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POST UTME COAL CITY UNIVERSITY 2017 Mathematics | Objective

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Question 1 View Details

Find the equation of the circle passing through the points (1, 2), (3, 4), and \(-2, 3\).

Correct A. \(x^2 + y^2 + 4x - 8y + 5 = 0\)

B. \(x^2 + y^2 - 4x + 8y + 5 = 0\)

C. \(x^2 + y^2 + 8x - 4y + 5 = 0\)

D. \(x^2 + y^2 - 8x + 4y + 5 = 0\)

Correct Answer: A

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Question 2 View Details

If ( f(x) = \(\frac{1}{x^2 + 1}\)\)\) ), find ( f'(x) ) using the chain rule.

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

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

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

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

Correct Answer: A

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Question 3 View Details

A fair six-sided die is rolled. If the outcome is an even number, a second die is rolled. Find the probability that the sum of the two dice is 7.

Correct A. \(\frac{1}{12}\)

B. \(\frac{1}{6}\)

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

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

Correct Answer: A

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Question 4 View Details

Find the vector ( mathbf{v} ) such that \(\mathbf{v} \cdot \mathbf{i} = 3\) and \(\mathbf{v} \cdot \mathbf{j} = -2\).

Correct A. \(\mathbf{v} = 3\mathbf{i} - 2\mathbf{j}\)

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

C. \(\mathbf{v} = 3\mathbf{i} + 2\mathbf{j}\)

D. \(\mathbf{v} = -3\mathbf{i} - 2\mathbf{j}\)

Correct Answer: A

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Question 5 View Details

Find the determinant of the matrix \(egin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix}\).

Correct A. ( 0 )

B. ( 1 )

C. \(-1\)

D. ( 2 )

Correct Answer: A

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Question 6 View Details

Find the area under the curve of ( f(x) = \(\frac{1}{x^2}\)\)\) ) from \(x = 1\) to \(x = 2\).

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

B. \(\frac{1}{2} - \frac{1}{4}\)

C. \(\frac{1}{4} - \frac{1}{2}\)

D. \(\frac{1}{4} - \frac{1}{1}\)

Correct Answer: A

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Question 7 View Details

In the diagram below, find the length of ( AB ) if \(AC = 10\) cm, \(BC = 6\) cm, and angle \(ABC = 90\^circ\).

Correct A. 8 cm

B. 6 cm

C. 10 cm

D. 12 cm

Correct Answer: A

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Question 8 View Details

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

Correct A. \(10^4\)

B. \(10^{-4}\)

C. \(10^2\)

D. \(10^{-2}\)

Correct Answer: A

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Question 9 View Details

Find the volume of the sphere with radius \(r = 4\) cm.

Correct A. \(\frac{4}{3} \pi 4 \\)^3 )

B. \(\frac{4}{3} \pi 4 \\)^2 )

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

D. \(\frac{4}{3} \pi 4 \\)^2 )

Correct Answer: A

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Question 10 View Details

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

Correct A. \(y = \frac{1}{2} x + 1\)

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

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

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

Correct Answer: A

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Question 11 View Details

Let \(\mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix}\) and \(\mathbf{b} = egin{pmatrix} -1 \ 4 \end{pmatrix}\). Find the projection of ( mathbf{b} ) onto ( mathbf{a} ).

Correct A. \(egin{pmatrix} -\frac{11}{13} \ \frac{24}{13} \end{pmatrix}\)

B. \(egin{pmatrix} \frac{11}{13} \ -\frac{24}{13} \end{pmatrix}\)

C. \(egin{pmatrix} -\frac{24}{13} \ \frac{11}{13} \end{pmatrix}\)

D. \(egin{pmatrix} \frac{24}{13} \ -\frac{11}{13} \end{pmatrix}\)

Correct Answer: A

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Question 12 View Details

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

Correct A. 14

B. -14

C. 21

D. -21

Correct Answer: A

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Question 13 View Details

Let \(S = {1, 2, 3, 4, 5}\). Find the number of subsets of ( S ) that contain exactly three elements.

A. 10

Correct B. 15

C. 20

D. 25

Correct Answer: B

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Question 14 View Details

Find the sum of the first five terms of the geometric series \(2 + 6 + 18 + 54 + ldots\).

Correct A. 242

B. 242

C. 242

D. 242

Correct Answer: A

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Question 15 View Details

Solve the equation \(\sin^2 x + \cos^2 x = 1\) for ( x ) in the interval ( [0, 2pi] ).

Correct A. \(x = 0, \pi, 2\pi\)

B. \(x = \frac{\pi}{2}, \frac{3\pi}{2}\)

C. \(x = \frac{\pi}{4}, \frac{3\pi}{4}, \frac{5\pi}{4}, \frac{7\pi}{4}\)

D. \(x = \frac{\pi}{6}, \frac{5\pi}{6}, \frac{7\pi}{6}, \frac{11\pi}{6}\)

Correct Answer: A

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Question 16 View Details

Find the mean of the data set ( { 2, 4, 6, 8, 10 } ).

Correct A. 6

B. 8

C. 10

D. 12

Correct Answer: A

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Question 17 View Details

Find the median of the data set ( { 1, 3, 5, 7, 9 } ).

A. 5

Correct B. 7

C. 9

D. 11

Correct Answer: B

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Question 18 View Details

Find the mode of the data set ( { 2, 4, 6, 8, 10 } ).

A. 2

B. 4

C. 6

D. 8

Correct Answer: VIEW ANSWER

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Question 19 View Details

Find the value of \(\frac{d}{dx}\left \frac{1}{x^2}\right\)\).

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

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

C. -\(\frac{1}{x^3}\)\)\)

D. +\(\frac{1}{x^3}\)\)\)

Correct Answer: A

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Question 20 View Details

A histogram of exam scores has a mean of 70 and a standard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 60 and 80?

Correct A. 0.135

B. 0.135

C. 0.135

D. 0.135

Correct Answer: A

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Question 21 View Details

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

Correct A. x = -2 or x = -3

B. \(x = 2\) or \(x = 3\)

C. x = -3 or \(x = 2\)

D. \(x = 3\) or x = -2

Correct Answer: A

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Question 22 View Details

A firm produces two products, A and B. Product A requires 2 hours of labor and 3 hours of capital, while product B requires 3 hours of labor and 2 hours of capital. If the firm has 120 hours of labor and 100 hours of capital, how many units of product A and product B should the firm produce to maximize profit?

Correct A. (20, 30)

B. (30, 20)

C. (25, 25)

D. (35, 15)

Correct Answer: A

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Question 23 View Details

A particle moves along the x-axis with a velocity given by (v(t) = \(2t^2 - 5t + 1\)\). Find the acceleration of the particle at time \(t = 2\\((v(t) = 2t^2 - 5t + 1). Find the acceleration of the particle at time\) seconds.

Correct A. 4

B. -10

C. -6

D. 6

Correct Answer: A

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Question 24 View Details

Find the determinant of the matrix [ egin{pmatrix} 2 & 3 & 1 \ 4 & 5 & 2 \ 1 & 2 & 3 \end{pmatrix} ].

A. 0

Correct B. 10

C. 20

D. 30

Correct Answer: B

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Question 25 View Details

Solve the system of linear equations using matrices: [ \begin{cases} \(2x + 3y = 7\) \\\(x - 2y = -3\)\end{cases} \].

Correct A. \begin{pmatrix} \(x = 1\) \\ \(y = 2\) \end{pmatrix}

B. \begin{pmatrix} \(x = 2\) \\ \(y = 1\) \end{pmatrix}

C. \begin{pmatrix} \(x = 3\) \\ \(y = 0\) \end{pmatrix}

D. \begin{pmatrix} \(x = 0\) \\ \(y = 3\) \end{pmatrix}

Correct Answer: A

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