Exam Body

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Subject

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POST UTME UNILORIN 2021 Mathematics | Objective

Are you preparing for POST UTME UNILORIN exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2021 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

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

A. 1

Correct B. -1

C. 2

D. 3

Correct Answer: B

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Question 2

A right circular cylinder has a height of 10 cm and a radius of 4 cm. Find the volume of the cylinder.

A. 80\pi

Correct B. 160\pi

C. 320\pi

D. 640\pi

Correct Answer: B

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Question 3

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

A. 0

B. \frac{\pi}{2}

Correct C. \frac{\pi}{4}

D. \frac{\pi}{6}

Correct Answer: C

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Question 4

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}{2}

Correct B. \frac{2}{7}

C. \frac{3}{8}

D. \frac{5}{12}

Correct Answer: B

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Question 5

Simplify the expression \( \sqrt{16x^2y^2} \ \).

Correct A. 4xy

B. 2xy

C. 4x^2y

D. 2x^2y^2

Correct Answer: A

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Question 6

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

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

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

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

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

Correct Answer: A

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Question 7

A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 60 and 90?

Correct A. 0.8413

B. 0.8413

C. 0.8413

D. 0.8413

Correct Answer: A

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Question 8

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

A. 2

Correct B. 3

C. 4

D. 5

Correct Answer: B

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Question 9

A company produces x units of a product, where the \cost of production is given by the function ( C(x) = 2x^2 + 5x + 1 ). Find the marginal \cost when x = 10.

A. 51

B. 52

Correct C. 53

D. 54

Correct Answer: C

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Question 10

A population of 1000 bacteria grows at a rate of 20% per hour. If the initial population is 100, what is the population after 5 hours?

A. 1000

B. 2000

Correct C. 3000

D. 4000

Correct Answer: C

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Question 11

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. What is the expected value of X?

Correct A. 1.1

B. 1.2

C. 1.3

D. 1.4

Correct Answer: A

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Question 12

Find the area under the curve y = x^2 from x = 0 to x = 4.

Correct A. 16

B. 32

C. 64

D. 128

Correct Answer: A

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Question 13

Solve the matrix equation \\begin{bmatrix} 1 & 2 \\ 3 & 4 \\end{bmatrix} \\begin{bmatrix} x \\ y \\end{bmatrix} = \\begin{bmatrix} 5 \\ 6 \\end{bmatrix}.

Correct A. x = 1, y = 2

B. x = 2, y = 3

C. x = 3, y = 4

D. x = 4, y = 5

Correct Answer: A

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Question 14

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

Correct A. y = 2x - 1

B. y = 2x + 1

C. y = x - 1

D. y = x + 1

Correct Answer: A

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Question 15

A circle has a radius of 4 units and a center at (0, 0). Find the equation of the circle.

Correct A. x^2 + y^2 = 16

B. x^2 + y^2 = 32

C. x^2 + y^2 = 64

D. x^2 + y^2 = 128

Correct Answer: A

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Question 16

Determine the value of x in the equation \( \frac{1}{2}x + 5 = \frac{3}{4}x - 3 \) in base 8.

Correct A. 6

B. 10

C. 12

D. 14

Correct Answer: A

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Question 17

A histogram of exam scores for a class of 50 students is shown below. What is the mean score?

A. 60

B. 65

Correct C. 70

D. 75

Correct Answer: C

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Question 18

Two events, A and B, are indep\endent. If P(A) = 0.4 and P(B) = 0.6, what is P(A ∩ B)?

Correct A. 0.2

B. 0.4

C. 0.6

D. 0.8

Correct Answer: A

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Question 19

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

A. 0.5

Correct B. 1.0

C. 1.5

D. 2.0

Correct Answer: B

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Question 20

Solve the system of linear equations \( egin{cases} x + y = 4 \ 2x - 3y = -3 \end{cases} \).

A. (1, 3)

Correct B. (2, 2)

C. (3, 1)

D. (4, 0)

Correct Answer: B

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Question 21

A random variable X has a probability distribution given by P\( X = 1 \) = 0.3, P\( X = 2 \) = 0.4, P\( X = 3 \) = 0.3. If Y = X^2, find E[Y].

A. 1.9

Correct B. 2.1

C. 2.3

D. 2.5

Correct Answer: B

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Question 22

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

A. 10

B. 100

Correct C. 1000

D. 10000

Correct Answer: C

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Question 23

Find the determinant of the matrix \[ \begin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix} \].

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 24

A histogram of exam scores has a mean of 60 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is greater than 70?

A. 0.25

Correct B. 0.5

C. 0.75

D. 0.9

Correct Answer: B

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Question 25

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

Correct A. \( x < -1 \) or \( x > \frac{3}{2} \)

B. \( x < -1 \) or \( x < \frac{3}{2} \)

C. \( x > -1 \) or \( x > \frac{3}{2} \)

D. \( x > -1 \) or \( x < \frac{3}{2} \)

Correct Answer: A

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