POST UTME PAN-ATLANTIC UNIVERSITY 2021 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.
A. 40\pi cm^3
B. 50\pi cm^3
C. 60\pi cm^3
D. 70\pi cm^3
Question 2
Find the mean of the data set {2, 4, 6, 8, 10}.
A. 5
B. 6
C. 7
D. 8
Question 3
In a geometric sequence, the first term is 2 and the common ratio is 3. Find the fifth term.
A. 486
B. 4860
C. 48600
D. 486000
Question 4
A rec\tangular box has a length of 6 cm, a width of 4 cm, and a height of 2 cm. What is the volume of the box in cubic centimeters?
A. 48
B. 64
C. 72
D. 96
Question 5
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( -∞, -1 \) ∪ (3, ∞)
B. \( -∞, -3 \) ∪ (1, ∞)
C. \( -∞, 1 \) ∪ (3, ∞)
D. \( -∞, -3 \) ∪ (1, ∞)
Question 6
A set A has 5 elements and a set B has 3 elements. Find the number of elements in the union of sets A and B.
A. 6
B. 7
C. 8
D. 9
Question 7
Find the derivative of the function \(f(x) = \frac{1}{x^2 + 1}\).
A. \frac{-2x}{\( x^2 + 1 \)^2}
B. \frac{2x}{\( x^2 + 1 \)^2}
C. \frac{-2}{\( x^2 + 1 \)^2}
D. \frac{2}{\( x^2 + 1 \)^2}
Question 8
Solve the equation \(x^2 + 4x + 4 = 0\).
A. \boxed{-2}
B. \boxed{-1}
C. \boxed{2}
D. \boxed{1}
Question 9
In a survey of 50 students, the heights of the students were recorded in centimeters. The mean height was 170 cm, and the s\tandard deviation was 5 cm. If the heights of the students were normally distributed, what is the probability that a randomly selected student has a height between 165 cm and 175 cm?
A. 0.9772
B. 0.6827
C. 0.3413
D. 0.1587
Question 10
A bakery sells a total of 480 loaves of bread per day. They sell a combination of whole wheat and white bread. If the ratio of whole wheat to white bread is 5:4, how many loaves of whole wheat bread are sold per day?
A. 200
B. 250
C. 300
D. 350
Question 11
Solve for x in the equation \( 2x^2 + 5x - 3 = 0 \).
A. -1.5
B. 1
C. 3
D. -2
Question 12
Let X and Y be indep\endent events with P(X) = 0.4 and P(Y) = 0.6. Find P(X ∩ Y).
A. 0.24
B. 0.36
C. 0.48
D. 0.60
Question 13
Solve for ( x ) in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. \( x = 10^2 \)
B. \( x = 10^4 \)
C. \( x = 10^{-2} \)
D. \( x = 10^{-4} \)
Question 14
A right triangle has a hypotenuse of 10 cm and one leg of 6 cm. What is the length of the other leg in centimeters?
A. 8
B. 6
C. 4
D. 2
Question 15
Find the determinant of the matrix \[ \begin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix} \].
A. 0
B. 1
C. 2
D. 3

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