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POST UTME LAUTECH 2024 Mathematics | Objective

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Question 1 View Details

A rectangular prism has a length of 10 cm, a width of 5 cm, and a height of 8 cm. Find the volume of the prism in cubic centimeters.

Correct A. 400

B. 500

C. 600

D. 800

Correct Answer: A

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Question 2 View Details

A fair six-sided die is rolled. What is the probability that the number rolled is greater than 4?

Correct A. \(1/3\)

B. \(1/2\)

C. \(2/3\)

D. \(1/6\)

Correct Answer: A

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Question 3 View Details

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

Correct A. -2

B. -1

C. 2

D. 3

Correct Answer: A

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Question 4 View Details

Find the determinant of the matrix: \(\begin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix}\)

Correct A. -120

B. 120

C. 0

D. 180

Correct Answer: A

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Question 5 View Details

A company produces two products, A and B. The profit from product A is 10 per unit, and the profit from product B is15 per unit. If the company produces 100 units of product A and 50 units of product B, what is the total profit?

A. 2500

Correct B. 3000

C. 3500

D. 4000

Correct Answer: B

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Question 6 View Details

Find the volume of the frustum of a cone with height 10cm, lower base radius 4cm, and upper base radius 6cm.

A. 100π cm³

Correct B. 150π cm³

C. 200π cm³

D. 250π cm³

Correct Answer: B

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Question 7 View Details

Solve for x in the matrix equation \(egin{bmatrix} 2 & 1 \ 1 & 2 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 3 \ 4 \end{bmatrix}\).

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

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

C. \(x = 3\), \(y = 4\)

D. \(x = 4\), \(y = 3\)

Correct Answer: B

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Question 8 View Details

Find the sum of the first 10 terms of the geometric progression 2, 6, 18, ...

Correct A. 1023

B. 1024

C. 1025

D. 1026

Correct Answer: A

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Question 9 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 10 View Details

Find the value of x in the polynomial equation \(x^3 - 6x^2 + 11x - 6 = 0\).

A. 1

B. 2

Correct C. 3

D. 4

Correct Answer: C

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Question 11 View Details

Determine the probability of the event that a randomly selected integer from the set {1, 2, 3, 4, 5, 6} is greater than 4, given that the integer is even.

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

Correct B. \(\frac{2}{3}\)\)

C. \(\frac{3}{4}\)\)

D. \(\frac{4}{5}\)\)

Correct Answer: B

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Question 12 View Details

Find the sum of the first 10 terms of the geometric series with first term 2 and common ratio \(\frac{1}{2}\)\).

Correct A. \(\frac{1023}{512}\)\)

B. \(\frac{1024}{512}\)\)

C. \(\frac{1025}{512}\)\)

D. \(\frac{1026}{512}\)\)

Correct Answer: A

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Question 13 View Details

Solve the equation \tan x + \cot \(x = 2\), where x is an acute angle.

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

B. \(\frac{\pi}{6}\)\)

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

D. \(\frac{\pi}{2}\)\)

Correct Answer: C

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Question 14 View Details

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

Correct A. 0.8413

B. 0.8419

C. 0.8423

D. 0.8427

Correct Answer: A

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Question 15 View Details

Find the vector overrightarrow{a} + \overrightarrow{b} if \overrightarrow{a}\(= 2\)\\(overrightarrow{a} + overrightarrow{b} if \hat{i} + 3\hat{j} and \overrightarrow{b}\(= -4\)\hat{i} + 5\hat{j}.

Correct A. -2\hat{i} + 8\hat{j}

B. 2\hat{i} - 8\hat{j}

C. -2\hat{i} - 8\hat{j}

D. 2\hat{i} + 8\hat{j}

Correct Answer: A

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Question 16 View Details

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

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

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

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

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

Correct Answer: A

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Question 17 View Details

Solve the inequality \(2x^2 - 5x - 3 > 0\) using the quadratic formula.

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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Question 18 View Details

Find the value of ( x ) in the equation \(2^x + 5^x = 7^x\) using \logarithms.

A. \(x = 2\)

Correct B. \(x = 3\)

C. \(x = 4\)

D. \(x = 5\)

Correct Answer: B

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Question 19 View Details

A histogram represents the distribution of exam scores in a class. 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. 0.25

B. 0.5

Correct C. 0.75

D. 0.9

Correct Answer: C

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Question 20 View Details

Solve the equation \(x^2 - 4x + 4 = 0\) using the quadratic formula.

Correct A. \(x = 2\)

B. \(x = -2\)

C. \(x = 1\)

D. \(x = -1\)

Correct Answer: A

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Question 21 View Details

Find the derivative of the function ( f(x) = \\(\sin^2\) x ) using the chain rule.

Correct A. f'\((x) = 2\)\sin x \cos x

B. f'\((x) = 2\)\\(\sin^2\) x

C. f'\((x) = 2\)\\(\cos^2\) x

D. f'\((x) = 2\)\sin x

Correct Answer: A

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Question 22 View Details

Solve the inequality \(x^2 - 6x + 8 > 0\) using the quadratic formula.

Correct A. \(x < 2\) or \(x > 4\)

B. \(x > 2\) or \(x < 4\)

C. \(x < 2\) or \(x < 4\)

D. \(x > 2\) or \(x > 4\)

Correct Answer: A

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Question 23 View Details

Find the value of ( x ) in the equation \(2^x + 3^x = 5^x\) using \logarithms.

A. \(x = 2\)

Correct B. \(x = 3\)

C. \(x = 4\)

D. \(x = 5\)

Correct Answer: B

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Question 24 View Details

A histogram represents the distribution of exam scores in a class. 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. 0.25

B. 0.5

C. 0.75

D. 0.9

Correct Answer: VIEW ANSWER

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Question 25 View Details

In a right-angled triangle, the length of the hypotenuse is 10 cm and one of the acute angles is 30°. Find the length of the side opposite the 30° angle.

A. 5 cm

Correct B. 7.07 cm

C. 10 cm

D. 15 cm

Correct Answer: B

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