POST UTME GREENFIELD UNIVERSITY 2017 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the value of x in the equation 2^x + 2^x = 64.
A. 5
B. 6
C. 7
D. 8
Question 2
A probability experiment consists of rolling a fair six-sided die. If the outcome is an even number, the experiment is repeated. If the outcome is an odd number, the experiment is stopped. What is the probability that the experiment will be stopped after exactly two rolls?
A. 1/6
B. 1/3
C. 1/2
D. 2/3
Question 3
Find the determinant of the matrix [ egin{pmatrix} 2 & 3 & 4 \ 5 & 6 & 7 \ 8 & 9 & 10 \end{pmatrix} ].
A. 0
B. 1
C. 2
D. 3
Question 4
Find the value of ( x ) in the quadratic equation \( x^2 + 5x + 6 = 0 \).
A. x = -2
B. x = -3
C. x = 2
D. x = 3
Question 5
In a right-angled triangle, the length of the hypotenuse is 10 cm and one of the acute angles is 30°. Find the length of the side opposite the 30° angle.
A. 5 cm
B. 5√3 cm
C. 10√3 cm
D. 20 cm
Question 6
Solve the equation \( x^2 - 4x + 4 = 0 \) u\sing the quadratic formula.
A. x = 2
B. x = 1
C. x = -1
D. x = -2
Question 7
A random variable ( X ) has a probability distribution given by \( P\( X = x \ \) = \frac{1}{2} \) for \( x = 1, 2, 3, 4 \). Find the probability that ( X ) is greater than 2.
A. 0.5
B. 0.75
C. 0.875
D. 0.9375
Question 8
Find the value of \( int_{0}^{1} \frac{1}{x^2 + 1} dx \) u\sing the method of substitution.
A. π/2
B. π/4
C. π/3
D. π/6
Question 9
A sequence is defined by the formula an = 2n + 1. Find the sum of the first 5 terms of the sequence.
A. 15
B. 21
C. 25
D. 30
Question 10
A histogram of the heights of students in a class is shown below. If the mean height is 175 cm, find the median height.
A. 170 cm
B. 175 cm
C. 180 cm
D. 185 cm
Question 11
Find the value of \( \cos \( 30^\circ \).
A. \frac{1}{2}
B. \frac{\sqrt{3}}{2}
C. \frac{1}{\sqrt{2}}
D. \frac{\sqrt{2}}{2}
Question 12
Let \( \mathbf{a} = \begin{pmatrix} 1 \ 2 \ 3 \end{pmatrix} \) and \( \mathbf{b} = \begin{pmatrix} 4 \ 5 \ 6 \end{pmatrix} \). Find the cross product \( \mathbf{a} \times \mathbf{b} \).
A. \[ \mathbf{a} \times \mathbf{b} = \begin{pmatrix} 5 \ 3 \ -7 \end{pmatrix} \]
B. \[ \mathbf{a} \times \mathbf{b} = \begin{pmatrix} 5 \ -3 \ 7 \end{pmatrix} \]
C. \[ \mathbf{a} \times \mathbf{b} = \begin{pmatrix} -5 \ 3 \ 7 \end{pmatrix} \]
D. \[ \mathbf{a} \times \mathbf{b} = \begin{pmatrix} 5 \ -3 \ -7 \end{pmatrix} \]
Question 13
Solve the inequality \( 2x - 5 > 3 \).
A. x > 4
B. x < 4
C. x > 2
D. x < 2
Question 14
Solve the equation \( 2^x + 2^{-x} = 4 \) for ( x ).
A. 1
B. 2
C. -1
D. -2
Question 15
Solve the inequality \( \frac{x}{x-2} > 1 \) for \( x > 2 \).
A. 2 < x < 3
B. x > 3
C. x < 2
D. x = 3

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