POST UTME RHEMA UNIVERSITY 2017 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Let \( S = {x in mathbb{R} : x^2 + 2x + 1 = 0} \). Find \( lim_{x \to 2} \frac{x^2 - 4}{x - 2} \) if it exists.
A. 4
B. 2
C. \frac{1}{2}
D. \frac{1}{4}
Question 2
A right triangle has a hypotenuse of length 10 and one leg of length 6. What is the length of the other leg?
A. 8
B. 10
C. 12
D. 14
Question 3
Find the value of x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 4
Solve the inequality \( x^2 - 4x - 5 > 0 \).
A. \( x < -1 \) or \( x > 5 \)
B. \( x < 1 \) or \( x > 5 \)
C. \( x < -1 \) or \( x < 5 \)
D. \( x < 1 \) or \( x < 5 \)
Question 5
Find the surface area of the solid formed by revolving the region bounded by the curve \( y = \sqrt{x} \), the x-axis, and the line \( x = 4 \) about the x-axis.
A. \( 16 \sqrt{2} \)
B. \( 32 \sqrt{2} \)
C. \( 64 \sqrt{2} \)
D. \( 128 \sqrt{2} \)
Question 6
A bakery sells 250 loaves of bread per day at ₦120 per loaf. If the \cost price per loaf is ₦80, calculate the profit per loaf and the total profit per day.
A. ₦40, ₦10,000
B. ₦30, ₦8,000
C. ₦20, ₦6,000
D. ₦10, ₦4,000
Question 7
A circle has a radius of 4 cm. Find the area of the sector with a central angle of 60°.
A. ( 12pi )
B. ( 16pi )
C. ( 20pi )
D. ( 24pi )
Question 8
Solve the quadratic equation \(x^2 + 5x + 6 = 0\).
A. x = -2, x = -3
B. x = -1, x = -6
C. x = 2, x = 3
D. x = 1, x = 4
Question 9
A company produces 240 units of a product per day. If the production rate is increased by 15% per day, how many units will be produced after 5 days?
A. 1,500
B. 1,600
C. 1,700
D. 1,800
Question 10
In the circuit below, identify the component labeled A.
A. Resistor
B. Battery
C. Capacitor
D. Inductor
Question 11
A box contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is not blue?
A. \( \frac{2}{3} \)
B. \( \frac{3}{5} \)
C. \( \frac{1}{3} \)
D. \( \frac{4}{5} \)
Question 12
Find the value of \( \log_{10} \( 1000 \ \) ).
A. ( 3 )
B. ( 4 )
C. ( 5 )
D. ( 6 )
Question 13
Find the area under the curve \( y = x^2 + 2x + 1 \) from \( x = 0 \) to \( x = 2 \).
A. 7
B. 6
C. 5
D. 4
Question 14
Find the equation of the circle with center (C(2, 3)) and radius 4.
A. \( x^2 + y^2 - 4x - 6y + 25 = 0 \)
B. \( x^2 + y^2 - 4x - 6y + 13 = 0 \)
C. \( x^2 + y^2 - 4x - 6y + 9 = 0 \)
D. \( x^2 + y^2 - 4x - 6y + 21 = 0 \)
Question 15
Solve the equation \( 2^x + 2^{x+1} = 3 cdot 2^{x+1} \) for ( x ).
A. \( x = -1 \)
B. \( x = 0 \)
C. \( x = 1 \)
D. \( x = 2 \)

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