POST UTME OAU 2017 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the value of ( x ) in the equation \( 2^x + 5^x = 3^x \).
A. 1
B. 2
C. 3
D. 4
Question 2
In the diagram below, the equation of the circle is given by \( x - 2 \ \)^2 + \( y - 3 \)^2 = 4 ). If the line \( y = x + 1 \) intersects the circle at two points, find the dis\tance between these two points.
A. 2√5
B. 2√3
C. 4√3
D. 4√5
Question 3
Solve the quadratic equation \( x^2 + 4x + 4 = 0 \).
A. x = -2
B. x = -1
C. x = 0
D. x = 1
Question 4
Determine the sum of the infinite geometric series ∫_{n=1}^{infty} \frac{1}{2^{n-1}}
A. 1
B. 2
C. 3
D. 4
Question 5
Solve the system of equations u\sing substitution: \( x + y = 4 \) and \( 2x - y = 2 \).
A. \( x = 2, y = 2 \)
B. \( x = 3, y = 1 \)
C. \( x = 1, y = 3 \)
D. \( x = 2, y = 3 \)
Question 6
Solve the inequality 2x^2 + 5x - 3 > 0
A. \( -\infty, -\frac{3}{2} \) \cup \( \frac{1}{2}, \infty \)
B. \( -\infty, -\frac{3}{2} \) \cup \( -\frac{1}{2}, \infty \)
C. \( -\infty, -\frac{1}{2} \) \cup \( \frac{3}{2}, \infty \)
D. \( -\infty, \frac{1}{2} \) \cup \( \frac{3}{2}, \infty \)
Question 7
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 8
Solve the matrix equation \( egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 5 \ 6 \end{bmatrix} \).
A. \( x = 1, y = 2 \)
B. \( x = 2, y = 1 \)
C. \( x = 3, y = 4 \)
D. \( x = 4, y = 3 \)
Question 9
Find the volume of the solid formed by revolving the region bounded by y = x^2, y = 0, and x = 2 about the x-axis
A. \frac{32}{3}\pi
B. \frac{64}{3}\pi
C. \frac{128}{3}\pi
D. \frac{256}{3}\pi
Question 10
Find the determinant of the matrix \( egin{bmatrix} 2 & 3 \ 4 & 5 \end{bmatrix} \).
A. -1
B. 1
C. 2
D. 3
Question 11
Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} ) u\sing the chain rule.
A. ( f'(x) = \frac{-2x}{\( x^2 + 1 \)^2} )
B. ( f'(x) = \frac{2x}{\( x^2 + 1 \)^2} )
C. ( f'(x) = \frac{-x}{\( x^2 + 1 \)^2} )
D. ( f'(x) = \frac{x}{\( x^2 + 1 \)^2} )
Question 12
A polynomial function ( f(x) ) is defined by ( f(x) = ax^3 + bx^2 + cx + d ). If ( f(1) = 4 ), \( f\( -1 \ \) = -4 ), and ( f(0) = 2 ), find the value of \( a + b + c + d \).
A. 4
B. 6
C. 8
D. 10
Question 13
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( x < -1 \) or \( x > \frac{3}{2} \)
B. \( x < -1 \) or \( x < \frac{3}{2} \)
C. \( x > -1 \) or \( x < \frac{3}{2} \)
D. \( x < -1 \) or \( x > \frac{3}{2} \)
Question 14
Find the sum of the first 5 terms of the geometric progression 2, 6, 18, ...
A. 124
B. 126
C. 128
D. 130
Question 15
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 )

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