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POST UTME RHEMA UNIVERSITY 2018 Mathematics | Objective

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Question 1 View Details

In a survey of 100 students, the mean height of the students is 170 cm. If the mean height of 20 students is 180 cm, and the mean height of the remaining 80 students is 160 cm, what is the mean height of all 100 students?

A. 168 cm

Correct B. 170 cm

C. 172 cm

D. 174 cm

Correct Answer: B

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Question 2 View Details

A rectangular solid has a length of 10 cm, a width of 5 cm, and a height of 8 cm. If the solid is cut into smaller cubes with a side length of 2 cm, how many cubes will be formed?

A. 20

B. 25

Correct C. 30

D. 35

Correct Answer: C

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Question 3 View Details

A car travels from city A to city B at an average speed of 60 $(km/h$\) and returns from city B to city A at an average speed of 40 $km/h\\((km/h) and returns from city B to city A at an average speed of 40$. What is the average speed of the car for the entire trip?

A. 48 $km/h$

B. 50 $km/h$

Correct C. 52 $km/h$

D. 55 $km/h$

Correct Answer: C

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Question 4 View Details

A company produces two products, X and Y. Product X requires 2 hours of labor and 3 hours of machine time, while product Y requires 3 hours of labor and 2 hours of machine time. If the company has 120 hours of labor and 180 hours of machine time available, how many units of product X and product Y should the company produce to maximize profit?

A. (20, 30)

B. (30, 20)

Correct C. (25, 25)

D. (35, 15)

Correct Answer: C

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Question 5 View Details

A random variable X has a probability distribution given by P$X = 1 = 0.3$, P$X = 2 = 0.4$, and P$X = 3 = 0.3$. What is the expected value of X?

A. 1.1

Correct B. 1.3

C. 1.5

D. 1.7

Correct Answer: B

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Question 6 View Details

Determine the value of x in the equation $\sin^2 x \$ + \$\cos^2(x)$ = 1 ) if $$1x \$ = $\frac{3}{5}$\) ).

Correct A. $\frac{4}{5}$

B. $\frac{3}{4}$

C. $\frac{5}{4}$

D. $\frac{4}{3}$

Correct Answer: A

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Question 7 View Details

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

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

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

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

D. $\frac{\pi}{6}$

Correct Answer: A

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Question 8 View Details

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

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

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

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

D. $x < 1$ or $x > 4$

Correct Answer: A

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Question 9 View Details

Find the sum of the first 5 terms of the geometric series ( 2, 6, 18, ... ).

Correct A. ( 242 )

B. ( 242 )

C. ( 242 )

D. ( 242 )

Correct Answer: A

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Question 10 View Details

Solve the system of equations $x + y = 4$ and $xy = 5$.

Correct A. $x = 1, y = 3$

B. $x = 2, y = 2$

C. $x = 3, y = 1$

D. $x = 4, y = 0$

Correct Answer: A

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Question 11 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. 24\pi $cm^3$

Correct B. 48\pi $cm^3$

C. 96\pi $cm^3$

D. 192\pi $cm^3$

Correct Answer: B

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Question 12 View Details

Solve the system of equations using matrices:\nbegin{align*}\n2x+3y&=7\nx-2y&=-3\nend{align*}

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

B. \begin{pmatrix}2\-3\end{pmatrix}

C. \begin{pmatrix}3\-2\end{pmatrix}

D. \begin{pmatrix}4\-1\end{pmatrix}

Correct Answer: A

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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.

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

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

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

D. $\frac{2x}{x^2+1$ ^3}\)\)

Correct Answer: A

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Question 14 View Details

A fair six-sided die is rolled. What is the probability that the number rolled is greater than 4?

A. $\frac{1}{6}$\)

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

C. $\frac{2}{3}$\)

Correct D. $\frac{5}{6}$\)

Correct Answer: D

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Question 15 View Details

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

Correct A. x=$\frac{\pi}{2}$\)

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

C. x=$\frac{\pi}{4}$\)

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

Correct Answer: A

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Question 16 View Details

Find the value of x in the equation $$1x = \frac{1}{\sqrt{3}}$ if ( x ) lies in the first quadrant.

Correct A. 30°

B. 45°

C. 60°

D. 90°

Correct Answer: A

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Question 17 View Details

Solve the matrix equation $\begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 3 \ 7 \end{bmatrix}$.

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

B. \begin{bmatrix} 2 \\ 3 \end{bmatrix}

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

D. \begin{bmatrix} 4 \\ 5 \end{bmatrix}

Correct Answer: A

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Question 18 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. $\frac{1}{x^2 + 1$ ^2}\)\)

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

Correct Answer: A

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Question 19 View Details

Evaluate the definite integral $\int_0^1 \frac{1}{x^2 + 1} dx$.

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

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

C. $\frac{\pi}{6}$\)

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

Correct Answer: A

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Question 20 View Details

Solve the system of equations $x + y = 3$ and $x - y = 1$.

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

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

C. \begin{bmatrix} 3 \\ 0 \end{bmatrix}

D. \begin{bmatrix} 0 \\ 3 \end{bmatrix}

Correct Answer: A

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Question 21 View Details

Find the value of x in the equation $$1x = \frac{1}{2}$ if ( x ) lies in the second quadrant.

A. 120°

Correct B. 150°

C. 180°

D. 210°

Correct Answer: B

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Question 22 View Details

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

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

B. \begin{bmatrix} 2 \\ 3 \end{bmatrix}

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

D. \begin{bmatrix} 4 \\ 5 \end{bmatrix}

Correct Answer: A

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Question 23 View Details

Find the derivative of the function ( f(x) = $\frac{1}{x^3 + 1}$\)\) ) using the chain rule.

A. -$\frac{3x^2}{$ $x^3 + 1$ ^2}\)\)

B. $\frac{3x^2}{$ $x^3 + 1$ ^2}\)\)

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

D. -$\frac{1}{x^3 + 1$ ^2}\)\)

Correct Answer: VIEW ANSWER

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Question 24 View Details

In the number system with base 8, what is the value of the digit $x$ such that $x_8 + 12_8 = 23_8$?

A. 4

Correct B. 5

C. 6

D. 7

Correct Answer: B

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Question 25 View Details

Find the value of $\frac{1}{2} \log_{10} x^2$$= 4$\).

A. 10

B. 100

Correct C. 1000

D. 10000

Correct Answer: C

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