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POST UTME AFE BABALOLA UNIVERSITY 2025 Mathematics | Objective

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Question 1 View Details

Let X and Y be independent random variables with probability distributions P\(X = 1 = 0\).4 and P\(Y = 1 = 0.3\). Find the probability that X and Y are both equal to 1.

Correct A. 0.12

B. 0.24

C. 0.36

D. 0.48

Correct Answer: A

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Question 2 View Details

Find the equation of the circle passing through the points (2, 3), (4, 1), and (6, 5).

Correct A. \left\(x - 4 \right\)^2 + \left\(y - 3 \right\)^\(2 = 5\)

B. \left\(x - 2 \right\)^2 + \left\(y - 1 \right\)^\(2 = 10\)

C. \left\(x - 6 \right\)^2 + \left\(y - 5 \right\)^\(2 = 15\)

D. \left\(x - 8 \right\)^2 + \left\(y - 7 \right\)^\(2 = 20\)

Correct Answer: A

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Question 3 View Details

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

Correct A. \left\(- \infty, - \frac{3}{2} \right\) \cup \left\(\frac{1}{2}, \infty \right\)

B. \left\(- \infty, - \frac{1}{2} \right\) \cup \left\(\frac{3}{2}, \infty \right\)

C. \left\(- \infty, \frac{1}{2} \right\) \cup \left\(\frac{3}{2}, \infty \right\)

D. \left\(- \infty, - \frac{3}{2} \right\) \cup \left\(\frac{1}{2}, \infty \right\)

Correct Answer: A

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Question 4 View Details

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

Correct A. 4

B. 6

C. 8

D. 10

Correct Answer: A

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Question 5 View Details

Let f(x) = \((x^2 + 2x - 3\)\). Find the value of f\(-1\\((x^2 + 2x - 3). Find the value of f\).

Correct A. -4

B. -3

C. -2

D. -1

Correct Answer: A

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Question 6 View Details

Find the value of x in the equation \(\log_{10} x^2 \\)\(= 4 ).\)

A. 10

B. 100

C. 1000

Correct D. 10000

Correct Answer: D

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Question 7 View Details

A circle has a radius of 5 cm. Find the area of the circle.

Correct A. 25π

B. 50π

C. 75π

D. 100π

Correct Answer: A

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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. 3050

B. 3060

C. 3070

D. 3080

Correct Answer: A

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Question 9 View Details

A set of 5 numbers has a mean of 10. Find the sum of the numbers.

Correct A. 50

B. 60

C. 70

D. 80

Correct Answer: A

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Question 10 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 11 View Details

In the number base (8\), what is the value of the expression \([3 \\((8), what is the value of the expression \times 2^2 + 5\)]_{8}\)?

A. 23

Correct B. 27

C. 31

D. 35

Correct Answer: B

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Question 12 View Details

The equation of the circle with center \(-2, 3\)\) and radius \(4) is given by \(\left x + 2\\() is given by (\right\)^2 + \left\(y - 3\right\)^\(2 = 16\)\). What is the equation of the circle with center \(1, -2\)\) and radius \(3\)?

Correct A. \left\(x - 1\right\)^2 + \left\(y + 2\right\)^\(2 = 9\)

B. \left\(x + 1\right\)^2 + \left\(y - 2\right\)^\(2 = 9\)

C. \left\(x - 1\right\)^2 + \left\(y + 2\right\)^\(2 = 16\)

D. \left\(x + 1\right\)^2 + \left\(y - 2\right\)^\(2 = 16\)

Correct Answer: A

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Question 13 View Details

A rectangular solid has dimensions \(10 \text{cm} \times 5 \text{cm} \times 3 \text{cm}\). What is the volume of the solid?

Correct A. 150

B. 200

C. 250

D. 300

Correct Answer: A

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Question 14 View Details

A vector \(\mathbf{a}\) has magnitude \(5\) and direction \(30^\circ\) counterclockwise from the positive \(x\)-axis. A vector \(\mathbf{b}\) has magnitude \(3\) and direction \(60^circ\) counterclockwise from the positive \(x\\(circ) counterclockwise from the positive\)-axis. What is the magnitude of the sum \(\mathbf{a} + \mathbf{b}\)?

A. 4

Correct B. 5

C. 6

D. 7

Correct Answer: B

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Question 15 View Details

Simplify the expression \(\frac{1}{1 + \sqrt{2}} + \frac{1}{1 - \sqrt{2}}\).

A. 0

Correct B. 1

C. 2

D. 3

Correct Answer: B

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Question 16 View Details

A random sample of 25 students from a university had a mean height of 175.5 cm with a standard deviation of 5.2 cm. If the population standard deviation is unknown, calculate the 95% confidence interval for the population mean.

Correct A. 170.3 cm, 180.7 cm

B. 168.1 cm, 182.9 cm

C. 169.5 cm, 181.5 cm

D. 171.1 cm, 179.9 cm

Correct Answer: A

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Question 17 View Details

A matrix A has the following elements: \(A = \begin{bmatrix} 2 & 3 \\ 4 & 5 end{bmatrix}\). If \(B = 2A\\(end{bmatrix}). If\), find the determinant of B.

A. 20

Correct B. 40

C. 60

D. 80

Correct Answer: B

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Question 18 View Details

A function f(x) = \((2x^2 + 3x - 1\)\) has a local maximum at x = -1. Find the value of the function at \(x = 0\\((2x^2 + 3x - 1) has a local maximum at x = -1. Find the value of the function at\).

Correct A. -1

B. 0

C. 1

D. 2

Correct Answer: A

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Question 19 View Details

A random variable X has a probability distribution given by: \(PX = 1 = 0.3\), P\(X = 2 = 0.4\), P\(X = 3 = 0\).3\). Find the expected value of X.

A. 1.1

Correct B. 1.3

C. 1.5

D. 1.7

Correct Answer: B

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Question 20 View Details

A circle has an equation of the form \(x - h\)^2 + \(y - k\)^\(2 = r\^2\). If the center of the circle is at (2, 3) and the radius is 4, find the equation of the circle.

Correct A. \(x - 2\)^2 + \(y - 3\)^\(2 = 16\)

B. \(x - 3\)^2 + \(y - 2\)^\(2 = 16\)

C. \(x - 4\)^2 + \(y - 3\)^\(2 = 16\)

D. \(x - 2\)^2 + \(y - 4\)^\(2 = 16\)

Correct Answer: A

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Question 21 View Details

A rectangular prism has a length of 6 cm, a width of 4 cm, and a height of 3 cm. Calculate the volume of the prism using the formula \(V = lwh\).

Correct A. 72

B. 96

C. 108

D. 120

Correct Answer: A

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Question 22 View Details

A circle has a radius of 4 cm. Calculate the area of the circle using the formula A = π\(r^2\).

A. 50.24

Correct B. 100.48

C. 200.96

D. 251.2

Correct Answer: B

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Question 23 View Details

A right-angled triangle has a base of 5 cm and a height of 12 cm. Calculate the length of the hypotenuse using the Pythagorean theorem.

A. 13

B. 14

Correct C. 15

D. 16

Correct Answer: C

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Question 24 View Details

A rectangular prism has a length of 8 cm, a width of 5 cm, and a height of 2 cm. Calculate the surface area of the prism using the formula \(SA = 2lw + 2lh + 2wh\).

A. 104

B. 120

Correct C. 136

D. 152

Correct Answer: C

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Question 25 View Details

A right-angled triangle has a base of 3 cm and a height of 4 cm. Calculate the area of the triangle using the formula \(A = 1/2bh\).\)

Correct A. 6

B. 12

C. 18

D. 24

Correct Answer: A

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