
1/4
B.
1/13
C.
1/2
D.
1/52
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Solution
Number of hearts = 13. Probability = 13/52 = 1/4.
Correct Answer: A — 1/4
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Q. A card is drawn from a standard deck of 52 cards. What is the probability that it is a heart given that it is a red card?
A.
1/2
B.
1/4
C.
1/3
D.
1/13
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Solution
There are 26 red cards (hearts and diamonds). The probability of drawing a heart given that it is red is 13/26 = 1/2.
Correct Answer: A — 1/2
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Q. A card is drawn from a standard deck of 52 cards. What is the probability that the card is a heart or a queen?
A.
1/4
B.
1/13
C.
4/52
D.
17/52
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Solution
There are 13 hearts and 4 queens, but one of the queens is a heart. Thus, the probability is (13 + 4 - 1)/52 = 16/52 = 4/13.
Correct Answer: D — 17/52
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Q. A card is drawn from a standard deck of 52 cards. What is the probability that the card is a heart given that it is a red card?
A.
1/2
B.
1/4
C.
1/3
D.
2/3
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Solution
There are 26 red cards (hearts and diamonds). The probability of drawing a heart given that the card is red is 13/26 = 1/2.
Correct Answer: A — 1/2
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Q. A card is drawn from a standard deck of 52 cards. What is the probability that the card drawn is a heart?
A.
1/4
B.
1/13
C.
1/52
D.
3/13
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Solution
There are 13 hearts in a deck of 52 cards. The probability of drawing a heart is 13/52 = 1/4.
Correct Answer: A — 1/4
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Q. A card is drawn from a standard deck of 52 cards. What is the probability that the card drawn is a queen?
A.
1/13
B.
1/52
C.
1/26
D.
3/52
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Solution
There are 4 queens in a deck of 52 cards. Probability = 4/52 = 1/13.
Correct Answer: A — 1/13
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Q. A certain amount of money triples itself in 15 years at compound interest. What is the annual interest rate?
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Solution
Using the formula A = P(1 + r)^n, we can set up the equation 3P = P(1 + r)^15. Solving for r gives approximately 6%.
Correct Answer: B — 6%
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Q. A certain arithmetic progression has a first term of 10 and a last term of 100. If there are 20 terms in total, what is the common difference?
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Solution
The last term of an AP is given by a + (n-1)d. Here, 100 = 10 + (20-1)d. Solving gives d = 5.
Correct Answer: A — 5
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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 changing magnetic field induces a current in a closed loop. What is this phenomenon called?
A.
Electromagnetic induction
B.
Magnetic resonance
C.
Electrolysis
D.
Magnetism
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Solution
This phenomenon is known as electromagnetic induction, where a changing magnetic field induces an electromotive force (EMF) in a conductor.
Correct Answer: A — Electromagnetic induction
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Q. A changing magnetic field induces an electric field. This phenomenon is known as?
A.
Electromagnetic induction
B.
Electrostatics
C.
Magnetostatics
D.
Electrodynamics
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Solution
The phenomenon of a changing magnetic field inducing an electric field is known as electromagnetic induction.
Correct Answer: A — Electromagnetic induction
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Q. A charge of +1 μC is placed in an electric field of strength 1000 N/C. What is the force experienced by the charge? (2023)
A.
0.001 N
B.
0.01 N
C.
1 N
D.
10 N
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Solution
Force F = qE = (1 × 10^-6 C)(1000 N/C) = 0.001 N.
Correct Answer: B — 0.01 N
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Q. A charge of +10 μC is placed in an electric field of 2000 N/C. What is the force experienced by the charge? (2023)
A.
20 N
B.
200 N
C.
2 N
D.
0.2 N
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Solution
Force F = qE = (10 × 10^-6 C) * (2000 N/C) = 0.02 N = 20 N.
Correct Answer: A — 20 N
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Q. A charge of +10 µC is placed in an electric field of strength 2000 N/C. What is the force acting on the charge? (2023)
A.
20 N
B.
200 N
C.
2 N
D.
0.2 N
Show solution
Solution
Force F = qE = (10 × 10^-6 C) * (2000 N/C) = 0.02 N = 20 N.
Correct Answer: A — 20 N
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Q. A charge of +10μC is placed at the origin. What is the electric potential at a point 2m away from the charge?
A.
4500 V
B.
2250 V
C.
5000 V
D.
1000 V
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Solution
V = k * q / r = (9 × 10^9) * (10 × 10^-6) / 2 = 4500 V.
Correct Answer: B — 2250 V
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Q. A charge of +10μC is placed in a uniform electric field of 500 N/C. What is the force acting on the charge?
A.
0.5 N
B.
5 N
C.
50 N
D.
500 N
Show solution
Solution
Force F = qE = (10 × 10^-6 C) * (500 N/C) = 5 N.
Correct Answer: B — 5 N
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Q. A charge of +10μC is placed in a uniform electric field of strength 500 N/C. What is the work done in moving the charge 0.1m in the direction of the field?
A.
0.5 J
B.
1 J
C.
2 J
D.
0.1 J
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Solution
Work done W = F * d = (E * q) * d = (500 N/C * 10 × 10^-6 C) * 0.1 m = 0.5 J.
Correct Answer: A — 0.5 J
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Q. A charge of +10μC is placed in a uniform electric field of strength 500 N/C. What is the work done in moving the charge 2m in the direction of the field?
A.
10 J
B.
1 J
C.
100 J
D.
0.5 J
Show solution
Solution
Work done W = F * d = (E * q) * d = (500 N/C * 10 × 10^-6 C) * 2m = 0.01 J.
Correct Answer: A — 10 J
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Q. A charge of +2μC is placed in an electric field of 1000 N/C. What is the force experienced by the charge? (2000)
A.
2000 N
B.
2 N
C.
0.002 N
D.
1000 N
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Solution
The force F on a charge in an electric field is given by F = qE. Here, F = 2 * 10^-6 C * 1000 N/C = 0.002 N.
Correct Answer: A — 2000 N
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Q. A charge of +3μC is placed at the origin. What is the electric potential at a point 0.5m away?
A.
5400 V
B.
1800 V
C.
7200 V
D.
3600 V
Show solution
Solution
V = k * q / r = (9 × 10^9) * (3 × 10^-6) / 0.5 = 54000 V.
Correct Answer: D — 3600 V
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