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POST UTME CALEB UNIVERSITY 2025 Mathematics | Objective

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Question 1 View Details

Determine the mean of the following dataset: {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.

A. 5

Correct B. 6

C. 7

D. 8

Correct Answer: B

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Question 2 View Details

Solve for x in the equation \(2^x + 5^x = 10^x\).

A. 2

B. 3

Correct C. 4

D. 5

Correct Answer: C

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Question 3 View Details

A histogram of exam scores is shown below. If the mean score is 60, what is the median?

A. 60

Correct B. 65

C. 70

D. 75

Correct Answer: B

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Question 4 View Details

Find the value of x in the equation \(\frac{x}{2} + 3 = 7\).

A. 4

Correct B. 5

C. 6

D. 7

Correct Answer: B

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Question 5 View Details

A vector ( vec{a} ) has a magnitude of 5 and makes an angle of 30 degrees with the positive x-axis. Find the x-component of ( vec{a} ).

Correct A. 3.54

B. 4.24

C. 4.65

D. 5.12

Correct Answer: A

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Question 6 View Details

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

Correct A. \(\frac{1}{2} \left \frac{4^3}{3} + 3 \cdot 4^2 - 2 \cdot 4 \right \\) )

B. \(\frac{1}{2} \left \frac{4^3}{3} + 3 \cdot 4^2 - 2 \cdot 4 \right \\) + 3 )

C. \(\frac{1}{2} \left \frac{4^3}{3} + 3 \cdot 4^2 - 2 \cdot 4 \right \\) - 2 )

D. \(\frac{1}{2} \left \frac{4^3}{3} + 3 \cdot 4^2 - 2 \cdot 4 \right \\) + 2 )

Correct Answer: A

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Question 7 View Details

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

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

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

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

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

Correct Answer: B

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Question 8 View Details

Solve the system of linear equations: \(2x + 3y = 7\) and \(x - 2y = -3\).

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

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

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

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

Correct Answer: A

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Question 9 View Details

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

Correct A. ( 0 )

B. ( 1 )

C. \(-1\)

D. ( 2 )

Correct Answer: A

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Question 10 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 + \(y - 3\)^\(2 = 4\) )

C. \(x - 2 \\)^2 + \(y - 3\)^\(2 = 9\) )

D. \(x - 2 \\)^2 + \(y - 3\)^\(2 = 25\) )

Correct Answer: A

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Question 11 View Details

Determine the value of x in the equation \(\frac{x}{2} + \frac{5}{3} = \frac{7}{6}\).

Correct A. 1

B. 2

C. 3

D. 4

Correct Answer: A

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Question 12 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 13 View Details

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

Correct A. \(1/6\)

B. \(1/12\)

C. \(1/2\)

D. \(2/3\)

Correct Answer: A

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Question 14 View Details

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

Correct A. \(-∞, -1\) ∪ (3, ∞)

B. \(-∞, 1\) ∪ (3, ∞)

C. \(-∞, -1\) ∪ (1, ∞)

D. \(-∞, 3\) ∪ (1, ∞)

Correct Answer: A

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Question 15 View Details

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

Correct A. -1

B. 0

C. 1

D. 2

Correct Answer: A

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Question 16 View Details

Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.

A. 24\pi

B. 48\pi

Correct C. 96\pi

D. 192\pi

Correct Answer: C

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Question 17 View Details

Solve the inequality \(\frac{x^2 - 4}{x^2 - 9}\)\)\\() > 0.\)

Correct A. \(-\infty, -3\) \cup \(-3, 2\) \cup \(2, \infty\)

B. \(-\infty, -3\) \cup \(2, \infty\)

C. \(-3, 2\)

D. \(2, \infty\)

Correct Answer: A

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Question 18 View Details

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

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 19 View Details

Solve the equation \\((x^2 + 4x + 4\)\(= 0.\)\)

Correct A. \(x = -2\)

B. \(x = -1\)

C. \(x = 1\)

D. \(x = 2\)

Correct Answer: A

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Question 20 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 21 View Details

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

Correct A. \(x^2\) + \\((y^2 - 6x - 2y + 12\)\(= 0\)\)

B. \(x^2\) + \\((y^2 + 6x - 2y + 12\)\(= 0\)\)

C. \(x^2\) + \\((y^2 - 6x + 2y + 12\)\(= 0\)\)

D. \(x^2\) + \\((y^2 + 6x + 2y + 12\)\(= 0\)\)

Correct Answer: A

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Question 22 View Details

A particle moves in a straight line with a velocity of 5 \((m/s\)\). If the acceleration is 2 \(m/s\\((m/s). If the acceleration is 2 \^2\), find the distance traveled in 4 seconds.

A. 20 m

B. 30 m

Correct C. 40 m

D. 50 m

Correct Answer: C

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Question 23 View Details

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

A. \(1/2\)

B. \(1/3\)

Correct C. \(2/3\)

D. \(1/6\)

Correct Answer: C

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Question 24 View Details

Find the derivative of the function f(x) = \(3x^2 + 2x - 5\) using the chain rule.

Correct A. 6x + 2

B. 6x - 2

C. \(6x^2 + 2x\)

D. \(6x^2 - 2x\)

Correct Answer: A

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Question 25 View Details

Solve the equation sin(x) = \cos(x) for \(0 \\(sin(x) = cos(x) for \le x\)\(\le 2\)π.

Correct A. π/4

B. 3π/4

C. π/2

D. 5π/4

Correct Answer: A

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