POST UTME VERITAS UNIVERSITY 2020 Mathematics | Objective

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Question 1
In a right-angled triangle, the length of the hypotenuse is 10 cm and one of the acute angles is 30°. What is the length of the side opposite the 30° angle?
A. 5
B. 5√3
C. 10
D. 10√3
Question 2
A sequence is defined by \( a_n = 2n^2 + 3n - 1 \). Find the sum of the first 5 terms of the sequence.
A. 45
B. 55
C. 65
D. 75
Question 3
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 4
Determine the value of ( x ) in the equation: \( \log_{10} \( x^2 \ \) = 4 ).
A. \( x = 10^2 \)
B. \( x = 10^4 \)
C. \( x = 10^{-2} \)
D. \( x = 10^{-4} \)
Question 5
Find the equation of the \tangent line to the curve \( y = \frac{1}{x} \) at the point where \( x = 2 \).
A. \( y = -\frac{1}{2}x + 1 \)
B. \( y = \frac{1}{2}x - 1 \)
C. \( y = -\frac{1}{2}x - 1 \)
D. \( y = \frac{1}{2}x + 1 \)
Question 6
Evaluate the definite integral: \( int_{0}^{1} x^2 \sin x , dx \).
A. \( -\cos x + \frac{1}{3} \sin x \)
B. \( \cos x + \frac{1}{3} \sin x \)
C. \( -\cos x - \frac{1}{3} \sin x \)
D. \( \cos x - \frac{1}{3} \sin x \)
Question 7
Determine the value of the infinite geometric series: \( \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + cdots \).
A. 1
B. \frac{1}{2}
C. \frac{1}{4}
D. \frac{1}{8}
Question 8
In a set of consecutive integers, the sum of the first 7 terms is 196. Find the sum of the next 7 terms.
A. 196
B. 196 + 7
C. 196 + 14
D. 196 + 21
Question 9
A company produces two products, A and B. The profit from the sale of product A is $10 per unit, and the profit from the sale of product B is $15 per unit. If the company produces 100 units of product A and 50 units of product B, what is the total profit?
A. $1500
B. $2500
C. $3500
D. $4500
Question 10
Find the area under the curve: \( y = x^2 \sin x \) from \( x = 0 \) to \( x = pi \).
A. \( -\frac{1}{3} pi^3 \)
B. \( \frac{1}{3} pi^3 \)
C. \( -\frac{1}{2} pi^3 \)
D. \( \frac{1}{2} pi^3 \)
Question 11
A histogram of exam scores is shown below. If the mean score is 60 and the s\tandard deviation is 10, what is the probability that a randomly selected student scored above 70?
A. 0.25
B. 0.5
C. 0.75
D. 0.9
Question 12
A probability experiment consists of rolling a fair six-sided die. Find the probability that the number rolled is greater than 4.
A. \frac{1}{6}
B. \frac{1}{3}
C. \frac{2}{3}
D. \frac{5}{6}
Question 13
Solve the quadratic equation x^2 + 4x + 4 = 0.
A. \\begin{pmatrix} -2 \\ 2 \\end{pmatrix}
B. \\begin{pmatrix} -1 \\ 1 \\end{pmatrix}
C. \\begin{pmatrix} 1 \\ -1 \\end{pmatrix}
D. \\begin{pmatrix} 2 \\ -2 \\end{pmatrix}
Question 14
A set of 5 numbers has a mean of 10 and a median of 8. Find the sum of the 5 numbers.
A. 50
B. 60
C. 70
D. 80
Question 15
Solve the inequality: \( 2x^2 + 5x - 3 > 0 \).
A. \( x < -1 \) or \( x > \frac{3}{2} \)
B. \( x < -\frac{1}{2} \) or \( x > 3 \)
C. \( x < -3 \) or \( x > \frac{1}{2} \)
D. \( x < -\frac{3}{2} \) or \( x > 1 \)

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