POST UTME NILE UNIVERSITY 2025 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
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 2
Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} ).
A. f'(x) = \frac{-2x}{\( x^2 + 1 \)^2}
B. f'(x) = \frac{2x}{\( x^2 + 1 \)^2}
C. f'(x) = \frac{-x}{\( x^2 + 1 \)^2}
D. f'(x) = \frac{x}{\( x^2 + 1 \)^2}
Question 3
Solve for x in the equation \( x^3 + 2x^2 - 7x - 12 = 0 \).
A. -3
B. -2
C. 3
D. 4
Question 4
Find the equation of the line pas\sing through the points ( (2, 3) ) and ( (4, 5) ).
A. y = \frac{2}{2}x + \frac{1}{2}
B. y = \frac{1}{2}x + \frac{2}{2}
C. y = \frac{2}{2}x + \frac{3}{2}
D. y = \frac{1}{2}x + \frac{3}{2}
Question 5
Find the vector ( mathbf{v} ) such that \( mathbf{v} cdot mathbf{i} = 3 \) and \( mathbf{v} cdot mathbf{j} = -2 \).
A. \mathbf{v} = \langle 3, -2 \rangle
B. \mathbf{v} = \langle -3, 2 \rangle
C. \mathbf{v} = \langle 3, 2 \rangle
D. \mathbf{v} = \langle -3, -2 \rangle
Question 6
Find the derivative of the function f(x) = \frac{\log x}{x^2} u\sing the quotient rule.
A. \frac{1}{x^3} - \frac{2\log x}{x^3}
B. \frac{2\log x}{x^3} - \frac{1}{x^3}
C. \frac{1}{x^3} + \frac{2\log x}{x^3}
D. \frac{2}{x^3} - \frac{\log x}{x^3}
Question 7
Find the sum of the infinite geometric series: \( sum_{n=1}^{infty} \frac{1}{2^n} \)
A. 1
B. 2
C. 3
D. 4
Question 8
Solve the inequality \frac{x}{x+1} > 0.
A. \( -\infty, -1 \) \cup \( 0, \infty \)
B. \( -\infty, 0 \) \cup \( 1, \infty \)
C. \( -\infty, 0 \) \cup \( 1, \infty \)
D. \( -\infty, -1 \) \cup (0, 1)
Question 9
A random variable ( X ) has a probability distribution given by \( P\( X = x \ \) = \frac{1}{2} ) for \( x = 1, 2, 3 \). Find the probability that ( X ) is greater than 2.
A. 0.5
B. 0.75
C. 0.25
D. 0.33
Question 10
Let \( mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix} \) and \( mathbf{b} = egin{pmatrix} 4 \ 5 \end{pmatrix} \). Find the projection of ( mathbf{b} ) onto ( mathbf{a} ) u\sing the formula \( mathrm{proj}_{mathbf{a}} mathbf{b} = \frac{mathbf{a} cdot mathbf{b}}{| mathbf{a} |^2} mathbf{a} \).
A. \begin{pmatrix} \frac{8}{13} \frac{12}{13} \end{pmatrix}
B. \begin{pmatrix} \frac{4}{13} \frac{6}{13} \end{pmatrix}
C. \begin{pmatrix} \frac{2}{13} \frac{3}{13} \end{pmatrix}
D. \begin{pmatrix} \frac{1}{13} \frac{1}{13} \end{pmatrix}
Question 11
Let X be a random variable with probability density function (pdf) given by f(x) = egin{cases} 2x & 0 leq x leq 1 \ 0 & \text{otherwise} \end{cases}. Find the probability that X is greater than 0.5.
A. 0.25
B. 0.5
C. 0.75
D. 1
Question 12
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. x < -1 or x > \frac{3}{2}
B. x < -1 or x < \frac{3}{2}
C. x > -1 or x > \frac{3}{2}
D. x > -1 or x < \frac{3}{2}
Question 13
Find the area under the curve \( y = \frac{1}{2}x^2 \) from \( x = 0 \) to \( x = 4 \).
A. 16
B. 32
C. 64
D. 128
Question 14
A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is greater than 85?
A. 0.1587
B. 0.3413
C. 0.4772
D. 0.6915
Question 15
In the diagram below, the equation of the circle is given by \( x - 2 \ \)^2 + \( y - 3 \)^2 = 16 ). Find the equation of the \tangent line to the circle at the point ( (5, 7) ).
A. y = -x + 12
B. y = x + 5
C. y = -x - 3
D. y = x - 2

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