POST UTME JOSEPH AYO BABALOLA UNIVERSITY 2021 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve for x in the equation 2^x + 2^x + 2^x = 3^x.
A. 2
B. 3
C. 4
D. 5
Question 2
Solve the equation \frac{1}{x + 1} + \frac{1}{x - 1} = \frac{1}{x^2 - 1}.
A. x = 2
B. x = -2
C. x = 1
D. x = -1
Question 3
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( -∞, -1 \) ∪ (3, ∞)
B. \( -∞, -3 \) ∪ (1, ∞)
C. \( -∞, 1 \) ∪ (3, ∞)
D. \( -∞, -3 \) ∪ (1, ∞)
Question 4
Find the area under the curve y = x^2 + 2x - 3 from x = 0 to x = 3.
A. 27
B. 30
C. 33
D. 36
Question 5
Solve the differential equation \frac{dy}{dx} = \frac{y}{x} + \frac{1}{x^2} with the initial condition y(1) = 1.
A. y = \frac{1}{x} + \frac{1}{x^2}
B. y = \frac{1}{x} - \frac{1}{x^2}
C. y = \frac{1}{x^2} + \frac{1}{x}
D. y = \frac{1}{x} + \frac{1}{x^3}
Question 6
Given the vectors θ = 2i + 3j and β = i - 2j, find the magnitude of the vector θ + β.
A. 3.60555
B. 4.47214
C. 5.38516
D. 6.40312
Question 7
Find the sum of the infinite geometric series 1 + 2x + 4x^2 + 8x^3 + ...
A. 1/\( 1-2x \)
B. 1/\( 1+x \)
C. 1/\( 1-2x \)^2
D. 1/\( 1+x \)^2
Question 8
Find the equation of the line pas\sing through the points (2,3) and (4,5).
A. y = x + 1
B. y = x - 1
C. y = 2x - 3
D. y = 2x + 3
Question 9
A box 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. 2/3
C. 3/4
D. 4/5
Question 10
Solve the inequality \( \frac{x^2 - 4}{x + 2} geq 0 \) for ( x in mathbb{R} ).
A. \( -∞, -2 \) ∪ [0, ∞)
B. \( -∞, -2 \) ∪ (0, ∞)
C. \( -∞, -2 \) ∪ [0, 2]
D. \( -∞, 2 \)
Question 11
Find the derivative of the function ( f(x) = 3x^2 \sin (2x) ) u\sing the product rule.
A. 6x^2 \sin (2x) + 12x \cos (2x)
B. 6x \sin (2x) + 12x^2 \cos (2x)
C. 6x^2 \cos (2x) - 12x \sin (2x)
D. 6x \cos (2x) - 12x^2 \sin (2x)
Question 12
Find the area under the curve y = x^3 from x = 0 to x = 2.
A. 8
B. 16
C. 32
D. 64
Question 13
Solve for x in the equation 2^x + 3^x = 5^x.
A. 1
B. 2
C. 3
D. 4
Question 14
A particle moves along the x-axis with its position given by the equation \( x(t) = 2t^2 - 5t + 1 \). Find the velocity of the particle at time t = 3.
A. v(3) = 7
B. v(3) = -7
C. v(3) = 14
D. v(3) = -14
Question 15
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. 16\pi
B. 32\pi
C. 64\pi
D. 128\pi

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