POST UTME UNN 2018 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the volume of the frustum of a cone with a height of 6 cm, a lower base radius of 4 cm, and an upper base radius of 2 cm.
A. 48\pi
B. 64\pi
C. 72\pi
D. 80\pi
Question 2
A random variable X has a probability distribution given by P(X) = \( 1/2 \)^\( X-1 \) for X = 1, 2, 3, ... . Find the probability that X is greater than 2.
A. 1/4
B. 1/2
C. 3/4
D. 1
Question 3
Determine the number of solutions to the equation x^2 + 2x + 2 = 0.
A. 0
B. 1
C. 2
D. 3
Question 4
Solve for ( x ) in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 5
Solve the equation \( \sin^2 x + \cos^2 x = 1 \) for (x).
A. 0
B. \frac{\pi}{2}
C. \frac{\pi}{4}
D. \frac{3\pi}{4}
Question 6
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( -∞, -1 \) ∪ (3, ∞)
B. \( -∞, -3 \) ∪ (1, ∞)
C. \( -∞, -1 \) ∪ (1, ∞)
D. \( -∞, 1 \) ∪ (3, ∞)
Question 7
Let X be a random variable with probability density function f(x) = \( \frac{1}{2}e^{-|x|} \) for -∞ < x < ∞. Find the probability that X is greater than 1.
A. 0.5
B. 0.6
C. 0.7
D. 0.8
Question 8
A solid cone has a radius of 4 cm and a height of 6 cm. Find the volume of the cone.
A. 48\pi
B. 64\pi
C. 80\pi
D. 96\pi
Question 9
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. 24
B. 28
C. 32
D. 36
Question 10
In a certain number base, the representation of the number 27 is 101. If the base is denoted by 'b', find the value of 'b' u\sing the formula for converting a number from base 'b' to base 10.
A. 3
B. 4
C. 5
D. 6
Question 11
Solve for ( x ) in the equation \( x^2 + 4x + 4 = 0 \).
A. -2
B. -1
C. 1
D. 2
Question 12
Solve the differential equation \frac{dy}{dx} = \frac{y}{x} u\sing the chain rule.
A. y = \ln|x|
B. y = \ln|x^2|
C. y = \ln|x^3|
D. y = \ln|x^4|
Question 13
A geometric sequence has a first term of 2 and a common ratio of 3. Find the 5th term of the sequence.
A. 243
B. 243
C. 243
D. 243
Question 14
Find the value of y in the equation \( y = 2x + 3 \), given that x = 2.
A. 7
B. 5
C. 3
D. 1
Question 15
Solve the equation 2x^2 + 5x - 3 = 0 u\sing the quadratic formula.
A. x = -1 ± √2
B. x = 1 ± √2
C. x = -1 ± √3
D. x = 1 ± √3

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