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POST UTME PAN-ATLANTIC UNIVERSITY 2018 Mathematics | Objective

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Question 1 View Details

Find the equation of the circle with center at ((2,3)) and passing through the point ((6,5)).

Correct A. \(x-2 \\)^2 + \(y-3\)^\(2 = 5\) )

B. \(x-2 \\)^2 + \(y-3\)^\(2 = 10\) )

C. \(x-2 \\)^2 + \(y-3\)^\(2 = 15\) )

D. \(x-2 \\)^2 + \(y-3\)^\(2 = 20\) )

Correct Answer: A

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Question 2 View Details

A random variable X has a probability distribution given by \(P X = x \\) = \(\frac{1}\){\(2^{x}}\)\) ) for \(x = 1, 2, 3, ..\).. Find the mean of X.

Correct A. \(\frac{4}{3}\)

B. \(\frac{5}{4}\)

C. \(\frac{6}{5}\)

D. \(\frac{7}{6}\)

Correct Answer: A

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Question 3 View Details

Solve the inequality \(\frac{x^2 - 4}{x^2 - 9} > 0\).

Correct A. x in \( -infty, -3 \ cup (3, infty) )

B. x in \( -infty, -3 \ cup (3, infty) cup (0, 2) )

C. x in \(-\infty, -3 \ cup (3, \infty) cup -2, 0\) )

D. x in \(-\infty, -3 \ cup (3, \infty) cup -2, 0\) cup (2, 4) )

Correct Answer: A

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Question 4 View Details

Find the area under the curve \(y = \frac{1}{x^2 + 1}\) from \(x = 0\) to \(x = 1\).

Correct A. \(\frac{\pi}{4} - 1\)

B. \(\frac{\pi}{4} - \frac{1}{2}\)

C. \(\frac{\pi}{4} - \frac{1}{3}\)

D. \(\frac{\pi}{4} - \frac{1}{4}\)

Correct Answer: A

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Question 5 View Details

A set A contains the elements ( { 1, 2, 3, 4, 5 } ). Find the number of subsets of A that contain exactly two elements.

A. ( 10 )

Correct B. ( 15 )

C. ( 20 )

D. ( 25 )

Correct Answer: B

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Question 6 View Details

A random variable X has a probability distribution given by P(X) = \(1/2\)^\(X-1\) for \(X = 1\), 2, 3, ... . Find the probability that X is greater than 2.

A. \(1/4\)

B. \(1/2\)

Correct C. \(3/4\)

D. 1

Correct Answer: C

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Question 7 View Details

In the diagram below, a circle with center O and radius 6 cm is inscribed in a square. Find the area of the shaded region.

A. 36π

B. 72π

Correct C. 108π

D. 144π

Correct Answer: C

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Question 8 View Details

Solve the equation \(x^2 - 4x - 5 = 0\) using the quadratic formula.

Correct A. \(x = 1\) ± \(√6\)

B. \(x = 2\) ± \(√3\)

C. \(x = 3\) ± \(√2\)

D. \(x = 4\) ± \(√1\)

Correct Answer: A

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Question 9 View Details

A vector ( vec{a} ) has a magnitude of 5 units and makes an angle of 30° with the positive x-axis. Find the x and y components of ( vec{a} ).

Correct A. \(x = 4\), \(y = 4√3\)\)

B. \(x = 3\), \(y = 3√3\)\)

C. \(x = 5\), \(y = 5√3\)\)

D. \(x = 2\), \(y = 2√3\)\)

Correct Answer: A

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Question 10 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. 250π \(cm^3\)

B. 500π \(cm^3\)

Correct C. 750π \(cm^3\)

D. 1000π \(cm^3\)

Correct Answer: C

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Question 11 View Details

Find the volume of the solid formed by revolving the region bounded by the curves \(y = x\^2\), \(y = 0\), and \(x = 2\) about the x-axis.

A. 16\pi

B. 32\pi

Correct C. 64\pi

D. 128\pi

Correct Answer: C

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Question 12 View Details

A box contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is blue?

Correct A. \(1/2\)

B. \(1/3\)

C. \(2/5\)

D. \(3/8\)

Correct Answer: A

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Question 13 View Details

Find the derivative of the function f(x) = \(2x^2 + 3x - 1\) / \(x^2 + 1\) using the quotient rule.

Correct A. \(4x + 3\) / \(x^2 + 1\)^2

B. \(4x^2 + 3x - 1\) / \(x^2 + 1\)^2

C. \(2x^2 + 3x - 1\) / \(x^2 + 1\)^2

D. \(4x^2 + 3x - 1\) / \(x^2 + 1\)^3

Correct Answer: A

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Question 14 View Details

A sequence is defined by the formula \(a_n = 2n + 1\). 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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Question 15 View Details

A set of 3 numbers has a mean of 10 and a median of 8. If the largest number is 12, what is the sum of the 3 numbers?

A. 30

B. 40

Correct C. 50

D. 60

Correct Answer: C

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Question 16 View Details

Find the value of \(\int_0^1 \frac{1}{x^2+4} dx\).

Correct A. \(\frac{\pi}{4}\)\)

B. \(\frac{\pi}{2}\)\)

C. \(\frac{\pi}{3}\)\)

D. \(\frac{\pi}{5}\)\)

Correct Answer: A

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Question 17 View Details

A rectangular box has a length of 5 cm, a width of 3 cm, and a height of 2 cm. Find its volume.

Correct A. 30

B. 40

C. 50

D. 60

Correct Answer: A

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Question 18 View Details

Solve the inequality \(2x^2-5x-3 > 0\).

Correct A. \(-\infty, -1\) \cup \(3, \infty\)

B. \(-\infty, -3\) \cup \(1, \infty\)

C. \(-\infty, -2\) \cup \(2, \infty\)

D. \(-\infty, -4\) \cup \(4, \infty\)

Correct Answer: A

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Question 19 View Details

Find the derivative of \(f(x) = \frac{1}{x^2+1}\).

A. -\(\frac{2x}{x^2+1\) ^2}\)\)

Correct B. \(\frac{2x}{x^2+1\) ^2}\)\)

C. -\(\frac{1}{x^2+1\) ^2}\)\)

D. \(\frac{1}{x^2+1\) ^2}\)\)

Correct Answer: B

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Question 20 View Details

A circle has a radius of 4 cm. Find its area.

Correct A. 16\pi

B. 32\pi

C. 64\pi

D. 128\pi

Correct Answer: A

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Question 21 View Details

Find the derivative of the function ( f(x) = \(\frac{1}\){\sqrt{\(x^2 + 1}}\)\) ) using the chain rule.

Correct A. \(\frac{-x}{x^2 + 1 \\)^{\(3/2\)}} )

B. \(\frac{x}{x^2 + 1 \\)^{\(3/2\)}} )

C. \(\frac{1}{x^2 + 1 \\)^{\(3/2\)}} )

D. \(\frac{-1}{x^2 + 1 \\)^{\(3/2\)}} )

Correct Answer: A

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Question 22 View Details

Solve the inequality \(2x^2 - 5x - 3 > 0\) using the quadratic formula.

Correct 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 \(x < \frac{3}{2}\)

Correct Answer: A

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Question 23 View Details

Find the value of \(\log_{10} 1000 \\) ) using the change of base formula.

A. 3

Correct B. 4

C. 5

D. 6

Correct Answer: B

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Question 24 View Details

A histogram of exam scores has a mean of 70 and a standard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 60 and 80?

A. 0.68

Correct B. 0.84

C. 0.95

D. 0.99

Correct Answer: B

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Question 25 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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