POST UTME UNIBEN 2024 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the surface area of the solid formed by revolving the region bounded by the curves $y = x^2$ and $y = 4 - x^2$ about the x-axis.
A. \frac{32\pi}{3}
B. \frac{64\pi}{3}
C. \frac{128\pi}{3}
D. \frac{256\pi}{3}
Question 2
Find the vector projection of the vector \vec{a} = 2\hat{i} + 3\hat{j} onto the vector \vec{b} = \hat{i} + 2\hat{j}.
A. 1.5\\hat{i} + 3\\hat{j}
B. 2\\hat{i} + 3\\hat{j}
C. 3\\hat{i} + 6\\hat{j}
D. 4\\hat{i} + 8\\hat{j}
Question 3
Find the value of x in the set {1, 2, 3, 4, 5} such that x is the median of the set.
A. 2
B. 3
C. 4
D. 5
Question 4
Find the volume of the solid formed by revolving the region bounded by the curves $y=x^2$ and $y=4x$ about the x-axis.
A. \frac{32}{15}\pi
B. \frac{64}{15}\pi
C. \frac{128}{15}\pi
D. \frac{256}{15}\pi
Question 5
A sequence is defined as \( a_n = 2n + 1 \). Find the sum of the first 5 terms of the sequence.
A. 15
B. 20
C. 25
D. 30
Question 6
Find the area under the curve $y=e^x$ from $x=0$ to $x=1$.
A. 1
B. e-1
C. e
D. e^2
Question 7
Find the sum of the first 10 terms of the arithmetic series 1, 3, 5, 7, ...
A. 100
B. 110
C. 120
D. 130
Question 8
Find the volume of the solid formed by revolving the region bounded by \( y = x^2 \) and \( y = 4 \) about the x-axis.
A. \( \frac{32}{3} \pi \)
B. \( \frac{16}{3} \pi \)
C. \( \frac{64}{3} \pi \)
D. \( \frac{128}{3} \pi \)
Question 9
Solve the inequality \( \frac{x}{x-2} > 0 \) for \( x in \( -infty, infty \ \) ).
A. \( -2, 2 \) \cup \( 2, \infty \)
B. \( -\infty, -2 \) \cup \( 2, \infty \)
C. \( -\infty, 2 \) \cup \( 2, \infty \)
D. \( -\infty, \infty \)
Question 10
Find the volume of the solid formed by revolving the region bounded by the curves $y = x^2$ and $y = 4 - x^2$ about the x-axis.
A. \frac{16\pi}{3}
B. \frac{32\pi}{3}
C. \frac{64\pi}{3}
D. \frac{128\pi}{3}
Question 11
Find the sum of the first 5 terms of the geometric series 2, 6, 18, 54, ...
A. 242
B. 242.5
C. 243
D. 243.5
Question 12
Solve the equation $\begin{vmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{vmatrix} = 0$.
A. 1
B. 2
C. 3
D. 4
Question 13
Find the sum of the infinite geometric series \( \sum_{n=1}^\infty \frac{1}{2^n} \ \).
A. 1
B. \( \frac{1}{2} \)
C. \( \frac{1}{4} \)
D. \( \frac{1}{8} \)
Question 14
A histogram shows the distribution of exam scores for a class of 50 students. The histogram has 5 bars, each representing a different score range. The heights of the bars are 8, 12, 15, 10, and 5 units, respectively. What is the mean score?
A. 12
B. 15
C. 18
D. 20
Question 15
A company produces two products, A and B. The profit from product A is $10 per unit, and the profit from product B is $15 per unit. If the company produces 100 units of product A and 50 units of product B, what is the total profit?
A. $1500
B. $2000
C. $2500
D. $3000

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