POST UTME JOSEPH AYO BABALOLA UNIVERSITY 2022 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
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 2
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. \( \begin{pmatrix} \frac{3}{13} \ \frac{2}{13} \end{pmatrix} \ \)
Question 3
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 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 car travels from city A to city B at an average speed of 60 km/h and returns at an average speed of 40 km/h. What is the average speed of the car for the entire trip?
A. 50 km/h
B. 55 km/h
C. 60 km/h
D. 65 km/h
Question 6
Solve the quadratic equation: x^2 + 5x + 6 = 0.
A. x = -2 or x = -3
B. x = 2 or x = 3
C. x = -1 or x = -6
D. x = 1 or x = 6
Question 7
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 8
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 9
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 10
Solve the trigonometric equation \( \sin^2 x + \cos^2 x = 1 \) for (0 ≤ x ≤ 2pi).
A. \( x = 0, \frac{pi}{2}, pi, \frac{3pi}{2} \)
B. \( x = 0, \frac{pi}{2}, pi, \frac{3pi}{2}, 2pi \)
C. \( x = 0, \frac{pi}{2}, pi, \frac{3pi}{2}, 2pi, \frac{5pi}{2} \)
D. \( x = 0, \frac{pi}{2}, pi, \frac{3pi}{2}, 2pi, \frac{5pi}{2}, \frac{7pi}{2} \)
Question 11
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 12
Find the derivative of the function (f(x) = \frac{1}{x^2 + 1}) u\sing the chain rule.
A. \( \frac{-2x}{\( x^2 + 1 \ \)^2} )
B. \( \frac{-2x^2}{\( x^2 + 1 \ \)^2} )
C. \( \frac{-2x^3}{\( x^2 + 1 \ \)^2} )
D. \( \frac{2x^3}{\( x^2 + 1 \ \)^2} )
Question 13
A random experiment consists of rolling a fair six-sided die. Find the probability that the sum of the numbers obtained is greater than 9.
A. 1/6
B. 1/3
C. 1/2
D. 2/3
Question 14
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 15
A random experiment consists of rolling a fair six-sided die and then flipping a fair coin. If the outcome of the die roll is even, the coin is flipped twice. Otherwise, the coin is flipped once. What is the probability that the outcome of the die roll is even and the outcome of the coin flip is heads?
A. \frac{1}{6}
B. \frac{1}{12}
C. \frac{1}{4}
D. \frac{1}{3}

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