POST UTME UNILORIN 2021 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the equation \( 2^x + 2^{-x} = 10 \) for x.
A. 2
B. 3
C. 4
D. 5
Question 2
A population of 1000 bacteria grows at a rate of 20% per hour. If the initial population is 100, what is the population after 5 hours?
A. 1000
B. 2000
C. 3000
D. 4000
Question 3
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 red?
A. 1/7
B. 1/8
C. 1/9
D. 1/10
Question 4
Simplify the expression \( \sqrt{16x^2y^2} \ \).
A. 4xy
B. 2xy
C. 4x^2y
D. 2x^2y^2
Question 5
Find the derivative of the function ( f(x) = \frac{1}{\sqrt{x^2 + 1}} ) u\sing the chain rule.
A. \frac{-x}{\( x^2 + 1 \)^{3/2}}
B. \frac{x}{\( x^2 + 1 \)^{3/2}}
C. \frac{1}{\( x^2 + 1 \)^{3/2}}
D. \frac{-1}{\( x^2 + 1 \)^{3/2}}
Question 6
Solve the system of equations \begin{align*} x + y &= 4 \ x - y &= 2 \end{align*}.
A. \begin{pmatrix} 3 \ 1 \end{pmatrix}
B. \begin{pmatrix} 1 \ 3 \end{pmatrix}
C. \begin{pmatrix} 2 \ 2 \end{pmatrix}
D. \begin{pmatrix} 4 \ 0 \end{pmatrix}
Question 7
A histogram of exam scores has a mean of 60 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is greater than 70?
A. 0.25
B. 0.5
C. 0.75
D. 0.9
Question 8
A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 60 and 90?
A. 0.8413
B. 0.8413
C. 0.8413
D. 0.8413
Question 9
In a set of 10 consecutive integers, the sum of the first and last terms is 57. If the sum of the first and last terms of another set of 10 consecutive integers is 67, what is the difference between the two sets?
A. 20
B. 30
C. 40
D. 50
Question 10
A random variable X has a probability distribution given by P\( X = 1 \) = 0.3, P\( X = 2 \) = 0.4, and P\( X = 3 \) = 0.3. What is the expected value of X?
A. 1.1
B. 1.2
C. 1.3
D. 1.4
Question 11
Find the equation of the line pas\sing through the points (2, 3) and (4, 5).
A. y = 2x - 1
B. y = 2x + 1
C. y = x - 1
D. y = x + 1
Question 12
Determine the value of x in the equation \( \frac{1}{2}x + 5 = \frac{3}{4}x - 3 \) in base 8.
A. 6
B. 10
C. 12
D. 14
Question 13
Solve for x in the equation \( \log_{10} \( x^2 \) = 4 \).
A. 10
B. 100
C. 1000
D. 10000
Question 14
Solve the matrix equation \\begin{bmatrix} 1 & 2 \\ 3 & 4 \\end{bmatrix} \\begin{bmatrix} x \\ y \\end{bmatrix} = \\begin{bmatrix} 5 \\ 6 \\end{bmatrix}.
A. x = 1, y = 2
B. x = 2, y = 3
C. x = 3, y = 4
D. x = 4, y = 5
Question 15
Find the sum of the first 10 terms of the geometric series with first term 2 and common ratio 3.
A. 2 \cdot \frac{3^{10} - 1}{3 - 1}
B. 2 \cdot \frac{3^{11} - 1}{3 - 1}
C. 2 \cdot \frac{3^{12} - 1}{3 - 1}
D. 2 \cdot \frac{3^{13} - 1}{3 - 1}

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