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POST UTME BOWEN UNIVERSITY 2021 Mathematics | Objective

Are you preparing for POST UTME BOWEN UNIVERSITY exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2021 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

A random variable X has a probability distribution given by P(X) = $ 1/2 $^$ X-1 $ for X = 1, 2, 3, ... . Find the probability that X is greater than 2.

A. 1/4

B. 1/2

Correct C. 3/4

D. 1

Correct Answer: C

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Question 2

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

Correct A. 4

B. 2

C. 8

D. 16

Correct Answer: A

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Question 3

Solve the inequality x^2 - 4x - 5 > 0.

Correct A. $ -∞, -1 $ ∪ (5, ∞)

B. $ -∞, -5 $ ∪ (1, ∞)

C. $ -∞, -1 $ ∪ (1, ∞)

D. $ -∞, 5 $ ∪ (1, ∞)

Correct Answer: A

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Question 4

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 5

A rec\tangular box has dimensions 5 cm x 8 cm x 10 cm. Find the volume of the box.

A. 200 cm^3

B. 400 cm^3

Correct C. 600 cm^3

D. 800 cm^3

Correct Answer: C

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Question 6

Let X be a random variable with probability density function f(x) = $ egin{cases} 2x & 0 leq x leq 1 \ 0 & \text{otherwise} \end{cases} $. Find the probability that X takes a value greater than 0.5.

A. 0.25

Correct B. 0.5

C. 0.75

D. 1

Correct Answer: B

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Question 7

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

A. 0

B. 1

Correct C. 2

D. 3

Correct Answer: C

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Question 8

Find the value of $ \sin 2\theta $ given that $ \sin \theta = \frac{3}{5} $ and $ \cos \theta = \frac{4}{5} $.

Correct A. $ \frac{24}{25} $

B. $ \frac{16}{25} $

C. $ \frac{12}{25} $

D. $ \frac{8}{25} $

Correct Answer: A

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Question 9

A binary operation $ * $ on the set of integers is defined as follows: for any two integers (a) and (b), $ a * b = a^2 + b^2 $. Find the value of $ 3 * 4 $.

A. 25

B. 36

C. 49

Correct D. 64

Correct Answer: D

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Question 10

Solve the inequality $ \log_2 \( x + 1 \ $ > 2).

Correct A. 0 < x < 3

B. x > 3

C. x < 3

D. x = 3

Correct Answer: A

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Question 11

Find the value of $\int_{0}^{\pi} \frac{1}{1+\sin^2 x} dx$.

Correct A. \frac{\pi}{2}

B. \frac{\pi}{4}

C. \frac{\pi}{3}

D. \frac{\pi}{6}

Correct Answer: A

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Question 12

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

Correct A. $ -\infty, -1 $ \cup $ 5, \infty $

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

C. $ -\infty, -5 $ \cup $ 1, \infty $

D. $ -\infty, 5 $ \cup $ 3, \infty $

Correct Answer: A

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Question 13

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 14

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

Correct A. x = -2

B. x = 2

C. x = -1

D. x = 1

Correct Answer: A

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Question 15

Find the value of $\sum_{n=1}^{\infty} \frac{1}{n^2}$.

Correct A. \frac{\pi^2}{6}

B. \frac{\pi^2}{12}

C. \frac{\pi^2}{24}

D. \frac{\pi^2}{48}

Correct Answer: A

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Question 16

In a binary system, what is the value of the number represented by the sequence 1011?

A. 11

B. 13

Correct C. 15

D. 17

Correct Answer: C

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Question 17

A circle has a radius of 5 cm. What is the area of the circle?

A. 25\pi

Correct B. 50\pi

C. 75\pi

D. 100\pi

Correct Answer: B

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Question 18

A vector \overrightarrow{a} has a magnitude of 10 units and is directed at an angle of 30\circ to the x-axis. What is the x-component of the vector?

Correct A. 5\sqrt{3}

B. 5\sqrt{2}

C. 10\sqrt{3}

D. 10\sqrt{2}

Correct Answer: A

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Question 19

A rec\tangular prism has a length of 6 cm, a width of 4 cm, and a height of 3 cm. What is the volume of the prism?

A. 72

Correct B. 96

C. 108

D. 120

Correct Answer: B

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Question 20

Two events, A and B, are indep\endent. If P(A) = 0.4 and P(B) = 0.6, what is the probability that both events occur?

Correct A. 0.12

B. 0.24

C. 0.36

D. 0.48

Correct Answer: A

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Question 21

Find the volume of the frustum of a cone with height 12 cm, lower base radius 6 cm, and upper base radius 3 cm.

Correct A. 288\pi

B. 288\pi + 36\pi

C. 288\pi - 36\pi

D. 288\pi + 72\pi

Correct Answer: A

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Question 22

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

Correct A. 10^4

B. 10^8

C. 10^2

D. 10^6

Correct Answer: A

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Question 23

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 24

Find the determinant of the matrix \begin{bmatrix} 2 & 3 & 4 \ 5 & 6 & 7 \ 8 & 9 & 10 \end{bmatrix}.

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 25

Solve the inequality \frac{x - 2}{x + 1} > 0.

Correct A. x < -1 \text{ or } x > 2

B. x < 2 \text{ or } x > -1

C. x < -1 \text{ and } x > 2

D. x > -1 \text{ and } x < 2

Correct Answer: A

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