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POST UTME IGBINEDION UNIVERSITY 2024 Mathematics | Objective

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Question 1 View Details

Find the value of \(int_{0}^{1} \frac{1}{x^2 + 1} dx\).

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

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

C. \(\frac{\pi}{6}\)\)

D. \(\frac{\pi}{8}\)\)

Correct Answer: A

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Question 2 View Details

Solve for ( x ) in the equation \(2x^2 + 5x - 3 = 0\).

Correct A. \(\frac{-5 \pm \sqrt{109}\)}{4}\)

B. \(\frac{-5 \pm \sqrt{25}\)}{4}\)

C. \(\frac{-5 \pm \sqrt{9}\)}{4}\)

D. \(\frac{-5 \pm \sqrt{1}\)}{4}\)

Correct Answer: A

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Question 3 View Details

Find the equation of the circle with center ( (2, 3) ) and radius ( 4 ).

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

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

C. \left\(x - 4 \right\)^2 + \left\(y - 5 \right\)^\(2 = 16\)

D. \left\(x - 5 \right\)^2 + \left\(y - 4 \right\)^\(2 = 16\)

Correct Answer: A

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Question 4 View Details

Find the derivative of ( f(x) = \(\frac{1}{x^2 + 1}\)\)\) ) using the chain 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 5 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 6 View Details

Find the sum of the first 10 terms of the geometric series with first term 2 and common ratio \(3/4\).

A. 2.9375

Correct B. 3.0625

C. 3.125

D. 3.1875

Correct Answer: B

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Question 7 View Details

Solve the inequality \(\frac{x-2}{x+1}\)\\()>0.\)

A. \(-1, 2\)

Correct B. \(-1, \infty\) \cup \(2, \infty\)

C. \(-1, \infty\) \cup \(-\infty, 2\)

D. \(-1, 2\)

Correct Answer: B

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Question 8 View Details

Find the equation of the circle with center \(-2, 3\) and radius 4.

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

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

C. \left\(x+2\right\)^2 + \left\(y+3\right\)^\(2 = 16\)

D. \left\(x-2\right\)^2 + \left\(y-3\right\)^\(2 = 16\)

Correct Answer: A

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Question 9 View Details

Solve the system of equations \begin{align*} x+y+z&=3, \ x+2y+3z&=6, \ x+3y+6z&=12. \end{align*}

Correct A. \begin{align*} x&=1, \ y&=1, \ z&=1. \end{align*}

B. \begin{align*} x&=2, \ y&=1, \ z&=0. \end{align*}

C. \begin{align*} x&=3, \ y&=0, \ z&=0. \end{align*}

D. \begin{align*} x&=0, \ y&=0, \ z&=0. \end{align*}

Correct Answer: A

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Question 10 View Details

Find the area of the triangle with vertices (0, 0), (3, 0), and (0, 4).

Correct A. 6

B. 12

C. 18

D. 24

Correct Answer: A

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Question 11 View Details

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

A. \(\frac{1}{2} 4^2 \\) + 3(4) - 2 )

B. \(\frac{1}{2} 0^2 \\) + 3(0) - 2 )

Correct C. \(\frac{1}{2} 4^2 \\) + 3(4) - 2 + \(\frac{1}{2}\)\)\(4^2\) + 3(4) - 2 )

D. \(\frac{1}{2} 4^2 \\) + 3(4) - 2 + \(\frac{1}{2}\)\)\(0^2\) + 3(0) - 2 )

Correct Answer: C

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Question 12 View Details

Solve for ( x ) in the equation \(\log_{10} x^2 \\)\(= 4 ).\)

Correct A. \(x = 10^4\)

B. \(x = 10^{-4}\)

C. \(x = 10^2\)

D. \(x = 10^{-2}\)

Correct Answer: A

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Question 13 View Details

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

A. \(\frac{1}{3} \pi\)

B. \(\frac{1}{2} \pi\)

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

D. \(\frac{1}{4} \pi\)

Correct Answer: C

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Question 14 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 15 View Details

Find the surface area of the solid formed by rotating the region bounded by \(y = x^2\) and \(y = x\) about the x-axis.

A. ( 2 pi )

B. ( 4 pi )

Correct C. ( 6 pi )

D. ( 8 pi )

Correct Answer: C

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Question 16 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 17 View Details

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

Correct A. \(-∞, -1\) ∪ (3, ∞)

B. \(-∞, -3\) ∪ (1, ∞)

C. \(-∞, 1\) ∪ (3, ∞)

D. \(-∞, -3\) ∪ (1, ∞)

Correct Answer: A

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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 + \(y + 3\)^\(2 = 16\)

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

Correct Answer: A

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Question 19 View Details

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

A. 8

Correct B. 10

C. 12

D. 14

Correct Answer: B

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Question 20 View Details

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

Correct A. \(-2, 0\)

B. \(-1, 0\)

C. \(0, -2\)

D. \(0, -1\)

Correct Answer: A

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Question 21 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 22 View Details

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

Correct A. \(-∞, -1\) ∪ (3, ∞)

B. \(-∞, -3\) ∪ (1, ∞)

C. \(-∞, 1\) ∪ (3, ∞)

D. \(-∞, -3\) ∪ (1, ∞)

Correct Answer: A

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Question 23 View Details

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

Correct A. \(y = x + 1\)

B. \(y = x - 1\)

C. \(y = -x + 1\)

D. \(y = x + 2\)

Correct Answer: A

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Question 24 View Details

A set A contains 5 elements. If 3 elements are randomly selected from set A, what is the probability that the selected elements are all distinct?

Correct A. \(1/10\)

B. \(1/5\)

C. \(1/2\)

D. \(3/5\)

Correct Answer: A

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Question 25 View Details

Find the sum of the first 10 terms of the geometric series with first term 2 and common ratio 3.

Correct A. 59048

B. 59049

C. 59050

D. 59051

Correct Answer: A

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