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POST UTME UNIBEN 2019 Mathematics | Objective

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Question 1 View Details

Find the volume of the frustum of a cone with height 6cm, lower base radius 4cm, and upper base radius 2cm.

A. 30π cm³

Correct B. 60π cm³

C. 90π cm³

D. 120π cm³

Correct Answer: B

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Question 2 View Details

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

Correct A. 16

B. 32

C. 64

D. 128

Correct Answer: A

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Question 3 View Details

Find the equation of the circle with center \(-2, 3\) and radius 4.

Correct A. \(x + 2 \\)^2 + \(y - 3\)^\(2 = 16\) )

B. \(x - 2 \\)^2 + \(y + 3\)^\(2 = 16\) )

C. \(x + 2 \\)^2 + \(y + 3\)^\(2 = 16\) )

D. \(x - 2 \\)^2 + \(y - 3\)^\(2 = 16\) )

Correct Answer: A

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Question 4 View Details

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

A. 20

B. 30

C. 40

Correct D. 50

Correct Answer: D

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Question 5 View Details

In the diagram below, ( AB ) is a diameter of the circle with center ( O ). If \(∠AOB = 60^{circ}\), find the measure of ( ∠ACB ).

A. \(30^{circ}\)

B. \(45^{circ}\)

Correct C. \(60^{circ}\)

D. \(90^{circ}\)

Correct Answer: C

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Question 6 View Details

A random variable X has a probability distribution given by P\(X = 1 = 0.3\), P\(X = 2 = 0.4\), and P\(X = 3 = 0.3\). Find the probability that X is greater than 2.

Correct A. 0.7

B. 0.4

C. 0.3

D. 0.2

Correct Answer: A

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Question 7 View Details

Find the vector projection of vector \(\vec{a} = 2\hat{i} + 3\hat{j} onto vector \vec{b} = \hat{i} + \hat{j}\).

Correct A. \(\frac{5}{6}\)\)\hat{i} + \(\frac{5}{6}\)\)\hat{j}

B. \(\frac{1}{6}\)\)\hat{i} + \(\frac{1}{6}\)\)\hat{j}

C. \(\frac{3}{4}\)\)\hat{i} + \(\frac{3}{4}\)\)\hat{j}

D. \(\frac{1}{2}\)\)\hat{i} + \(\frac{1}{2}\)\)\hat{j}

Correct Answer: A

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Question 8 View Details

Solve the quadratic equation \(\frac{x^2 + 2x - 3}{x + 1}\)\)\\() = 0.\)

Correct A. \(x = -3\)

B. \(x = 1\)

C. \(x = -1\)

D. \(x = 2\)

Correct Answer: A

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Question 9 View Details

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

Correct A. \(10^8\)

B. \(10^4\)

C. \(10^2\)

D. \(10^6\)

Correct Answer: A

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Question 10 View Details

A set A contains the elements {1, 2, 3, 4, 5}. Find the number of subsets of A that contain exactly two elements.

A. 10

Correct B. 15

C. 20

D. 25

Correct Answer: B

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Question 11 View Details

Solve for x in the equation \(x^2 + 5x + 6 = 0\).

A. -2

Correct B. -3

C. 1

D. 2

Correct Answer: B

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Question 12 View Details

Find the equation of the circle with center \(-2, 3\) and radius 4.

Correct A. \(x + 2 \\)^2 + \(y - 3\)^\(2 = 16\) \)

B. \(x - 2 \\)^2 + \(y + 3\)^\(2 = 16\) \)

C. \(x + 2 \\)^2 + \(y + 3\)^\(2 = 16\) \)

D. \(x - 2 \\)^2 + \(y - 3\)^\(2 = 16\) \)

Correct Answer: A

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Question 13 View Details

Solve the inequality \(2x^2 + 5x - 3 > 0\).

Correct A. \(x < -1 \\) or \(x > \frac{3}{2} \\)

B. \(x < -1 \\) or \(x < \frac{3}{2} \\)

C. \(x > -1 \\) or \(x < \frac{3}{2} \\)

D. \(x > -1 \\) or \(x > \frac{3}{2} \\)

Correct Answer: A

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Question 14 View Details

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

A. 8

B. 10

Correct C. 12

D. 16

Correct Answer: C

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Question 15 View Details

Solve for x in the equation \(x^3 - 6x^2 + 11x - 6 = 0\).

A. 1

B. 2

Correct C. 3

D. 4

Correct Answer: C

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Question 16 View Details

Solve for x in the equation \(\frac{1}{2}x^2 + 5x - 3 = 0\).

A. \(x = -10\)

Correct B. \(x = 1\)

C. \(x = -1\)

D. \(x = 2\)

Correct Answer: B

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Question 17 View Details

A circle with center (0, 0) and radius 5 passes through which of the following points?

A. (3, 4)

B. (4, 3)

Correct C. (5, 0)

D. (0, 5)

Correct Answer: C

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Question 18 View Details

Solve the inequality \(2x^2 - 5x - 3 > 0\).

Correct A. \(x < -1\) or \(x > 3\)

B. \(x < 1\) or \(x > 3\)

C. \(x < -1\) or \(x < 3\)

D. \(x > 1\) or \(x > 3\)

Correct Answer: A

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Question 19 View Details

Find the equation of the line passing through the points (2, 3) and (4, 5).

Correct A. \(y = 2x - 1\)

B. \(y = 2x + 1\)

C. \(y = -2x + 1\)

D. \(y = -2x - 1\)

Correct Answer: A

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Question 20 View Details

Solve for x in the equation \(x^2 + 5x + 6 = 0\).

A. \(x = -2\)

Correct B. \(x = -3\)

C. \(x = 2\)

D. \(x = 3\)

Correct Answer: B

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Question 21 View Details

Find the value of x in the equation \(\frac{x}{2} + 5 = 11\).

Correct A. 6

B. 8

C. 10

D. 12

Correct Answer: A

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Question 22 View Details

Solve the inequality \(2x^2 + 5x - 3 > 0\).

Correct A. x < -1 or \(x > 3\)

B. \(x < 1\) or \(x > 3\)

C. x < -3 or \(x > 1\)

D. \(x < 3\) or \(x > 1\)

Correct Answer: A

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Question 23 View Details

Find the sum of the first 5 terms of the geometric series ( 2, 6, 18, 54, ... ).

Correct A. 120

B. 150

C. 180

D. 200

Correct Answer: A

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Question 24 View Details

Solve the system of equations \(x + y = 4\) and \(x - y = 2\).

Correct A. \(x = 3\), \(y = 1\)

B. \(x = 1\), \(y = 3\)

C. \(x = 2\), \(y = 2\)

D. \(x = 4\), \(y = 0\)

Correct Answer: A

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Question 25 View Details

Find the determinant of the matrix \(\begin{bmatrix} 2 & 3 \ 4 & 5 \end{bmatrix}\).

Correct A. 1

B. 2

C. 3

D. 4

Correct Answer: A

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