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POST UTME UNILORIN 2017 Mathematics | Objective

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Question 1 View Details

In the diagram below, the circle with center (O\) has a radius of 4 cm. If \(AB\\((O) has a radius of 4 cm. If\) is a chord of the circle such that \(OA = 3\) cm and \(OB = 5\) cm, find the length of \(AB\).

A. 6 cm

Correct B. 8 cm

C. 10 cm

D. 12 cm

Correct Answer: B

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Question 2 View Details

If \((x^2+2x+1\) = 0\), find the value of \(x\\((x^2+2x+1 = 0), find the value of\).

Correct A. -1

B. 0

C. 1

D. 2

Correct Answer: A

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Question 3 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. \(1/2\)

B. \(2/3\)

C. \(3/4\)

D. \(4/5\)

Correct Answer: A

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Question 4 View Details

In the diagram below, the line (l\) has a slope of 2 and passes through the point \((1,3)\\((l) has a slope of 2 and passes through the point\). Find the equation of the line.

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

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

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

D. \(y = 2x+2\)

Correct Answer: B

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Question 5 View Details

If \((x^2+4x+4\) = 0\), find the value of \(x\\((x^2+4x+4 = 0), find the value of\).

Correct A. -2

B. -1

C. 0

D. 1

Correct Answer: A

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Question 6 View Details

A random sample of 25 students from a university had a mean height of 175 cm with a standard deviation of 5 cm. If the population standard deviation is 6 cm, calculate the standard error of the mean.

A. 2.4 cm

Correct B. 2.7 cm

C. 3.1 cm

D. 3.5 cm

Correct Answer: B

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Question 7 View Details

A firm has two production plants, A and B. The cost function for plant A is C_\(A(x) =\)\(2x^2 + 10x + 5\), and for plant B is C_\(B(x) =\)\\(cost function for plant A is C_A(x) = (2x^2 + 10x + 5\(3x^2 + 5x + 2\). If the firm produces 20 units, what is the total \cost of production?

A. 1500

B. 1600

Correct C. 1700

D. 1800

Correct Answer: C

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Question 8 View Details

A sequence is defined as: \(a_n = 2n\^2 + 3n - 1\). Find the sum of the first 10 terms of the sequence.

A. 1040

B. 1080

Correct C. 1120

D. 1160

Correct Answer: C

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Question 9 View Details

A histogram of exam scores is shown below. If the mean score is 60 and the standard deviation is 10, what is the probability that a randomly selected student scored above 70?

A. 0.2

B. 0.3

Correct C. 0.4

D. 0.5

Correct Answer: C

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Question 10 View Details

A matrix A is given by:\(A =\)\begin{bmatrix} 2 & 1 \ 3 & 2 \end{bmatrix}. Find the determinant of matrix A.

A. 1

Correct B. 2

C. 3

D. 4

Correct Answer: B

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Question 11 View Details

Find the determinant of the matrix [ egin{array}{ccc} 2 & 3 & 4 \ 5 & 6 & 7 \ 8 & 9 & 10 \end{array} ].

Correct A. 0

B. -1

C. 1

D. 2

Correct Answer: A

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Question 12 View Details

Solve the inequality \(\frac{x}{2} - 3 > 7\).

A. \(x < -16\)

Correct B. \(x > 16\)

C. \(x < 16\)

D. \(x > -16\)

Correct Answer: B

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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. \(x - 2\)^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 14 View Details

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

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

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

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

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

Correct Answer: A

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Question 15 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?

A. \(\frac{1}{4}\)\)

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

Correct C. \(\frac{3}{8}\)\)

D. \(\frac{5}{8}\)\)

Correct Answer: C

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Question 16 View Details

Let X and Y be independent random variables with probability density functions f_\(X(x) = 2x\), \(0 < x\)\(< 1\), and f_\(Y(y) =\)\(3y^2\),\((0 < y\)\) < 1. Find the probability that \(X + Y < 1\\((0 < y) < 1. Find the probability that\).

Correct A. \(1/2\)

B. \(1/3\)

C. \(2/3\)

D. \(1/4\)

Correct Answer: A

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Question 17 View Details

Find the vector projection of the vector \(\vec{a} = \begin{pmatrix} 1 \ 2 3 \end{pmatrix} onto the vector \vec{b} = \\( 3 end{pmatrix} onto the vector \begin{pmatrix} 4 \ 5 \ 6 \end{pmatrix}\).

Correct A. \begin{pmatrix} \(20/61\) \ \(25/61\) \ \(30/61\) \end{pmatrix}

B. \begin{pmatrix} \(20/61\) \ \(25/61\) \ \(30/61\) \end{pmatrix}

C. \begin{pmatrix} \(20/61\) \ \(25/61\) \ \(30/61\) \end{pmatrix}

D. \begin{pmatrix} \(20/61\) \ \(25/61\) \ \(30/61\) \end{pmatrix}

Correct Answer: A

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Question 18 View Details

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

Correct A. \boxed{ -3, -2 \cup ( 2, 3 )}

B. \boxed{ -3, -2 \cup ( 2, 3 )}

C. \boxed{ -3, -2 \cup ( 2, 3 )}

D. \boxed{ -3, -2 \cup ( 2, 3 )}

Correct Answer: A

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Question 19 View Details

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

Correct A. \(\frac{3x^4 - 2x^4}{\) \(x^2 + 1\) ^2}\)\)

B. \(\frac{3x^4 - 2x^4}{\) \(x^2 + 1\) ^2}\)\)

C. \(\frac{3x^4 - 2x^4}{\) \(x^2 + 1\) ^2}\)\)

D. \(\frac{3x^4 - 2x^4}{\) \(x^2 + 1\) ^2}\)\)

Correct Answer: A

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Question 20 View Details

Let f(x) = \(\frac{x^2}{x + 1}\)\)\). Find the equation of the \tangent line to the graph of f at the point (0, 0).

Correct A. \(y = x\)

B. \(y = x + 1\)

C. \(y = x - 1\)

D. \(y = x + 2\)

Correct Answer: A

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Question 21 View Details

A histogram is a graphical representation of the distribution of a set of data. Which of the following is NOT a characteristic of a histogram?

A. It is a type of bar chart.

B. It is used to show the frequency distribution of a set of data.

C. It is a graphical representation of the distribution of a set of data.

Correct D. It is always a vertical bar chart.

Correct Answer: D

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Question 22 View Details

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

Correct A. 0.5

B. 1.0

C. 1.5

D. 2.0

Correct Answer: A

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Question 23 View Details

A rectangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. What is its volume?

A. 30 \(cm^3\)

B. 40 \(cm^3\)

Correct C. 50 \(cm^3\)

D. 60 \(cm^3\)

Correct Answer: C

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Question 24 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 25 View Details

A company produces two products, A and B. The profit from product A is ₦100 per unit, and the profit from product B is ₦150 per unit. If the company produces 100 units of product A and 50 units of product B, what is the total profit?

A. ₦15,000

B. ₦20,000

Correct C. ₦25,000

D. ₦30,000

Correct Answer: C

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