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POST UTME IGBINEDION UNIVERSITY 2025 Mathematics | Objective

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Question 1 View Details

Let ( X ) and ( Y ) be independent random variables with probability density functions \(f_X x \\) = egin{cases} 2x, & 0 leq x leq 1 \ 0, & \text{otherwise} \end{cases} ) and \(f_Y y \\) = egin{cases} \(3y^2\), & 0 leq y leq 1 \ 0, & text{otherwise} \end{cases} ). Find the probability that \(X + Y \\(text{otherwise} end{cases} ). Find the probability that \leq 1\).

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

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

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

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

Correct Answer: A

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Question 2 View Details

Find the determinant of the matrix \(A = \begin{bmatrix} 2 & 1 & 3 \ 4 & 2 & 5 \ 6 & 3 & 7 \end{bmatrix}\).

A. -3

Correct B. 0

C. 3

D. 6

Correct Answer: B

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Question 3 View Details

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

Correct A. \(\frac{1}{x^3}\)\)\) - \(\frac{2\ln(x)}{x^3}\)\)\)

B. \(\frac{1}{x^3}\)\)\) + \(\frac{2\ln(x)}{x^3}\)\)\)

C. \(\frac{1}{x^3}\)\)\) - \(\frac{\ln(x)}{x^3}\)\)\)

D. \(\frac{1}{x^3}\)\)\) + \(\frac{\ln(x)}{x^3}\)\)\)

Correct Answer: A

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Question 4 View Details

Solve the equation \(2^x + 3^x = 5^x\) for ( x ).

A. 1

Correct B. 2

C. 3

D. 4

Correct Answer: B

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Question 5 View Details

Find the value of ( x ) in the equation \(\sin^2 x \\) + \\(\cos^2(x)\)\(= 1 ).\)

A. 0

Correct B. \(\frac{\pi}{4}\)\)

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

D. \(\frac{3\pi}{4}\)\)

Correct Answer: B

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Question 6 View Details

Find the volume of the solid formed by revolving the region bounded by the curves \(y = x\^2\), \(y = 0\), and \(x = 2\) about the x-axis.

A. 32\pi

B. 64\pi

Correct C. 128\pi

D. 256\pi

Correct Answer: C

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Question 7 View Details

Solve the inequality \(\frac{x^2 - 4}{x^2 - 2x - 3}\)\)\\() > 0.\)

A. x \in \(-\infty, -1\) \cup \(1, \infty\)

Correct B. x \in \(-\infty, -3\) \cup \(-1, 1\) \cup \(3, \infty\)

C. x \in \(-\infty, -3\) \cup \(-1, 1\) \cup \(3, \infty\)

D. x \in \(-\infty, -1\) \cup \(1, \infty\)

Correct Answer: B

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Question 8 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 9 View Details

Solve the equation \(x^3\) + \\((2x^2 - 7x - 12\)\(= 0.\)\)

Correct A. \(x = -3\)

B. \(x = -1\)

C. \(x = 1\)

D. \(x = 4\)

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. \(y = x + 2\)

D. \(y = x - 2\)

Correct Answer: A

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Question 11 View Details

Solve the quadratic equation \(x^2 + 5x + 6 = 0\) using the quadratic formula. What is the value of ( x )?

A. 2

Correct B. -3

C. -2

D. 1

Correct Answer: B

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Question 12 View Details

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

Correct A. 7

B. 9

C. 11

D. 13

Correct Answer: A

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Question 13 View Details

Solve the system of linear equations using matrices: \(\begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 7 \ 10 \end{bmatrix}\).

Correct A. \begin{bmatrix} 1 \ 2 \end{bmatrix}

B. \begin{bmatrix} 3 \ 4 \end{bmatrix}

C. \begin{bmatrix} 5 \ 6 \end{bmatrix}

D. \begin{bmatrix} 7 \ 8 \end{bmatrix}

Correct Answer: A

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Question 14 View Details

Find the value of ( x ) in the inequality \(2x - 5 > 3\).

A. 4

B. 5

Correct C. 6

D. 7

Correct Answer: C

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Question 15 View Details

Find the area of the triangle with vertices ( (0, 0) ), ( (2, 0) ), and ( (1, 3) ).

Correct A. 3

B. 4

C. 5

D. 6

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 \(x = 1\) to \(x = 4\).

Correct A. ( 20 )

B. ( 30 )

C. ( 40 )

D. ( 50 )

Correct Answer: A

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Question 17 View Details

Solve for ( x ) in the equation \(\sin^2 x \\) + \\(\cos^2(x)\)\(= 1 ).\)

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

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

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

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

Correct Answer: B

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Question 18 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 - 3 \\)^2 + \(y - 2\)^\(2 = 16\) )

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

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

Correct Answer: A

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Question 19 View Details

A histogram has a mean of ( 20 ) and a standard deviation of ( 5 ). Find the area under the curve from \(x = 15\) to \(x = 25\).

A. ( 0.5 )

B. ( 0.6 )

Correct C. ( 0.7 )

D. ( 0.8 )

Correct Answer: C

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Question 20 View Details

Solve for ( x ) in the equation \(\log_{10} x \\)\(= 2 ).\)

Correct A. \(x = 10^2\)

B. \(x = 10^3\)

C. \(x = 10^4\)

D. \(x = 10^5\)

Correct Answer: A

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Question 21 View Details

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

Correct A. \left\(x - 1 \right\)^2 + \left\(y - 2 \right\)^\(2 = 13\)

B. \left\(x + 1 \right\)^2 + \left\(y - 2 \right\)^\(2 = 13\)

C. \left\(x - 1 \right\)^2 + \left\(y + 2 \right\)^\(2 = 13\)

D. \left\(x + 1 \right\)^2 + \left\(y + 2 \right\)^\(2 = 13\)

Correct Answer: A

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Question 22 View Details

A rectangular water \tank has a length of 5 m, a width of 3 m, and a height of 2 m. Find the volume of water in the \tank.

Correct A. 30 \(m^3\)

B. 40 \(m^3\)

C. 50 \(m^3\)

D. 60 \(m^3\)

Correct Answer: A

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Question 23 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. \(3x^2 + 2\)

D. \(3x^2 - 2\)

Correct Answer: A

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Question 24 View Details

Solve the system of equations using matrices:

Correct A. \begin{bmatrix} 1 & -2 \ 3 & 4 \end{bmatrix}

B. \begin{bmatrix} 2 & -1 \ 3 & 4 \end{bmatrix}

C. \begin{bmatrix} 1 & 2 \ 3 & -4 \end{bmatrix}

D. \begin{bmatrix} 2 & 1 \ 3 & -4 \end{bmatrix}

Correct Answer: A

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Question 25 View Details

Find the value of sin(2x) if \\(sin(x) =\)\(3/5\\(sin(2x) if sin(x) =\).

Correct A. \(24/25\)

B. \(12/25\)

C. \(16/25\)

D. \(20/25\)

Correct Answer: A

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