POST UTME BELLS UNIVERSITY 2021 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A bakery sells 250 loaves of bread per day. If they make a profit of ₦5 per loaf, how much profit do they make in a day?
A. ₦1250
B. ₦12500
C. ₦125000
D. ₦1250000
Question 2
Find the magnitude of the vector \( \vec{a} = \begin{pmatrix} 3 \ 4 \end{pmatrix} \) and the angle it makes with the x-axis.
A. 5, \tan^{-1} \frac{4}{3}
B. 5, \tan^{-1} \frac{3}{4}
C. 7, \tan^{-1} \frac{4}{3}
D. 7, \tan^{-1} \frac{3}{4}
Question 3
Find the equation of the circle with center at ((2,3)) and radius 4.
A. \( x-2 \ \)^2 + \( y-3 \)^2 = 16 )
B. \( x-3 \ \)^2 + \( y-2 \)^2 = 16 )
C. \( x+2 \ \)^2 + \( y-3 \)^2 = 16 )
D. \( x-2 \ \)^2 + \( y+3 \)^2 = 16 )
Question 4
Solve the equation \( \sin^2 x + \cos^2 x = 1 \) for x.
A. \sin x = \cos x
B. \sin x = -\cos x
C. \cos x = \sin x
D. \cos x = -\sin x
Question 5
Find the sum of the first 10 terms of the geometric series 2, 6, 18, ...
A. 121
B. 123
C. 125
D. 127
Question 6
Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} \) u\sing the chain rule.
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 7
Solve the system of equations \begin{align*} x + y &= 3 \ x - y &= 1 \end{align*}.
A. x = 2, y = 1
B. x = 1, y = 2
C. x = 2, y = 2
D. x = 1, y = 1
Question 8
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 9
Solve for (x) in the equation \( 2^x + 2^{x+1} = 3 cdot 2^x \).
A. \( x = 2 \)
B. \( x = 1 \)
C. \( x = 0 \)
D. \( x = -1 \)
Question 10
Determine the value of x in the equation \( \frac{x}{2} + \frac{3}{4} = \frac{7}{8} \).
A. 1
B. 2
C. 3
D. 4
Question 11
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 12
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. 24\pi cm^3
B. 30\pi cm^3
C. 36\pi cm^3
D. 48\pi cm^3
Question 13
Find the volume of the cylinder with radius 6 cm and height 10 cm.
A. \( 180 \pi \) cm³
B. \( 360 \pi \) cm³
C. \( 600 \pi \) cm³
D. \( 1200 \pi \) cm³
Question 14
Find the derivative of the function y = x^4 - 2x^2 + 1.
A. 4x^3 - 4x
B. 2x^3 - 2x
C. x^3 - x
D. x^2 - 1
Question 15
Solve the matrix equation \( \begin{bmatrix} 2 & 1 \ 1 & 3 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 3 \ 7 \end{bmatrix} \).
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}

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