POST UTME NILE UNIVERSITY 2021 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the derivative of the function ( f(x) = 3x^2 + 2x - 5 ).
A. 6x + 2
B. 6x + 4
C. 6x - 2
D. 6x - 4
Question 2
Let X and Y be indep\endent random variables with mean 0 and variance 1. What is the probability that X + Y is greater than 2?
A. 0.5
B. 0.25
C. 0.75
D. 0.125
Question 3
Solve the inequality \( \frac{2x+3}{x-1} > 0 \) u\sing interval notation.
A. ( (1, infty) )
B. \( -infty, 1 \ \) )
C. \( -infty, 1 \ \) cup (1, infty) )
D. \( -infty, 1 \ \) cap (1, infty) )
Question 4
A rec\tangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. Find its volume.
A. 30
B. 40
C. 50
D. 60
Question 5
Find the determinant of the matrix \( egin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix} \).
A. 0
B. 1
C. -1
D. 2
Question 6
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. \( \frac{16pi}{3} \)
B. \( \frac{32pi}{3} \)
C. \( \frac{64pi}{3} \)
D. \( \frac{128pi}{3} \)
Question 7
Determine the value of x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 8
Let X be a random variable with probability density function f(x) = \( egin{cases} 2x, & 0 leq x leq 1 \ 0, & \text{otherwise} \end{cases} \). Find the probability that X is greater than 0.5.
A. 0.25
B. 0.5
C. 0.75
D. 1
Question 9
Find the volume of the solid formed by rotating the area under the curve y = x^2 from x = 0 to x = 2 about the x-axis.
A. \frac{8\pi}{5}
B. \frac{10\pi}{3}
C. \frac{12\pi}{5}
D. \frac{14\pi}{3}
Question 10
Find the volume of the frustum of a cone with height 8 cm, lower base radius 4 cm, and upper base radius 2 cm.
A. 64\pi cm^3
B. 128\pi cm^3
C. 256\pi cm^3
D. 512\pi cm^3
Question 11
In the diagram below, what is the value of x?
A. 30
B. 60
C. 90
D. 120
Question 12
Find the sum of the first 10 terms of the geometric series \( 2x + 3x^2 + 4x^3 + ldots \).
A. 2x + 3x^2 + 4x^3 + ldots + 20x^9
B. 2x + 3x^2 + 4x^3 + ldots + 21x^9
C. 2x + 3x^2 + 4x^3 + ldots + 22x^9
D. 2x + 3x^2 + 4x^3 + ldots + 23x^9
Question 13
Find the equation of the \tangent to the curve y = x^2 - 2x + 1 at the point (1, 0).
A. y = x - 1
B. y = x + 1
C. y = x - 2
D. y = x + 2
Question 14
Solve for x in the equation \( x^2 - 6x + 8 = 0 \).
A. 2
B. 3
C. 4
D. 5
Question 15
Find the derivative of the function ( f(x) = \frac{1}{\sqrt{x}} ) u\sing the chain rule.
A. ( f'(x) = -\frac{1}{2x^{\frac{3}{2}}} )
B. ( f'(x) = -\frac{1}{2x^{\frac{1}{2}}} )
C. ( f'(x) = \frac{1}{2x^{\frac{3}{2}}} )
D. ( f'(x) = \frac{1}{2x^{\frac{1}{2}}} )

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