POST UTME UNIBEN 2020 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A vector ( vec{a} ) has a magnitude of 5 units and makes an angle of 60° with the positive x-axis. Find the x-component of ( vec{a} ).
A. 2.5
B. 3.75
C. 4.33
D. 5.00
Question 2
A sequence is defined as: \[ a_n = \frac{1}{n} + \frac{1}{n+1} \]. Find the sum of the first 5 terms of the sequence.
A. 2.5
B. 2.6
C. 2.7
D. 2.8
Question 3
A random experiment has 3 possible outcomes: A, B, and C. The probability of outcome A is 0.4, the probability of outcome B is 0.3, and the probability of outcome C is 0.3. What is the probability that outcome A occurs?
A. 0.4
B. 0.3
C. 0.2
D. 0.1
Question 4
In a set of 5 numbers, the mean is 10 and the median is 8. If the largest number is 15, find the sum of the remaining 3 numbers.
A. 25
B. 30
C. 35
D. 40
Question 5
A random variable X has a probability distribution given by P\( X = 1 \) = 0.4, P\( X = 2 \) = 0.3, P\( X = 3 \) = 0.2, and P\( X = 4 \) = 0.1. If two indep\endent random variables X and Y have the same probability distribution as X, find the probability that X + Y is greater than 5.
A. 0.2
B. 0.3
C. 0.4
D. 0.5
Question 6
A quadratic equation is given by: \[ x^2 + 4x + 4 = 0 \]. Find the roots of the equation.
A. 0
B. -2
C. -1
D. 1
Question 7
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( -∞, -1 \) ∪ (3, ∞)
B. \( -∞, -3 \) ∪ (1, ∞)
C. \( -∞, 1 \) ∪ (3, ∞)
D. \( -∞, -3 \) ∪ (1, ∞)
Question 8
Find the equation of the circle pas\sing through the points (1, 2), (2, 3), and (3, 4).
A. \( x - 2 \)^2 + \( y - 3 \)^2 = 1
B. \( x - 2 \)^2 + \( y - 3 \)^2 = 4
C. \( x - 2 \)^2 + \( y - 3 \)^2 = 9
D. \( x - 2 \)^2 + \( y - 3 \)^2 = 16
Question 9
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( -∞, -1 \) ∪ (3, ∞)
B. \( -∞, -3 \) ∪ (1, ∞)
C. \( -∞, 1 \) ∪ (3, ∞)
D. \( -∞, -3 \) ∪ (1, ∞)
Question 10
Find the derivative of the function ( f(x) = \frac{x^2}{x+1} ) u\sing the quotient rule.
A. \frac{2x\( x+1 \) - x^2}{\( x+1 \)^2}
B. \frac{x^2}{\( x+1 \)^2}
C. \frac{2x}{\( x+1 \)^2}
D. \frac{2x\( x+1 \) + x^2}{\( x+1 \)^2}
Question 11
A binary operation \( * \) on the set of real numbers is defined as \( a * b = a^2 + b^2 \). Find the value of \( 2 * 3 \).
A. 13
B. 17
C. 19
D. 21
Question 12
Find the area of the triangle with vertices ( (0, 0), (3, 0), (0, 4) ).
A. 6
B. 8
C. 10
D. 12
Question 13
Find the area of the region bounded by the curves y = x^2, y = 0, and x = 2.
A. 8/3
B. 16/3
C. 32/3
D. 64/3
Question 14
A histogram is shown below: \[ \begin{array}{|c|c|c|c|} \hline \text{Class} & 0-10 & 10-20 & 20-30 \ \hline \text{Frequency} & 5 & 10 & 15 \ \hline \end{array} \]. Find the mean of the data.
A. 20
B. 21
C. 22
D. 23
Question 15
Find the equation of the plane pas\sing through the points (1, 2, 3), (2, 3, 4), and (3, 4, 5).
A. x + y + z = 6
B. x - y + z = 6
C. x + y - z = 6
D. x - y - z = 6

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