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POST UTME BELLS UNIVERSITY 2019 Mathematics | Objective

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Question 1 View Details

Find the value of x in the equation \(2x^2 + 5x - 3 = 0\).

A. 1

Correct B. -1

C. 2

D. -2

Correct Answer: B

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Question 2 View Details

A set of exam scores has a mean of 85 and a standard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score will be between 70 and 90?

A. 0.135

B. 0.25

Correct C. 0.5

D. 0.75

Correct Answer: C

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Question 3 View Details

Solve the system of equations using matrices: \(egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 5 \ 6 \end{bmatrix}\).

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

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

C. \(x = 3\), \(y = 4\)

D. \(x = 4\), \(y = 3\)

Correct Answer: A

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Question 4 View Details

Find the sum of the first 10 terms of the geometric series: \(2 + 6 + 18 + ..\)..

A. 123

B. 124

Correct C. 125

D. 126

Correct Answer: C

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Question 5 View Details

In the diagram below, \(\(1\theta = \frac{3}{5}\). Find the value of 1\theta\).

A. 0.6

Correct B. 0.8

C. 0.4

D. 0.2

Correct Answer: B

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Question 6 View Details

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

Correct A. 14

B. -14

C. 16

D. -16

Correct Answer: A

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Question 7 View Details

The equation of a circle is given by \(x - h \\)^2 + \(y - k\)^\(2 = r\^2\) ). If the center of the circle is at ( (3, 4) ) and the radius is 5, find the equation of the circle.

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

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

C. \(x - 3\)^2 + \(y - 4\)^\(2 = 20\)

D. \(x - 3\)^2 + \(y - 4\)^\(2 = 35\)

Correct Answer: A

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Question 8 View Details

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

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 9 View Details

Solve the inequality \(2x^2 + 3x - 1 > 0\).

Correct A. \(-\infty, -\frac{1}{2}\) \cup \(\frac{1}{3}, \infty\)

B. \(-\infty, -\frac{1}{2}\) \cup \(\frac{1}{3}, 0\)

C. \(-\infty, 0\) \cup \(\frac{1}{3}, \infty\)

D. \(-\infty, -\frac{1}{2}\) \cup \(0, \infty\)

Correct Answer: A

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Question 10 View Details

Find the value of ( x ) in the equation \(2^x + 3^x = 5^x\).

Correct A. 1

B. 2

C. 3

D. 4

Correct Answer: A

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Question 11 View Details

Find the equation of the circle passing through the points ( (2,3) ), ( (4,5) ), and ( (6,7) ).

Correct A. \(x^2 + y^2 - 10x - 2y + 23 = 0\)

B. \(x^2 + y^2 - 12x - 4y + 35 = 0\)

C. \(x^2 + y^2 - 14x - 6y + 47 = 0\)

D. \(x^2 + y^2 - 16x - 8y + 59 = 0\)

Correct Answer: A

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Question 12 View Details

Evaluate the definite integral \(int_{0}^{2} 2x^3 - 5x^2 + 3x - 1 \\) dx ).

A. ( 2 )

B. ( 4 )

Correct C. ( 6 )

D. ( 8 )

Correct Answer: C

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Question 13 View Details

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

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

Correct 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: B

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Question 14 View Details

Solve the vector equation \(\mathbf{a} \times \mathbf{b} + mathbf{c} \\)\(= mathbf\){0} ) for ( mathbf{a} ), given that \\(mathbf{c} \(\mathbf{b} = egin{pmatrix} 2 \ 3 \ 4 \end{pmatrix}\) and \(\mathbf{c} = egin{pmatrix} 1 \ 2 \ 3 \end{pmatrix}\).

Correct A. \(\mathbf{a} = egin{pmatrix} 0 \ 0 \ 0 \end{pmatrix}\)

B. \(\mathbf{a} = egin{pmatrix} 3 \ 4 \ 5 \end{pmatrix}\)

C. \(\mathbf{a} = egin{pmatrix} 4 \ 5 \ 6 \end{pmatrix}\)

D. \(\mathbf{a} = egin{pmatrix} 5 \ 6 \ 7 \end{pmatrix}\)

Correct Answer: A

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Question 15 View Details

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

Correct A. \(x = \frac{\pi}{6}\)

B. \(x = \frac{\pi}{4}\)

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

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

Correct Answer: A

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Question 16 View Details

Find the area under the curve \(y = x\^2 + 2x + 1\) from \(x = 0\) to \(x = 3\).

Correct A. 27

B. 30

C. 36

D. 45

Correct Answer: A

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Question 17 View Details

A fair six-sided die is rolled. What is the probability that the number obtained is a multiple of 3?

A. \(1/2\)

B. \(1/3\)

C. \(2/3\)

Correct D. \(1/6\)

Correct Answer: D

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Question 18 View Details

Find the volume of the solid formed by rotating the region bounded by \(y = x\^2\), \(y = 0\), and \(x = 2\) about the x-axis.

A. 32\\(\pi/5\)

B. 64\\(\pi/5\)

Correct C. 128\\(\pi/5\)

D. 256\\(\pi/5\)

Correct Answer: C

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Question 19 View Details

A vector \(\vec{a} = 2\hat{i} + 3\hat{j} and a vector \vec{b} = -4\hat{i} + 5\hat{j}\). Find the magnitude of the cross product of \(\vec{a}\) and \(\vec{b}\).

A. 13

Correct B. 15

C. 17

D. 19

Correct Answer: B

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Question 20 View Details

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

Correct A. -2

B. 0

C. 2

D. 4

Correct Answer: A

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Question 21 View Details

Find the area under the curve \(y = \frac{1}{2}x^2 + 3x - 2\) from \(x = 1\) to \(x = 4\).

Correct A. \(\frac{29}{3}\)

B. \(\frac{31}{3}\)

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

D. \(\frac{33}{3}\)

Correct Answer: A

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Question 22 View Details

Solve the inequality \(\frac{2x + 1}{x - 1} > 0\).

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

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

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

D. \(x < 1\) or \(x = -1\)

Correct Answer: A

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Question 23 View Details

Find the value of ( x ) in the equation \(x^3 - 6x^2 + 11x - 6 = 0\).

A. \(x = 1\)

B. \(x = 2\)

Correct C. \(x = 3\)

D. \(x = 4\)

Correct Answer: C

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Question 24 View Details

Find the area of the triangle with vertices ( A(1, 2) ), ( B(3, 4) ), and ( C(2, 1) ).

Correct A. ( 5 )

B. ( 6 )

C. ( 7 )

D. ( 8 )

Correct Answer: A

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Question 25 View Details

Solve the system of equations \(x + y = 4\) and \(xy = 5\).

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

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

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

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

Correct Answer: A

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