NDA
Q. A rectangle has a length of 10 cm and a width of 5 cm. What is its area? (2022)
A.
50 cm²
B.
60 cm²
C.
40 cm²
D.
30 cm²
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Solution
Area = Length * Width = 10 cm * 5 cm = 50 cm².
Correct Answer: A — 50 cm²
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Q. A rectangle has a length of 10 cm and a width of 5 cm. What is the area of the rectangle? (2022)
A.
50 cm²
B.
25 cm²
C.
15 cm²
D.
30 cm²
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Solution
Area = Length × Width = 10 cm × 5 cm = 50 cm².
Correct Answer: A — 50 cm²
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Q. A rectangle has a length of 12 cm and a width of 5 cm. What is its perimeter? (2021)
A.
34 cm
B.
30 cm
C.
24 cm
D.
40 cm
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Solution
Perimeter = 2(length + width) = 2(12 + 5) = 2 * 17 = 34 cm
Correct Answer: B — 30 cm
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Q. A river basin has an area of 500 km². If the average rainfall is 800 mm per year, what is the total volume of water received by the basin in a year? (2019)
A.
400,000,000 m³
B.
500,000,000 m³
C.
600,000,000 m³
D.
700,000,000 m³
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Solution
Volume = area × rainfall = 500 km² × 800 mm = 500,000,000 m³.
Correct Answer: A — 400,000,000 m³
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Q. A river carries 1500 m³ of water per second. If the river's width is 25 m, what is the average depth of the river?
A.
6 m
B.
5 m
C.
4 m
D.
3 m
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Solution
Discharge = Width × Depth × Velocity. Assuming velocity = 1 m/s, Depth = Discharge / (Width × Velocity) = 1500 m³/s / (25 m × 1 m/s) = 60 m.
Correct Answer: B — 5 m
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Q. A river flows at a speed of 3 m/s. How far will it travel in 2 hours? (2020)
A.
21600 m
B.
7200 m
C.
10800 m
D.
3600 m
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Solution
Distance = speed × time = 3 m/s × 7200 s = 21600 m.
Correct Answer: A — 21600 m
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Q. A river flows through a region with a soil erosion rate of 5 tons per hectare per year. If the area of the watershed is 100 hectares, how much soil is eroded in a year?
A.
500 tons
B.
1000 tons
C.
200 tons
D.
300 tons
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Solution
Soil eroded = Erosion rate × Area = 5 tons/hectare/year × 100 hectares = 500 tons/year.
Correct Answer: B — 1000 tons
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Q. A river has a cross-sectional area of 150 m² and flows at a velocity of 4 m/s. What is the discharge of the river? (2021)
A.
600 m³/s
B.
400 m³/s
C.
300 m³/s
D.
200 m³/s
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Solution
Discharge = area × velocity = 150 m² × 4 m/s = 600 m³/s.
Correct Answer: A — 600 m³/s
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Q. A river has a length of 100 km and a drainage area of 500 km². What is the average discharge per square kilometer?
A.
0.2 m³/s
B.
0.5 m³/s
C.
1 m³/s
D.
1.5 m³/s
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Solution
Average discharge = Total discharge / Drainage area. Assuming total discharge = 250 m³/s, Average discharge = 250 m³/s / 500 km² = 0.5 m³/s.
Correct Answer: B — 0.5 m³/s
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Q. A river's velocity is measured at 2 m/s. If the river's width is 10 m and depth is 3 m, what is the discharge?
A.
60 m³/s
B.
30 m³/s
C.
20 m³/s
D.
10 m³/s
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Solution
Discharge = Velocity × Area. Area = Width × Depth = 10 m × 3 m = 30 m². Discharge = 2 m/s × 30 m² = 60 m³/s.
Correct Answer: B — 30 m³/s
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Q. A river's width is 15 m and its average depth is 2 m. What is the cross-sectional area of the river?
A.
30 m²
B.
15 m²
C.
45 m²
D.
60 m²
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Solution
Cross-sectional area = Width × Depth = 15 m × 2 m = 30 m².
Correct Answer: D — 60 m²
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Q. A runner completes a 400 m lap in 50 seconds. What is the average speed of the runner in m/s? (2019)
A.
6 m/s
B.
7 m/s
C.
8 m/s
D.
9 m/s
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Solution
Average speed = Total distance / Total time = 400 m / 50 s = 8 m/s.
Correct Answer: A — 6 m/s
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Q. A school awards a trophy to the top 10% of students. If there are 200 students, how many students receive the trophy?
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Solution
Number of students receiving trophy = 10% of 200 = 0.1 * 200 = 20.
Correct Answer: C — 20
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Q. A set of numbers has a mean of 20. If one number is removed, the mean becomes 18. What was the number removed? (2022)
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Solution
Let the number of elements be n. Then, 20n - x = 18(n - 1). Solving gives x = 22.
Correct Answer: A — 22
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Q. A set of numbers has the following frequencies: 10 (1), 20 (2), 30 (3), 40 (4). What is the mode of this set? (2021)
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Solution
The number 40 appears most frequently (4 times), so the mode is 40.
Correct Answer: D — 40
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Q. A shopkeeper sells a shirt for Rs. 800 after giving a discount of 20%. What was the marked price of the shirt? (2020)
A.
Rs. 1000
B.
Rs. 900
C.
Rs. 800
D.
Rs. 750
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Solution
Let marked price = x. Then, 0.8x = 800 => x = 800/0.8 = 1000.
Correct Answer: A — Rs. 1000
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Q. A shopkeeper sells an article for Rs. 800, making a profit of 20%. What was the cost price of the article? (2020)
A.
Rs. 600
B.
Rs. 640
C.
Rs. 500
D.
Rs. 700
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Solution
Let CP = x. Then, 800 = x + 0.20x = 1.20x. Therefore, x = 800 / 1.20 = 666.67.
Correct Answer: A — Rs. 600
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Q. A snack contains 150 calories, with 10% from protein, 50% from carbohydrates, and 40% from fats. How many calories are from fats?
A.
40 calories
B.
50 calories
C.
60 calories
D.
70 calories
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Solution
40% of 150 calories = 0.40 * 150 = 60 calories from fats.
Correct Answer: C — 60 calories
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Q. A soil sample contains 40% sand, 30% silt, and 30% clay. What is the percentage of clay in the sample? (2022)
A.
30%
B.
40%
C.
50%
D.
20%
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Solution
The percentage of clay is given as 30%.
Correct Answer: A — 30%
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Q. A soldier runs 12 km in 1 hour and 15 minutes. What is his speed in km/h? (2023)
A.
8 km/h
B.
9 km/h
C.
10 km/h
D.
11 km/h
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Solution
Time = 1 hour + 15 minutes = 1.25 hours. Speed = Distance / Time = 12 km / 1.25 h = 9.6 km/h.
Correct Answer: B — 9 km/h
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Q. A soldier runs 5 km in 30 minutes. What is his speed in km/h? (2019)
A.
8 km/h
B.
10 km/h
C.
12 km/h
D.
15 km/h
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Solution
Speed = Distance / Time = 5 km / (30/60) h = 10 km/h
Correct Answer: B — 10 km/h
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Q. A sound wave has a frequency of 440 Hz. What is its period?
A.
0.00227 s
B.
0.00455 s
C.
0.01 s
D.
0.1 s
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Solution
The period (T) is the inverse of frequency (f), T = 1/f = 1/440 ≈ 0.00227 s.
Correct Answer: B — 0.00455 s
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Q. A stone is thrown vertically upwards with a speed of 15 m/s. How long will it take to reach the highest point? (Take g = 10 m/s²) (2023)
A.
1.5 s
B.
2 s
C.
3 s
D.
4 s
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Solution
Time to reach highest point = u/g = 15/10 = 1.5 s.
Correct Answer: B — 2 s
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Q. A student must score at least 60% to pass an exam. If the exam is out of 250 marks, what is the minimum score required to pass? (2019)
A.
140
B.
150
C.
160
D.
170
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Solution
Minimum Score = (60 / 100) * 250 = 150.
Correct Answer: B — 150
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Q. A student needs to score at least 75% to qualify for a scholarship. If the total marks are 400, what is the minimum score required? (2022)
A.
250
B.
300
C.
350
D.
375
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Solution
Minimum Score = (75 / 100) * 400 = 300.
Correct Answer: B — 300
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Q. A student needs to score at least 80% in an exam of 500 marks to get a scholarship. What is the minimum score required? (2023)
A.
350
B.
400
C.
450
D.
500
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Solution
Minimum Score = (80 / 100) * 500 = 400.
Correct Answer: B — 400
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Q. A student received a prize for scoring 92 marks out of 120. What is the percentage of marks? (2021)
A.
75%
B.
76.67%
C.
78.33%
D.
80%
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Solution
Percentage = (92 / 120) * 100 = 76.67%.
Correct Answer: B — 76.67%
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Q. A student received a scholarship for scoring 95 marks out of 150 in an exam. What is the percentage of marks? (2020)
A.
60%
B.
65%
C.
70%
D.
75%
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Solution
Percentage = (95 / 150) * 100 = 63.33%.
Correct Answer: C — 70%
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Q. A student received a scholarship of $1200. If he spends 30% of it on tuition fees, how much does he spend?
A.
$300
B.
$360
C.
$400
D.
$450
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Solution
Amount spent on tuition fees = 30% of 1200 = 0.3 * 1200 = $360.
Correct Answer: B — $360
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Q. A student received an award for scoring the highest marks in a subject. If he scored 95 out of 100, what is his score in percentage?
A.
90%
B.
92%
C.
95%
D.
98%
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Solution
Percentage = (95 / 100) * 100 = 95%
Correct Answer: C — 95%
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