POST UTME UNIBEN 2021 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the vector ( mathbf{a} ) such that \( mathbf{a} cdot mathbf{b} = 10 \) and \( mathbf{a} cdot mathbf{c} = 5 \), where \( mathbf{b} = 2mathbf{i} + 3mathbf{j} \) and \( mathbf{c} = mathbf{i} - 2mathbf{j} \).
A. \( 3mathbf{i} - mathbf{j} \)
B. \( 2mathbf{i} + mathbf{j} \)
C. \( mathbf{i} + 2mathbf{j} \)
D. \( mathbf{i} - 2mathbf{j} \)
Question 2
A histogram is shown below. What is the mean of the data?
A. 5
B. 10
C. 15
D. 20
Question 3
Determine the value of x in the equation \( \sin^2 x + \cos^2 x = 1 \) if \( \sin x = \frac{3}{5} \).
A. \( \frac{pi}{4} \)
B. \( \frac{pi}{3} \)
C. \( \frac{pi}{2} \)
D. \( \frac{pi}{6} \)
Question 4
Solve for x in the equation \( 2^x + 3^x = 5^x \)
A. 1
B. 2
C. 3
D. 4
Question 5
Solve the inequality \( 2x^2 - 5x - 3 > 0 \).
A. \( x < -1 \) or \( x > \frac{3}{2} \)
B. \( x < -1 \) or \( x < \frac{3}{2} \)
C. \( x > -1 \) or \( x < \frac{3}{2} \)
D. \( x > -1 \) or \( x > \frac{3}{2} \)
Question 6
Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.
A. 24π cm³
B. 48π cm³
C. 96π cm³
D. 192π cm³
Question 7
Find the area under the curve \( y = x^2 \) from x = 0 to x = 4.
A. 16
B. 32
C. 64
D. 128
Question 8
A set A contains 5 elements. If we select 2 elements from set A, what is the number of ways to do this?
A. 10
B. 15
C. 20
D. 25
Question 9
Find the volume of the solid formed by revolving the region bounded by the curve \( y = \frac{1}{2}x^2 + 1 \) about the x-axis.
A. \( \frac{5pi}{6} \)
B. \( \frac{7pi}{6} \)
C. \( \frac{11pi}{6} \)
D. \( \frac{13pi}{6} \)
Question 10
A sequence is defined as \( a_n = 2n + 1 \). Find the sum of the first 5 terms of the sequence.
A. 15
B. 25
C. 35
D. 45
Question 11
Let ( S ) be the set of all real numbers ( x ) such that \( x^2 + 2x - 3 > 0 \). Find the set ( S ) in interval notation.
A. \( -∞, -1 \) ∪ (3, ∞)
B. \( -∞, 1 \) ∪ (3, ∞)
C. \( -∞, -1 \) ∪ (1, ∞)
D. \( -∞, 1 \) ∪ (1, ∞)
Question 12
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. 0.8419
C. 0.8423
D. 0.8431
Question 13
A fair six-sided die is rolled. What is the probability that the number appearing is a multiple of 3?
A. \( \frac{1}{6} \)
B. \( \frac{1}{3} \)
C. \( \frac{2}{3} \)
D. \( \frac{5}{6} \)
Question 14
A triangle has angles 30°, 60°, and 90°. What is the length of the side opposite the 30° angle?
A. 1
B. 2
C. 3
D. 4
Question 15
A particle moves in a straight line with a velocity of ( v(t) = 2t + 1 ) m/s. Find the acceleration of the particle at time \( t = 2 \) s.
A. ( 4 ) m/s^2
B. ( 2 ) m/s^2
C. ( 1 ) m/s^2
D. ( 3 ) m/s^2

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