POST UTME UNN 2021 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A solid sphere of radius 4 cm is inscribed in a cube. Find the volume of the sphere.
A. 268.08
B. 268.1
C. 268.12
D. 268.14
Question 2
Find the derivative of ( f(x) = \frac{1}{\sqrt{x}} ) u\sing the chain rule.
A. \( \frac{-1}{2}x^{-\frac{3}{2}} \)
B. \( \frac{1}{2}x^{-\frac{1}{2}} \)
C. \( -\frac{1}{2}x^{-\frac{3}{2}} \)
D. \( \frac{1}{2}x^{-\frac{3}{2}} \)
Question 3
Solve the matrix equation AX = B, where A = \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix}, X = \begin{bmatrix} x \ y \end{bmatrix}, and B = \begin{bmatrix} 5 \ 6 \end{bmatrix}.
A. \begin{bmatrix} 1 \ 2 \end{bmatrix}
B. \begin{bmatrix} 2 \ 3 \end{bmatrix}
C. \begin{bmatrix} 3 \ 4 \end{bmatrix}
D. \begin{bmatrix} 4 \ 5 \end{bmatrix}
Question 4
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. 0.8413
C. 0.8413
D. 0.8413
Question 5
A rec\tangular garden measures 15 m by 8 m. If a path that is 2 m wide is built around the garden, what is the area of the path?
A. 48 m^2
B. 64 m^2
C. 80 m^2
D. 96 m^2
Question 6
A circle has a diameter of 10 cm. Find the area of the circle.
A. 78.5
B. 78.55
C. 78.6
D. 78.65
Question 7
Find the sum of the first 10 terms of the geometric series with first term 2 and common ratio 3.
A. 12143
B. 12145
C. 12147
D. 12149
Question 8
Find the value of \( int_{0}^{1} \frac{1}{x^2 + 1} dx \) u\sing the method of substitution.
A. \frac{\pi}{2}
B. \frac{\pi}{4}
C. \frac{\pi}{6}
D. \frac{\pi}{8}
Question 9
Solve the inequality \( 2x^2 - 5x - 3 > 0 \) u\sing the quadratic formula.
A. \left\( -\infty, \frac{3}{2} \right \) \cup \left\( 1, \infty \right \)
B. \left\( -\infty, -1 \right \) \cup \left\( 2, \infty \right \)
C. \left\( -\infty, -2 \right \) \cup \left\( 3, \infty \right \)
D. \left\( -\infty, -3 \right \) \cup \left\( 4, \infty \right \)
Question 10
A random sample of 25 students from a university had a mean height of 175 cm with a s\tandard deviation of 5 cm. If the population s\tandard deviation is unknown, calculate the 95% confidence interval for the mean height of the university students.
A. 170.5 cm, 179.5 cm
B. 172.5 cm, 177.5 cm
C. 174.5 cm, 175.5 cm
D. 176.5 cm, 173.5 cm
Question 11
Find the derivative of the function $f(x) = \frac{1}{x^2 + 1}$.
A. f'(x) = \frac{-2x}{\( x^2 + 1 \)^2}
B. f'(x) = \frac{2x}{\( x^2 + 1 \)^2}
C. f'(x) = \frac{1}{\( x^2 + 1 \)^2}
D. f'(x) = \frac{-1}{\( x^2 + 1 \)^2}
Question 12
Find the area under the curve \( y = x^3 - 6x^2 + 9x + 2 \) from \( x = 0 \) to \( x = 2 \).
A. 14
B. 16
C. 18
D. 20
Question 13
A water \tank can hold 2400 liters of water. If 3/5 of the \tank is already filled, how many more liters of water can be added?
A. 1440 liters
B. 1600 liters
C. 1800 liters
D. 2000 liters
Question 14
Find the equation of the circle with center $\( -2, 3 \)$ and radius $4$.
A. \( x + 2 \)^2 + \( y - 3 \)^2 = 16
B. \( x - 2 \)^2 + \( y + 3 \)^2 = 16
C. \( x + 2 \)^2 + \( y + 3 \)^2 = 16
D. \( x - 2 \)^2 + \( y - 3 \)^2 = 16
Question 15
Determine the value of $\int_{0}^{\pi} \frac{\sin^2 x}{\sin^2 x + 1} dx$.
A. \frac{\pi}{2}
B. \frac{\pi}{4}
C. \frac{\pi}{3}
D. \frac{\pi}{6}

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