POST UTME VERITAS UNIVERSITY 2018 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A bag contains 5 red balls and 3 blue balls. If a ball is drawn at random, find the probability that it is blue.
A. \frac{1}{5}
B. \frac{1}{2}
C. \frac{3}{8}
D. \frac{3}{5}
Question 2
Solve for x in the inequality \( \frac{1}{x+1} + \frac{1}{x-2} geq 1 \).
A. [-1, -2] cup [2, infty)
B. [-2, -1] cup [2, infty)
C. [-2, 2]
D. [-2, -1] cup [2, infty]
Question 3
Find the sum of the first 10 terms of the geometric series \( 2 + 6 + 18 + ldots \).
A. 195
B. 205
C. 215
D. 225
Question 4
A solid right circular cone has a height of 10 cm and a base radius of 4 cm. Find the volume of the cone in terms of π.
A. \frac{160\pi}{3} cm^3
B. \frac{320\pi}{3} cm^3
C. \frac{80\pi}{3} cm^3
D. \frac{40\pi}{3} cm^3
Question 5
Find the area under the curve \( y = x^2 + 2x - 3 \) from \( x = 0 \) to \( x = 2 \).
A. 4
B. 6
C. 8
D. 10
Question 6
Determine the value of x in the equation \( egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ 1 \end{bmatrix} = egin{bmatrix} 7 \ 11 \end{bmatrix} \).
A. 2
B. 3
C. 4
D. 5
Question 7
A set of 5 points [ A, B, C, D, E \] are chosen at random from the set of points [ (0,0), (1,0), (2,0), (3,0), (4,0), (5,0), (6,0), (7,0), (8,0), (9,0) \]. What is the probability that the points [ A, B, C, D, E \] are in increa\sing order?
A. \frac{1}{252}
B. \frac{1}{126}
C. \frac{1}{63}
D. \frac{1}{32}
Question 8
Find the area under the curve \( y = x^2 - 2x + 1 \) from \( x = 0 \) to \( x = 2 \).
A. \frac{4}{3}
B. \frac{5}{3}
C. \frac{6}{3}
D. \frac{7}{3}
Question 9
Find the volume of the frustum of a cone with height 8 cm, lower base radius 4 cm, and upper base radius 2 cm.
A. 256\pi cm^3
B. 512\pi cm^3
C. 768\pi cm^3
D. 1024\pi cm^3
Question 10
Solve the equation \( x^2 + 2x - 6 = 0 \) u\sing the quadratic formula.
A. x = 2 \pm \sqrt{7}
B. x = -2 \pm \sqrt{7}
C. x = 2 \pm \sqrt{5}
D. x = -2 \pm \sqrt{5}
Question 11
A fair six-sided die is rolled. What is the probability that the number rolled is greater than 4?
A. 1/2
B. 1/3
C. 2/3
D. 1/6
Question 12
A circle has a radius of 4 cm. What is the area of the circle?
A. 16π
B. 32π
C. 64π
D. 128π
Question 13
The mean of a set of numbers is 25. If one of the numbers is increased by 5, the mean becomes 26. How many numbers are in the set?
A. 5
B. 10
C. 15
D. 20
Question 14
Find the value of \( \log_{10} \( 1000 \ \) ).
A. 3
B. 4
C. 5
D. 6
Question 15
Solve the equation \( x^2 + 4x + 4 = 0 \).
A. x = -2
B. x = 0
C. x = -1
D. x = 1

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