POST UTME UNILORIN 2017 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the value of ( x ) in the equation \( 2^x + 3^x = 10^x \).
A. 2
B. 3
C. 4
D. 5
Question 2
In the diagram below, the line $l$ has a slope of 2 and passes through the point $(1,3)$. Find the equation of the line.
A. y=2x-1
B. y=2x+1
C. y=2x-2
D. y=2x+2
Question 3
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 between 50 and 70?
A. 0.68
B. 0.85
C. 0.95
D. 0.98
Question 4
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 5
A histogram is constructed from the following data: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20. If the mean is 12, what is the value of the mis\sing number in the set?
A. 22
B. 20
C. 18
D. 16
Question 6
Find the derivative of the function f(x) = \frac{x^3}{x^2 + 1} u\sing the quotient rule.
A. \frac{3x^4 - 2x^4}{\( x^2 + 1 \)^2}
B. \frac{3x^4 - 2x^4}{\( x^2 + 1 \)^2}
C. \frac{3x^4 - 2x^4}{\( x^2 + 1 \)^2}
D. \frac{3x^4 - 2x^4}{\( x^2 + 1 \)^2}
Question 7
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 8
In the diagram below, the circle with center $O$ has a radius of 4 cm. If $AB$ is a chord of the circle such that $OA=3$ cm and $OB=5$ cm, find the length of $AB$.
A. 6 cm
B. 8 cm
C. 10 cm
D. 12 cm
Question 9
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 10
A vector is defined by the equation: \( vec{a} = 2hat{i} + 3hat{j} \). Find the magnitude of the vector.
A. √13
B. √15
C. √17
D. √19
Question 11
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 12
If $x^2+4x+4=0$, find the value of $x$.
A. -2
B. -1
C. 0
D. 1
Question 13
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 14
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 15
If $x^2+2x+1=0$, find the value of $x$.
A. -1
B. 0
C. 1
D. 2

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