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POST UTME AL-HIKMAH UNIVERSITY 2023 Mathematics | Objective

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Question 1 View Details

Find the value of x in the equation \(\frac{1}{2}x^2 + 5x - 3 = 0\)

A. 1

Correct B. -2

C. 3

D. -3

Correct Answer: B

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Question 2 View Details

Solve for y: \(\sin^2 y + \cos^2 y = 1\)

A. 0

Correct B. π/2

C. π

D. 3π/2

Correct Answer: B

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Question 3 View Details

Find the derivative of ( f(x) = \(3x^2 - 2x + 1\) )

Correct A. 6x - 2

B. 6x + 2

C. \(3x^2 - 2\)

D. \(3x^2 + 2\)

Correct Answer: A

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Question 4 View Details

A rectangular prism 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 5 View Details

Solve for x: \(2^x = 16\)

A. 2

Correct B. 3

C. 4

D. 5

Correct Answer: B

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Question 6 View Details

Find the determinant of the matrix [ egin{pmatrix} 2 & 3 & 1 \ 4 & 5 & 2 \ 1 & 2 & 3 \end{pmatrix} ].

Correct A. -1

B. 1

C. 2

D. 3

Correct Answer: A

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Question 7 View Details

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

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

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

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

D. \(-3, -1\) \cup (1, 3) \cup \(-\infty, -3\) \cup \(3, \infty\) \cup (0, 1)

Correct Answer: B

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Question 8 View Details

Find the equation of the line passing through the points (2, 3) and (4, 5).

Correct A. \(y = 2x + 1\)

B. \(y = 2x - 1\)

C. \(y = -2x + 1\)

D. \(y = -2x - 1\)

Correct Answer: A

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Question 9 View Details

Find the area of the triangle with vertices (0, 0), (3, 0), and (0, 4).

A. 6

B. 8

Correct C. 12

D. 18

Correct Answer: C

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Question 10 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 + \(y - 3\)^\(2 = 9\)

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

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

Correct Answer: A

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Question 11 View Details

Determine the value of \(int_{0}^{2} 2x^2 + 3x - 4 \\) dx ).

A. 4

Correct B. 6

C. 8

D. 10

Correct Answer: B

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Question 12 View Details

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

A. 1

B. 5

Correct C. 7

D. 9

Correct Answer: C

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Question 13 View Details

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

A. 5

B. 10

Correct C. 15

D. 20

Correct Answer: C

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Question 14 View Details

A geometric sequence has first term \(a = 2\) and common ratio \(r = 3\). Find the sum of the first five terms of the sequence.

A. 155

Correct B. 160

C. 165

D. 170

Correct Answer: B

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Question 15 View Details

A polynomial function ( f(x) = \(x^3 - 2x^2 + 3x - 1\) ) has a root at \(x = 1\). Find the value of ( f(2) ).

A. 3

Correct B. 5

C. 7

D. 9

Correct Answer: B

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Question 16 View Details

A random variable X has a probability distribution given by P\(X = 1 = 0.3\), P\(X = 2 = 0.4\), and P\(X = 3 = 0.3\). If two independent random variables X and Y have the same probability distribution, what is the probability that X + Y is greater than 4?

A. 0.4

Correct B. 0.5

C. 0.6

D. 0.7

Correct Answer: B

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Question 17 View Details

The volume of a sphere (V) is given by the formula V = \(\frac{4}{3}\)\)\pi \(r^3\), where r is the radius of the sphere. If the radius of a sphere is increased by 20%, what is the percentage increase in its volume?

A. 10%

B. 20%

C. 30%

Correct D. 520%

Correct Answer: D

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Question 18 View Details

Solve the system of linear equations: \begin{align*} x + y &= 4 \ 2x - 3y &= 5 \end{align*}

A. \left\(3, \frac{1}{3} \right\)

Correct B. \left\(\frac{17}{5}, 4 - \frac{17}{5} \right\)

C. \left\(2, 2 \right\)

D. \left\(1, 3 \right\)

Correct Answer: B

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Question 19 View Details

A matrix A is given by \begin{pmatrix} 1 & 2 \ 3 & 4 \end{pmatrix}. Find the determinant of A.

A. -1

Correct B. -2

C. 2

D. 4

Correct Answer: B

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Question 20 View Details

Solve the quadratic equation: \\((x^2 + 5x + 6\)\(= 0\)\)

Correct A. \left\(-3, -2 \right\)

B. \left\(-2, -3 \right\)

C. \left\(1, 2 \right\)

D. \left\(2, 1 \right\)

Correct Answer: A

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