POST UTME UNILORIN 2017 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the vector projection of the vector \vec{a} = \begin{pmatrix} 1 \ 2 \ 3 \end{pmatrix} onto the vector \vec{b} = \begin{pmatrix} 4 \ 5 \ 6 \end{pmatrix}.
A. \begin{pmatrix} 20/61 \ 25/61 \ 30/61 \end{pmatrix}
B. \begin{pmatrix} 20/61 \ 25/61 \ 30/61 \end{pmatrix}
C. \begin{pmatrix} 20/61 \ 25/61 \ 30/61 \end{pmatrix}
D. \begin{pmatrix} 20/61 \ 25/61 \ 30/61 \end{pmatrix}
Question 2
A bag contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is blue?
A. 1/2
B. 2/3
C. 3/4
D. 4/5
Question 3
Find the value of ( x ) in the equation \( 2^x + 3^x = 10^x \).
A. 2
B. 3
C. 4
D. 5
Question 4
In a geometric sequence with first term $a$ and common ratio $r$, the sum of the first $n$ terms is given by $S_n = \frac{a\( r^n - 1 \)}{r - 1}$. If $a = 2$, $r = 3$, and $n = 5$, find the value of $S_5$.
A. 120
B. 121
C. 122
D. 123
Question 5
A company produces two products, A and B. The profit from product A is ₦100 per unit, and the profit from product B is ₦150 per unit. If the company produces 100 units of product A and 50 units of product B, what is the total profit?
A. ₦15,000
B. ₦20,000
C. ₦25,000
D. ₦30,000
Question 6
A histogram of exam scores is shown below. If the mean score is 60 and the s\tandard deviation is 10, what is the probability that a randomly selected student scored above 70?
A. 0.2
B. 0.3
C. 0.4
D. 0.5
Question 7
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. 1/2
B. 1/3
C. 2/3
D. 1/4
Question 8
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 on the first roll?
A. 0.5
B. 0.6
C. 0.7
D. 0.8
Question 9
A random experiment has two indep\endent events, A and B, with probabilities 0.4 and 0.6, respectively. What is the probability that both events occur?
A. 0.2
B. 0.4
C. 0.6
D. 0.8
Question 10
A set of 5 numbers has a mean of 10 and a s\tandard deviation of 2. If the largest number is 15, find the sum of the remaining 4 numbers.
A. 35
B. 36
C. 37
D. 38
Question 11
A histogram is constructed with 5 classes, each of width 2. The first class has a frequency of 3, the second class has a frequency of 5, the third class has a frequency of 2, the fourth class has a frequency of 4, and the fifth class has a frequency of 6. What is the value of the class mark for the third class?
A. 4
B. 5
C. 6
D. 7
Question 12
A firm has two production plants, A and B. The \cost function for plant A is C_A(x) = 2x^2 + 10x + 5, and for plant B is C_B(x) = 3x^2 + 5x + 2. If the firm produces 20 units, what is the total \cost of production?
A. 1500
B. 1600
C. 1700
D. 1800
Question 13
Solve the inequality \frac{x^2 - 4}{x^2 - 9} > 0.
A. \boxed{\( -3, -2 \) \cup ( 2, 3 )}
B. \boxed{\( -3, -2 \) \cup ( 2, 3 )}
C. \boxed{\( -3, -2 \) \cup ( 2, 3 )}
D. \boxed{\( -3, -2 \) \cup ( 2, 3 )}
Question 14
Solve the inequality \( \frac{x}{2} - 3 > 7 \).
A. x < -16
B. x > 16
C. x < 16
D. x > -16
Question 15
If $x^2+4x+4=0$, find the value of $x$.
A. -2
B. -1
C. 0
D. 1

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