POST UTME PAN-ATLANTIC UNIVERSITY 2018 Mathematics | Objective

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Question 1
A sequence is defined by the formula a_n = 2n + 1. Find the sum of the first 5 terms of the sequence.
A. 15
B. 25
C. 35
D. 45
Question 2
Solve the inequality \( \frac{x^2 - 4}{x^2 - 9} > 0 \).
A. \( x in \( -infty, -3 \ \) cup (3, infty) )
B. \( x in \( -infty, -3 \ \) cup (3, infty) cup (0, 2) )
C. \( x in \( -infty, -3 \ \) cup (3, infty) cup \( -2, 0 \) )
D. \( x in \( -infty, -3 \ \) cup (3, infty) cup \( -2, 0 \) cup (2, 4) )
Question 3
Find the determinant of the matrix \( egin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix} \).
A. 0
B. 1
C. 2
D. 3
Question 4
A sequence is defined by the recurrence relation \( a_n = 2a_{n-1} + 3 \) with initial term \( a_1 = 2 \). Find the value of \( a_{10} \).
A. 123
B. 125
C. 127
D. 129
Question 5
A set A contains the elements ( { 1, 2, 3, 4, 5 } ). Find the number of subsets of A that contain exactly two elements.
A. ( 10 )
B. ( 15 )
C. ( 20 )
D. ( 25 )
Question 6
A circle has equation \( x - 1 \ \)^2 + \( y - 2 \)^2 = 4 ). Find the coordinates of the center of the circle.
A. (1, 2)
B. (2, 1)
C. (1, 1)
D. (2, 2)
Question 7
In the diagram below, a circle with center O and radius 6 cm is inscribed in a square. Find the area of the shaded region.
A. 36π
B. 72π
C. 108π
D. 144π
Question 8
A set [ A \] contains [ 5 \] elements. If [ n(A) = 5 \], find the number of subsets of [ A \].
A. 32
B. 31
C. 30
D. 29
Question 9
Solve the matrix equation \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 3 \ 7 \end{bmatrix}.
A. x = 1, y = 2
B. x = 2, y = 1
C. x = 1, y = 1
D. x = 2, y = 2
Question 10
Find the value of \sin(3x) + \cos(2x) when x = \frac{\pi}{4}.
A. \frac{1}{\sqrt{2}}
B. \frac{1}{2}
C. \frac{1}{\sqrt{2}} + \frac{1}{2}
D. \frac{1}{\sqrt{2}} - \frac{1}{2}
Question 11
Solve the inequality \( 2x^2 - 5x - 3 > 0 \) u\sing the quadratic formula.
A. \( x < -1 \) or \( x > \frac{3}{2} \)
B. \( x < -1 \) or \( x < \frac{3}{2} \)
C. \( x > -1 \) or \( x > \frac{3}{2} \)
D. \( x < -1 \) or \( x < \frac{3}{2} \)
Question 12
Find the equation of the circle with center at ((2,3)) and pas\sing through the point ((6,5)).
A. \( x-2 \ \)^2 + \( y-3 \)^2 = 5 )
B. \( x-2 \ \)^2 + \( y-3 \)^2 = 10 )
C. \( x-2 \ \)^2 + \( y-3 \)^2 = 15 )
D. \( x-2 \ \)^2 + \( y-3 \)^2 = 20 )
Question 13
A random variable X has a probability distribution given by P(X) = \( 1/2 \)^\( X-1 \) for X = 1, 2, 3, ... . Find the probability that X is greater than 2.
A. 1/4
B. 1/2
C. 3/4
D. 1
Question 14
Find the volume of the solid formed by revolving the region bounded by the curves y = x^2, y = 0, and x = 2 about the x-axis.
A. 16\pi
B. 32\pi
C. 64\pi
D. 128\pi
Question 15
Solve the inequality $2x^2-5x-3>0$.
A. \( -\infty, -1 \) \cup \( 3, \infty \)
B. \( -\infty, -3 \) \cup \( 1, \infty \)
C. \( -\infty, -2 \) \cup \( 2, \infty \)
D. \( -\infty, -4 \) \cup \( 4, \infty \)

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