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POST UTME IGBINEDION UNIVERSITY 2025 Mathematics | Objective

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Question 1

Let ( X ) and ( Y ) be indep\endent 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 \( X + Y leq 1 \).

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

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

Find the derivative of the function ( f(x) = \frac{\ln(x)}{x^2} ) u\sing 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

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

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

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

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

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

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

Find the equation of the line pas\sing 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

Solve the quadratic equation \( x^2 + 5x + 6 = 0 \) u\sing 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

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

Solve the system of linear equations u\sing 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

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

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

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

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

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

Correct Answer: B

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Question 18

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

A histogram has a mean of ( 20 ) and a s\tandard 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

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

Find the equation of the circle pas\sing 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

A rec\tangular 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

Find the derivative of the function f(x) = 3x^2 + 2x - 5 u\sing 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

Solve the system of equations u\sing 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

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

Correct A. 24/25

B. 12/25

C. 16/25

D. 20/25

Correct Answer: A

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