NDA
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
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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 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
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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 cricket team has 11 players. If 3 players are injured, what percentage of the team is still available to play? (2021)
A.
27%
B.
73%
C.
30%
D.
70%
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Solution
If 3 players are injured, then 11 - 3 = 8 players are available. The percentage of players available is (8/11) * 100 = 72.73%, which rounds to 73%.
Correct Answer: B — 73%
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Q. A cyclist covers a distance of 30 km at a speed of 15 km/h. How long does it take to complete the journey? (2022)
A.
1 hour
B.
2 hours
C.
2.5 hours
D.
3 hours
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Solution
Time = Distance / Speed = 30 km / 15 km/h = 2 hours.
Correct Answer: B — 2 hours
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Q. A cyclist travels 15 km in 30 minutes. What is the speed of the cyclist in km/h? (2019)
A.
25 km/h
B.
30 km/h
C.
35 km/h
D.
40 km/h
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Solution
Speed = Distance / Time = 15 km / 0.5 hours = 30 km/h.
Correct Answer: A — 25 km/h
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Q. A data set has values: 10, 12, 14, 16. What is the variance? (2021)
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Solution
Mean = (10 + 12 + 14 + 16) / 4 = 13. Variance = [(10-13)² + (12-13)² + (14-13)² + (16-13)²] / 4 = 2.5.
Correct Answer: B — 4
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Q. A diet consists of 60% carbohydrates, 25% proteins, and 15% fats. If a person consumes 2000 calories, how many calories come from proteins? (2000)
A.
300 calories
B.
400 calories
C.
500 calories
D.
600 calories
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Solution
25% of 2000 calories = 0.25 * 2000 = 500 calories.
Correct Answer: B — 400 calories
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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
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Solution
Height = Rate × Time = 300 m/min × 10 min = 3000 m
Correct Answer: C — 3000 m
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Q. A jar contains 5 red, 3 blue, and 2 yellow marbles. If one marble is drawn, what is the probability that it is either red or yellow?
A.
1/2
B.
2/5
C.
4/10
D.
7/10
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Solution
Total marbles = 5 + 3 + 2 = 10. Probability of red or yellow = (Number of red + Number of yellow) / Total = (5 + 2) / 10 = 7/10.
Correct Answer: D — 7/10
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Q. A lens forms a real image that is twice the size of the object. If the object distance is 10 cm, what is the image distance? (2021)
A.
10 cm
B.
15 cm
C.
20 cm
D.
25 cm
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Solution
Using the magnification formula m = -v/u, where m = 2 and u = -10 cm, we find v = -2 * (-10) = 20 cm.
Correct Answer: C — 20 cm
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Q. A man invests Rs. 5000 at a rate of 5% per annum compounded annually. What will be the amount after 3 years? (2020)
A.
Rs. 5750
B.
Rs. 6300
C.
Rs. 5000
D.
Rs. 5798.75
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Solution
Amount = P(1 + r)^n = 5000(1 + 0.05)^3 = 5000(1.157625) = 5798.75.
Correct Answer: D — Rs. 5798.75
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Q. A marathon is 42 kilometers long. If a runner completes it in 3 hours, what is his average speed in km/h? (2023)
A.
12 km/h
B.
14 km/h
C.
15 km/h
D.
13 km/h
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Solution
Average speed = Total distance / Total time = 42 km / 3 hours = 14 km/h.
Correct Answer: A — 12 km/h
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Q. A meal contains 800 calories, with 40% from carbohydrates, 30% from proteins, and 30% from fats. How many calories are from carbohydrates?
A.
240 calories
B.
320 calories
C.
400 calories
D.
480 calories
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Solution
40% of 800 calories = 0.40 * 800 = 320 calories.
Correct Answer: B — 320 calories
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Q. A military base has a rectangular area of 200 m by 150 m. What is the area of the base? (2019)
A.
30000 m²
B.
25000 m²
C.
20000 m²
D.
15000 m²
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Solution
Area = Length × Width = 200 m × 150 m = 30000 m²
Correct Answer: B — 25000 m²
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Q. A national event is expected to attract 1,200 visitors. If 15% of them are expected to be children, how many children are expected?
A.
180
B.
150
C.
200
D.
120
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Solution
Number of children expected = 1,200 * 0.15 = 180.
Correct Answer: A — 180
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Q. A national festival lasts for 5 days. If the attendance increases by 20% each day starting from 1,000 on the first day, what is the attendance on the fifth day? (2073)
A.
2,488
B.
2,000
C.
2,400
D.
2,500
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Solution
Attendance on the fifth day = 1000 * (1 + 0.20)^4 = 1000 * 2.0736 = 2073.6 ≈ 2074.
Correct Answer: A — 2,488
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Q. A pendulum swings with a period of 2 seconds. What is the length of the pendulum? (Take g = 10 m/s²)
A.
1 m
B.
2 m
C.
0.5 m
D.
0.25 m
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Solution
Using the formula T = 2π√(l/g), we have l = (T² * g)/(4π²) = (2² * 10)/(4π²) = 1 m.
Correct Answer: B — 2 m
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Q. A person drives 180 km at a speed of 90 km/h. How long does the journey take? (2021)
A.
1 hour
B.
1.5 hours
C.
2 hours
D.
2.5 hours
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Solution
Time = Distance / Speed = 180 km / 90 km/h = 2 hours.
Correct Answer: C — 2 hours
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Q. A person is on a diet that consists of 50% carbohydrates, 30% fats, and 20% proteins. If they consume 1800 calories, how many calories are from carbohydrates?
A.
600 calories
B.
700 calories
C.
800 calories
D.
900 calories
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Solution
50% of 1800 calories = 0.50 * 1800 = 900 calories from carbohydrates.
Correct Answer: C — 800 calories
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Q. A person jogs at a speed of 8 km/h for 45 minutes. How far does he jog? (2022)
A.
5 km
B.
6 km
C.
7 km
D.
8 km
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Solution
Time = 45 minutes = 0.75 hours. Distance = Speed * Time = 8 km/h * 0.75 hours = 6 km.
Correct Answer: B — 6 km
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Q. A person needs 2000 calories a day and wants to get 15% of their calories from fats. How many grams of fat should they consume (1 gram of fat = 9 calories)? (2000)
A.
33 grams
B.
40 grams
C.
50 grams
D.
60 grams
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Solution
15% of 2000 calories = 0.15 * 2000 = 300 calories from fats. 300 calories / 9 calories per gram = 33.33 grams, rounded to 33 grams.
Correct Answer: B — 40 grams
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Q. A person walks 3 km north and then 4 km east. What is the straight-line distance from the starting point? (2021)
A.
5 km
B.
6 km
C.
7 km
D.
8 km
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Solution
Using Pythagoras theorem, distance = √(3² + 4²) = √(9 + 16) = √25 = 5 km.
Correct Answer: A — 5 km
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Q. A person walks 3 km towards the north and then 4 km towards the east. What is the straight-line distance from the starting point? (2020)
A.
5 km
B.
6 km
C.
7 km
D.
8 km
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Solution
Using Pythagoras theorem, distance = √(3² + 4²) = √(9 + 16) = √25 = 5 km.
Correct Answer: A — 5 km
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Q. A person walks 4 km in 50 minutes. What is his speed in m/s? (2022)
A.
1.2 m/s
B.
1.5 m/s
C.
2.0 m/s
D.
2.5 m/s
Show solution
Solution
Speed = Distance / Time = 4 km = 4000 m; Time = 50 minutes = 3000 seconds. Speed = 4000 m / 3000 s = 1.33 m/s, which rounds to 1.5 m/s.
Correct Answer: B — 1.5 m/s
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Q. A player has a batting average of 50 runs. If he has played 20 matches, how many runs has he scored in total? (2019)
A.
800
B.
1000
C.
900
D.
700
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Solution
Total runs scored = Batting average * Number of matches = 50 * 20 = 1000 runs.
Correct Answer: A — 800
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Q. A player runs 100 meters in 12 seconds. What is his average speed in m/s? (2019)
A.
8.33
B.
9.00
C.
7.50
D.
8.00
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Solution
Average speed = Distance / Time = 100 meters / 12 seconds = 8.33 m/s.
Correct Answer: A — 8.33
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Q. A player scores 15 points in a game. If he plays 10 games, what is the total number of points scored? (2023)
A.
150
B.
120
C.
130
D.
140
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Solution
Total points scored = 15 points/game * 10 games = 150 points.
Correct Answer: A — 150
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Q. A projectile is launched at an angle of 30° with the horizontal with an initial velocity of 40 m/s. What is the horizontal range of the projectile? (Take g = 10 m/s²)
A.
160 m
B.
200 m
C.
80 m
D.
120 m
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Solution
Range R = (u² * sin(2θ))/g = (40² * sin(60°))/10 = (1600 * √3/2)/10 = 80√3 m ≈ 138.56 m.
Correct Answer: B — 200 m
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Q. A radar system can detect objects up to 100 km away. If an object is detected at 75 km, how far is it from the radar? (2022)
A.
25 km
B.
50 km
C.
75 km
D.
100 km
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Solution
Distance from Radar = Maximum Range - Detected Distance = 100 km - 75 km = 25 km
Correct Answer: A — 25 km
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Q. A ray of light strikes a plane mirror at an angle of 30 degrees to the normal. What is the angle of reflection? (2022)
A.
30 degrees
B.
45 degrees
C.
60 degrees
D.
90 degrees
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Solution
According to the law of reflection, the angle of reflection is equal to the angle of incidence. Therefore, the angle of reflection is 30 degrees.
Correct Answer: A — 30 degrees
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