POST UTME BABCOCK UNIVERSITY 2020 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the volume of the solid formed by revolving the region bounded by y = x^2, x = 0, and x = 2 about the x-axis.
A. 16\pi
B. 32\pi
C. 64\pi
D. 128\pi
Question 2
A box contains 5 red balls and 3 blue balls. If two balls are drawn at random, what is the probability that they are of different colors?
A. 1/4
B. 1/3
C. 2/5
D. 3/5
Question 3
Find the derivative of ( f(x) = x^3 - 2x^2 + 3x - 1 ) u\sing the chain rule.
A. 3x^2 - 4x + 3
B. 3x^2 - 4x + 2
C. 3x^2 - 4x - 3
D. 3x^2 - 4x - 2
Question 4
Find the derivative of the function f(x) = x^3 + 2x^2 - 5x + 1.
A. 3x^2 + 4x - 5
B. 2x^2 + 3x - 1
C. x^2 + 2x - 1
D. x^2 + 3x - 2
Question 5
Find the area under the curve of ( f(x) = \frac{1}{x^2} ) from \( x = 1 \) to \( x = 2 \).
A. 0.5
B. 1
C. 1.5
D. 2
Question 6
Find the area under the curve y = 2x^2 + 3x - 1 from x = 0 to x = 2
A. 14.67
B. 14.67 m^2
C. 14.67 km^2
D. 14.67 cm^2
Question 7
Find the determinant of the matrix \( egin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix} \).
A. 0
B. 1
C. 2
D. 3
Question 8
Solve for x in the equation \( \sin^2 x + \cos^2 x = 1 \).
A. \( x = \frac{pi}{2} \)
B. \( x = \frac{pi}{4} \)
C. \( x = \frac{3pi}{4} \)
D. \( x = \frac{5pi}{4} \)
Question 9
A random sample of 25 students from a university had a mean height of 175.5 cm with a s\tandard deviation of 5.2 cm. Calculate the coefficient of variation (CV) of the sample.
A. 12.5%
B. 15%
C. 17.5%
D. 20%
Question 10
Solve the equation x^3 - 6x^2 + 11x - 6 = 0.
A. 1
B. 2
C. 3
D. 4
Question 11
A circle with center ( C ) and radius ( r ) is shown below. If \( OC = 6 \), find the length of ( AB ).
A. 4
B. 6
C. 8
D. 10
Question 12
A cylindrical \tank with a radius of 5m and a height of 10m is filled with water. If the density of water is 1000 kg/m^3, calculate the volume of water in the \tank.
A. 785.4 m^3
B. 785.4 m^2
C. 785.4 m
D. 785.4 km^3
Question 13
In the diagram below, ( ABC ) is a right-angled triangle with \( angle B = 90^circ \). If \( AB = 3 \) and \( BC = 4 \), find the length of ( AC ).
A. 5
B. 6
C. 7
D. 8
Question 14
A circle has a radius of 4 cm. Find the area of the circle.
A. 16\pi
B. 32\pi
C. 64\pi
D. 128\pi
Question 15
Find the area under the curve y = x^2 + 2x - 3 from x = 0 to x = 2.
A. 10
B. 12
C. 14
D. 16

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