POST UTME AFE BABALOLA 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 8cm, lower base radius 4cm, and upper base radius 2cm.
A. 64\pi cm^3
B. 128\pi cm^3
C. 256\pi cm^3
D. 512\pi cm^3
Question 2
Find the area under the curve \( y = \sin x \) from \( x = 0 \) to \( x = \frac{pi}{2} \).
A. \( \frac{1}{2} \)
B. \( \frac{pi}{2} \)
C. \( \frac{1}{2} pi \)
D. \( \frac{2}{pi} \)
Question 3
Two events, A and B, are indep\endent. If P(A) = 0.4 and P(B) = 0.6, what is P(A and B)?
A. 0.2
B. 0.4
C. 0.6
D. 0.8
Question 4
A polynomial $p(x)$ has degree $n$ and has roots $r_1, r_2, \dots, r_n$. If $p(x) = \( x - r_1 \)\( x - r_2 \) \dots \( x - r_n \)$, find the coefficient of the $x^{n-1}$ term.
A. -r_1 - r_2 - \dots - r_n
B. r_1r_2 + r_2r_3 + \dots + r_{n-1}r_n
C. r_1 + r_2 + \dots + r_n
D. -r_1r_2r_3 \dots r_n
Question 5
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 6
Find the value of \(\sin 2\theta\) if \(\sin \theta = \frac{3}{5}\).
A. \frac{3}{5}
B. \frac{4}{5}
C. \frac{6}{5}
D. \frac{12}{5}
Question 7
Find the volume of the solid formed by revolving the region bounded by the curves \( y = x^2 \) and \( y = 2x \) about the x-axis.
A. \frac{28\pi}{3}
B. \frac{32\pi}{3}
C. \frac{40\pi}{3}
D. \frac{48\pi}{3}
Question 8
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. 0.68
B. 0.80
C. 0.90
D. 0.95
Question 9
Simplify the expression \( 2x^2 + 3x - 1 \)^2 \) u\sing the binomial theorem.
A. \( 4x^4 + 12x^3 - 9x^2 - 6x + 1 \)
B. \( 4x^4 + 12x^3 - 9x^2 + 6x + 1 \)
C. \( 4x^4 + 12x^3 + 9x^2 - 6x + 1 \)
D. \( 4x^4 + 12x^3 + 9x^2 + 6x + 1 \)
Question 10
A sequence $a_n$ is defined by $a_n = 2^n + 3^n$. Find the sum of the first $n$ terms of the sequence.
A. 2^n\( 2^n - 1 \)
B. 3^n\( 3^n - 1 \)
C. 2^n + 3^n
D. n\( 2^n + 3^n \)
Question 11
Let $S_n = 1 + 2 + 3 + \cdots + n$. Find the value of $S_{10}$.
A. 55
B. 65
C. 75
D. 85
Question 12
Find the derivative of the function ( f(x) = \sin^2 x ) u\sing the chain rule.
A. f'(x) = 2 \sin x \cos x
B. f'(x) = 2 \sin x \cos x + \sin^2 x
C. f'(x) = 2 \sin x \cos x - \sin^2 x
D. f'(x) = 2 \sin x \cos x - 2 \sin^2 x
Question 13
Solve the system of equations \( x + y = 2 \) and \( xy = 1 \) u\sing substitution.
A. x = 1, y = 1
B. x = 1, y = -1
C. x = -1, y = 1
D. x = -1, y = -1
Question 14
Solve the equation \sin^2 x + \cos^2 x = 1 for x in the interval [0, 2\pi].
A. 0
B. \frac{\pi}{4}
C. \frac{\pi}{2}
D. \pi
Question 15
Find the determinant of the matrix \( egin{bmatrix} 2 & 3 \ 4 & 5 \end{bmatrix} \).
A. ( 1 )
B. ( 2 )
C. ( 3 )
D. ( 4 )

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