POST UTME BELLS UNIVERSITY 2024 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the equation \[ \sin^2(x) + \cos^2(x) = 1 \] for x.
A. \frac{\pi}{4}
B. \frac{\pi}{2}
C. \frac{3\pi}{4}
D. \frac{\pi}{6}
Question 2
Given that \( \sin^2 x + \cos^2 x = 1 \), find the value of \( \tan x \) when \( \sin x = \frac{3}{5} \).
A. 0.6
B. 0.8
C. 1.2
D. 1.5
Question 3
A particle moves in a straight line with a velocity of 5 m/s. If the acceleration is 2 m/s^2, find the dis\tance traveled in 3 seconds.
A. 15
B. 20
C. 25
D. 30
Question 4
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. Find the expected value of X.
A. 1.1
B. 1.2
C. 1.3
D. 1.4
Question 5
Find the derivative of the function ( f(x) = \frac{x^2 + 2x - 3}{x^2 - 4} ) u\sing the quotient rule.
A. \frac{\( x^2 - 4 \)\( 2x + 2 \) - \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2}
B. \frac{\( x^2 - 4 \)\( 2x + 2 \) + \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2}
C. \frac{\( x^2 - 4 \)\( 2x + 2 \) - \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2}
D. \frac{\( x^2 - 4 \)\( 2x + 2 \) + \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2}
Question 6
Let A = \( egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \) and B = \( egin{bmatrix} 5 & 6 \ 7 & 8 \end{bmatrix} \). Find the product AB.
A. \( egin{bmatrix} 19 & 22 \ 43 & 50 \end{bmatrix} \)
B. \( egin{bmatrix} 21 & 24 \ 45 & 52 \end{bmatrix} \)
C. \( egin{bmatrix} 23 & 26 \ 47 & 54 \end{bmatrix} \)
D. \( egin{bmatrix} 25 & 28 \ 49 & 56 \end{bmatrix} \)
Question 7
Find the determinant of the matrix \( \begin{bmatrix} 2 & 3 \ 4 & 5 \end{bmatrix} \).
A. 1
B. 2
C. 3
D. 4
Question 8
The equation of a circle is \( x^2 + y^2 = 16 \). Find the equation of the line pas\sing through the point ( (4, 0) ) that is \tangent to the circle.
A. y = 4x + 16
B. y = 4x - 16
C. y = 4x + 4
D. y = 4x - 4
Question 9
Find the value of x in the quadratic equation \( x^2 + 4x + 4 = 0 \).
A. x = -2
B. x = -1
C. x = 0
D. x = 1
Question 10
A circle has a radius of 4 cm. Find the area of the circle.
A. 16\pi
B. 4\pi
C. 2\pi
D. \pi
Question 11
Solve the inequality \( 2x - 5 > 3 \).
A. x > 4
B. x < 4
C. x > 2
D. x < 2
Question 12
Find the vector \[ \vec{a} \times \vec{b} \] given that \[ \vec{a} = \begin{pmatrix} 2 \ 3 \ 4 \end{pmatrix} \] and \[ \vec{b} = \begin{pmatrix} 1 \ 2 \ 3 \end{pmatrix} \].
A. \begin{pmatrix} -1 \ 8 \ -5 \end{pmatrix}
B. \begin{pmatrix} 1 \ -8 \ 5 \end{pmatrix}
C. \begin{pmatrix} -1 \ -8 \ 5 \end{pmatrix}
D. \begin{pmatrix} 1 \ 8 \ -5 \end{pmatrix}
Question 13
Find the equation of the line pas\sing through the points (2, 3) and (4, 5).
A. y = 2x - 1
B. y = 2x + 1
C. y = x + 2
D. y = x - 2
Question 14
A fair six-sided die is rolled. What is the probability that the number rolled is a multiple of 3 or 5?
A. 1/3
B. 1/2
C. 2/3
D. 5/6
Question 15
A curve is defined by the equation \( y = \frac{1}{x^2 + 1} \). Find the area under the curve between \( x = 0 \) and \( x = 1 \).
A. 1/2
B. 1/3
C. 2/3
D. 1/4

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