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POST UTME BOWEN UNIVERSITY 2018 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

Solve the inequality $\frac{x^2 - 4}{x^2 - 9}$\)\$) > 0.$

Correct A. $-3, -2$ \cup $-1, 1$ \cup (2, 3)

B. $-3, -2$ \cup (1, 2)

C. $-3, -2$ \cup (1, 3)

D. $-3, 3$

Correct Answer: A

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Question 3 View Details

Find the area of the region bounded by the parabola (y = x\^2\), the line \$(y = x^2\(y = 4$, and the x-axis.

A. 8\pi

B. 16\pi

Correct C. 24\pi

D. 32\pi

Correct Answer: C

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Question 4 View Details

Solve the system of equations \begin{align*} x + y &= 4 \ x - 2y &= 3 \end{align*}

Correct A. \begin{pmatrix} 1 \ 3 \end{pmatrix}

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

C. \begin{pmatrix} 2 \ 2 \end{pmatrix}

D. \begin{pmatrix} -2 \ -2 \end{pmatrix}

Correct Answer: A

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Question 5 View Details

A box contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is red?

A. $\frac{1}{2}$\)

B. $\frac{3}{8}$\)

Correct C. $\frac{5}{8}$\)

D. $\frac{7}{8}$\)

Correct Answer: C

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Question 6 View Details

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

A. 10

B. 100

C. 1000

Correct D. 10000

Correct Answer: D

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Question 7 View Details

A histogram of exam scores has a mean of 75 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 90?

A. 0.5

B. 0.6

Correct C. 0.7

D. 0.8

Correct Answer: C

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Question 8 View Details

Solve the equation $x^2 + 4x + 4 = 0$.

A. $x = 0$

Correct B. $x = -2$

C. $x = -1$

D. $x = 1$

Correct Answer: B

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Question 9 View Details

Find the area under the curve $y = x^2$ from $x = 0$ to $x = 4$.

A. 16

B. 32

Correct C. 64

D. 128

Correct Answer: C

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Question 10 View Details

A circle has a radius of 5 cm. Find the area of the circle.

A. 10\pi

B. 20\pi

Correct C. 50\pi

D. 100\pi

Correct Answer: C

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Question 11 View Details

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

A. 1

Correct B. -1

C. 2

D. 3

Correct Answer: B

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Question 12 View Details

A rectangular solid has dimensions 3 cm, 4 cm, and 5 cm. Find its surface area.

A. 94

Correct B. 96

C. 98

D. 100

Correct Answer: B

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Question 13 View Details

Solve the equation [ \$(2x^2 + 3x - 1$$= 0$\) ].

A. $x =$$-1/2$

Correct B. $x = 1/2$\)

C. $x = -1$

D. $x = 1$

Correct Answer: B

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Question 14 View Details

A curve has equation [$(y = x$\^2 + 2x + 1\) ]. Find the area under the curve between \$(y = x^2 + 2x + 1\(x = 0$ and $x = 2$.

A. 7

Correct B. 8

C. 9

D. 10

Correct Answer: B

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Question 15 View Details

Two events are independent. If the probability of one event is $(1/2$\) and the probability of the other event is $3/4\\((1/2) and the probability of the other event is$, find the probability that both events occur.

Correct A. $3/8$

B. $1/2$

C. $3/4$

D. $5/8$

Correct Answer: A

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Question 16 View Details

A random sample of 25 students from a university had a mean height of 175.5 cm with a standard deviation of 5.2 cm. Calculate the coefficient of variation (CV) of the sample.

A. 10%

Correct B. 15%

C. 20%

D. 25%

Correct Answer: B

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Question 17 View Details

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

A. $\frac{1}{x^3}$\)\)

Correct B. $\frac{2x}{x^4}$\)\)

C. $\frac{x^2}{x$^4}\)\)

D. $\frac{x^3}{x$^4}\)\)

Correct Answer: B

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Question 18 View Details

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

Correct A. $\frac{\pi}{4}$\)

B. $\frac{\pi}{2}$\)

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

D. $\frac{5\pi}{4}$\)

Correct Answer: A

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Question 19 View Details

A force of 10 N acts on an object, causing it to accelerate at 2 $m/s\^2$. What is the mass of the object?

A. 5 kg

Correct B. 10 kg

C. 15 kg

D. 20 kg

Correct Answer: B

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Question 20 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. $x - 3$^2 + $y - 2$^$2 = 16$

C. $x - 4$^2 + $y - 3$^$2 = 16$

D. $x - 2$^2 + $y - 4$^$2 = 16$

Correct Answer: A

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Question 21 View Details

Let $\mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix}$ and $\mathbf{b} = egin{pmatrix} -1 \ 4 end{pmatrix}$. Find the vector $\\(end{pmatrix}). Find the vector \mathbf{a} \times \mathbf{b}$ using the determinant method.

Correct A. $egin{pmatrix} 10 \ -14 \end{pmatrix}$

B. $egin{pmatrix} -10 \ 14 \end{pmatrix}$

C. $egin{pmatrix} 14 \ 10 \end{pmatrix}$

D. $egin{pmatrix} 0 \ 0 \end{pmatrix}$

Correct Answer: A

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Question 22 View Details

Solve the equation $2^x + 2^{x+1} = 3 \cdot 2^x$ for ( x ).

Correct A. $x = 1$

B. $x = 2$

C. $x = 3$

D. $x = 4$

Correct Answer: A

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Question 23 View Details

Find the value of $\log_{10} 1000 \$ ).

A. ( 3 )

Correct B. ( 4 )

C. ( 5 )

D. ( 6 )

Correct Answer: B

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Question 24 View Details

Solve the inequality $\frac{x}{2} - 1 > 3$.

Correct A. $x > 8$

B. $x < 8$

C. $x > 6$

D. $x < 6$

Correct Answer: A

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Question 25 View Details

Find the value of ($12x \$ ) given that \$($12x $\(1x \$ = $\frac{1}{2}$\) ) and 1x \\) = $\frac{\sqrt{3}}{2}$ ).

Correct A. $\frac{\sqrt{3}}{2}$

B. $\frac{1}{2}$

C. $-\frac{1}{2}$

D. $-\frac{\sqrt{3}}{2}$

Correct Answer: A

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