POST UTME NILE UNIVERSITY 2023 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A rec\tangular prism has a length of 10 cm, a width of 5 cm, and a height of 8 cm. Find the volume of the prism.
A. 400 cm^3
B. 500 cm^3
C. 600 cm^3
D. 800 cm^3
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
A circle has a radius of 4 cm. Find the area of the circle.
A. 16π
B. 32π
C. 64π
D. 128π
Question 4
Find the area of the triangle with vertices (0, 0), (3, 0), and (0, 4).
A. 6
B. 12
C. 18
D. 24
Question 5
Find the equation of the circle with center \( -2, 3 \) and radius 4.
A. \boxed{\( x + 2 \)^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 6
Solve the inequality \( \frac{x}{x - 2} > 0 \) for \( x \neq 2 \).
A. x < 0 or x > 2
B. x < 2
C. x > 2
D. x < 0
Question 7
Find the value of x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 8
Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.
A. 32\pi
B. 64\pi
C. 96\pi
D. 128\pi
Question 9
Evaluate the definite integral \(int_0^1 x^2 dx\).
A. 1/3
B. 1/2
C. 2/3
D. 1
Question 10
A circle passes through the points (2, 3), (4, 5), and (6, 7). Find the equation of the circle.
A. \( x - 4 \)^2 + \( y - 5 \)^2 = 9
B. \( x - 3 \)^2 + \( y - 4 \)^2 = 16
C. \( x - 5 \)^2 + \( y - 6 \)^2 = 25
D. \( x - 6 \)^2 + \( y - 7 \)^2 = 36
Question 11
A circle has a diameter of 10 cm. If a chord of the circle is 8 cm long, find the dis\tance from the center of the circle to the chord.
A. 4 cm
B. 5 cm
C. 6 cm
D. 7 cm
Question 12
Solve the equation \[ \sin^2 x + \cos^2 x = 1 \] for x.
A. \[ x = \frac{\pi}{4} \]
B. \[ x = \frac{\pi}{2} \]
C. \[ x = \frac{3\pi}{4} \]
D. \[ x = \frac{5\pi}{4} \]
Question 13
Find the sum of the first 10 terms of the geometric progression 2, 6, 18, ...
A. 1023
B. 1024
C. 1025
D. 1026
Question 14
Solve for y in the equation \( y = \frac{1}{2} \left\( x + \frac{1}{x} \right \ \) ).
A. \frac{x^2 + 1}{2x}
B. \frac{x^2 - 1}{2x}
C. \frac{x^2 + 2}{2x}
D. \frac{x^2 - 2}{2x}
Question 15
Let ( S ) be the set of all real numbers ( x ) such that \( x^2 - 6x + 8 = 0 \). Find the set ( S ) in interval notation.
A. \( -\infty, 2 \) \cup \( 4, \infty \)
B. \( -\infty, 4 \) \cup \( 2, \infty \)
C. \( -\infty, 2 \) \cup (2, 4) \cup \( 4, \infty \)
D. \( -\infty, 4 \) \cup \( 2, \infty \)

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