NDA Exam Preparation Resources | Soulshift Education

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English General Knowledge Mathematics

Q. Determine the maximum value of the function f(x) = -x^2 + 6x - 8. (2022)

A. 0
B. 4
C. 6
D. 8

Solution

The vertex is at x = -6/(2*(-1)) = 3. The maximum value is f(3) = -3^2 + 6*3 - 8 = 1.

Correct Answer: B — 4

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Q. Determine the median of the following numbers: 9, 7, 5, 3, 1.

A. 5
B. 6
C. 7
D. 8

Solution

Arrange the numbers: 1, 3, 5, 7, 9. The median is the middle value, which is 5.

Correct Answer: A — 5

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Q. Determine the median of the following set: 1, 2, 3, 4, 5, 6, 7, 8. (2020)

A. 4
B. 4.5
C. 5
D. 6

Solution

Arrange the numbers: 1, 2, 3, 4, 5, 6, 7, 8. The median is the average of the 4th and 5th numbers: (4 + 5) / 2 = 4.5.

Correct Answer: B — 4.5

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Q. Determine the minimum value of f(x) = x^2 - 6x + 10. (2019)

A. 2
B. 3
C. 4
D. 5

Solution

The minimum occurs at x = -b/(2a) = 6/(2*1) = 3. f(3) = 3^2 - 6(3) + 10 = 3.

Correct Answer: B — 3

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Q. Determine the minimum value of the function f(x) = x^2 - 4x + 6. (2020)

A. 2
B. 3
C. 4
D. 5

Solution

The function is a upward-opening parabola. The minimum occurs at x = -b/(2a) = 4/(2*1) = 2. f(2) = 2^2 - 4(2) + 6 = 2.

Correct Answer: A — 2

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Q. Determine the mode of the following data: {1, 2, 2, 3, 4, 4, 4, 5, 5}.

A. 2
B. 3
C. 4
D. 5

Solution

The mode is 4, as it appears 3 times, more than any other number.

Correct Answer: C — 4

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Q. Determine the slope of the tangent line to f(x) = x^2 at x = 3. (2023)

A. 3
B. 6
C. 9
D. 12

Solution

f'(x) = 2x; thus, f'(3) = 2(3) = 6.

Correct Answer: B — 6

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Q. Determine the solution of the differential equation dy/dx = y^2 - 1.

A. y = tan(x + C)
B. y = 1/(C - x)
C. y = 1/(C + x)
D. y = e^(x + C)

Solution

This is separable. Separating and integrating gives y = 1/(C - x).

Correct Answer: B — y = 1/(C - x)

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Q. Determine the x-intercept of the line given by the equation 5x + 2y - 10 = 0. (2023)

A. 2
B. 0
C. 5
D. 10

Solution

Setting y = 0 in the equation gives 5x = 10, thus x = 2. The x-intercept is 2.

Correct Answer: C — 5

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Q. Determine the y-intercept of the line given by the equation 5x + 2y - 10 = 0. (2021)

A. 5
B. 2
C. 10
D. 0

Solution

Setting x = 0 in the equation gives 2y = 10, thus y = 5. The y-intercept is 5.

Correct Answer: B — 2

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Q. Differentiate f(x) = 4x^2 * e^x. (2022)

A. 4e^x + 4x^2e^x
B. 4x^2e^x + 4xe^x
C. 4e^x + 2x^2e^x
D. 8xe^x

Solution

Using the product rule, f'(x) = 4e^x + 4x^2e^x.

Correct Answer: A — 4e^x + 4x^2e^x

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Q. Differentiate f(x) = 4x^2 + 3x - 5. (2019)

A. 8x + 3
B. 4x + 3
C. 2x + 3
D. 8x - 3

Solution

Using the power rule, f'(x) = 8x + 3.

Correct Answer: A — 8x + 3

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Q. Differentiate f(x) = 4x^5 - 2x^3 + x. (2022)

A. 20x^4 - 6x^2 + 1
B. 20x^4 - 6x^2
C. 4x^4 - 2x^2 + 1
D. 5x^4 - 2x^2

Solution

Using the power rule, f'(x) = 20x^4 - 6x^2 + 1.

Correct Answer: A — 20x^4 - 6x^2 + 1

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Q. Differentiate f(x) = ln(x^2 + 1). (2022)

A. 2x/(x^2 + 1)
B. 1/(x^2 + 1)
C. 2x/(x^2 - 1)
D. x/(x^2 + 1)

Solution

Using the chain rule, f'(x) = 2x/(x^2 + 1).

Correct Answer: A — 2x/(x^2 + 1)

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Q. Differentiate f(x) = x^2 * e^x. (2022)

A. x^2 * e^x + 2x * e^x
B. 2x * e^x + x^2 * e^x
C. x^2 * e^x + e^x
D. 2x * e^x

Solution

Using the product rule, f'(x) = x^2 * e^x + 2x * e^x.

Correct Answer: A — x^2 * e^x + 2x * e^x

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Q. Differentiate f(x) = x^2 * ln(x).

A. 2x * ln(x) + x
B. x * ln(x) + 2x
C. 2x * ln(x)
D. x^2/x

Solution

Using the product rule, f'(x) = 2x * ln(x) + x.

Correct Answer: A — 2x * ln(x) + x

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Q. Differentiate the function f(x) = ln(x^2 + 1).

A. 2x/(x^2 + 1)
B. 2/(x^2 + 1)
C. 1/(x^2 + 1)
D. x/(x^2 + 1)

Solution

Using the chain rule, f'(x) = (1/(x^2 + 1)) * (2x) = 2x/(x^2 + 1).

Correct Answer: A — 2x/(x^2 + 1)

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Q. Differentiate the function f(x) = x^2 * e^x.

A. x^2 * e^x + 2x * e^x
B. 2x * e^x + x^2 * e^x
C. x^2 * e^x + e^x
D. 2x * e^x + e^x

Solution

Using the product rule, f'(x) = (x^2)' * e^x + x^2 * (e^x)' = 2x * e^x + x^2 * e^x.

Correct Answer: A — x^2 * e^x + 2x * e^x

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Q. During a global conference, 40% of the attendees were women. If there were 500 attendees, how many were men? (2023)

A. 200
B. 250
C. 300
D. 350

Solution

Number of women = 40% of 500 = 200. Number of men = 500 - 200 = 300.

Correct Answer: C — 300

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Q. During a national celebration, 25% of the attendees are children. If there are 800 attendees, how many are adults? (2020)

A. 600
B. 200
C. 400
D. 300

Solution

Number of children = 25% of 800 = 0.25 * 800 = 200. Number of adults = 800 - 200 = 600.

Correct Answer: A — 600

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Q. During a national event, 25% of the attendees are from outside the country. If there are 800 attendees, how many are from outside the country? (2021)

A. 200
B. 250
C. 300
D. 350

Solution

Number of attendees from outside = 25% of 800 = 0.25 * 800 = 200.

Correct Answer: A — 200

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Q. During a national event, 25% of the attendees are from outside the country. If there are 1,200 attendees, how many are from outside the country?

A. 300
B. 250
C. 400
D. 350

Solution

Number of attendees from outside = 25% of 1,200 = 0.25 * 1,200 = 300.

Correct Answer: A — 300

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Q. During a national event, 25% of the attendees are from rural areas. If there are 800 attendees, how many are from urban areas?

A. 600
B. 200
C. 400
D. 300

Solution

Number of attendees from urban areas = 800 * (1 - 0.25) = 800 * 0.75 = 600.

Correct Answer: A — 600

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Q. During a national event, 25% of the attendees are students. If there are 1,600 attendees, how many are not students?

A. 1,200
B. 1,000
C. 1,400
D. 1,600

Solution

Number of non-students = 1,600 * (1 - 0.25) = 1,600 * 0.75 = 1,200.

Correct Answer: A — 1,200

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Q. During a national event, 30% of the attendees are from abroad. If there are 1,000 attendees, how many are from abroad? (2021)

A. 300
B. 400
C. 500
D. 600

Solution

Number of attendees from abroad = 30% of 1,000 = 0.3 * 1,000 = 300.

Correct Answer: A — 300

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Q. During a national event, if 70% of the attendees are adults and there are 350 attendees, how many are children?

A. 105
B. 245
C. 70
D. 140

Solution

Number of adults = 70% of 350 = 0.70 * 350 = 245. Number of children = 350 - 245 = 105.

Correct Answer: A — 105

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Q. During a national event, if 70% of the attendees are adults and there are 500 attendees, how many are children? (2022)

A. 150
B. 200
C. 100
D. 250

Solution

Number of adults = 70% of 500 = 0.70 * 500 = 350. Number of children = 500 - 350 = 150.

Correct Answer: B — 200

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Q. During a peacekeeping mission, 120 soldiers were deployed. If 25% of them were from country A, how many soldiers were from country A?

A. 20
B. 25
C. 30
D. 35

Solution

Number of soldiers from country A = 25% of 120 = 0.25 * 120 = 30.

Correct Answer: C — 30

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Q. Evaluate the integral ∫ (3x^2 - 4) dx.

A. x^3 - 4x + C
B. x^3 - 2x + C
C. 3x^3 - 4x + C
D. x^3 - 4x

Solution

The integral evaluates to x^3 - 4x + C, where C is the constant of integration.

Correct Answer: A — x^3 - 4x + C

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Q. Evaluate the integral ∫ (4x^3 - 2x) dx.

A. x^4 - x^2 + C
B. x^4 - x^2
C. x^4 - x^2 + 2C
D. 4x^4 - x^2 + C

Solution

The integral is (4/4)x^4 - (2/2)x^2 + C = x^4 - x^2 + C.

Correct Answer: A — x^4 - x^2 + C

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