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POST UTME UNN 2017 Mathematics | Objective

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Question 1 View Details

Let ( f(x) = \(\frac{x^2 - 4}{x^2 - 9}\)\)) ). Find the value of \(f -3 \\\() ). Find the value of (f -3\) ).

Correct A. \(\frac{5}{-18}\)

B. \(\frac{-5}{18}\)

C. \(\frac{5}{18}\)

D. \(\frac{-5}{-18}\)

Correct Answer: A

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Question 2 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 3 View Details

In the diagram below, ( ABC ) is a right-angled triangle with \(AB = 6\) cm and \(BC = 8\) cm. Find the length of the hypotenuse ( AC ).

A. 10

B. 12

C. 14

Correct D. 16

Correct Answer: D

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Question 4 View Details

A sequence is defined by the recurrence relation \(a_n = 2a_{n-1} + 3\) with initial term \(a_1 = 2\). Find the value of \(a_5\).

A. 37

B. 41

C. 45

Correct D. 49

Correct Answer: D

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Question 5 View Details

A random experiment consists of rolling a fair six-sided die. Find the probability that the sum of the numbers on the two dice is greater than 9.

A. \(\frac{1}{6}\)

B. \(\frac{1}{3}\)

C. \(\frac{1}{2}\)

Correct D. \(\frac{2}{3}\)

Correct Answer: D

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Question 6 View Details

Find the equation of the circle with center at (2, 3) and radius 4.

Correct A. \boxed{ x - 2 ^2 + y - \(3 ^2 = 16\)}

B. \(x - 2\)^2 + \(y - 3\)^\(2 = 25\)

C. \(x - 2\)^2 + \(y - 3\)^\(2 = 9\)

D. \(x - 2\)^2 + \(y - 3\)^\(2 = 36\)

Correct Answer: A

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Question 7 View Details

Solve for x in the equation \(\log_{10} x^2\)\(= 4\)\).

Correct A. \boxed{\(x = 10\^2}\)

B. \(x = 10\^4\)

C. \(x = 10\^8\)

D. \(x = 10\^16\)

Correct Answer: A

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Question 8 View Details

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

Correct A. \boxed{f'\((x) =\)\(\frac{-2x}{x^2 + 1\) ^2}\)\)}

B. f'\((x) =\)\(\frac{2x}{x^2 + 1\) ^2}\)\)

C. f'\((x) =\)\(\frac{1}{x^2 + 1\) ^2}\)\)

D. f'\((x) =\)\(\frac{-1}{x^2 + 1\) ^2}\)\)

Correct Answer: A

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Question 9 View Details

A fair six-sided die is rolled. What is the probability that the number rolled is greater than 4?

Correct A. \boxed{\(\frac{1}{3}\)\)}

B. \(\frac{1}{2}\)\)

C. \(\frac{2}{3}\)\)

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

Correct Answer: A

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Question 10 View Details

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

Correct A. \boxed{ -\infty, -1 \cup 3, \infty }

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

C. \(-\infty, -1\) \cup \(1, \infty\)

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

Correct Answer: A

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Question 11 View Details

Solve for x in the equation \(\sin^2 x + \cos^2 x = 1\) using the identity \(\sin^2 x + \cos^2 x = 1\).

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

B. \(x =\)\(\frac{3\pi}{4}\)\)

C. \(x =\)\(\frac{5\pi}{4}\)\)

D. \(x =\)\(\frac{7\pi}{4}\)\)

Correct Answer: A

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Question 12 View Details

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

A. \(\frac{32}{3}\)\)\pi

Correct B. \(\frac{64}{3}\)\)\pi

C. \(\frac{128}{3}\)\)\pi

D. \(\frac{256}{3}\)\)\pi

Correct Answer: B

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Question 13 View Details

Solve the equation \(2^x + 2^{-x} = 10\) for x.

Correct A. \(x =\)\log_2 5

B. \(x =\)\log_2 2

C. \(x =\)\log_2 4

D. \(x =\)\log_2 8

Correct Answer: A

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Question 14 View Details

Find the surface area of the solid formed by revolving the region bounded by the curve (y = \(x^3\)\) and the line \(x = 1\\((y = x^3) and the line\) about the x-axis.

A. 6\sqrt{2}

B. 12\sqrt{2}

Correct C. 24\sqrt{2}

D. 48\sqrt{2}

Correct Answer: C

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Question 15 View Details

Solve the inequality \(\log_2 x > 2\) for x.

A. \(x > 4\)

B. \(x > 8\)

C. \(x > 16\)

Correct D. \(x > 32\)

Correct Answer: D

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Question 16 View Details

Find the mean of the set of numbers: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20.

A. 10

Correct B. 12

C. 14

D. 16

Correct Answer: B

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Question 17 View Details

Solve the inequality: \(2x^2 + 5x - 3 \geq 0\).

Correct A. \(x \leq -3\) or \(x \geq \frac{3}{2}\)

B. \(x \leq -3\) or \(x \geq 1\)

C. \(x \leq 1\) or \(x \geq -3\)

D. \(x \leq -1\) or \(x \geq 3\)

Correct Answer: A

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Question 18 View Details

Find the derivative of the function: \(f(x) = 3x^2 + 2x - 5\).

Correct A. \(f'(x) = 6x + 2\)

B. \(f'(x) = 6x - 2\)

C. \(f'(x) = 3x^2 + 2\)

D. \(f'(x) = 3x^2 - 2\)

Correct Answer: A

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Question 19 View Details

A set of numbers has a mean of 10 and a standard deviation of 2. Find the probability that a randomly selected number from the set is greater than 12.

A. \(PX > 12 = 0\).25 \)

B. \(PX > 12 = 0\).5 \)

Correct C. \(PX > 12 = 0\).75 \)

D. \(PX > 12 = 0\).9 \)

Correct Answer: C

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Question 20 View Details

Solve the quadratic equation: \(x^2 + 4x + 4 = 0\).

Correct A. \(x = -2\)

B. \(x = -1\)

C. \(x = 0\)

D. \(x = 2\)

Correct Answer: A

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Question 21 View Details

A binary operation (\ast\) is defined as: \\((ast\(a ast b = a^2 + b^2\). Find the value of \(2 \\(ast b = a^2 + b^2). Find the value of \ast 3\).

Correct A. 13

B. 15

C. 17

D. 19

Correct Answer: A

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Question 22 View Details

Find the value of (x\) in the equation: \(2x + 5 = 11\\((x) in the equation:\).

A. 2

Correct B. 3

C. 4

D. 5

Correct Answer: B

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Question 23 View Details

A sequence is defined as: (a_\(n = 2n + 1\)\). Find the value of \(a_5\\((a_n = 2n + 1). Find the value of\).

A. 9

Correct B. 11

C. 13

D. 15

Correct Answer: B

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Question 24 View Details

Find the value of (x\) in the equation: \(x^2 - 4x - 3 = 0\\((x) in the equation:\).

A. 3

B. -1

C. 5

D. -3

Correct Answer: VIEW ANSWER

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Question 25 View Details

Find the determinant of the matrix [ egin{array}{ccc} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{array} ] using the expansion by minors method.

Correct A. -120

B. 120

C. -60

D. 60

Correct Answer: A

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