POST UTME OAU 2022 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the value of ( x ) in the equation \( 2^x + 5^x = 3^x \).
A. x = 2
B. x = 3
C. x = 4
D. x = 5
Question 2
A circle with center ( C(0,0) ) and radius 4 passes through the point ( P(3,4) ). Find the equation of the circle.
A. \( x^2 + y^2 = 16 \)
B. \( x^2 + y^2 = 20 \)
C. \( x^2 + y^2 = 24 \)
D. \( x^2 + y^2 = 28 \)
Question 3
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( x < -3/2 \) or \( x > 1/2 \)
B. \( x < -3/2 \) or \( x < 1/2 \)
C. \( x > -3/2 \) or \( x > 1/2 \)
D. \( x < -3/2 \) or \( x < 1/2 \)
Question 4
If \( \sin x = \frac{3}{5} \), find \( \cos x \).
A. \( \frac{4}{5} \ \)
B. \( \frac{3}{5} \ \)
C. \( \frac{4}{3} \ \)
D. \( \frac{3}{4} \ \)
Question 5
Find the volume of the solid formed by revolving the region bounded by the curves \( y = x^2 \) and \( y = 2x \) 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 6
A matrix ( A ) is given by \( A = \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \). Find the determinant of ( A ).
A. 1
B. 2
C. 3
D. 4
Question 7
A binary operation ( ast ) on the set of integers is defined as \( a ast b = a^2 + b^2 \). Find the value of ( 2 ast 3 ).
A. 11
B. 13
C. 17
D. 19
Question 8
Let \( S = {1, 2, 3, 4, 5} \) and \( T = {2, 3, 5, 7, 11} \). Find the symmetric difference of sets S and T.
A. S \cup T
B. S \cap T
C. S \triangle T
D. S \oplus T
Question 9
Solve the quadratic equation \( x^2 + 4x + 4 = 0 \).
A. x = -2
B. x = 2
C. x = -1
D. x = 1
Question 10
A fair six-sided die is rolled. What is the probability that the number rolled is greater than 4?
A. \frac{1}{6}
B. \frac{1}{3}
C. \frac{2}{3}
D. \frac{5}{6}
Question 11
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 12
Find the derivative of the function ( f(x) = \frac{1}{\sqrt{x}} ) u\sing the chain rule.
A. \frac{-1}{2x^{3/2}}
B. \frac{1}{2x^{3/2}}
C. \frac{-1}{x^{3/2}}
D. \frac{1}{x^{3/2}}
Question 13
A random experiment consists of rolling a fair six-sided die. If the number rolled is even, the experiment is repeated. If the number rolled is odd, the experiment stops. What is the probability that the experiment will stop on the first roll?
A. 1/2
B. 1/3
C. 2/3
D. 1/6
Question 14
Solve the quadratic equation \( x^2 + 4x + 4 = 0 \).
A. \( x = -2 \pm 0 \ \)
B. \( x = -2 \pm 2 \ \)
C. \( x = -2 \pm 1 \ \)
D. \( x = -2 \pm 4 \ \)
Question 15
Solve the inequality \( \frac{x}{x-2} > 2 \) for \( x > 2 \).
A. x > 4
B. x > 6
C. x < 4
D. x < 6

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