POST UTME VERITAS UNIVERSITY 2023 Mathematics | Objective

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Question 1 View Details
A random sample of 25 students from a university had a mean height of 175 cm with a standard deviation of 5 cm. If the population standard deviation is unknown, calculate the 95% confidence interval for the population mean.
Correct A. 170.35 cm, 179.65 cm
B. 170.15 cm, 179.85 cm
C. 170.25 cm, 179.75 cm
D. 170.45 cm, 179.55 cm

Correct Answer: A

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Question 2 View Details
Find the volume of the solid formed by revolving the region bounded by the parabola (y = x\^2\), the x-axis, and the line \\((y = x^2\(x = 2\) about the x-axis.
Correct A. 32\\(\pi/5\)
B. 16\\(\pi/3\)
C. 32\\(\pi/3\)
D. 16\\(\pi/5\)

Correct Answer: A

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Question 3 View Details
A particle moves along the x-axis with a velocity given by v(t) = \((2t^2 - 5t + 3\)\). Find the position of the particle at \(t = 3\\((2t^2 - 5t + 3). Find the position of the particle at\) seconds, given that the initial position is 2 meters.
A. 13
B. 14
Correct C. 15
D. 16

Correct Answer: C

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Question 4 View Details
Find the area of the region bounded by the curve (y = x\^3 - \(6x^2 + 9x + 2\)\), the x-axis, and the lines \\((y = x^3 - 6x^2 + 9x + 2\(x = 1\) and \(x = 4\).
A. 20
B. 30
Correct C. 40
D. 50

Correct Answer: C

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Question 5 View Details
A circle has a radius of 4 cm. Find the area of the sector formed by the central angle of 60 degrees.
Correct A. 8\\(\pi/3\)
B. 16\\(\pi/3\)
C. 32\\(\pi/3\)
D. 64\\(\pi/3\)

Correct Answer: A

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Question 6 View Details
Find the equation of the line passing through the points ( (2,3) ) and ( (4,5) ).
Correct A. \(y = x + 1\)
B. \(y = x - 1\)
C. \(y = -x + 1\)
D. \(y = x - 2\)

Correct Answer: A

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Question 7 View Details
A histogram of exam scores is shown below. What is the mean score?
A. 40
Correct B. 50
C. 60
D. 70

Correct Answer: B

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Question 8 View Details
Solve for ( x ) in the equation \(2^x + 5^x = 7^x\).
A. \(x = 2\)
B. \(x = 3\)
Correct C. \(x = 4\)
D. \(x = 5\)

Correct Answer: C

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Question 9 View Details
Find the determinant of the matrix \(egin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix}\).
Correct A. 0
B. 1
C. 2
D. 3

Correct Answer: A

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Question 10 View Details
A circle with center ( (0,0) ) and radius 5 passes through the point ( (3,4) ). Find the equation of the circle.
Correct A. \(x^2 + y^2 = 25\)
B. \(x^2 + y^2 = 16\)
C. \(x^2 + y^2 = 9\)
D. \(x^2 + y^2 = 4\)

Correct Answer: A

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Question 11 View Details
Let ( f(x) = \(\frac{x^2 - 4}{x - 2}\)\)\) ). Find the derivative of ( f(x) ) using the quotient rule.
Correct A. ( f'\((x) =\)\(\frac{2x x - 2 - x^2 - 4\) }{ x - 2 ^2}\)\) \)
B. ( f'\((x) =\)\(\frac{x^2 - 4}{\) x - 2 ^2}\)\) \)
C. ( f'\((x) =\)\(\frac{2x}{x - 2}\)\) \)
D. ( f'\((x) =\)\(\frac{x^2 - 4}{x}\)\)\) \)

Correct Answer: A

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Question 12 View Details
A histogram of exam scores is shown below. If the mean score is 75, and the standard deviation is 10, what is the probability that a randomly selected student scored above 85?
A. 0.25
B. 0.30
Correct C. 0.35
D. 0.40

Correct Answer: C

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Question 13 View Details
Two events, A and B, are independent. If P(A) = 0.4 and P(B) = 0.6, what is the probability that both events occur?
A. 0.12
Correct B. 0.24
C. 0.36
D. 0.48

Correct Answer: B

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Question 14 View Details
Solve the equation \(2^x + 3^x = 5^x\) for x.
A. \(x = 2\)
B. \(x = 3\)
Correct C. \(x = 4\)
D. \(x = 5\)

Correct Answer: C

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Question 15 View Details
A sequence is defined as \(a_n = 2n + 1\). Find the sum of the first 5 terms of the sequence.
A. 15
B. 25
Correct C. 35
D. 45

Correct Answer: C

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