POST UTME UNILORIN 2019 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A circle has a radius of 4 cm. If a chord of the circle subt\ends an angle of 60° at the center, what is the length of the chord?
A. 4 cm
B. 6 cm
C. 8 cm
D. 10 cm
Question 2
Find the volume of the solid formed by revolving the region bounded by y = x^2, y = 0, and x = 2 about the x-axis.
A. \frac{32\pi}{5}
B. \frac{16\pi}{3}
C. \frac{32\pi}{3}
D. \frac{64\pi}{5}
Question 3
Solve for x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 2
B. 4
C. 8
D. 16
Question 4
In a random sample of 100 students, the mean height is 175 cm with a s\tandard deviation of 5 cm. If the distribution of heights is approximately normal, what is the probability that a randomly selected student will be taller than 180 cm?
A. 0.1587
B. 0.3413
C. 0.4772
D. 0.6179
Question 5
Solve the inequality: \frac{x}{x-1} > 0.
A. \( -\infty, 0 \) \cup \( 1, \infty \)
B. \( -\infty, 1 \) \cup \( 1, \infty \)
C. \( -\infty, 0 \) \cup (0, 1)
D. (0, 1)
Question 6
Find the area under the curve \( y = x^2 \) from x = 0 to x = 4.
A. 32
B. 64
C. 128
D. 256
Question 7
Find the equation of the line pas\sing through the point ( (1, 2) ) with slope 3.
A. \( y = 3x + 1 \)
B. \( y = 3x - 1 \)
C. \( y = 3x + 2 \)
D. \( y = 3x - 2 \)
Question 8
Find the surface area of the solid formed by revolving the region bounded by y = x^2, y = 0, and x = 2 about the x-axis.
A. 16\pi
B. 32\pi
C. 64\pi
D. 128\pi
Question 9
Solve the system of equations u\sing matrices: \begin{bmatrix} 2 & 1 \\ 1 & 2 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 3 \\ 4 \end{bmatrix}.
A. \\begin{bmatrix} 1 \\\\ 2 \\end{bmatrix}
B. \\begin{bmatrix} 2 \\\\ 1 \\end{bmatrix}
C. \\begin{bmatrix} 3 \\\\ 4 \\end{bmatrix}
D. \\begin{bmatrix} 4 \\\\ 3 \\end{bmatrix}
Question 10
Find the mean deviation about the median for the data set: 2, 4, 6, 8, 10.
A. 2
B. 4
C. 6
D. 8
Question 11
Determine 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 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 will be between 60 and 90?
A. 0.8413
B. 0.9772
C. 0.9986
D. 0.9999
Question 13
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 less than 60?
A. 0.1587
B. 0.6915
C. 0.8413
D. 0.9772
Question 14
Find the volume of the solid formed by revolving the region bounded by y = x^3, y = 0, and x = 2 about the x-axis.
A. \frac{64\pi}{7}
B. \frac{32\pi}{3}
C. \frac{64\pi}{5}
D. \frac{128\pi}{7}
Question 15
A solid is formed by revolving the region bounded by the curves y = x^2 and y = 4 - x^2 about the x-axis. Find the volume of the solid.
A. \frac{16\pi}{3}
B. \frac{32\pi}{3}
C. \frac{64\pi}{3}
D. \frac{128\pi}{3}

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