POST UTME BELLS UNIVERSITY 2023 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 \( mathbf{c} = mathbf{i} - mathbf{j} \).
A. \mathbf{a} = 3mathbf{i} + 2mathbf{j}
B. \mathbf{a} = 2mathbf{i} + 3mathbf{j}
C. \mathbf{a} = mathbf{i} + 2mathbf{j}
D. \mathbf{a} = 4mathbf{i} + mathbf{j}
Question 2
Solve the inequality $|x-2| > 3$.
A. \( -\infty, -1 \) \cup \( 5, \infty \)
B. \( -\infty, 1 \) \cup \( 3, \infty \)
C. \( -\infty, -5 \) \cup \( 1, \infty \)
D. \( -\infty, 5 \) \cup \( 1, \infty \)
Question 3
A surd \( \sqrt[3]{27} \) can be expressed in the form \( a + b\sqrt[3]{c} \). Find the values of ( a ), ( b ), and ( c ).
A. \( a = 3, b = 1, c = 3 \)
B. \( a = 3, b = 2, c = 3 \)
C. \( a = 2, b = 1, c = 3 \)
D. \( a = 1, b = 2, c = 3 \)
Question 4
A binary operation $\circ$ is defined as $a \circ b = ab + 2$. Find the value of $2 \circ 3$.
A. 8
B. 10
C. 12
D. 14
Question 5
A histogram of exam scores is shown below. What is the mean score?
A. 60
B. 70
C. 80
D. 90
Question 6
Find the volume of the solid formed by revolving the region bounded by the parabola \( y = x^2 \) and the line \( y = 2x \) about the x-axis.
A. \frac{8}{3}
B. \frac{16}{3}
C. \frac{32}{3}
D. \frac{64}{3}
Question 7
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \left\( -\infty, -\frac{3}{2} \right \) \cup \left\( \frac{1}{2}, \infty \right \)
B. \left\( -\infty, -\frac{1}{2} \right \) \cup \left\( \frac{3}{2}, \infty \right \)
C. \left\( -\infty, \frac{1}{2} \right \) \cup \left\( \frac{3}{2}, \infty \right \)
D. \left\( -\infty, -\frac{3}{2} \right \) \cup \left\( \frac{1}{2}, \infty \right \)
Question 8
Find the value of $\int_{0}^{\pi} \frac{1}{1+\sin^2x} dx$.
A. \frac{\pi}{2}
B. \frac{\pi}{4}
C. \frac{\pi}{3}
D. \frac{\pi}{6}
Question 9
Find the sum of the first 10 terms of the geometric series 2 + 6 + 18 + ...
A. 1023
B. 1024
C. 1025
D. 1026
Question 10
In a geometric sequence with first term 2 and common ratio 3, find the sum of the first 5 terms.
A. 2 + 6 + 18 + 54 + 162
B. 2 + 6 + 18 + 54 + 162 + 486
C. 2 + 6 + 18 + 54 + 162 + 486 + 1458
D. 2 + 6 + 18 + 54 + 162 + 486 + 1458 + 4374
Question 11
A histogram of exam scores has a mean of 60 and a s\tandard deviation of 10. If the scores are normally distributed, find the probability that a randomly selected score is greater than 70.
A. ( 0.1587 )
B. ( 0.3413 )
C. ( 0.5 )
D. ( 0.8413 )
Question 12
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. 64
B. 80
C. 96
D. 112
Question 13
Find the derivative of the function ( f(x) = \frac{x^2}{x^2 + 1} ) u\sing the quotient rule.
A. ( f'(x) = \frac{2x\( x^2 + 1 \) - 2x^2}{\( x^2 + 1 \)^2} )
B. ( f'(x) = \frac{2x^2}{\( x^2 + 1 \)^2} )
C. ( f'(x) = \frac{2x}{\( x^2 + 1 \)^2} )
D. ( f'(x) = \frac{2x^2 + 2}{\( x^2 + 1 \)^2} )
Question 14
Find the equation of the circle with center ( (2, 3) ) and radius ( 4 ).
A. \left\( x - 2 \right \)^2 + \left\( y - 3 \right \)^2 = 16
B. \left\( x - 3 \right \)^2 + \left\( y - 2 \right \)^2 = 16
C. \left\( x - 4 \right \)^2 + \left\( y - 3 \right \)^2 = 16
D. \left\( x - 2 \right \)^2 + \left\( y - 4 \right \)^2 = 16
Question 15
In a 3x3 matrix, if the determinant is 0, what can be concluded about the linear indep\endence of the column vectors?
A. The column vectors are linearly dep\endent
B. The column vectors are linearly indep\endent
C. The determinant is not 0
D. The matrix is \singular

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