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POST UTME BELLS UNIVERSITY 2021 Mathematics | Objective

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Question 1 View Details

Determine the value of x in the equation $\frac{x}{2} + \frac{3}{4} = \frac{7}{8}$.

Correct A. 1

B. 2

C. 3

D. 4

Correct Answer: A

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Question 2 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 - 2 \$^2 + $y + 3$^$2 = 16$ )

C. $x + 2 \$^2 + $y + 3$^$2 = 16$ )

D. $x - 2 \$^2 + $y - 3$^$2 = 16$ )

Correct Answer: A

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Question 3 View Details

Solve for x in the inequality $2x - 5 > 3$.

Correct A. $x > 4$

B. $x < 4$

C. $x > 2$

D. $x < 2$

Correct Answer: A

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Question 4 View Details

A bakery sells 250 loaves of bread per day. If they make a profit of ₦5 per loaf, how much profit do they make in a day?

Correct A. ₦1250

B. ₦12500

C. ₦125000

D. ₦1250000

Correct Answer: A

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Question 5 View Details

Find the volume of the cylinder with radius 6 cm and height 10 cm.

A. $180 \pi$ cm³

B. $360 \pi$ cm³

Correct C. $600 \pi$ cm³

D. $1200 \pi$ cm³

Correct Answer: C

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Question 6 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-3 \$^2 + $y-2$^$2 = 16$ )

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

D. $x-2 \$^2 + $y+3$^$2 = 16$ )

Correct Answer: A

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Question 7 View Details

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

Correct A. $x = 2$

B. $x = 1$

C. $x = 0$

D. $x = -1$

Correct Answer: A

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Question 8 View Details

Find the volume of the solid formed by revolving the region bounded by the curves $y = x^2$ and $y = x^3$ about the x-axis.

Correct A. $\frac{1}{6} \pi$

B. $\frac{1}{3} \pi$

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

D. $\frac{2}{3} \pi$

Correct Answer: A

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Question 9 View Details

A circle with center at ((0,0)) and radius 5 passes through the point ((3,4)). Find the equation of the circle.

Correct A. $x^2 + y^2 = 25$

B. $x^2 + y^2 = 9$

C. $x^2 + y^2 = 16$

D. $x^2 + y^2 = 36$

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. $y = 2x - 1$

B. $y = 2x + 1$

C. $y = x - 1$

D. $y = x + 1$

Correct Answer: A

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Question 11 View Details

Find the area under the curve $y = \frac{1}{2}x^2 + 3x - 2$ from $x = 0$ to $x = 4$.

A. 64

B. 80

Correct C. 96

D. 112

Correct Answer: C

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Question 12 View Details

Solve the matrix equation $\begin{bmatrix} 2 & 1 \ 1 & 3 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 3 \ 7 \end{bmatrix}$.

Correct A. \begin{bmatrix} 1 \ 2 \end{bmatrix}

B. \begin{bmatrix} 2 \ 1 \end{bmatrix}

C. \begin{bmatrix} 3 \ 4 \end{bmatrix}

D. \begin{bmatrix} 4 \ 3 \end{bmatrix}

Correct Answer: A

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Question 13 View Details

Find the sum of the first 10 terms of the geometric series $2 + 6 + 18 + \cdots$.

Correct A. 1023

B. 1024

C. 1025

D. 1026

Correct Answer: A

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Question 14 View Details

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

Correct A. -$\frac{2x}{x^2 + 1$ ^2}\)\)

B. $\frac{2x}{x^2 + 1$ ^2}\)\)

C. -$\frac{2}{x^2 + 1$ ^2}\)\)

D. $\frac{2}{x^2 + 1$ ^2}\)\)

Correct Answer: A

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Question 15 View Details

Solve the inequality $2x^2 + 5x - 3 > 0$.

Correct A. $-\infty, -1$ \cup $3, \infty$

B. $-\infty, -3$ \cup $1, \infty$

C. $-\infty, 1$ \cup $3, \infty$

D. $-\infty, -3$ \cup $1, \infty$

Correct Answer: A

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Question 16 View Details

Find the area under the curve $y = \frac{1}{2}x^2$ from $x = 0$ to $x = 4$.

Correct A. 16

B. 32

C. 64

D. 128

Correct Answer: A

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Question 17 View Details

Solve the inequality $|x - 2| > 3$.

Correct A. $x < -1$ or $x > 5$

B. $x < -1$ or $x > 4$

C. $x < -5$ or $x > 1$

D. $x < 1$ or $x > 5$

Correct Answer: A

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Question 18 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 - 2 \$^2 + $y - 3$^$2 = 9$ )

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

Correct Answer: A

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Question 19 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 20 View Details

Solve the equation $\sin^2 x + \cos^2 x = 1$.

A. $$1x = 1$

B. $$1x = 1$

Correct C. $$1x = 0$

D. $$1x = 0$

Correct Answer: C

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Question 21 View Details

Find the volume of the solid formed by revolving the region bounded by the curve (y = x\^2\), the x-axis, and the line \$(y = x^2\(x = 2$ about the x-axis.

A. 16\pi

B. 32\pi

Correct C. 64\pi

D. 128\pi

Correct Answer: C

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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 180 hours of capital available, how many units of product A and product B should the firm produce to maximize profit?

Correct A. 10 units of A and 15 units of B

B. 15 units of A and 10 units of B

C. 20 units of A and 5 units of B

D. 5 units of A and 20 units of B

Correct Answer: A

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Question 23 View Details

Find the area under the curve $y = 2x\^3 - 5x^2 + x + 1$ from $x = 0$ to $x = 2$.

A. 14

B. 28

Correct C. 42

D. 56

Correct Answer: C

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Question 24 View Details

A right circular cone has a height of 10 cm and a base radius of 5 cm. Find the volume of the cone.

A. 250\pi

B. 500\pi

Correct C. 750\pi

D. 1000\pi

Correct Answer: C

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Question 25 View Details

Find the derivative of the function $y = x\^4 - 2x^2 + 1$.

Correct A. $4x^3 - 4x$

B. $2x^3 - 2x$

C. $x^3 - x$

D. $x^2 - 1$

Correct Answer: A

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