POST UTME JOSEPH AYO BABALOLA UNIVERSITY 2023 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the derivative of the function ( f(x) = \frac{1}{\sqrt{1 + x^2}} ) u\sing the chain rule.
A. f'(x) = \frac{-x}{\( 1 + x^2 \)^{3/2}}
B. f'(x) = \frac{x}{\( 1 + x^2 \)^{3/2}}
C. f'(x) = \frac{1}{\( 1 + x^2 \)^{3/2}}
D. f'(x) = \frac{-1}{\( 1 + x^2 \)^{3/2}}
Question 2
Find the determinant of the matrix \( \begin{bmatrix} 2 & 1 & 3 \ 4 & 2 & 1 \ 3 & 1 & 2 \end{bmatrix} \).
A. 0
B. 1
C. 2
D. 3
Question 3
A random variable X has a probability distribution given by P\( X = 1 \) = 1/4, P\( X = 2 \) = 1/2, P\( X = 3 \) = 1/4. Find the probability that X is greater than 2.
A. 1/2
B. 3/4
C. 1/4
D. 3/8
Question 4
Find the equation of the circle pas\sing through the points (2, 3), (4, 5), and (6, 7).
A. x^2 + y^2 + 4x + 6y - 11 = 0
B. x^2 + y^2 + 2x + 4y - 9 = 0
C. x^2 + y^2 + 6x + 2y - 13 = 0
D. x^2 + y^2 + 8x + 10y - 15 = 0
Question 5
Find the derivative of the function ( f(x) = \frac{1}{x^2} ).
A. f'(x) = \frac{-2}{x^3}
B. f'(x) = \frac{2}{x^3}
C. f'(x) = \frac{-1}{x^3}
D. f'(x) = \frac{1}{x^3}
Question 6
A random variable X has a probability distribution given by ( P(X) = egin{cases} 0.2 & \text{if } X = 1 \ 0.8 & \text{if } X = 2 \ 0 & \text{otherwise} \end{cases} ). Find the probability that X is greater than 1.
A. 0.2
B. 0.8
C. 1
D. 0.6
Question 7
Find the equation of the line pas\sing through the points ( (2, 3) ) and ( (4, 5) ).
A. y = \frac{2}{2}x + \frac{1}{2}
B. y = \frac{1}{2}x + \frac{3}{2}
C. y = 2x - 1
D. y = 2x + 1
Question 8
A circuit consists of a 12V battery, a 4Ω resistor, and a 6Ω resistor connected in series. Find the current flowing through the circuit.
A. 1.5A
B. 2A
C. 2.5A
D. 3A
Question 9
A bag contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is blue?
A. 1/2
B. 1/3
C. 2/5
D. 3/8
Question 10
Find the derivative of the function ( f(x) = \frac{x^2 + 2x - 3}{x^2 - 4} ) u\sing the quotient rule.
A. \frac{2x\( x^2 - 4 \) - \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2}
B. \frac{2x\( x^2 - 4 \) + \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2}
C. \frac{2x\( x^2 - 4 \) - \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2}
D. \frac{2x\( x^2 - 4 \) + \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2}
Question 11
Find the sum of the first 5 terms of the geometric progression ( 2, 6, 18, ... ).
A. 124
B. 126
C. 128
D. 130
Question 12
A vector \( \vec{a} \) has magnitude 5 units and direction 30° north of east. Find the magnitude of the vector \( \vec{a} \) if it is rotated 60° counterclockwise.
A. 5\sqrt{3} units
B. 10 units
C. 5\sqrt{2} units
D. 5 units
Question 13
A circle has a radius of 5 units. Find the area of the circle u\sing the formula \( A = \pi r^2 \).
A. 25\pi
B. 50\pi
C. 75\pi
D. 100\pi
Question 14
Solve the equation \( \sin^2 x + \cos^2 x = 1 \).
A. \( \sin x = \cos x \)
B. \( \sin x = -\cos x \)
C. \( \cos x = -\sin x \)
D. \( \cos x = \sin x \)
Question 15
In a binary number system, what is the value of the digit in the 5th position from the right in the number 1011011101?
A. 1
B. 0
C. 1
D. 2

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