NDA
Q. If a disease has an incidence rate of 0.1% in a population of 1,000,000, how many new cases are expected in a year? (2022)
A.
100
B.
200
C.
300
D.
400
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Solution
Expected new cases = 0.1% of 1,000,000 = 0.001 * 1,000,000 = 100 cases.
Correct Answer: A — 100
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Q. If a disease spreads at a rate of 3% per week, what will be the total percentage of the population infected after 4 weeks, assuming no recovery? (2021)
A.
12.36%
B.
10.5%
C.
11.5%
D.
15%
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Solution
Using the formula for compound growth: Total infected = 100 × (1 - (1 - 0.03)^4) = 100 × (1 - 0.88) = 12.36%.
Correct Answer: A — 12.36%
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Q. If a drone can cover 120 km in 1.5 hours, what is its average speed? (2022)
A.
70 km/h
B.
80 km/h
C.
90 km/h
D.
100 km/h
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Solution
Average Speed = Total Distance / Total Time = 120 km / 1.5 h = 80 km/h
Correct Answer: B — 80 km/h
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Q. If a food item contains 10 grams of protein per serving and a person needs 60 grams of protein daily, how many servings must they consume?
A.
4 servings
B.
5 servings
C.
6 servings
D.
7 servings
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Solution
60 grams / 10 grams per serving = 6 servings.
Correct Answer: B — 5 servings
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Q. If a food label states that a serving contains 5 grams of sugar and the daily recommended intake is 25 grams, what percentage of the daily intake does one serving represent?
A.
10%
B.
15%
C.
20%
D.
25%
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Solution
(5 grams / 25 grams) * 100 = 20%.
Correct Answer: A — 10%
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Q. If a football team has 22 players and 5 are substitutes, what fraction of the team are substitutes? (2022)
A.
1/4
B.
1/5
C.
1/3
D.
1/2
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Solution
Fraction of substitutes = Number of substitutes / Total players = 5 / 22.
Correct Answer: A — 1/4
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Q. If a football team has a win rate of 40% and they played 30 matches, how many matches did they win? (2022)
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Solution
Matches won = 40% of 30 = 0.4 * 30 = 12.
Correct Answer: A — 10
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Q. If 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. If A is a 2x2 matrix and B is a 2x3 matrix, what is the order of the product AB? (2019)
A.
2x2
B.
2x3
C.
3x2
D.
2x5
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Solution
The order of the product of two matrices is determined by the outer dimensions. Here, A (2x2) and B (2x3) can be multiplied, resulting in a matrix of order 2x3.
Correct Answer: B — 2x3
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Q. If A is a 3x3 matrix, how many elements does it have? (2023)
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Solution
A 3x3 matrix has 3 rows and 3 columns, resulting in a total of 3 * 3 = 9 elements.
Correct Answer: B — 9
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Q. If a line has an equation of the form y = mx + c, what does 'c' represent? (2023)
A.
Slope
B.
Y-intercept
C.
X-intercept
D.
None of the above
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Solution
'c' represents the y-intercept of the line, which is the point where the line crosses the y-axis.
Correct Answer: B — Y-intercept
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Q. If a line has the equation 4x - y + 8 = 0, what is its y-intercept? (2019)
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Solution
Setting x = 0 in the equation gives y = 8. Thus, the y-intercept is -8.
Correct Answer: D — -4
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Q. If a line has the equation y = -3x + 6, what is the y-intercept?
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Solution
The y-intercept is the constant term in the equation, which is 6.
Correct Answer: A — 6
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Q. If a location is at 120 degrees West longitude, what is its time zone relative to GMT? (2023)
A.
GMT-8
B.
GMT-7
C.
GMT-6
D.
GMT-5
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Solution
120 degrees West corresponds to GMT-8, as each 15 degrees represents one hour.
Correct Answer: A — GMT-8
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Q. If a matrix is diagonal, what can be said about its non-diagonal elements? (2020)
A.
They are all zero
B.
They are all one
C.
They can be any value
D.
They are negative
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Solution
In a diagonal matrix, all non-diagonal elements are zero.
Correct Answer: A — They are all zero
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Q. If a member of Parliament serves a term of 5 years and is re-elected for another term, how many years will they serve in total?
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Solution
Total years served = 5 years + 5 years = 10 years.
Correct Answer: B — 10
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Q. If a military vehicle 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. If a national event has a budget of $50,000 and 40% is allocated for marketing, how much is allocated for marketing?
A.
$20,000
B.
$25,000
C.
$30,000
D.
$15,000
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Solution
Amount allocated for marketing = $50,000 * 0.40 = $20,000.
Correct Answer: A — $20,000
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Q. If a national event has a total of 500 volunteers and 60% of them are from colleges, how many volunteers are from colleges?
A.
300
B.
250
C.
200
D.
350
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Solution
Number of volunteers from colleges = 500 * 0.60 = 300.
Correct Answer: A — 300
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Q. If a national event is attended by 1,500 people and 30% of them are students, how many students attended the event?
A.
300
B.
450
C.
500
D.
600
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Solution
Number of students = 1,500 * 0.30 = 450.
Correct Answer: B — 450
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Q. If a parabola opens to the left, which of the following is its standard form?
A.
y^2 = -4px
B.
x^2 = -4py
C.
y^2 = 4px
D.
x^2 = 4py
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Solution
The standard form of a parabola that opens to the left is y^2 = -4px.
Correct Answer: A — y^2 = -4px
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Q. If a person consumes 2500 calories a day and 30% of those calories come from fats, how many calories are derived from fats?
A.
500 calories
B.
600 calories
C.
700 calories
D.
750 calories
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Solution
30% of 2500 calories = 0.30 * 2500 = 750 calories.
Correct Answer: A — 500 calories
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Q. If a person consumes 3000 calories a day and wants to ensure that 25% of their intake is from proteins, how many grams of protein should they consume (1 gram of protein = 4 calories)?
A.
150 grams
B.
200 grams
C.
250 grams
D.
300 grams
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Solution
25% of 3000 calories = 0.25 * 3000 = 750 calories from proteins. 750 calories / 4 calories per gram = 187.5 grams, rounded to 188 grams.
Correct Answer: B — 200 grams
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Q. If a person has a 20% chance of contracting a disease and a 30% chance of recovery, what is the probability that the person will contract the disease and not recover? (2022)
A.
0.14
B.
0.06
C.
0.1
D.
0.2
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Solution
Probability of contracting and not recovering = Probability of contracting × (1 - Probability of recovery) = 0.20 × (1 - 0.30) = 0.20 × 0.70 = 0.14.
Correct Answer: A — 0.14
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Q. If a person needs 2500 calories a day and wants to get 20% of their calories from fats, how many grams of fat should they consume (1 gram of fat = 9 calories)?
A.
55 grams
B.
60 grams
C.
70 grams
D.
75 grams
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Solution
20% of 2500 calories = 0.20 * 2500 = 500 calories from fats. 500 calories / 9 calories per gram = 55.56 grams, rounded to 56 grams.
Correct Answer: C — 70 grams
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Q. If a place is located at 120°W longitude, what is its time difference from GMT?
A.
-8 hours
B.
-7 hours
C.
-6 hours
D.
-5 hours
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Solution
120°W corresponds to 120 / 15 = 8 hours behind GMT, hence -8 hours.
Correct Answer: A — -8 hours
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Q. If a plane travels from 60°E to 60°W, how many hours will it take to cross this distance if it travels at a speed of 15° per hour?
A.
8 hours
B.
10 hours
C.
12 hours
D.
15 hours
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Solution
The total distance is 60° + 60° = 120°. At 15° per hour, it will take 120 / 15 = 8 hours.
Correct Answer: B — 10 hours
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Q. If a radar can detect objects up to a distance of 50 km, what is the maximum area it can cover? (2022)
A.
7850 km²
B.
5000 km²
C.
10000 km²
D.
15000 km²
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Solution
Area = πr² = π(50 km)² ≈ 7850 km²
Correct Answer: A — 7850 km²
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Q. If a rectangle has a length of 10 cm and a width of 5 cm, what is its perimeter? (2022)
A.
30 cm
B.
25 cm
C.
20 cm
D.
15 cm
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Solution
Perimeter of a rectangle = 2(length + width) = 2(10 + 5) = 30 cm.
Correct Answer: A — 30 cm
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Q. If a rectangle has a length of 10 m and a width of 5 m, what is its perimeter? (2023)
A.
30 m
B.
25 m
C.
20 m
D.
15 m
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Solution
Perimeter = 2(length + width) = 2(10 + 5) = 30 m.
Correct Answer: A — 30 m
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