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POST UTME BOWEN UNIVERSITY 2021 Mathematics | Objective

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Question 1 View Details

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 View Details

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 View Details

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 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 5 View Details

A rectangular 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 View Details

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 View Details

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 View Details

Find the value of (\(12\theta\) given that \\((\)12theta\(\(1\theta = \frac{3}{5}\) and 1\\(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 View Details

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

A. 25

B. 36

C. 49

Correct D. 64

Correct Answer: D

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Question 10 View Details

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 View Details

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 View Details

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 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 14 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

A rectangular 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 View Details

Two events, A and B, are independent. 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 View Details

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 View Details

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 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 24 View Details

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 View Details

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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