POST UTME WELLSPRING UNIVERSITY 2020 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A random experiment consists of rolling a fair six-sided die and then flipping a fair coin. If the number on the die is even, the coin is flipped twice; otherwise, the coin is flipped only once. Let X be the number of heads obtained from the coin flips. What is E[X]?
A. 1
B. 1.5
C. 2
D. 2.5
Question 2
A set ( A ) contains the elements \( \{ 1, 2, 3, 4, 5 \} \). Find the number of subsets of ( A ) that contain exactly three elements.
A. 10
B. 15
C. 20
D. 25
Question 3
Solve for x in the equation \( \log_{10} \( x^2 \) = 4 \)
A. 10
B. 100
C. 1000
D. 10000
Question 4
Find the area of the triangle with vertices (0, 0), (3, 0), and (0, 2).
A. 3
B. 6
C. 9
D. 12
Question 5
A sequence is defined by \( a_n = 2n + 1 \). Find the sum of the first five terms of the sequence.
A. 30
B. 35
C. 40
D. 45
Question 6
Let X and Y be indep\endent random variables with probability density functions f_X(x) = 2x, 0 < x < 1 and f_Y(y) = 3y^2, 0 < y < 1. Find the probability that X + Y < 1.
A. 1/4
B. 1/2
C. 3/4
D. 1
Question 7
Find the equation of the circle with center (2, 3) and radius 4.
A. \( x - 2 \)^2 + \( y - 3 \)^2 = 16
B. \( x + 2 \)^2 + \( y - 3 \)^2 = 16
C. \( x - 2 \)^2 + \( y + 3 \)^2 = 16
D. \( x + 2 \)^2 + \( y + 3 \)^2 = 16
Question 8
A set of 10 points is chosen at random from a circle of radius 1. What is the probability that the dis\tance between the two closest points is greater than \( \frac{1}{2} \)?
A. 0
B. \frac{1}{2}
C. \frac{3}{4}
D. 1
Question 9
A random experiment consists of rolling a fair six-sided die. Find 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 10
Find the sum of the infinite geometric series \( \sum_{n=1}^\infty \frac{1}{2^n} \)
A. 1
B. \frac{1}{2}
C. \frac{2}{3}
D. \frac{3}{4}
Question 11
Solve the system of equations \[\begin{cases} x + y = 4 \ 2x - 3y = -3 \end{cases}\] u\sing matrices.
A. \boxed{\begin{pmatrix} x \ y \end{pmatrix} = \begin{pmatrix} 1 \ 3 \end{pmatrix}}
B. \begin{pmatrix} x \ y \end{pmatrix} = \begin{pmatrix} 2 \ 2 \end{pmatrix}
C. \begin{pmatrix} x \ y \end{pmatrix} = \begin{pmatrix} 3 \ 1 \end{pmatrix}
D. \begin{pmatrix} x \ y \end{pmatrix} = \begin{pmatrix} 4 \ 0 \end{pmatrix}
Question 12
A set of 5 points is chosen at random from a circle of radius 4. What is the probability that the 5 points form a convex pentagon?
A. 0.1
B. 0.2
C. 0.3
D. 0.4
Question 13
If ( f(x) = \frac{1}{x} ), find ( f'(x) ) u\sing the chain rule.
A. \( -\frac{1}{x^2} \)
B. \( \frac{1}{x^2} \)
C. \( -\frac{1}{x} \)
D. \( \frac{1}{x} \)
Question 14
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}{\( x^2 + 1 \)^2}
C. -\frac{2}{\( x^2 + 1 \)^2}
D. \frac{2}{\( x^2 + 1 \)^2}
Question 15
Solve the equation \[\sqrt{x + 5} + \sqrt{x - 3} = 7\] for x.
A. \boxed{x = 16}
B. x = 10
C. x = 20
D. x = 22

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