POST UTME DELSU 2025 Mathematics | Objective

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Question 1
Solve the equation \log_2 \( x + 1 \) = 3.
A. 7
B. 8
C. 9
D. 10
Question 2
A solid sphere of radius 4 cm is inscribed in a cube. Find the volume of the sphere.
A. 268.08 cm^3
B. 268.08 cm^3
C. 268.08 cm^3
D. 268.08 cm^3
Question 3
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 4
Solve the equation [ 2 \sin^2 x + \cos 2x = 1 ] for x in the interval [0, 2π].
A. x = π/4, 3π/4
B. x = π/4, 5π/4
C. x = π/4, 3π/4, 5π/4
D. x = π/4, 3π/4, 5π/4, 7π/4
Question 5
In the diagram below, find the equation of the circle with center ( C(2,3) ) and radius ( 4 ).
A. \( x-2 \ \)^2 + \( y-3 \)^2 = 16 )
B. \( x-2 \ \)^2 + \( y-3 \)^2 = 4 )
C. \( x-3 \ \)^2 + \( y-2 \)^2 = 16 )
D. \( x-3 \ \)^2 + \( y-2 \)^2 = 4 )
Question 6
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. \( x + 3 \)^2 + \( y - 2 \)^2 = 16
D. \( x - 3 \)^2 + \( y + 2 \)^2 = 16
Question 7
Find the area under the curve \( y = x^2 - 4x + 3 \) from \( x = 0 \) to \( x = 2 \).
A. \( \frac{5}{3} \)
B. \( \frac{7}{3} \)
C. \( \frac{9}{3} \)
D. \( \frac{11}{3} \)
Question 8
Find the sum of the first 10 terms of the geometric series \( 2x^2 + 4x^3 + 8x^4 + ldots \).
A. \( 2x^2 left\( \frac{1 - 2^{10} x^{10}}{1 - 2x} \right \ \) )
B. \( 2x^2 left\( \frac{1 - 2^{10} x^{10}}{1 + 2x} \right \ \) )
C. \( 2x^2 left\( \frac{1 - 2^{10} x^{10}}{1 - 2x} \right \ \) + 4x^3 left\( \frac{1 - 2^{10} x^{10}}{1 - 2x} \right \) )
D. \( 2x^2 left\( \frac{1 - 2^{10} x^{10}}{1 + 2x} \right \ \) + 4x^3 left\( \frac{1 - 2^{10} x^{10}}{1 + 2x} \right \) )
Question 9
Find the derivative of the function ( f(x) = \frac{1}{\sqrt{1-x^2}} ) u\sing the chain rule.
A. \( \frac{-x}{\( 1-x^2 \ \)^{3/2}} )
B. \( \frac{x}{\( 1-x^2 \ \)^{3/2}} )
C. \( \frac{1}{\( 1-x^2 \ \)^{3/2}} )
D. \( \frac{-1}{\( 1-x^2 \ \)^{3/2}} )
Question 10
Find the mean deviation of the data set ( 2, 4, 6, 8, 10 ).
A. \( \frac{20}{5} \)
B. \( \frac{40}{5} \)
C. \( \frac{60}{5} \)
D. \( \frac{80}{5} \)
Question 11
Find the value of \sin (2x) given that \sin (x) = 1/2.
A. 1
B. 1/2
C. 1/3
D. 1/4
Question 12
Find the derivative of the function ( f(x) = \frac{x^2 + 2x - 3}{x^2 - 4} ) u\sing the quotient rule.
A. \( \frac{\( x^2 - 4 \)\( 2x + 2 \ \) - \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2} )
B. \( \frac{\( x^2 - 4 \)\( 2x + 2 \ \) + \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2} )
C. \( \frac{\( x^2 - 4 \)\( 2x + 2 \ \) - \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2} )
D. \( \frac{\( x^2 - 4 \)\( 2x + 2 \ \) + \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2} )
Question 13
Find the derivative of the function ( f(x) = \sin^2 x ) u\sing the chain rule.
A. \( 2 \sin x \cos x \)
B. \( 2 \sin x \cos^2 x \)
C. \( 2 \cos x \sin^2 x \)
D. \( 2 \sin^2 x \cos x \)
Question 14
A vector \mathbf{a} has a magnitude of 5 and makes an angle of 30° with the positive x-axis. Find the magnitude of the vector \mathbf{a} + \mathbf{b}, where \mathbf{b} is a unit vector in the direction of the negative y-axis.
A. 5.83
B. 6.07
C. 6.35
D. 6.67
Question 15
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. 0.84
C. 0.95
D. 0.99

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