POST UTME COAL CITY UNIVERSITY 2018 Mathematics | Objective

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Question 1 View Details
Let X be a random variable with probability density function ( f(x) = egin{cases} 2x, & 0 leq x leq 1 \ 0, & \text{otherwise} \end{cases} ). Find the probability that X is greater than 0.5.
A. \(\frac{1}{2}\)
Correct B. \(\frac{3}{4}\)
C. \(\frac{1}{4}\)
D. \(\frac{3}{8}\)

Correct Answer: B

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Question 2 View Details
Find the area under the curve \(y = \sin^2 x\) from \(x = 0\) to \(x = \frac{\pi}{2}\).
Correct A. \(\frac{1}{2}\)
B. \(\frac{\pi}{4}\)
C. \(\frac{\pi}{2}\)
D. \(\frac{3\pi}{4}\)

Correct Answer: A

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Question 3 View Details
Solve the equation \(\(12x =\)1x\) for ( 0 leq x leq 2pi ).
A. \(x = \frac{\pi}{6}\)
B. \(x = \frac{\pi}{4}\)
Correct C. \(x = \frac{\pi}{3}\)
D. \(x = \frac{\pi}{2}\)

Correct Answer: C

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Question 4 View Details
A right circular cone has a height of 10 cm and a base radius of 5 cm. Find the volume of the cone.
A. ( 100pi ) \(cm^3\)
B. ( 200pi ) \(cm^3\)
Correct C. ( 300pi ) \(cm^3\)
D. ( 400pi ) \(cm^3\)

Correct Answer: C

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Question 5 View Details
A histogram of exam scores has a mean of 60 and a standard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is greater than 70?
A. \(\frac{1}{4}\)
B. \(\frac{1}{2}\)
Correct C. \(\frac{3}{4}\)
D. \(\frac{3}{5}\)

Correct Answer: C

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Question 6 View Details
Find the derivative of the function ( f(x) = \(\frac{x^2}{x\)^2 + 1}\)\) ) using the chain rule.
Correct A. ( f'\((x) =\)\(\frac{2x x^2 + 1 - x^2(2x)}{\) \(x^2 + 1\) ^2}\)\) )
B. ( f'\((x) =\)\(\frac{2x}{x^2 + 1\) ^2}\)\) )
C. ( f'\((x) =\)\(\frac{2x^2}{\) \(x^2 + 1\) ^2}\)\) )
D. ( f'\((x) =\)\(\frac{2x^3}{\) \(x^2 + 1\) ^2}\)\) )

Correct Answer: A

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Question 7 View Details
Solve the matrix equation \(egin{bmatrix} 2 & 1 \ 1 & 2 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 3 \ 4 \end{bmatrix}\).
A. \(x = 1, y = 2\)
Correct B. \(x = 2, y = 1\)
C. \(x = 1, y = 1\)
D. \(x = 2, y = 2\)

Correct Answer: B

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Question 8 View Details
Find the mean and standard deviation of the data set ( { 2, 4, 6, 8, 10 } ).
Correct A. Mean: 6, Standard Deviation: 2
B. Mean: 5, Standard Deviation: 2
C. Mean: 6, Standard Deviation: 3
D. Mean: 5, Standard Deviation: 3

Correct Answer: A

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Question 9 View Details
Solve the trigonometric equation \(\sin^2 x + \cos^2 x = 1\) for ( x ) in the interval ( [0, 2pi] ).
Correct A. \(x = \frac{\pi}{4}, \frac{3\pi}{4}\)
B. \(x = \frac{\pi}{4}, \frac{5\pi}{4}\)
C. \(x = \frac{\pi}{4}, \frac{7\pi}{4}\)
D. \(x = \frac{\pi}{4}, \frac{9\pi}{4}\)

Correct Answer: A

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Question 10 View Details
Find the derivative of the function ( f(x) = \(\frac{1}{x^2 + 1}\)\)\) ) using the chain rule.
A. ( f'\((x) =\)\(\frac{-2x}{x^2 + 1\) ^2}\)\) )
Correct B. ( f'\((x) =\)\(\frac{2x}{x^2 + 1\) ^2}\)\) )
C. ( f'\((x) =\)\(\frac{-2}{x^2 + 1\) ^2}\)\) )
D. ( f'\((x) =\)\(\frac{2}{x^2 + 1\) ^2}\)\) )

Correct Answer: B

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Question 11 View Details
Determine the value of x in the equation \(\sin^2 x \\) + \\(\cos^2(x)\) = 1 ) if \($1x \\) = \(\frac{3}{4}\)\) ).
Correct A. \(\frac{\pi}{4}\)\)
B. \(\frac{3\pi}{4}\)\)
C. \(\frac{5\pi}{4}\)\)
D. \(\frac{7\pi}{4}\)\)

Correct Answer: A

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Question 12 View Details
A histogram of exam scores for a class of 100 students is shown below. What is the mean score?
A. 60
B. 70
Correct C. 80
D. 90

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 P(A and B)?
Correct A. 0.2
B. 0.4
C. 0.6
D. 0.8

Correct Answer: A

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Question 14 View Details
Find the magnitude of the vector \(egin{pmatrix} 3 \ 4 \ 0 \end{pmatrix}\).
A. 5
B. \(\sqrt{5}\)
Correct C. \(\sqrt{29}\)
D. \(\sqrt{41}\)

Correct Answer: C

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Question 15 View Details
Solve the equation \(x^2 + 6x + 8 = 0\) using the quadratic formula.
Correct A. \(\frac{-6 \pm \sqrt{6^2 - 4(1)(8)}\)\)}{2(1)}\)
B. \(\frac{-6 \pm \sqrt{6^2 - 4(1)(8)}\)\)}{2(1)}\)
C. \(\frac{-6 \pm \sqrt{6^2 - 4(1)(8)}\)\)}{2(1)}\)
D. \(\frac{-6 \pm \sqrt{6^2 - 4(1)(8)}\)\)}{2(1)}\)

Correct Answer: A

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