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POST UTME UNILORIN 2017 Mathematics | Objective

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Question 1

In the diagram below, the circle with center $O$ has a radius of 4 cm. If $AB$ 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

If $x^2+2x+1=0$, find the value of $x$.

Correct A. -1

B. 0

C. 1

D. 2

Correct Answer: A

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Question 3

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

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

If $x^2+4x+4=0$, find the value of $x$.

Correct A. -2

B. -1

C. 0

D. 1

Correct Answer: A

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Question 6

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

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) = 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

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

A histogram of exam scores is shown below. If the mean score is 60 and the s\tandard 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

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

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

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

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

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

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

Let X and Y be indep\endent 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.

Correct A. 1/2

B. 1/3

C. 2/3

D. 1/4

Correct Answer: A

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Question 17

Find the vector projection of the vector \vec{a} = \begin{pmatrix} 1 \ 2 \ 3 \end{pmatrix} onto the vector \vec{b} = \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

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

Find the derivative of the function f(x) = \frac{x^3}{x^2 + 1} u\sing 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

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

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

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

A rec\tangular 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

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

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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