POST UTME RSU 2017 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
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. 24π cm³
B. 48π cm³
C. 96π cm³
D. 192π cm³
Question 2
Two events A and B are indep\endent. If P(A) = 0.4 and P(B) = 0.6, find P(A ∩ B).
A. 0.12
B. 0.24
C. 0.36
D. 0.48
Question 3
Let X be a random variable with probability density function (pdf) given by f(x) = \( \frac{1}{2}e^{-|x|} \) for -∞ < x < ∞. Find the probability that X lies between -1 and 1.
A. 0.5
B. 0.6
C. 0.7
D. 0.8
Question 4
Solve the inequality \( \frac{x^2 - 4}{x^2 - 9} > 0 \) for x ≠ ±3.
A. \( -∞, -3 \) ∪ \( -3, -1 \) ∪ (1, 3) ∪ (3, ∞)
B. \( -∞, -3 \) ∪ \( -1, 1 \) ∪ (3, ∞)
C. \( -∞, -3 \) ∪ \( -1, 3 \) ∪ (3, ∞)
D. \( -∞, -3 \) ∪ \( -1, 1 \) ∪ (1, 3) ∪ (3, ∞)
Question 5
Solve for x in the equation \( 2^x + 2^{x+1} = 3 \cdot 2^x \).
A. -1
B. 0
C. 1
D. 2
Question 6
A bag contains 5 red marbles, 4 blue marbles, and 3 green marbles. If a marble is drawn at random, what is the probability that it is not blue?
A. \frac{1}{2}
B. \frac{2}{5}
C. \frac{3}{5}
D. \frac{4}{5}
Question 7
Find the derivative of the function ( f(x) = \sin^2 x ) u\sing the chain rule.
A. \( 2 \sin x \cos x \)
B. \( -2 \sin x \cos x \)
C. \( 2 \sin^2 x \)
D. \( -2 \sin^2 x \)
Question 8
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 9
Find the area of the triangle with vertices ( A(0, 0) ), ( B(3, 0) ), and ( C(0, 2) ).
A. ( 6 )
B. ( 9 )
C. ( 12 )
D. ( 15 )
Question 10
Find the sum of the first 5 terms of the geometric progression \( 2, 6, 18, \ldots \)
A. 62
B. 64
C. 66
D. 68
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 - 2
D. y = x + 2
Question 12
Solve the equation \( \cos^2 x = \frac{3}{4} \) for ( x ).
A. \( x = \frac{pi}{6} \)
B. \( x = \frac{pi}{4} \)
C. \( x = \frac{pi}{3} \)
D. \( x = \frac{pi}{2} \)
Question 13
Find the derivative of the function ( f(x) = \frac{1}{\sqrt{x^2 + 1}} ) u\sing the chain rule.
A. \( \frac{-x}{\( x^2 + 1 \ \)^{3/2}} )
B. \( \frac{x}{\( x^2 + 1 \ \)^{3/2}} )
C. \( \frac{1}{\( x^2 + 1 \ \)^{3/2}} )
D. \( \frac{-1}{\( x^2 + 1 \ \)^{3/2}} )
Question 14
Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm. The slant height of the frustum is 8 cm.
A. 48\pi cm^3
B. 64\pi cm^3
C. 80\pi cm^3
D. 96\pi cm^3
Question 15
Solve the equation \( \log_{10} \( x^2 \ \) = 4 ) for ( x ).
A. \( x = 10^4 \)
B. \( x = 10^2 \)
C. \( x = 10^{-2} \)
D. \( x = 10^{-4} \)

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