POST UTME JOSEPH AYO BABALOLA UNIVERSITY 2022 Mathematics | Objective

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Question 1
Determine the value of x in the equation \( \sin\( 2x \ \) = \frac{1}{2} ) given that \( \sin\( x \ \) = \frac{\sqrt{3}}{2} ).
A. \frac{\pi}{6}
B. \frac{\pi}{4}
C. \frac{\pi}{3}
D. \frac{\pi}{2}
Question 2
A solid right circular cone has a height of 12 cm and a base radius of 6 cm. Find the volume of the cone in terms of π.
A. \frac{288\pi}{\pi}
B. \frac{288\pi}{3}
C. \frac{288\pi}{\pi}
D. \frac{288\pi}{3}
Question 3
A binary operation \( * \) on the set of real numbers is defined as \( a * b = a^2 + b^2 \). Find the value of ( x ) such that \( x * \( x + 1 \ \) = 25 ).
A. 4
B. 5
C. 6
D. 7
Question 4
Find the determinant of the matrix \( egin{bmatrix} 2 & 3 \ 4 & 5 \end{bmatrix} \).
A. 1
B. 2
C. 3
D. 4
Question 5
A particle moves along the x-axis with its position given by the equation (x(t) = 2t^2 - 5t + 1). Find the velocity of the particle at time \( t = 2 \).
A. 3
B. 4
C. 5
D. 6
Question 6
Solve the inequality \( \frac{x^2 - 4}{x^2 - 9} > 0 \).
A. \( -∞, -3 \) ∪ (3, ∞)
B. \( -3, 3 \)
C. \( -∞, -3 \) ∪ (3, ∞) ∪ (0, 3)
D. \( -∞, -3 \) ∪ (3, ∞) ∪ (0, 3) ∪ (4, ∞)
Question 7
Find the equation of the circle with center \( -2, 3 \) and radius 4.
A. \( x + 2 \)^2 + \( y - 3 \)^2 = 16
B. \( x - 2 \)^2 + \( y + 3 \)^2 = 16
C. \( x + 2 \)^2 + \( y + 3 \)^2 = 16
D. \( x - 2 \)^2 + \( y - 3 \)^2 = 16
Question 8
Solve for x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 9
In a circle with center ( O ) and radius ( 4 ), a chord ( AB ) is drawn such that \( OA = 3 \). Find the length of ( AB ).
A. 5
B. 6
C. 7
D. 8
Question 10
A binary operation ∗ is defined as: a ∗ b = a^2 + 2ab + b^2. Find the value of (2 ∗ 3) ∗ 4.
A. (2 ∗ 3) ∗ 4 = 4^2 + 2(4)(3) + 3^2
B. (2 ∗ 3) ∗ 4 = 2^2 + 2(2)(3) + 3^2
C. (2 ∗ 3) ∗ 4 = 4^2 + 2(4)(2) + 2^2
D. (2 ∗ 3) ∗ 4 = 2^2 + 2(2)(2) + 2^2
Question 11
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( x < -1 \) or \( x > \frac{3}{2} \)
B. \( x < -\frac{1}{2} \) or \( x > 3 \)
C. \( x < -3 \) or \( x > \frac{1}{2} \)
D. \( x < 3 \) or \( x > -\frac{1}{2} \)
Question 12
A box contains 5 red balls and 3 blue balls. If a ball is selected at random, what is the probability that it is blue?
A. 1/2
B. 1/3
C. 2/5
D. 3/8
Question 13
A solid cone has a base radius of 4 cm and a height of 6 cm. Find the volume of the cone in cubic centimeters.
A. 48π cm^3
B. 64π cm^3
C. 96π cm^3
D. 128π cm^3
Question 14
Simplify the expression: \frac{2x^2 + 3x - 1}{x^2 - 4}
A. \frac{2x + 1}{x - 2}
B. \frac{2x - 1}{x + 2}
C. \frac{2x + 1}{x + 2}
D. \frac{2x - 1}{x - 2}
Question 15
Let \( mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix} \) and \( mathbf{b} = egin{pmatrix} 1 \ -2 \end{pmatrix} \). Find the projection of ( mathbf{b} ) onto ( mathbf{a} ).
A. \( \begin{pmatrix} \frac{7}{13} \ \frac{12}{13} \end{pmatrix} \ \)
B. \( \begin{pmatrix} \frac{1}{13} \ \frac{-2}{13} \end{pmatrix} \ \)
C. \( \begin{pmatrix} \frac{2}{13} \ \frac{-3}{13} \end{pmatrix} \ \)
D. \( \begin{pmatrix} \frac{3}{13} \ \frac{2}{13} \end{pmatrix} \ \)

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