POST UTME BELLS UNIVERSITY 2019 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the vector equation \( mathbf{a} \times \( mathbf{b} + mathbf{c} \ \) = mathbf{0} ) for ( mathbf{a} ), given that \( mathbf{b} = egin{pmatrix} 2 \ 3 \ 4 \end{pmatrix} \) and \( mathbf{c} = egin{pmatrix} 1 \ 2 \ 3 \end{pmatrix} \).
A. \( mathbf{a} = egin{pmatrix} 0 \ 0 \ 0 \end{pmatrix} \)
B. \( mathbf{a} = egin{pmatrix} 3 \ 4 \ 5 \end{pmatrix} \)
C. \( mathbf{a} = egin{pmatrix} 4 \ 5 \ 6 \end{pmatrix} \)
D. \( mathbf{a} = egin{pmatrix} 5 \ 6 \ 7 \end{pmatrix} \)
Question 2
Find the volume of the solid formed by rotating the region bounded by y = x^2, y = 0, and x = 2 about the x-axis.
A. 32\pi/5
B. 64\pi/5
C. 128\pi/5
D. 256\pi/5
Question 3
Solve the inequality \( 2x^2 + 3x - 1 > 0 \).
A. \( -\infty, -\frac{1}{2} \) \cup \( \frac{1}{3}, \infty \)
B. \( -\infty, -\frac{1}{2} \) \cup \( \frac{1}{3}, 0 \)
C. \( -\infty, 0 \) \cup \( \frac{1}{3}, \infty \)
D. \( -\infty, -\frac{1}{2} \) \cup \( 0, \infty \)
Question 4
A fair six-sided die is rolled. What is the probability that the number obtained is a multiple of 3?
A. 1/2
B. 1/3
C. 2/3
D. 1/6
Question 5
Find the sum of the first 10 terms of the geometric series: \( 2 + 6 + 18 + ... \).
A. 123
B. 124
C. 125
D. 126
Question 6
Convert the decimal number 0.75 to binary.
A. 0.11
B. 0.10
C. 0.01
D. 0.00
Question 7
The equation of a circle is given by \( x - h \ \)^2 + \( y - k \)^2 = r^2 ). If the center of the circle is at ( (3, 4) ) and the radius is 5, find the equation of the circle.
A. \( x - 3 \)^2 + \( y - 4 \)^2 = 25
B. \( x - 3 \)^2 + \( y - 4 \)^2 = 30
C. \( x - 3 \)^2 + \( y - 4 \)^2 = 20
D. \( x - 3 \)^2 + \( y - 4 \)^2 = 35
Question 8
Solve the inequality \( \frac{2x + 1}{x - 1} > 0 \).
A. \( x < -1 \) or \( x > 1 \)
B. \( x < 1 \) or \( x > -1 \)
C. \( x < -1 \) or \( x = 1 \)
D. \( x < 1 \) or \( x = -1 \)
Question 9
Find the value of x in the equation \( 2x^2 + 5x - 3 = 0 \).
A. 1
B. -1
C. 2
D. -2
Question 10
Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} ) u\sing the chain rule.
A. ( f'(x) = \frac{-2x}{\( x^2 + 1 \)^2} )
B. ( f'(x) = \frac{2x}{\( x^2 + 1 \)^2} )
C. ( f'(x) = \frac{2}{\( x^2 + 1 \)^2} )
D. ( f'(x) = \frac{-2}{\( x^2 + 1 \)^2} )
Question 11
Find the area of the triangle with vertices ( A(1, 2) ), ( B(3, 4) ), and ( C(2, 1) ).
A. ( 5 )
B. ( 6 )
C. ( 7 )
D. ( 8 )
Question 12
In the diagram below, \( \sin \theta = \frac{3}{5} \). Find the value of \( \cos \theta \).
A. 0.6
B. 0.8
C. 0.4
D. 0.2
Question 13
A bag contains 5 red marbles, 4 blue marbles, and 6 green marbles. If a marble is drawn at random, what is the probability that it is not blue?
A. \frac{11}{15}
B. \frac{13}{15}
C. \frac{14}{15}
D. \frac{16}{15}
Question 14
Solve the inequality \( \frac{x - 2}{x + 1} > 0 \)
A. \( -∞, -1 \) ∪ (1, ∞)
B. \( -∞, -1 \) ∪ (2, ∞)
C. \( -∞, 1 \) ∪ (2, ∞)
D. \( -∞, 1 \) ∪ (2, ∞)
Question 15
If ( f(x) = \frac{1}{x^2 + 1} ), find ( f'(x) ).
A. -\frac{2x}{\( x^2 + 1 \)^2}
B. \frac{2x}{\( x^2 + 1 \)^2}
C. -\frac{1}{\( x^2 + 1 \)^2}
D. \frac{1}{\( x^2 + 1 \)^2}

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