POST UTME UNN 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. If the outcome is an even number, the experimenter wins a prize. If the outcome is an odd number, the experimenter loses a prize. If the outcome is a six, the experimenter gets a second chance to roll the die. Find the probability that the experimenter wins a prize.
A. \frac{1}{2}
B. \frac{1}{3}
C. \frac{2}{3}
D. \frac{3}{4}
Question 2
Solve the inequality \( \frac{x}{x-2} > 1 \) for \( x > 2 \).
A. 2 < x < 3
B. x > 3
C. x < 2
D. x = 3
Question 3
A set ( A ) contains the elements ( { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 } ). Find the number of subsets of ( A ) that contain exactly 3 elements.
A. \( 2^3 \ \)
B. \( 3^3 \ \)
C. \( 10 \ \)
D. \( 5 \ \)
Question 4
Solve for x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10^4
B. 10^8
C. 10^12
D. 10^16
Question 5
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 \( 4, \infty \)
Question 6
Solve for x in the equation \( \log_{10} \( x^2 \ \) = 4 )
A. 10
B. 100
C. 1000
D. 10000
Question 7
Solve the quadratic equation \( x^2 - 6x + 8 = 0 \).
A. x = 2
B. x = 4
C. x = 3
D. x = 1
Question 8
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 9
A fair six-sided die is rolled twice. What is the probability that the sum of the two numbers rolled is $7$?
A. \frac{1}{6}
B. \frac{1}{12}
C. \frac{1}{24}
D. \frac{1}{36}
Question 10
A binary operation ( odot ) on the set of real numbers is defined as \( a odot b = a^2 + b^2 \). Find the value of ( x ) such that \( x odot \( x-1 \ \) = 4 ).
A. x = 2
B. x = -1
C. x = 1
D. x = 3
Question 11
A polynomial function is defined by ( f(x) = x^3 - 6x^2 + 11x - 6 ). Find the value of ( f(2) ).
A. \( 0 \ \)
B. \( 2 \ \)
C. \( 4 \ \)
D. \( 6 \ \)
Question 12
A triangle has angles A, B, and C. If angle A is 30° and angle B is 60°, find angle C
A. 90°
B. 60°
C. 30°
D. 120°
Question 13
A box contains 5 red balls and 3 blue balls. If 2 balls are drawn at random, what is the probability that both balls are blue?
A. \frac{1}{14}
B. \frac{1}{7}
C. \frac{3}{14}
D. \frac{1}{2}
Question 14
A sequence is defined as \( a_n = 2n + 1 \). Find the sum of the first 5 terms of the sequence.
A. 15
B. 20
C. 25
D. 30
Question 15
A geometric progression is defined by \( a_n = 2a_{n-1} \) with \( a_1 = 2 \). Find the sum of the first 5 terms of the progression.
A. \( 62 \ \)
B. \( 63 \ \)
C. \( 64 \ \)
D. \( 65 \ \)

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