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POST UTME ELIZADE UNIVERSITY 2018 Mathematics | Objective

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Question 1 View Details

A rectangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. Find the volume of the prism in cubic centimeters.

Correct A. 30

B. 60

C. 90

D. 120

Correct Answer: A

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Question 2 View Details

Find the surface area of the sphere with a radius of 4 cm.

A. 201.06

Correct B. 314.16

C. 502.65

D. 804.25

Correct Answer: B

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Question 3 View Details

A vector \overrightarrow{a} has a magnitude of 5 units and makes an angle of 60° with the positive x-axis. Find the x-component of the vector.

Correct A. 2.5

B. 3.75

C. 4.33

D. 5.00

Correct Answer: A

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Question 4 View Details

Two events, A and B, are independent. The probability of event A occurring is 0.4, and the probability of event B occurring is 0.6. Find the probability that both events occur.

Correct A. 0.24

B. 0.36

C. 0.48

D. 0.60

Correct Answer: A

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Question 5 View Details

Find the determinant of the matrix \begin{bmatrix} 2 & 3 \ 4 & 5 \end{bmatrix}.

Correct A. 1

B. 2

C. 3

D. 4

Correct Answer: A

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Question 6 View Details

Let A be a 3x3 matrix with determinant 6. If A is multiplied by a scalar k, what is the determinant of kA?

Correct A. 6k

B. \(k^3\)

C. \(6k^3\)

D. \(k^2\)

Correct Answer: A

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Question 7 View Details

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

A. \(-3, -2\) \cup (2, 3)

B. \(-3, -2\) \cup \(2, \infty\)

Correct C. \(-\infty, -3\) \cup \(-2, 2\) \cup \(3, \infty\)

D. \(-\infty, -3\) \cup \(-2, 2\) \cup \(3, \infty\)

Correct Answer: C

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Question 8 View Details

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

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

B. \(x - 2\)^2 + \(y - 3\)^\(2 = 4\)

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

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

Correct Answer: A

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Question 9 View Details

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

A. \(x =\)\pm 10

Correct B. \(x =\)\pm 100

C. \(x =\)\pm 1000

D. \(x =\)\pm 10000

Correct Answer: B

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Question 10 View Details

Find the value of x in the equation \(\frac{1}{x}\)\) + \(\frac{1}{x + 2}\)\) = \(\frac{1}{2}\)\).

Correct A. \(x = -1\)

B. \(x = 1\)

C. \(x = 2\)

D. \(x = 3\)

Correct Answer: A

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Question 11 View Details

Find the area under the curve \(y = \frac{1}{2}x^2 + 3x - 2\) from \(x = 0\) to \(x = 4\).

A. 64

B. 80

Correct C. 96

D. 112

Correct Answer: C

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Question 12 View Details

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

Correct A. \(-∞, -1\) ∪ (3, ∞)

B. \(-∞, -3\) ∪ (1, ∞)

C. \(-∞, 1\) ∪ (3, ∞)

D. \(-∞, -3\) ∪ (1, ∞)

Correct Answer: A

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Question 13 View Details

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

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

B. \(x - 3\)^2 + \(y - 2\)^\(2 = 16\)

C. \(x + 2\)^2 + \(y - 3\)^\(2 = 16\)

D. \(x - 2\)^2 + \(y + 3\)^\(2 = 16\)

Correct Answer: A

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Question 14 View Details

A bag 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. \(3/8\)

B. \(1/2\)

C. \(3/5\)

D. \(5/8\)

Correct Answer: A

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Question 15 View Details

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

Correct A. \(x = -2\)

B. \(x = -1\)

C. \(x = 0\)

D. \(x = 1\)

Correct Answer: A

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Question 16 View Details

Find the value of x in the equation \(\log_{10} x^2 \\)\(= 4 ).\)

A. 10

B. 100

C. 1000

Correct D. 10000

Correct Answer: D

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Question 17 View Details

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

Correct A. \(-∞, -1\) ∪ (3, ∞)

B. \(-∞, 1\) ∪ (3, ∞)

C. \(-∞, -1\) ∪ (1, ∞)

D. \(-∞, 3\) ∪ (1, ∞)

Correct Answer: A

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Question 18 View Details

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

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

B. \(x - 2\)^2 + \(y + 3\)^\(2 = 16\)

C. \(x + 2\)^2 + \(y + 3\)^\(2 = 16\)

D. \(x - 2\)^2 + \(y - 3\)^\(2 = 16\)

Correct Answer: A

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Question 19 View Details

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

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

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

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

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

Correct Answer: A

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Question 20 View Details

Solve the system of equations \(x + y = 4\) and \(x - y = 2\).

Correct A. \(x = 3\), \(y = 1\)

B. \(x = 1\), \(y = 3\)

C. \(x = 2\), \(y = 2\)

D. \(x = 4\), \(y = 0\)

Correct Answer: A

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Question 21 View Details

Find the area under the curve \(y = \frac{1}{2}x^2 + 3x - 2\) from \(x = 0\) to \(x = 4\).

A. 40

B. 50

Correct C. 60

D. 70

Correct Answer: C

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Question 22 View Details

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

A. 13

B. 14

Correct C. 15

D. 16

Correct Answer: C

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Question 23 View Details

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

Correct A. \(-∞, -1\) ∪ (3, ∞)

B. \(-∞, 1\) ∪ (3, ∞)

C. \(-∞, -1\) ∪ (1, ∞)

D. \(-∞, 1\) ∪ (3, ∞)

Correct Answer: A

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Question 24 View Details

A random experiment consists of rolling a fair six-sided die. If the number rolled is even, the experimenter wins. If the number rolled is odd, the experimenter loses. Find the probability of winning.

Correct A. \(1/2\)

B. \(1/3\)

C. \(2/3\)

D. \(3/4\)

Correct Answer: A

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Question 25 View Details

Find the value of ( x ) in the equation \(2x^2 + 5x - 3 = 0\).

A. 1

Correct B. -1

C. 2

D. -2

Correct Answer: B

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