POST UTME BABCOCK UNIVERSITY 2023 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the value of \( \sin 2\theta \) given that \( \sin \theta = \frac{3}{5} \) and \( \cos \theta = \frac{4}{5} \).
A. 24/25
B. 16/25
C. 20/25
D. 12/25
Question 2
Find the volume of the solid formed by rotating the region bounded by $y=x^2$ and $y=4-x^2$ about the x-axis.
A. \frac{16\pi}{3}
B. \frac{32\pi}{3}
C. \frac{64\pi}{3}
D. \frac{128\pi}{3}
Question 3
Solve the inequality \( 2x^2 + 5x - 3 \geq 0 \) u\sing the quadratic formula.
A. \( x \leq -1.5 \) or \( x \geq 1 \)
B. \( x \leq -1 \) or \( x \geq 1.5 \)
C. \( x \leq -1.5 \) or \( x \geq 1.5 \)
D. \( x \leq 1 \) or \( x \geq 1.5 \)
Question 4
Let X and Y be indep\endent random variables with probability density functions f_X(x) = 2x, 0 < x < 1 and f_Y(y) = 3y^2, 0 < y < 1. Find the probability that X + Y < 1.
A. 1/4
B. 1/2
C. 3/4
D. 1
Question 5
Solve the system of equations \( x + y = 4 \) and \( xy = 5 \).
A. \( x = 1, y = 3 \)
B. \( x = 2, y = 2 \)
C. \( x = 3, y = 1 \)
D. \( x = 4, y = 0 \)
Question 6
Find the sum of the first 5 terms of the geometric series ( 2, 6, 18, ... ).
A. ( 62 )
B. ( 64 )
C. ( 66 )
D. ( 68 )
Question 7
Determine the value of $\int_{0}^{\pi} \frac{1}{1+\sin^2x} dx$.
A. \frac{\pi}{2}
B. \frac{\pi}{4}
C. \frac{\pi}{3}
D. \frac{\pi}{6}
Question 8
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. 40
B. 50
C. 60
D. 70
Question 9
A binary operation ( odot ) is defined as \( a odot b = ab + 2 \). Find the value of ( 3 odot 4 ).
A. 14
B. 16
C. 18
D. 20
Question 10
Find the area under the curve y = x^2 from x = 0 to x = 2.
A. 4
B. 6
C. 8
D. 10
Question 11
Find the sum of the first 5 terms of the geometric series $\sum_{n=1}^5 \frac{2}{3^n}$.
A. \frac{2}{3} + \frac{2}{9} + \frac{2}{27} + \frac{2}{81} + \frac{2}{243}
B. \frac{2}{3} + \frac{2}{9} + \frac{2}{27} + \frac{2}{81} + \frac{2}{243}
C. \frac{2}{3} + \frac{2}{9} + \frac{2}{27} + \frac{2}{81}
D. \frac{2}{3} + \frac{2}{9} + \frac{2}{27}
Question 12
A fair six-sided die is rolled twice. What is the probability that the sum of the two numbers is 7?
A. 1/6
B. 1/3
C. 1/2
D. 2/3
Question 13
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 4 \) from \( x = 0 \) to \( x = 2 \).
A. \( \frac{1}{2} \)
B. ( 4 )
C. ( 6 )
D. ( 8 )
Question 14
Find the volume of the solid formed by revolving the region bounded by the parabola \( y = x^2 \) and the line \( y = 2x \) about the x-axis.
A. 16/3
B. 32/3
C. 64/3
D. 128/3
Question 15
Find the value of ( x ) in the equation \( x^2 - 4x - 5 = 0 \).
A. 5
B. -1
C. 2
D. 3

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