POST UTME COAL CITY UNIVERSITY 2024 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the volume of the cylinder with radius 6 and height 8.
A. 288\pi
B. 288\pi^2
C. 288\pi^3
D. 288\pi^4
Question 2
Find the equation of the circle with center \( -2, 3 \) and radius 4.
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
Question 3
Solve the system of equations \[ x + y = 2 \] and \[ x - y = 1 \].
A. x = 1, y = 1
B. x = 1, y = -1
C. x = -1, y = 1
D. x = -1, y = -1
Question 4
Solve the trigonometric equation \( 2 \sin^2 x + 3 \cos x - 1 = 0 \).
A. \frac{\pi}{6}
B. \frac{\pi}{4}
C. \frac{\pi}{3}
D. \frac{\pi}{2}
Question 5
Find the determinant of the matrix [ egin{pmatrix} 2 & 3 & 4 \ 5 & 6 & 7 \ 8 & 9 & 10 \end{pmatrix} ].
A. -1
B. 1
C. 0
D. 2
Question 6
A box contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is blue, given that it is not red?
A. \frac{1}{2}
B. \frac{2}{5}
C. \frac{3}{8}
D. \frac{5}{7}
Question 7
If \( f(x) = \frac{1}{x^2 + 1} \), find \( f'(x) \) u\sing the chain rule.
A. \frac{-2x}{\( x^2 + 1 \)^2}
B. \frac{2x}{\( x^2 + 1 \)^2}
C. \frac{-2}{\( x^2 + 1 \)^2}
D. \frac{2}{\( x^2 + 1 \)^2}
Question 8
A line passes through the points (1, 2) and (4, 6). Find the equation of the line in slope-intercept form.
A. y = 2x - 2
B. y = 2x + 2
C. y = -2x + 2
D. y = -2x - 2
Question 9
Two events A and B are indep\endent. If P(A) = 0.4 and P(B) = 0.6, find P(A ∩ B).
A. 0.2
B. 0.4
C. 0.6
D. 0.8
Question 10
A function f(x) is defined as \(f(x) = 2x^2 + 3x - 1\). Find the derivative of f(x) u\sing the power rule.
A. 4x + 3
B. 2x + 3
C. 4x - 3
D. 2x - 3
Question 11
Solve for x in the equation [ 2x^2 + 5x - 3 = 0 ].
A. 1
B. -1
C. 2
D. -2
Question 12
Find the sum of the first 10 terms of the geometric series \( 2 + 6 + 18 + \cdots \).
A. \( 3094 \ \)
B. \( 3095 \ \)
C. \( 3096 \ \)
D. \( 3097 \ \)
Question 13
Find the mean of the data set \[ 2, 4, 6, 8, 10 \].
A. 4
B. 5
C. 6
D. 7
Question 14
Find the determinant of the matrix \( \begin{bmatrix} 2 & 1 & 3 \ 4 & 2 & 1 \ 3 & 1 & 2 \end{bmatrix} \ \).
A. \( 0 \ \)
B. \( 1 \ \)
C. \( 2 \ \)
D. \( 3 \ \)
Question 15
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{\( x^2 + 2x - 3 \)\( 2x + 2 \) - \( x^2 - 4 \)(2x)}{\( x^2 - 4 \)^2}
C. \frac{\( x^2 - 4 \)\( 2x + 2 \) + \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2}
D. \frac{\( x^2 + 2x - 3 \)\( 2x + 2 \) + \( x^2 - 4 \)(2x)}{\( x^2 - 4 \)^2}

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