POST UTME MADONNA UNIVERSITY 2025 Mathematics | Objective

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Question 1
Let A = \{1, 2, 3, 4, 5\} and B = \{2, 3, 5, 6, 7\}. Find the symmetric difference of A and B.
A. \{1, 4, 6, 7\}
B. \{1, 4, 6, 7, 8\}
C. \{1, 4, 6, 7, 8, 9\}
D. \{1, 4, 6, 7, 8, 9, 10\}
Question 2
A sequence is defined by \( a_n = n^2 - 2n + 1 \). Find the sum of the first 5 terms of the sequence.
A. ( 45 )
B. ( 55 )
C. ( 65 )
D. ( 75 )
Question 3
A sequence is defined by \( a_n = 2n + 1 \). Find the sum of the first 5 terms of the sequence.
A. ( 15 )
B. ( 25 )
C. ( 35 )
D. ( 45 )
Question 4
Solve for ( x ) in the equation \( 2^x + 3^x = 5^x \).
A. 1
B. 2
C. 3
D. 4
Question 5
Let ( f(x) = \frac{x^2 - 4}{x - 2} ). Find the derivative of ( f(x) ) u\sing the quotient rule.
A. \frac{2x\( x - 2 \) - \( x^2 - 4 \)}{\( x - 2 \)^2}
B. \frac{2x\( x - 2 \) + \( x^2 - 4 \)}{\( x - 2 \)^2}
C. \frac{2x\( x - 2 \) - \( x^2 - 4 \)}{\( x - 2 \)^2}
D. \frac{2x\( x - 2 \) + \( x^2 - 4 \)}{\( x - 2 \)^2}
Question 6
A random experiment has two indep\endent events, A and B. The probability of event A occurring is 0.4, and the probability of event B occurring is 0.6. What is the probability that both events A and B occur?
A. 0.24
B. 0.24
C. 0.24
D. 0.24
Question 7
Find the sum of the first 10 terms of the geometric series \( 2x^2 + 4x^3 + 8x^4 + ... \).
A. 2x^2\( 1 + 2 + 4 + ... + 512 \)
B. 2x^2\( 1 - 2 + 4 - ... + 512 \)
C. 2x^2\( 1 + 2 + 4 + ... + 512 \)
D. 2x^2\( 1 - 2 + 4 - ... + 512 \)
Question 8
Solve the inequality \( \frac{x - 2}{x + 1} > 0 \).
A. x < -1 or x > 2
B. x < 1 or x > 2
C. x < -1 or x < 2
D. x > -1 or x < 2
Question 9
A vector ( vec{a} ) has a magnitude of 5 and makes an angle of 30° with the positive x-axis. Find the magnitude of the vector \( vec{a} + vec{b} \), where ( vec{b} ) is a vector with a magnitude of 3 and is perp\endicular to ( vec{a} ).
A. 8
B. 6
C. 8
D. 6
Question 10
A fair six-sided die is rolled. What is the probability that the number rolled is a multiple of 3?
A. \frac{1}{2}
B. \frac{1}{3}
C. \frac{2}{3}
D. \frac{4}{5}
Question 11
Solve for ( x ) in the equation \( 2^x = 64 \)
A. \( x = 3 \ \)
B. \( x = 4 \ \)
C. \( x = 5 \ \)
D. \( x = 6 \ \)
Question 12
Find the equation of the circle with center \( C\( -2, 3 \ \) ) and radius \( r = 4 \).
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 13
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 14
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( x < -\frac{5}{4} \) or \( x > \frac{3}{2} \)
B. \( x < -\frac{3}{2} \) or \( x > \frac{5}{4} \)
C. \( x < -\frac{5}{4} \) or \( x < \frac{3}{2} \)
D. \( x > -\frac{5}{4} \) or \( x < \frac{3}{2} \)
Question 15
Find the sum of the infinite geometric series \sum_{n=1}^\infty \frac{2}{3^n}.
A. \frac{2}{3}
B. \frac{4}{3}
C. \frac{6}{3}
D. \frac{8}{3}

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