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POST UTME CALEB UNIVERSITY 2019 Mathematics | Objective

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Question 1 View Details

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

A. 48\pi \(cm^3\)

B. 64\pi \(cm^3\)

Correct C. 80\pi \(cm^3\)

D. 96\pi \(cm^3\)

Correct Answer: C

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Question 2 View Details

If \overrightarrow{a} = \begin{pmatrix} 2 \ 3 \ 4 \end{pmatrix} and \overrightarrow{b} = \begin{pmatrix} -1 \ 2 1 \end{pmatrix}, find the cross product \overrightarrow{a} \\( 1 end{pmatrix}, find the cross product \times \overrightarrow{b}.

Correct A. \begin{pmatrix} 5 \ -11 \ -1 \end{pmatrix}

B. \begin{pmatrix} -5 \ 11 \ 1 \end{pmatrix}

C. \begin{pmatrix} 5 \ 11 \ 1 \end{pmatrix}

D. \begin{pmatrix} -5 \ -11 \ 1 \end{pmatrix}

Correct Answer: A

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Question 3 View Details

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

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

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

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

D. \(x =\)\(\frac{7\pi}{4}\)\)

Correct Answer: B

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Question 4 View Details

Find the area under the curve \(y = x\^2\) from \(x = 0\) to \(x = 4\).

A. 64

B. 128

Correct C. 192

D. 256

Correct Answer: C

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Question 5 View Details

If f(x) = \(2x^2 + 3x - 1\), find the derivative f'(x).

Correct A. 4x + 3

B. 2x + 1

C. 4x - 3

D. 2x - 1

Correct Answer: A

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Question 6 View Details

Solve the inequality (\(\frac{x-2}{x+1}\(> 0\)\) for x in \\((frac{x-2}{x+1} > 0\(-\infty, -1 \ cup -1, 2\) cup (2\), infty) ).

A. \(-\infty, -1\) \cup \(2, \infty\)

B. \(-\infty, -1\) \cup \(-1, 2\)

Correct C. \(-\infty, -1\) \cup \(2, \infty\)

D. \(-\infty, -1\) \cup \(2, \infty\)

Correct Answer: C

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Question 7 View Details

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

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

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

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

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

Correct Answer: C

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Question 8 View Details

A histogram of exam scores has a mean of 60 and a standard deviation of 10. If the highest score is 90, find the number of students who scored 80.

A. 2

B. 3

Correct C. 4

D. 5

Correct Answer: C

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Question 9 View Details

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

A. 1950

B. 1960

Correct C. 1970

D. 1980

Correct Answer: C

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Question 10 View Details

Solve the equation \(x^2 - 6x + 8 = 0\).

Correct A. (2, 4)

B. (3, 2)

C. (4, 3)

D. (2, 2)

Correct Answer: A

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Question 11 View Details

Find the value of (x\) in the equation \(2^x + 2^{x+1} = 3 \\((x) in the equation \cdot 2^{x+1}\).

A. 1

B. 2

Correct C. 3

D. 4

Correct Answer: C

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Question 12 View Details

Solve the inequality \(\left| x - 2 \right| \geq 3\).

Correct A. \(x \leq -1\) or \(x \geq 5\)

B. \(x \leq 1\) or \(x \geq 5\)

C. \(x \leq -1\) or \(x \geq 2\)

D. \(x \leq 1\) or \(x \geq 2\)

Correct Answer: A

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Question 13 View Details

In the diagram below, (ABCD\) is a rectangle and \(E\\((ABCD) is a rectangle and\) is the midpoint of (AD\). If \(AB = 6\\((AD). If\) and (BC = 8\), find the area of triangle \(ADE\\((BC = 8), find the area of triangle\).

Correct A. 24

B. 30

C. 36

D. 40

Correct Answer: A

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Question 14 View Details

Find the value of (x\) in the equation \(\\((x) in the equation \frac{1}{x} + \frac{1}{x+1} = \frac{1}{2}\).

A. -1

Correct B. 1

C. 2

D. 3

Correct Answer: B

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Question 15 View Details

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

Correct A. \(x = -2\)

B. \(x = -1\)

C. \(x = 1\)

D. \(x = 2\)

Correct Answer: A

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Question 16 View Details

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

A. 64\pi

B. 96\pi

Correct C. 128\pi

D. 192\pi

Correct Answer: C

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Question 17 View Details

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

A. \(10^4\)

B. \(10^8\)

Correct C. \(10^{16}\)

D. \(10^{32}\)

Correct Answer: C

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Question 18 View Details

Find the area under the curve \(y = x\^2\) from \(x = 0\) to \(x = 4\).

A. 64

B. 128

Correct C. 256

D. 512

Correct Answer: C

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Question 19 View Details

Find the sum of the first 10 terms of the geometric progression 3, 6, 12, ...

A. 3120

B. 3240

Correct C. 3360

D. 3480

Correct Answer: C

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Question 20 View Details

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

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

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

Correct C. \(x - 2\)^2 + \(y - 3\)^\(2 = 36\)

D. \(x - 2\)^2 + \(y - 3\)^\(2 = 49\)

Correct Answer: C

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Question 21 View Details

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

A. \(egin{pmatrix} 0 \ 0 \end{pmatrix}\)

Correct B. \(egin{pmatrix} 1 \ -\frac{1}{2} \end{pmatrix}\)

C. \(egin{pmatrix} \frac{1}{2} \ -\frac{3}{2} \end{pmatrix}\)

D. \(egin{pmatrix} 1 \ -1 \end{pmatrix}\)

Correct Answer: B

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Question 22 View Details

A fair six-sided die is rolled. What is the probability that the number obtained is a multiple of 3 or 5?

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

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

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

D. \(\frac{5}{6}\)

Correct Answer: C

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Question 23 View Details

Let \(A = {1, 2, 3, 4, 5}\) and \(B = {2, 4, 6, 8, 10}\). Find ( A cap B ).

A. ( { 1, 2, 3, 4, 5 } )

B. ( { 2, 4, 6, 8, 10 } )

C. ( { 1, 2, 3, 4, 5, 6, 8, 10 } )

Correct D. ( { 2, 4 } )

Correct Answer: D

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Question 24 View Details

The sum of the first 10 terms of the arithmetic progression ( 1, 3, 5, ldots ) is ( 100 ). Find the first term.

Correct A. ( 1 )

B. ( 2 )

C. ( 3 )

D. ( 4 )

Correct Answer: A

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Question 25 View Details

Simplify \(\frac{3x^2 + 2x - 1}{2x^2 - 5x + 1}\).

Correct A. \(\frac{3x + 1}{2x - 1}\)

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

C. \(\frac{3x + 1}{2x + 1}\)

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

Correct Answer: A

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