POST UTME UNIPORT 2018 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Let \( S = {1, 2, 3, 4, 5} \) be a finite set. Find the number of elements in the power set of ( S ), denoted as ( P(S) ).
A. 32
B. 31
C. 30
D. 29
Question 2
Solve the inequality \( 2x^2 + 5x - 3 \geq 0 \).
A. \( x \leq -3 \) or \( x \geq \frac{3}{2} \)
B. \( x \leq -3 \) or \( x \geq 1 \)
C. \( x \leq 1 \) or \( x \geq -3 \)
D. \( x \leq -1 \) or \( x \geq 3 \)
Question 3
A geometric progression is defined as \( a_n = 2a_{n-1} + 1 \) for \( n = 2, 3, 4, ldots \) with \( a_1 = 2 \). Find the sum of the first five terms of this progression.
A. 63
B. 62
C. 61
D. 60
Question 4
Find the sum of the first $10$ terms of the geometric series $1 + 2 + 4 + 8 + \dotsb$.
A. 1023
B. 1024
C. 1025
D. 1026
Question 5
A random variable X has a probability distribution given by ( P(X) = egin{cases} 0.2 & \text{if } X = 1 \ 0.3 & \text{if } X = 2 \ 0.5 & \text{if } X = 3 \end{cases} ). Find the expected value of X.
A. 1.5
B. 2
C. 2.5
D. 3
Question 6
Find the equation of the circle with center ( (2, 3) ) and radius ( 4 ).
A. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 16 )
B. \( x - 3 \ \)^2 + \( y - 2 \)^2 = 16 )
C. \( x - 4 \ \)^2 + \( y - 3 \)^2 = 16 )
D. \( x - 2 \ \)^2 + \( y - 4 \)^2 = 16 )
Question 7
Find the area under the curve y = x^2 + 2x - 3 from x = 1 to x = 4.
A. 20
B. 30
C. 40
D. 50
Question 8
A sequence is defined as \( a_n = 2n + 1 \) for \( n = 1, 2, 3, ldots \). Find the sum of the first five terms of this sequence.
A. 30
B. 31
C. 32
D. 33
Question 9
Find the sum of the first 10 terms of the arithmetic progression 2, 5, 8, ...
A. 50
B. 55
C. 60
D. 65
Question 10
A binary number is represented as \( 1011_2 \). Convert it to decimal.
A. 3
B. 5
C. 7
D. 9
Question 11
Find the determinant of the matrix \begin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix}
A. 0
B. 1
C. 2
D. 3
Question 12
A circle passes through the points (2, 3), (4, 1), and (6, 5). Find the equation of the circle.
A. x^2 + y^2 - 4x - 2y - 5 = 0
B. x^2 + y^2 + 4x + 2y - 5 = 0
C. x^2 + y^2 - 6x - 4y + 11 = 0
D. x^2 + y^2 + 6x + 4y - 11 = 0
Question 13
Find the area under the curve \( y = \frac{1}{x^2} \) from \( x = 1 \) to \( x = 2 \).
A. \( \frac{1}{2} \)
B. \( \frac{1}{3} \)
C. \( \frac{1}{4} \)
D. \( \frac{1}{5} \)
Question 14
Find the area under the curve \( y = \frac{1}{2}x^2 \) from \( x = 0 \) to \( x = 4 \).
A. 16
B. 32
C. 64
D. 128
Question 15
Solve for ( x ) in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. \( x = 10^4 \)
B. \( x = 10^2 \)
C. \( x = 10^{-2} \)
D. \( x = 10^{-4} \)

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