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POST UTME BABCOCK UNIVERSITY 2023 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 circle has a radius of 4 cm. Find the area of the circle.

Correct A. 50.24 \(cm^2\)

B. 100.48 \(cm^2\)

C. 50.24 \(cm^3\)

D. 100.48 \(cm^3\)

Correct Answer: A

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Question 3 View Details

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

Correct A. 32

B. 64

C. 16

D. 128

Correct Answer: A

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Question 4 View Details

Solve the equation \(2x + 5 = 11\).

Correct A. 3

B. 2

C. 4

D. 5

Correct Answer: A

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Question 5 View Details

Find the value of ( x ) in the equation \(x^2 - 4x - 5 = 0\).

Correct A. 5

B. -1

C. 2

D. 3

Correct Answer: A

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Question 6 View Details

Find the value of \(\frac{d}{dx} \left \frac{1}{x^2 + 1} \right\)\) using the quotient rule.

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

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

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

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

Correct Answer: A

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Question 7 View Details

Solve the inequality \(\left| x - 2 \right| > 3\).

Correct A. \(x < -1\) or \(x > 5\)

B. \(x < 1\) or \(x > 5\)

C. \(x < -1\) or \(x > 2\)

D. \(x < 1\) or \(x > 2\)

Correct Answer: A

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Question 8 View Details

Find the sum of the first 5 terms of the geometric series \(\sum_{n = 1}^5 \frac{2}{3^n}\).

Correct A. \(\frac{2}{3}\)\) + \(\frac{2}{9}\)\) + \(\frac{2}{27}\)\) + \(\frac{2}{81}\)\) + \(\frac{2}{243}\)\)

B. \(\frac{2}{3}\)\) + \(\frac{2}{9}\)\) + \(\frac{2}{27}\)\) + \(\frac{2}{81}\)\) + \(\frac{2}{243}\)\)

C. \(\frac{2}{3}\)\) + \(\frac{2}{9}\)\) + \(\frac{2}{27}\)\) + \(\frac{2}{81}\)\)

D. \(\frac{2}{3}\)\) + \(\frac{2}{9}\)\) + \(\frac{2}{27}\)\)

Correct Answer: A

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Question 9 View Details

Solve the matrix equation \(\begin{bmatrix} 2 & 1 \ 1 & 2 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 3 \ 3 \end{bmatrix}\).

Correct A. \begin{bmatrix} 1 \ 1 \end{bmatrix}

B. \begin{bmatrix} 1 \ 2 \end{bmatrix}

C. \begin{bmatrix} 2 \ 1 \end{bmatrix}

D. \begin{bmatrix} 2 \ 2 \end{bmatrix}

Correct Answer: A

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Question 10 View Details

A set of 5 numbers has a mean of 10. If 2 is added to each number, what is the new mean?

Correct A. 12

B. 13

C. 14

D. 15

Correct Answer: A

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Question 11 View Details

A random sample of 25 students from a population of 1000 students had a mean height of 175 cm with a standard deviation of 5 cm. Calculate the 95% confidence interval for the population mean.

Correct A. 170.4 cm, 179.6 cm

B. 172.5 cm, 177.5 cm

C. 174.5 cm, 175.5 cm

D. 171.2 cm, 178.8 cm

Correct Answer: A

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Question 12 View Details

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

Correct A. \(x \leq -1.5\) or \(x \geq 1\)

B. \(x \leq -1\) or \(x \geq 1.5\)

C. \(x \leq -1.5\) or \(x \geq 1.5\)

D. \(x \leq 1\) or \(x \geq 1.5\)

Correct Answer: A

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Question 13 View Details

Find the determinant of the matrix \(\begin{bmatrix} 2 & 3 & 1 \\ 4 & 1 & 2 \\ 3 & 2 & 1 \end{bmatrix}\).

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 14 View Details

A company produces two products, A and B. The profit from the sale of product A is ₦200 per unit, while the profit from the sale of 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. ₦25000

Correct B. ₦30000

C. ₦35000

D. ₦40000

Correct Answer: B

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Question 15 View Details

A histogram of the heights of 100 students is shown below. If the mean height of the students is 175 cm, what is the standard deviation?

Correct A. 5 cm

B. 10 cm

C. 15 cm

D. 20 cm

Correct Answer: A

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Question 16 View Details

Find the area under the curve \(y = \frac{1}{2}x^2 + 3x - 2\) from \(x = 0\) to \(x = 4\).

A. 40

B. 50

Correct C. 60

D. 70

Correct Answer: C

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Question 17 View Details

A fair six-sided die is rolled twice. What is the probability that the sum of the two numbers is 7?

A. \(1/6\)

B. \(1/3\)

C. \(1/2\)

Correct D. \(2/3\)

Correct Answer: D

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Question 18 View Details

Find the volume of the solid formed by revolving the region bounded by the parabola (y = \(x^2\)\) and the line \(y = 2x\\((y = x^2) and the line\) about the x-axis.

A. \(16/3\)

Correct B. \(32/3\)

C. \(64/3\)

D. \(128/3\)

Correct Answer: B

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Question 19 View Details

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

Correct A. \(-∞, -3\) ∪ (1, ∞)

B. \(-∞, -1\) ∪ (3, ∞)

C. \(-∞, 1\) ∪ (3, ∞)

D. \(-∞, -3\) \cup \(-1, ∞\)\)

Correct Answer: A

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Question 20 View Details

Find the value of (\(12\theta\) given that \\((\)12theta\(\(1\theta = \frac{3}{5}\) and 1\\(theta =\)\(\frac{4}{5}\)\).

Correct A. \(24/25\)

B. \(16/25\)

C. \(20/25\)

D. \(12/25\)

Correct Answer: A

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Question 21 View Details

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

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

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

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

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

Correct Answer: A

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Question 22 View Details

A binary operation ( odot ) is defined as \(a odot b = ab + 2\). Find the value of ( 3 odot 4 ).

A. 14

Correct B. 16

C. 18

D. 20

Correct Answer: B

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Question 23 View Details

Solve the trigonometric equation \(\sin^2 x + \cos^2 x = 1\) for ( x ) in the interval ( [0, 2pi] ).

Correct A. \(x = \frac{\pi}{4}\)

B. \(x = \frac{\pi}{2}\)

C. \(x = \frac{3\pi}{4}\)

D. \(x = \frac{5\pi}{4}\)

Correct Answer: A

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Question 24 View Details

A random experiment consists of rolling a fair six-sided die. Find the probability that the sum of the numbers on the two dice is 7.

A. \(\frac{1}{6}\)\)

Correct B. \(\frac{1}{3}\)\)

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

D. \(\frac{2}{3}\)\)

Correct Answer: B

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Question 25 View Details

Convert the decimal number 0.000123 to a binary number.

A. 0.000123

Correct B. 0.00011011

C. 0.00010101

D. 0.00011101

Correct Answer: B

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