POST UTME REDEEMERS UNIVERSITY 2023 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A set A contains 5 elements. If B is a subset of A, what is the maximum number of elements in B?
A. 3
B. 4
C. 5
D. 6
Question 2
A random experiment has two indep\endent events, A and B. The probability of event A occurring is 0.4, and the probability of event B occurring is 0.6. What is the probability that both events occur?
A. 0.24
B. 0.36
C. 0.48
D. 0.60
Question 3
A survey of 100 students found that 60 students preferred Mathematics, 30 students preferred Science, and 10 students preferred both. What is the probability that a randomly selected student prefers either Mathematics or Science?
A. 0.7
B. 0.8
C. 0.9
D. 0.95
Question 4
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( x < -\frac{5}{4} \) or \( x > \frac{3}{2} \)
B. \( x < -\frac{3}{2} \) or \( x > \frac{5}{4} \)
C. \( x < -\frac{5}{4} \) or \( x < \frac{3}{2} \)
D. \( x > -\frac{5}{4} \) or \( x < \frac{3}{2} \)
Question 5
Find the surface area 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. ( 16pi )
B. ( 32pi )
C. ( 64pi )
D. ( 128pi )
Question 6
Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} ) u\sing the chain rule.
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 7
A vector \( \vec{a} \) has a magnitude of 5 and is directed at an angle of 30° to the positive x-axis. Find the x and y components of the vector.
A. 4.33, 4.33
B. 4.33, 2.67
C. 2.67, 4.33
D. 2.67, 2.67
Question 8
A set of 5 numbers has a mean of 10. If 2 is added to each number, what is the new mean?
A. 12
B. 14
C. 16
D. 18
Question 9
Solve the system of equations \( egin{cases} x + y = 4 \ 2x - 3y = 5 \end{cases} \).
A. \( x = 2, y = 2 \)
B. \( x = 3, y = 1 \)
C. \( x = 1, y = 3 \)
D. \( x = 4, y = 0 \)
Question 10
Find the volume of the cylinder with radius 4 cm and height 10 cm.
A. 400\pi
B. 500\pi
C. 600\pi
D. 800\pi
Question 11
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 - 1
D. y = x + 1
Question 12
Find the value of x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 13
Solve the inequality \( \frac{x^2 - 4}{x + 2} > 0 \) for \( x in \( -infty, -2 \ \) cup \( -2, infty \) ).
A. \( x < -2 \) or \( x > 2 \)
B. \( x > -2 \) or \( x < 2 \)
C. \( x < -2 \) and \( x > 2 \)
D. \( x > -2 \) and \( x < 2 \)
Question 14
A function f(x) is defined as (f(x) = \frac{1}{x^2 + 1}). Find the derivative of f(x) u\sing the chain rule.
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 15
A probability experiment consists of rolling a fair six-sided die. If the outcome is an even number, the player wins a prize. Find the probability of winning the prize.
A. 1/2
B. 1/3
C. 2/3
D. 1/6

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