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POST UTME IGBINEDION UNIVERSITY 2020 Mathematics | Objective

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Question 1 View Details

Determine the equation of the circle with center at ((2,3)) and radius (5).

Correct A. \(x^2 + y^2 - 4x + 6y + 4 = 0\)

B. \(x^2 + y^2 + 4x - 6y + 4 = 0\)

C. \(x^2 + y^2 - 4x - 6y + 4 = 0\)

D. \(x^2 + y^2 + 4x + 6y + 4 = 0\)

Correct Answer: A

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Question 2 View Details

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

Correct A. (f'\((x) = -\)\(\frac{2x}{x^2 + 1\) ^2}\)\))

B. (f'\((x) =\)\(\frac{2x}{x^2 + 1\) ^2}\)\))

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

D. (f'\((x) = -\)\(\frac{2}{x^2 + 1\) ^2}\)\))

Correct Answer: A

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Question 3 View Details

Solve the inequality \(x^2 - 6x + 8 > 0\).

Correct A. \(x < 2\) or \(x > 4\)

B. \(x > 2\) or \(x < 4\)

C. \(x < 4\) or \(x > 2\)

D. \(x > 4\) or \(x < 2\)

Correct Answer: A

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Question 4 View Details

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

Correct A. \(y = \frac{1}{2}x + \frac{1}{2}\)

B. \(y = \frac{1}{2}x - \frac{1}{2}\)

C. \(y = 2x - 1\)

D. \(y = 2x + 1\)

Correct Answer: A

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Question 5 View Details

A vector (mathbf{a}) has magnitude (5) and direction \(60^circ\) from the positive x-axis. Find the vector (mathbf{a}).

Correct A. \(\mathbf{a} = egin{pmatrix} 4 \ 3 \end{pmatrix}\)

B. \(\mathbf{a} = egin{pmatrix} 3 \ 4 \end{pmatrix}\)

C. \(\mathbf{a} = egin{pmatrix} 5 \ 0 \end{pmatrix}\)

D. \(\mathbf{a} = egin{pmatrix} 0 \ 5 \end{pmatrix}\)

Correct Answer: A

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Question 6 View Details

A random experiment consists of rolling a fair six-sided die and then tossing a fair coin. If the number on the die is even, the coin is tossed twice; otherwise, the coin is tossed only once. What is the probability that the number of heads observed is at least 2?

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

Correct B. \(\frac{2}{3}\)\)

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

D. \(\frac{4}{5}\)\)

Correct Answer: B

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Question 7 View Details

Let \(\mathbf{a} = \begin{pmatrix} 1 \ 2 \ 3 \end{pmatrix}\) and \(\mathbf{b} = \begin{pmatrix} 4 \ 5 \ 6 end{pmatrix}\). Find the cross product \(\\(end{pmatrix}). Find the cross product \mathbf{a} \times \mathbf{b}\).

Correct A. \begin{pmatrix} -3 \ 6 \ -6 \end{pmatrix}

B. \begin{pmatrix} 6 \ -3 \ 6 \end{pmatrix}

C. \begin{pmatrix} 3 \ -6 \ 3 \end{pmatrix}

D. \begin{pmatrix} -6 \ 3 \ -3 \end{pmatrix}

Correct Answer: A

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Question 8 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 9 View Details

Let \(S = \{1, 2, 3, \ldots, 10 \}\). Find the number of subsets of \(S\) that contain exactly three elements.

A. 120

B. 210

Correct C. 252

D. 300

Correct Answer: C

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Question 10 View Details

Find the sum of the first (n\) terms of the geometric series \(2 + 6 + 18 + \\((n) terms of the geometric series \ldots\).

Correct A. \(\frac{2 r^n - 1\) }{r - 1}\)\)

B. \(\frac{2 r^n - 1\) }{r + 1}\)\)

C. \(\frac{2 r^n + 1\) }{r - 1}\)\)

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

Correct Answer: A

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