POST UTME RHEMA UNIVERSITY 2018 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the value of $\frac{1}{2} \log_{10} \( x^2 \) = 4$.
A. 10
B. 100
C. 1000
D. 10000
Question 2
Solve the inequality \( |x - 2| > 3 \).
A. \( x < -1 \) or \( x > 5 \)
B. \( x < 1 \) or \( x > 5 \)
C. \( x < -1 \) or \( x > 4 \)
D. \( x < 1 \) or \( x > 4 \)
Question 3
A car travels from city A to city B at an average speed of 60 km/h and returns from city B to city A at an average speed of 40 km/h. What is the average speed of the car for the entire trip?
A. 48 km/h
B. 50 km/h
C. 52 km/h
D. 55 km/h
Question 4
A random variable X has a probability distribution given by P\( X = 1 \) = 0.3, P\( X = 2 \) = 0.4, and P\( X = 3 \) = 0.3. What is the expected value of X?
A. 1.1
B. 1.3
C. 1.5
D. 1.7
Question 5
Find the equation of the circle with centre at ((2,3)) and radius (4).
A. \( x-2 \ \)^2 + \( y-3 \)^2 = 16 )
B. \( x-3 \ \)^2 + \( y-2 \)^2 = 16 )
C. \( x-4 \ \)^2 + \( y-5 \)^2 = 16 )
D. \( x-5 \ \)^2 + \( y-4 \)^2 = 16 )
Question 6
Find the volume of the solid formed by revolving the region bounded by the parabola \( y = x^2 \), the x-axis, and the line \( x = 2 \) about the x-axis.
A. \( \frac{32}{15} pi \)
B. \( \frac{64}{15} pi \)
C. \( \frac{128}{15} pi \)
D. \( \frac{256}{15} pi \)
Question 7
Find the sum of the infinite geometric series $\sum_{n=1}^\infty \frac{1}{2^n} \left\( \frac{1}{2}\right \)^n$.
A. 1
B. 2
C. 3
D. 4
Question 8
Find the value of x in the equation \( \sin x = \frac{1}{2} \) if ( x ) lies in the second quadrant.
A. 120°
B. 150°
C. 180°
D. 210°
Question 9
Solve the inequality \( |2x - 5| geq 3 \).
A. \( x leq -1 \) or ( x geq 4 )
B. ( x leq 1 ) or ( x geq 4 )
C. \( x leq -1 \) or ( x geq 3 )
D. ( x leq 1 ) or ( x geq 3 )
Question 10
Solve the equation \sin^2 x + \cos^2 x = 1 for x in the interval [0, 2\pi].
A. x=\frac{\pi}{2}
B. x=\frac{3\pi}{2}
C. x=\frac{\pi}{4}
D. x=\frac{5\pi}{4}
Question 11
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}{\( x^2+1 \)^3}
C. \frac{2x}{\( x^2+1 \)^2}
D. \frac{2x}{\( x^2+1 \)^3}
Question 12
A company produces two products, X and Y. Product X requires 2 hours of labor and 3 hours of machine time, while product Y requires 3 hours of labor and 2 hours of machine time. If the company has 120 hours of labor and 180 hours of machine time available, how many units of product X and product Y should the company produce to maximize profit?
A. (20, 30)
B. (30, 20)
C. (25, 25)
D. (35, 15)
Question 13
Let $S = \{1, 2, 3, 4, 5, 6, 7, 8, 9\}$. Find the number of subsets of $S$ that contain exactly three odd numbers.
A. 10
B. 20
C. 30
D. 40
Question 14
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 15
Solve for ( x ) in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. \( x = 10^4 \)
B. \( x = 10^{-4} \)
C. \( x = 10^2 \)
D. \( x = 10^{-2} \)

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