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POST UTME AFE BABALOLA UNIVERSITY 2020 Mathematics | Objective

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Question 1 View Details

Solve for x in the equation \(\log_{10} x^2 \\)\(= 4 ).\)

Correct A. 10

B. 100

C. 1000

D. 10000

Correct Answer: A

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Question 2 View Details

Find the value of \(\frac{1}{2} \int_{0}^{1} x^2 dx\).

Correct A. 0.5

B. 1

C. 1.5

D. 2

Correct Answer: A

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Question 3 View Details

A circle has a radius of 5cm. Find the area of the circle.

A. 25π

Correct B. 50π

C. 75π

D. 100π

Correct Answer: B

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Question 4 View Details

A die is rolled. What is the probability that the number obtained is greater than 4?

A. \(1/6\)

B. \(1/3\)

C. \(1/2\)

Correct D. \(2/3\)

Correct Answer: D

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Question 5 View Details

Solve the equation \(2x^2 + 5x - 3 = 0\).

A. \(-1/2\)

Correct B. \(1/2\)

C. -3

D. 3

Correct Answer: B

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Question 6 View Details

Find the value of x in the equation \(\log_{10} x^2 \\)\(= 4 ).\)

A. 10

B. 100

C. 1000

Correct D. 10000

Correct Answer: D

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Question 7 View Details

Solve the quadratic equation \(x^2 + 5x + 6 = 0\) using the quadratic formula.

A. \(x = -2\)

Correct B. \(x = -3\)

C. \(x = 2\)

D. \(x = 3\)

Correct Answer: B

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Question 8 View Details

A vector ( mathbf{a} ) has a magnitude of 5 units and makes an angle of 30° with the positive x-axis. Find the x and y components of ( mathbf{a} ).

Correct A. \(x = 4.33\), \(y = 2.5\)

B. \(x = 2.5\), \(y = 4.33\)

C. \(x = 3.54\), \(y = 2.5\)

D. \(x = 2.5\), \(y = 3.54\)

Correct Answer: A

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Question 9 View Details

A right-angled triangle has a hypotenuse of length 10 units and one leg of length 6 units. Find the length of the other leg.

Correct A. 8

B. 6

C. 4

D. 2

Correct Answer: A

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Question 10 View Details

Solve the inequality \(x^2 - 4x + 4 > 0\).

A. \(x < 2\)

Correct B. \(x > 2\)

C. \(x < 1\)

D. \(x > 1\)

Correct Answer: B

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Question 11 View Details

Let X be a random variable with probability density function f(x) = \begin{cases} 2x & \(0 < x\)\(< 1\)\\ 0 & \text{otherwise} \end{cases}. Find the probability that X is greater than 0.5.

Correct A. 0.25

B. 0.5

C. 0.75

D. 1.0

Correct Answer: A

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Question 12 View Details

Find the derivative of the function f(x) = \(\frac{1}{x^2 + 1}\)\)\) using the chain rule.

Correct A. \(\frac{-2x}{x^2 + 1\) ^2}\)\)

B. \(\frac{2x}{x^2 + 1\) ^2}\)\)

C. \(\frac{1}{x^2 + 1\) ^2}\)\)

D. \(\frac{-1}{x^2 + 1\) ^2}\)\)

Correct Answer: A

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Question 13 View Details

Solve the inequality \\((x^2 - 4x - 5\)\(> 0.\)\)

Correct A. \(-\infty, -1\) \cup \(5, \infty\)

B. \(-\infty, 1\) \cup \(5, \infty\)

C. \(-\infty, -1\) \cup (1, 5)

D. \(-\infty, 1\) \cup \(-5, \infty\)

Correct Answer: A

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Question 14 View Details

Find the area under the curve \(y = x\^2\) from \(x = 0\) to \(x = 2\).

Correct A. \(\frac{8}{3}\)\)

B. \(\frac{16}{3}\)\)

C. \(\frac{24}{3}\)\)

D. \(\frac{32}{3}\)\)

Correct Answer: A

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Question 15 View Details

Solve the equation \\(\sin^2\) x + \\(\cos^2\) \(x = 1\).

Correct A. \(x =\)\(\frac{\pi}{4}\)\)

B. \(x =\)\(\frac{\pi}{2}\)\)

C. \(x =\)\(\frac{3\pi}{4}\)\)

D. \(x =\)\(\frac{5\pi}{4}\)\)

Correct Answer: A

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Question 16 View Details

Solve the inequality \(\frac{x^2 - 4}{x + 2} > 0\) for ( x in mathbb{R} ).

Correct A. \(-\infty, -2 \\) cup (2, infty) )

B. \(-\infty, -2 \\) cup (2, infty) ) and \(x = -2\)

C. \(-\infty, -2 \\) cup (2, infty) ) and \(x = 2\)

D. \(-\infty, -2 \\) cup (2, infty) )

Correct Answer: A

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Question 17 View Details

Find the derivative of the function ( f(x) = \(\frac{1}{x^2 + 1}\)\)\) ) using the chain rule.

Correct A. ( f'\((x) =\)\(\frac{-2x}{x^2 + 1\) ^2}\)\) )

B. ( f'\((x) =\)\(\frac{-2x}{x^2 + 1}\)\)\) )

C. ( f'\((x) =\)\(\frac{2x}{x^2 + 1\) ^2}\)\) )

D. ( f'\((x) =\)\(\frac{2x}{x^2 + 1}\)\)\) )

Correct Answer: A

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Question 18 View Details

A histogram of exam scores is shown below. What is the mean score?

A. 60

Correct B. 70

C. 80

D. 90

Correct Answer: B

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Question 19 View Details

Solve the equation \(2^x + 2^x = 2^{x+1}\) for ( x in mathbb{R} ).

A. \(x = 0\)

Correct B. \(x = 1\)

C. \(x = -1\)

D. \(x = 2\)

Correct Answer: B

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Question 20 View Details

Find the derivative of the function ( f(x) = \\(\sin^2(x)\) ) using the chain rule.

Correct A. ( f'\((x) = 2\)\sin\(x)\cos(x\) )

B. ( f'\((x) =\)\sin(x) )

C. ( f'\((x) =\)\cos(x) )

D. ( f'\((x) = 2\)\\(\sin^2(x)\) )

Correct Answer: A

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Question 21 View Details

Find the derivative of the function ( f(x) = \(\frac{x^2 + 2x - 3}{x^2 - 4}\)\)\) ) using the quotient rule.

A. \(\frac{2x x^2 - 4 - x^2 + 2x - 3\) (2x)}{ \(x^2 - 4\) ^2}\)\)

B. \(\frac{2x x^2 - 4 + x^2 + 2x - 3\) (2x)}{ \(x^2 - 4\) ^2}\)\)

Correct C. \(\frac{2x x^2 - 4 - x^2 + 2x - 3\) (2x)}{ \(x^2 - 4\) ^2}\)\)

D. \(\frac{2x x^2 - 4 + x^2 + 2x - 3\) (2x)}{ \(x^2 - 4\) ^2}\)\)

Correct Answer: C

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Question 22 View Details

A set of 10 numbers has a mean of 20. If 5 is added to each number, what is the new mean?

A. 22

Correct B. 25

C. 28

D. 30

Correct Answer: B

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Question 23 View Details

Find the volume of the frustum of a cone with radii 6 cm and 3 cm and height 8 cm.

A. 120\pi

B. 150\pi

Correct C. 180\pi

D. 200\pi

Correct Answer: C

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Question 24 View Details

A sequence is defined by the formula \(a_n = 2n^2 - 5n + 1\). Find the sum of the first 5 terms.

A. 15

B. 20

Correct C. 25

D. 30

Correct Answer: C

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Question 25 View Details

A histogram has a mean of 25 and a standard deviation of 5. If the data is normally distributed, what is the probability that a randomly selected value is greater than 30?

A. 0.1587

B. 0.3413

C. 0.5000

Correct D. 0.8413

Correct Answer: D

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