NDA
Q. If a rectangle has a length of 10 units and a width of 5 units, what is its perimeter?
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Solution
Perimeter = 2 * (length + width) = 2 * (10 + 5) = 30 units.
Correct Answer: A — 30
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Q. If a rectangle has a length of 8 cm and a width of 5 cm, what is its perimeter? (2022)
A.
26 cm
B.
30 cm
C.
40 cm
D.
20 cm
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Solution
Perimeter = 2(length + width) = 2(8 + 5) = 26 cm.
Correct Answer: A — 26 cm
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Q. If a river has a sediment transport capacity of 200 kg/m³ and flows at a rate of 10 m³/s, what is the total sediment transported in one hour? (2000)
A.
72000 kg
B.
60000 kg
C.
360000 kg
D.
120000 kg
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Solution
Total sediment = Sediment capacity × Flow rate × Time = 200 kg/m³ × 10 m³/s × 3600 s = 7200000 kg.
Correct Answer: C — 360000 kg
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Q. If a river's flow rate increases by 20% and its original flow rate was 50 m³/s, what is the new flow rate?
A.
60 m³/s
B.
70 m³/s
C.
80 m³/s
D.
90 m³/s
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Solution
New flow rate = Original flow rate + (20% of Original flow rate) = 50 m³/s + (0.2 × 50 m³/s) = 60 m³/s.
Correct Answer: A — 60 m³/s
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Q. If a river's flow rate is 500 cubic meters per second, how many liters of water flow in 10 minutes? (2019)
A.
300,000 L
B.
300,000,000 L
C.
1,800,000 L
D.
1,500,000 L
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Solution
Flow in 10 minutes = 500 m³/s × 600 s = 300,000 m³ = 300,000,000 L.
Correct Answer: B — 300,000,000 L
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Q. If a river's sediment load is 200 kg/m³ and the river has a flow rate of 10 m³/s, what is the total sediment transported in one hour? (2022)
A.
720,000 kg
B.
600,000 kg
C.
1,200,000 kg
D.
1,440,000 kg
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Solution
Sediment transported = sediment load × flow rate × time = 200 kg/m³ × 10 m³/s × 3600 s = 720,000 kg.
Correct Answer: D — 1,440,000 kg
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Q. If a riverbank erodes at a rate of 2 meters per year, how much will it erode in 5 years? (2023)
A.
5 m
B.
10 m
C.
15 m
D.
20 m
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Solution
Erosion = rate × time = 2 m/year × 5 years = 10 m.
Correct Answer: B — 10 m
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Q. If a runner completes a 10 km race in 40 minutes, what is his average speed in km/h? (2021)
A.
12 km/h
B.
13 km/h
C.
14 km/h
D.
15 km/h
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Solution
Time = 40 minutes = 40/60 hours = 2/3 hours. Speed = Distance / Time = 10 km / (2/3) hours = 10 * (3/2) = 15 km/h.
Correct Answer: C — 14 km/h
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Q. If a soldier can carry a load of 40 kg and he carries 5 such loads, what is the total weight he carries? (2019)
A.
150 kg
B.
200 kg
C.
250 kg
D.
300 kg
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Solution
Total Weight = Load × Number of Loads = 40 kg × 5 = 200 kg
Correct Answer: B — 200 kg
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Q. If a soldier can carry a load of 40 kg for 5 km, how much weight can he carry for 10 km if the weight carried is directly proportional to the distance? (2020)
A.
20 kg
B.
30 kg
C.
40 kg
D.
50 kg
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Solution
If distance doubles, weight carried is halved. So, 40 kg / 2 = 20 kg.
Correct Answer: A — 20 kg
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Q. If a sound wave travels from air into water, what happens to its speed?
A.
Increases
B.
Decreases
C.
Remains the same
D.
Becomes zero
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Solution
Sound travels faster in water than in air due to higher density.
Correct Answer: A — Increases
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Q. If a square has a perimeter of 32 cm, what is the length of one side? (2023)
A.
8 cm
B.
10 cm
C.
12 cm
D.
6 cm
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Solution
The perimeter P of a square is given by P = 4 * side. If P = 32 cm, then side = 32/4 = 8 cm.
Correct Answer: A — 8 cm
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Q. If a student is awarded a medal for scoring 85% in an exam, and the total marks are 200, how many marks did he score?
A.
150
B.
160
C.
170
D.
180
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Solution
Marks scored = 85% of 200 = 0.85 * 200 = 170.
Correct Answer: B — 160
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Q. If a student received an award of $3000 and decided to save 25% of it, how much money will he save?
A.
$500
B.
$750
C.
$1000
D.
$1500
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Solution
Amount saved = 25% of 3000 = 0.25 * 3000 = $750.
Correct Answer: C — $1000
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Q. If a student scored 45 out of 60 in an exam, what is the percentage of marks obtained? (2023)
A.
70%
B.
75%
C.
80%
D.
85%
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Solution
Percentage = (45 / 60) * 100 = 75%.
Correct Answer: B — 75%
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Q. If a student scored 80 marks out of 100 in Mathematics and received a merit award, what is the percentage of marks obtained? (2021)
A.
70%
B.
80%
C.
90%
D.
100%
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Solution
Percentage = (Marks Obtained / Total Marks) * 100 = (80 / 100) * 100 = 80%.
Correct Answer: B — 80%
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Q. If a student scored 80 marks out of 100 in Mathematics and received a scholarship award of $2000, what is the percentage of marks scored by the student? (2000)
A.
70%
B.
80%
C.
90%
D.
100%
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Solution
Percentage = (Marks obtained / Total marks) * 100 = (80 / 100) * 100 = 80%
Correct Answer: B — 80%
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Q. If a student scored 88 marks out of 120, what is the percentage of marks obtained? (2022)
A.
70%
B.
72%
C.
73.33%
D.
75%
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Solution
Percentage = (88 / 120) * 100 = 73.33%.
Correct Answer: C — 73.33%
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Q. If a tank uses 15 liters of fuel to travel 100 km, how much fuel will it need to travel 250 km? (2023)
A.
30 liters
B.
35 liters
C.
40 liters
D.
45 liters
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Solution
Fuel needed = (Fuel per 100 km) × (Distance / 100) = 15 liters × (250 km / 100) = 37.5 liters, rounded to 40 liters
Correct Answer: C — 40 liters
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Q. If a test for a disease has a sensitivity of 90% and a specificity of 95%, what is the probability that a person who tests positive actually has the disease, given that the prevalence is 1%? (2022)
A.
0.018
B.
0.1
C.
0.5
D.
0.9
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Solution
Using Bayes' theorem, P(Disease | Positive) = (Sensitivity × Prevalence) / ((Sensitivity × Prevalence) + (1 - Specificity) × (1 - Prevalence)) = (0.9 × 0.01) / ((0.9 × 0.01) + (0.05 × 0.99)) = 0.018.
Correct Answer: A — 0.018
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Q. If a train travels 120 km in 1.5 hours, what is its speed in km/h? (2023)
A.
70 km/h
B.
75 km/h
C.
80 km/h
D.
85 km/h
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Solution
Speed = Distance / Time = 120 km / 1.5 hours = 80 km/h.
Correct Answer: C — 80 km/h
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Q. If a train travels at a speed of 60 km/h, how far will it travel in 2.5 hours?
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. If a transversal intersects two parallel lines, what can be said about the same-side interior angles? (2023)
A.
They are equal
B.
They are supplementary
C.
They are complementary
D.
They are unequal
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Solution
When a transversal intersects two parallel lines, the same-side interior angles are supplementary, meaning they add up to 180 degrees.
Correct Answer: B — They are supplementary
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Q. If a triangle has angles of 30° and 60°, what is the measure of the third angle?
A.
90°
B.
60°
C.
30°
D.
120°
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Solution
The sum of angles in a triangle is 180°. Therefore, the third angle is 180° - 30° - 60° = 90°.
Correct Answer: A — 90°
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Q. If a triangle has sides of lengths 3 cm, 4 cm, and 5 cm, is it a right triangle?
A.
Yes
B.
No
C.
Not enough information
D.
Only if angles are known
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Solution
Yes, because 3² + 4² = 5² (9 + 16 = 25).
Correct Answer: A — Yes
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Q. If a triangle has sides of lengths 3 cm, 4 cm, and 5 cm, what is its area? (2021)
A.
6 cm²
B.
12 cm²
C.
8 cm²
D.
10 cm²
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Solution
Area = 1/2 × base × height = 1/2 × 3 cm × 4 cm = 6 cm².
Correct Answer: A — 6 cm²
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Q. If a triangle has sides of lengths 7 cm, 24 cm, and 25 cm, is it a right triangle? (2020)
A.
Yes
B.
No
C.
Cannot be determined
D.
Only if angles are known
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Solution
Using the Pythagorean theorem, 7² + 24² = 49 + 576 = 625 = 25², thus it is a right triangle.
Correct Answer: A — Yes
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Q. If a vaccine reduces the risk of infection by 75%, what is the probability of infection after vaccination if the initial probability of infection is 0.2? (2020)
A.
0.05
B.
0.1
C.
0.15
D.
0.2
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Solution
The probability of infection after vaccination = Initial probability × (1 - reduction) = 0.2 × (1 - 0.75) = 0.2 × 0.25 = 0.05.
Correct Answer: B — 0.1
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Q. If a wire carries a current of 3 A and has a resistance of 2 ohms, what is the power dissipated in the wire?
A.
6 W
B.
9 W
C.
12 W
D.
15 W
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Solution
Power is given by P = I^2 * R. Here, P = (3 A)^2 * 2 Ω = 9 * 2 = 18 W.
Correct Answer: C — 12 W
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Q. If B = [[2, 3], [5, 7]], what is the value of det(B)? (2020)
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Solution
The determinant of B is calculated as (2*7) - (3*5) = 14 - 15 = -1.
Correct Answer: A — -1
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