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POST UTME BELLS UNIVERSITY 2018 Mathematics | Objective

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Question 1 View Details

Determine the mean of the following set of numbers: 2, 4, 6, 8, 10. If the mean is increased by 2, what is the new mean?

A. 6

B. 8

C. 10

Correct D. 12

Correct Answer: D

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Question 2 View Details

A histogram is constructed with the following data: 2, 4, 6, 8, 10. The height of the bars is proportional to the frequency of the data. What is the mode of the data?

A. 2

Correct B. 4

C. 6

D. 8

Correct Answer: B

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Question 3 View Details

A dependent event is defined as an event whose probability of occurrence is affected by the occurrence of another event. What is the probability of drawing a red card from a deck of 52 cards if the first card drawn is a red card?

Correct A. $1/2$

B. $1/3$

C. $2/3$

D. $3/4$

Correct Answer: A

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Question 4 View Details

A 3x3 matrix is given by the following equation: [$A =$egin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix} ]. What is the determinant of matrix A?

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 5 View Details

A sequence is given by the following equation: [ $a_n = 2n + 1$ ]. What is the 5th term of the sequence?

A. 11

B. 13

Correct C. 15

D. 17

Correct Answer: C

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Question 6 View Details

In a survey of 100 students, the mean height was 170 cm with a standard deviation of 5 cm. If the heights of the students are normally distributed, what is the probability that a randomly selected student will be taller than 180 cm?

Correct A. 0.1587

B. 0.3413

C. 0.4772

D. 0.6827

Correct Answer: A

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Question 7 View Details

A rectangular prism has a length of 10 cm, a width of 5 cm, and a height of 8 cm. What is the volume of the prism?

A. 400 $cm^3$

B. 500 $cm^3$

Correct C. 600 $cm^3$

D. 800 $cm^3$

Correct Answer: C

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Question 8 View Details

Solve the system of equations using matrices:\n$egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 3 \ 7 \end{bmatrix}$

Correct A. $egin{bmatrix} -1 \ 2 \end{bmatrix}$

B. $egin{bmatrix} 1 \ -2 \end{bmatrix}$

C. $egin{bmatrix} 2 \ -1 \end{bmatrix}$

D. $egin{bmatrix} -2 \ 1 \end{bmatrix}$

Correct Answer: A

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Question 9 View Details

A circle has a radius of 4 cm. What is the area of the circle?

A. 50.24 $cm^2$

Correct B. 100.48 $cm^2$

C. 200.96 $cm^2$

D. 50.24 $cm^2$

Correct Answer: B

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Question 10 View Details

A histogram shows the distribution of exam scores for a class of 100 students. The histogram has 5 bars, with the heights of the bars being 10, 20, 30, 20, and 20. What is the mean of the exam scores?

A. 20

B. 22

Correct C. 25

D. 28

Correct Answer: C

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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. 40

B. 50

Correct C. 60

D. 70

Correct Answer: C

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Question 12 View Details

Solve the matrix equation $\begin{bmatrix} 2 & 1 \ 3 & 2 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 5 \ 8 \end{bmatrix}$.

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 value of ( x ) in the equation $2^x = 16$.

A. 2

Correct B. 3

C. 4

D. 5

Correct Answer: B

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Question 14 View Details

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

Correct A. $-∞, -1$ ∪ (3, ∞)

B. $-∞, 1$ ∪ (3, ∞)

C. $-∞, -1$ ∪ (1, ∞)

D. $-∞, 1$ ∪ (1, ∞)

Correct Answer: A

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Question 15 View Details

Find the area of the triangle with vertices ( A(0, 0) ), ( B(3, 0) ), and ( C(0, 4) ).

A. 6

B. 8

Correct C. 10

D. 12

Correct Answer: C

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Question 16 View Details

Let X and Y be independent random variables with probability density functions f_$X(x) = 2x$, $0 < x$ < 1 and f_$Y(y) =$$3y^2$,$(0 < y$\) < 1. Find the probability that $X + Y < 1\\((0 < y) < 1. Find the probability that$.

Correct A. $\frac{1}{4}$\)

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

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

D. $\frac{5}{8}$\)

Correct Answer: A

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Question 17 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 18 View Details

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

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

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

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

D. $x =$\pi

Correct Answer: A

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Question 19 View Details

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

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

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

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

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

Correct Answer: C

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Question 20 View Details

Evaluate the definite integral \int_$0^1$ $x^2$ dx.

Correct A. $\frac{1}{3}$\)

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

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

D. 1

Correct Answer: A

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Question 21 View Details

A random experiment consists of rolling a fair six-sided die and then flipping a fair coin. If the number on the die is even, the coin is flipped twice; otherwise, the coin is flipped only once. What is the probability that at least one of the coin flips shows heads?

A. $1/4$

Correct B. $1/2$

C. $3/4$

D. $2/3$

Correct Answer: B

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Question 22 View Details

The volume of a sphere (V) is given by the formula $V = \frac{4}{3} \pi r^3 \$. If the radius of the sphere is increased by 20%, what percentage increase will occur in its volume?

A. 4%

B. 12%

Correct C. 24%

D. 48%

Correct Answer: C

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Question 23 View Details

The mean of five numbers is 20. If one of the numbers is increased by 10, what will be the new mean?

A. 20

Correct B. 21

C. 22

D. 23

Correct Answer: B

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Question 24 View Details

Solve the system of equations: $x + y = 4$ and $2x - 3y = - 6$.

Correct A. $x = 2, y = 2$

B. $x = 3, y = 1$

C. $x = 4, y = 0$

D. $x = 5, y = -1$

Correct Answer: A

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Question 25 View Details

Find the derivative of the function $f(x) = 3x^2 $1x$.

Correct A. $f'(x) = 3x^2 \(1x + 6x$1x\)

B. $f'(x) = 3x^2 $1x$

C. $f'(x) = 3x $1x$

D. $f'(x) = 3x $1x$

Correct Answer: A

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