POST UTME BOWEN UNIVERSITY 2021 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the value of $\int_{0}^{\pi} \frac{1}{1+\sin^2 x} dx$.
A. \frac{\pi}{2}
B. \frac{\pi}{4}
C. \frac{\pi}{3}
D. \frac{\pi}{6}
Question 2
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?
A. 0.12
B. 0.24
C. 0.36
D. 0.48
Question 3
Find the area under the curve $y = \frac{1}{x^2+1}$ from $x = 0$ to $x = 1$.
A. \frac{\pi}{4}
B. \frac{\pi}{2}
C. \frac{\pi}{3}
D. \frac{\pi}{6}
Question 4
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
B. 0.5
C. 0.75
D. 1
Question 5
Solve the polynomial equation \( x^3 - 2x^2 - 5x + 6 = 0 \).
A. x = 1
B. x = -1
C. x = 2
D. x = -2
Question 6
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?
A. 5\sqrt{3}
B. 5\sqrt{2}
C. 10\sqrt{3}
D. 10\sqrt{2}
Question 7
A histogram of exam scores is shown below. If the mean score is 60, what is the median score?
A. 55
B. 60
C. 65
D. 70
Question 8
In a binary system, what is the value of the number represented by the sequence 1011?
A. 11
B. 13
C. 15
D. 17
Question 9
Solve the inequality x^2 - 4x - 5 > 0.
A. \( -∞, -1 \) ∪ (5, ∞)
B. \( -∞, -5 \) ∪ (1, ∞)
C. \( -∞, -1 \) ∪ (1, ∞)
D. \( -∞, 5 \) ∪ (1, ∞)
Question 10
Solve the inequality \frac{x - 2}{x + 1} > 0.
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
Question 11
Find the determinant of the matrix \begin{bmatrix} 2 & 3 & 4 \ 5 & 6 & 7 \ 8 & 9 & 10 \end{bmatrix}.
A. 0
B. 1
C. 2
D. 3
Question 12
Find the value of \( \sin 2\theta \) given that \( \sin \theta = \frac{3}{5} \) and \( \cos \theta = \frac{4}{5} \).
A. \( \frac{24}{25} \)
B. \( \frac{16}{25} \)
C. \( \frac{12}{25} \)
D. \( \frac{8}{25} \)
Question 13
Solve the inequality $|x-2| > 3$.
A. \( -\infty, -1 \) \cup \( 5, \infty \)
B. \( -\infty, 1 \) \cup \( 3, \infty \)
C. \( -\infty, -5 \) \cup \( 1, \infty \)
D. \( -\infty, 5 \) \cup \( 3, \infty \)
Question 14
Solve the quadratic equation \( x^2 + 4x + 4 = 0 \).
A. x = -2
B. x = 0
C. x = -1
D. x = 2
Question 15
A circle has a radius of 5 cm. What is the area of the circle?
A. 25\pi
B. 50\pi
C. 75\pi
D. 100\pi

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