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POST UTME UNILORIN 2021 Mathematics | Objective

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Question 1 View Details

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 View Details

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 View Details

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

Correct B. \(\frac{2}{7}\)\)

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

D. \(\frac{5}{12}\)\)

Correct Answer: B

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Question 5 View Details

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 View Details

Find the derivative of the function ( f(x) = \(\frac{1}\){\sqrt{\(x^2 + 1}}\)\) ) using 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 View Details

A histogram of exam scores has a mean of 75 and a standard 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 View Details

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 View Details

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 of production is given by the function ( C(x) = (2x^2 + 5x + 1\cost when \(x = 10\).

A. 51

B. 52

Correct C. 53

D. 54

Correct Answer: C

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Question 10 View Details

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 View Details

A random variable X has a probability distribution given by P\(X = 1 = 0.3\), P\(X = 2 = 0.4\), and P\(X = 3 = 0.3\). 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 View Details

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 View Details

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 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. \(y = x - 1\)

D. \(y = x + 1\)

Correct Answer: A

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Question 15 View Details

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 View Details

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 View Details

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 View Details

Two events, A and B, are independent. If P(A) = 0.4 and P(B) = 0.6, what is P(\(A \cap B\))?

Correct A. 0.2

B. 0.4

C. 0.6

D. 0.8

Correct Answer: A

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Question 19 View Details

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 View Details

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 View Details

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 \(Y = X\\((X = 3 = 0.3). If \^2\), 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 View Details

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 View Details

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 View Details

A histogram of exam scores has a mean of 60 and a standard 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 View Details

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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