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POST UTME UNIBEN 2022 Mathematics | Objective

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Question 1 View Details

A random variable X has a probability distribution given by P\(X = 1 = 0.3\), P\(X = 2 = 0.4\),\(P(X = 3\)= 0.3\). If Y is another random variable such that \(Y = 2X - 1\\((X = 3 = 0.3). If Y is another random variable such that\), find the probability that Y is greater than 3.

A. 0.2

B. 0.4

Correct C. 0.6

D. 0.8

Correct Answer: C

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Question 2 View Details

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

A. \(x = 1\)

B. \(x = -1\)

Correct C. \(x =\)\(\frac{1}{2}\)\)

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

Correct Answer: C

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Question 3 View Details

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

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

B. \(x - 2\)^2 + \(y - 3\)^\(2 = 4\)

C. \(x - 2\)^2 + \(y - 3\)^\(2 = 9\)

D. \(x - 2\)^2 + \(y - 3\)^\(2 = 25\)

Correct Answer: A

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Question 4 View Details

Find the determinant of the matrix \(\begin{bmatrix} 2 & 1 & 3 \ 4 & 2 & 1 \ 3 & 4 & 2 \end{bmatrix}\).

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 5 View Details

A sequence is defined by the recurrence relation \(a_n = 2a_{n-1} + 1\) with initial term \(a_1 = 3\). Find the sum of the first 5 terms of the sequence.

Correct A. 65

B. 75

C. 85

D. 95

Correct Answer: A

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Question 6 View Details

Given that \(\mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix}\) and \(\mathbf{b} = egin{pmatrix} 1 \ -2 end{pmatrix}\), find the vector \(\\(end{pmatrix}), find the vector \mathbf{a} \times \mathbf{b}\).

Correct A. \(egin{pmatrix} 7 \ -6 \end{pmatrix}\)

B. \(egin{pmatrix} -6 \ 7 \end{pmatrix}\)

C. \(egin{pmatrix} 6 \ -7 \end{pmatrix}\)

D. \(egin{pmatrix} -7 \ 6 \end{pmatrix}\)

Correct Answer: A

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Question 7 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. \(y = x - 2\)

D. \(y = x + 2\)

Correct Answer: A

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Question 8 View Details

Find the sum of the first 5 terms of the geometric series with first term \(a = 2\) and common ratio \(r = 3\).

Correct A. \(2 3^5 - 1 \\) )

B. \(2 3^5 + 1 \\) )

C. \(2 3^5 - 2 \\) )

D. \(2 3^5 + 2 \\) )

Correct Answer: A

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Question 9 View Details

Solve the quadratic equation \(x^2 + 4x + 4 = 0\).

Correct A. \(x = -2\)

B. \(x = 2\)

C. \(x = -1\)

D. \(x = 1\)

Correct Answer: A

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Question 10 View Details

Find the area of the triangle with vertices ( (0, 0) ), ( (3, 0) ), and ( (0, 4) ).

Correct A. ( 6 )

B. ( 12 )

C. ( 18 )

D. ( 24 )

Correct Answer: A

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Question 11 View Details

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

A. \(\frac{1}{3} \pi 6^2 + 3^2 + 6 \cdot 3 \\) cdot 8 )

B. \(\frac{1}{3} \pi 6^2 + 3^2 - 6 \cdot 3 \\) cdot 8 )

Correct C. \(\frac{1}{3} \pi 6^2 + 3^2 + 6 \cdot 3 \\) cdot 8 )

D. \(\frac{1}{3} \pi 6^2 + 3^2 - 6 \cdot 3 \\) cdot 8 )

Correct Answer: C

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Question 12 View Details

Solve for x in the equation \(egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ 1 \end{bmatrix} = egin{bmatrix} 7 \ 10 \end{bmatrix}\).

Correct A. \(x = 3\)

B. \(x = 4\)

C. \(x = 5\)

D. \(x = 6\)

Correct Answer: A

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Question 13 View Details

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

A. \(\frac{1}{3}\)

Correct B. \(\frac{2}{3}\)

C. \(\frac{1}{2}\)

D. \(\frac{2}{5}\)

Correct Answer: B

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Question 14 View Details

Find the mean and standard deviation of the data set { 2, 4, 6, 8, 10 }.

Correct A. \(ar{x} = 6, \sigma = 2\)

B. \(ar{x} = 5, \sigma = 1\)

C. \(ar{x} = 6, \sigma = 1\)

D. \(ar{x} = 5, \sigma = 2\)

Correct Answer: A

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Question 15 View Details

A histogram of exam scores has a mean of 60 and a standard deviation of 10. If the histogram is symmetric, what is the probability that a randomly selected score is greater than 70?

A. \(\frac{1}{4}\)

B. \(\frac{1}{2}\)

Correct C. \(\frac{3}{4}\)

D. \(\frac{2}{3}\)

Correct Answer: C

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Question 16 View Details

Given that \(\sin^2 x + \cos^2 x = 1\), find (\\(tan^2\) x\) in terms of \\((tan^2 x\(\sin^2 x\) and \(\cos^2 x\).

Correct A. \(\frac{\sin^2 x}{\cos^2 x}\)

B. \(\sin^2 x + \cos^2 x\)

C. \(\frac{\cos^2 x}{\sin^2 x}\)

D. \(\sin^2 x \cos^2 x\)

Correct Answer: A

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Question 17 View Details

Solve for ( x ) in the equation \(2^{2x} = 8\).

A. \(x = 2\)

B. \(x = 3\)

Correct C. \(x = \frac{3}{2}\)

D. \(x = \frac{1}{2}\)

Correct Answer: C

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Question 18 View Details

Find the equation of the circle with center ( (3, 4) ) and radius ( 5 ).

Correct A. \(x - 3\)^2 + \(y - 4\)^\(2 = 25\) \)

B. \(x - 4\)^2 + \(y - 3\)^\(2 = 25\) \)

C. \(x - 3\)^2 + \(y - 4\)^\(2 = 30\) \)

D. \(x - 4\)^2 + \(y - 3\)^\(2 = 30\) \)

Correct Answer: A

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Question 19 View Details

Find the vector ( mathbf{a} ) given that \(\mathbf{a} \cdot \mathbf{b} = 6\) and \(\mathbf{a} \cdot \mathbf{c} = 3\), where \(\mathbf{b} = 2\mathbf{i} + 3\mathbf{j}\) and \(\mathbf{c} = \mathbf{i} - 2\mathbf{j}\).

Correct A. \(3\mathbf{i} + 2\mathbf{j}\)

B. \(2\mathbf{i} + 3\mathbf{j}\)

C. \(\mathbf{i} - 2\mathbf{j}\)

D. \(4\mathbf{i} - \mathbf{j}\)

Correct Answer: A

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Question 20 View Details

Solve the inequality \(|x - 2| > 3\).

Correct A. \(x < -1\) or \(x > 5\)

B. \(x < 1\) or \(x > 5\)

C. \(x < -1\) or \(x > 2\)

D. \(x < 1\) or \(x > 2\)

Correct Answer: A

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Question 21 View Details

Find the volume of the frustum of a cone with height 8 cm, lower base radius 4 cm, and upper base radius 6 cm.

A. 256\pi \(cm^3\)

B. 512\pi \(cm^3\)

Correct C. 768\pi \(cm^3\)

D. 1024\pi \(cm^3\)

Correct Answer: C

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Question 22 View Details

Solve the equation \(\frac{1}{x+1} + \frac{1}{x-1} = \frac{1}{2}\) for x.

Correct A. \(x = 2\)

B. \(x = -2\)

C. \(x = 1\)

D. \(x = -1\)

Correct Answer: A

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Question 23 View Details

Find the area of the region bounded by the curves \(y = x\^2\) and \(y = 2x\).

A. \(4/3\)

B. \(8/3\)

Correct C. \(16/3\)

D. \(32/3\)

Correct Answer: C

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Question 24 View Details

Solve the matrix equation \(\begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 3 \ 7 \end{bmatrix}\) for x and y.

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

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

C. \(x = 1\), \(y = 1\)

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

Correct Answer: A

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Question 25 View Details

Find the derivative of the function f(x) = \(x^3 + 2x^2 - 5x + 1\).

Correct A. \(3x^2 + 4x - 5\)

B. \(3x^2 + 4x + 5\)

C. \(3x^2 - 4x - 5\)

D. \(3x^2 - 4x + 5\)

Correct Answer: A

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