POST UTME COAL CITY UNIVERSITY 2025 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A fair six-sided die is rolled. What is the probability that the number rolled is greater than 4?
A. \( \frac{1}{6} \)
B. \( \frac{1}{3} \)
C. \( \frac{2}{3} \)
D. \( \frac{5}{6} \)
Question 2
Solve the inequality \frac{x}{x-1} > 2.
A. x < -1 or x > 2
B. x < 1 or x > 2
C. x < -1 or x < 2
D. x > -1 or x > 2
Question 3
Find the volume of the solid formed by rotating the region bounded by the curves y = x^2 and y = 4 - x^2 about the x-axis.
A. 16\pi
B. 32\pi
C. 64\pi
D. 128\pi
Question 4
Solve for ( x ) in the equation \( 2^x + 2^x = 2^{x+2} \).
A. 0
B. 1
C. 2
D. 3
Question 5
In a histogram, the mean is 25, the median is 20, and the mode is 15. Find the value of the class width.
A. 5
B. 10
C. 15
D. 20
Question 6
A rec\tangular prism has a length of 6 units, a width of 4 units, and a height of 3 units. Find the volume of the prism.
A. 72
B. 80
C. 90
D. 100
Question 7
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 8
Determine the value of x in the equation \( egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ 1 \end{bmatrix} = egin{bmatrix} 7 \ 11 \end{bmatrix} \).
A. 3
B. 4
C. 5
D. 6
Question 9
Find the mean of the data set: 2, 4, 6, 8, 10.
A. 6
B. 8
C. 10
D. 12
Question 10
A set of 10 points is chosen at random from a circle of radius 5. What is the probability that the dis\tance between the two farthest points is less than 5?
A. 0.1
B. 0.2
C. 0.3
D. 0.4
Question 11
A circle with center (0, 0) and radius 4 passes through the point (3, 4). Find the equation of the circle.
A. x^2 + y^2 = 16
B. x^2 + y^2 = 20
C. x^2 + y^2 = 24
D. x^2 + y^2 = 28
Question 12
A fair six-sided die is rolled. What is the probability that the number obtained is a multiple of 3?
A. 1/3
B. 1/6
C. 1/2
D. 2/3
Question 13
Find the derivative of ( f(x) = \frac{1}{\sqrt{x}} ) u\sing the chain rule.
A. \( \frac{-1}{2}x^{-\frac{3}{2}} \)
B. \( \frac{1}{2}x^{-\frac{3}{2}} \)
C. \( \frac{1}{2}x^{-\frac{1}{2}} \)
D. \( \frac{-1}{2}x^{-\frac{1}{2}} \)
Question 14
A rec\tangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. What is its volume?
A. 30
B. 40
C. 50
D. 60
Question 15
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

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