POST UTME UNN 2017 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the volume of the solid formed by revolving the region bounded by the curve \( y = x^2 \) and the line \( x = 2 \) about the x-axis.
A. \frac{32}{3}\pi
B. \frac{64}{3}\pi
C. \frac{128}{3}\pi
D. \frac{256}{3}\pi
Question 2
A random experiment consists of rolling a fair six-sided die. Find the probability that the sum of the numbers on the two dice is greater than 9.
A. \( \frac{1}{6} \)
B. \( \frac{1}{3} \)
C. \( \frac{1}{2} \)
D. \( \frac{2}{3} \)
Question 3
Find the value of \( x \) in the equation: \( 2x + 5 = 11 \).
A. 2
B. 3
C. 4
D. 5
Question 4
Simplify the expression \( \frac{\log_2 16}{\log_2 4} \).
A. 2
B. 3
C. 4
D. 5
Question 5
Find the sum of the first 5 terms of the geometric series with first term \( a = 2 \) and common ratio \( r = \frac{1}{2} \).
A. \frac{31}{16}
B. \frac{63}{32}
C. \frac{127}{64}
D. \frac{255}{128}
Question 6
A set ( A ) contains the elements \( \{ 1, 2, 3, 4, 5 \} \). Find the number of subsets of ( A ) that contain exactly two elements.
A. 10
B. 15
C. 20
D. 25
Question 7
A binary operation \( \ast \) is defined as: \( a \ast b = a^2 + b^2 \). Find the value of \( 2 \ast 3 \).
A. 13
B. 15
C. 17
D. 19
Question 8
Find the determinant of the matrix \( \begin{bmatrix} 2 & 3 & 4 \ 5 & 6 & 7 \ 8 & 9 & 10 \end{bmatrix} \).
A. 0
B. 1
C. 2
D. 3
Question 9
Find the sum of the first 10 terms of the geometric series \( 2 + 6 + 18 + \cdots \).
A. 1023
B. 1024
C. 1025
D. 1026
Question 10
A sequence is defined as: \( a_n = 2n + 1 \). Find the value of \( a_5 \).
A. 9
B. 11
C. 13
D. 15
Question 11
Find the derivative of ( f(x) = \frac{x^2 + 2x - 3}{x^2 - 4} ) u\sing the quotient rule.
A. \frac{2x\( x^2 - 4 \) - \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2}
B. \frac{2x\( x^2 - 4 \) + \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2}
C. \frac{2x\( x^2 - 4 \) - \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2}
D. \frac{2x\( x^2 - 4 \) + \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2}
Question 12
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. x < -1
B. x > -1
C. x < 1
D. x > 1
Question 13
Solve the inequality: \( 2x^2 + 5x - 3 \geq 0 \).
A. \( x \leq -3 \) or \( x \geq \frac{3}{2} \)
B. \( x \leq -3 \) or \( x \geq 1 \)
C. \( x \leq 1 \) or \( x \geq -3 \)
D. \( x \leq -1 \) or \( x \geq 3 \)
Question 14
Find the derivative of the function \( f(x) = \frac{1}{x^2 + 1} \).
A. \boxed{f'(x) = \frac{-2x}{\( x^2 + 1 \)^2}}
B. f'(x) = \frac{2x}{\( x^2 + 1 \)^2}
C. f'(x) = \frac{1}{\( x^2 + 1 \)^2}
D. f'(x) = \frac{-1}{\( x^2 + 1 \)^2}
Question 15
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \boxed{\( -\infty, -1 \) \cup \( 3, \infty \)}
B. \( -\infty, 1 \) \cup \( 3, \infty \)
C. \( -\infty, -1 \) \cup \( 1, \infty \)
D. \( -\infty, 1 \) \cup \( -3, \infty \)

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