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POST UTME WELLSPRING UNIVERSITY 2021 Mathematics | Objective

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Question 1 View Details

Find the volume of the frustum of a cone with height 8 cm, lower base radius 4 cm, and upper base radius 2 cm.

A. 64\pi \(cm^3\)

Correct B. 128\pi \(cm^3\)

C. 256\pi \(cm^3\)

D. 512\pi \(cm^3\)

Correct Answer: B

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Question 2 View Details

Solve for x in the equation \(\frac{1}{2}x^2 + 3x - 5 = 0\).

Correct A. -2

B. -1

C. 4

D. 5

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. \(x + 2\)^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 4 View Details

Find the vector projection of vector \(\vec{a} = 2\hat{i} + 3\hat{j}\) onto vector \(\vec{b} = \hat{i} + \hat{j}\).

Correct A. \(\frac{5}\){\(\sqrt{2}\)}\)\hat{i} + \(\frac{5}\){\(\sqrt{2}\)}\)\hat{j}

B. \(\frac{5}\){\(\sqrt{2}\)}\)\hat{i} - \(\frac{5}\){\(\sqrt{2}\)}\)\hat{j}

C. \(\frac{5}\){\(\sqrt{2}\)}\)\hat{i} + \(\frac{5}\){\(\sqrt{2}\)}\)\hat{j}

D. \(\frac{5}\){\(\sqrt{2}\)}\)\hat{i} - \(\frac{5}\){\(\sqrt{2}\)}\)\hat{j}

Correct Answer: A

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Question 5 View Details

Find the derivative of the function (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 6 View Details

Let X and Y be independent random variables with probability density functions f_\(X(x) = 2x\), \(0 < x\) < 1 and f_\(Y(y) =\)\(3y^2\),\((0 < y\)\) < 1. Find the probability that \(X + Y < 1\\((0 < y) < 1. Find the probability that\).

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 7 View Details

Find the area of the region bounded by the curves \(y = x\^2\) and \(y = 2x - 1\).

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

Correct B. \(\frac{3}{4}\)\)

C. \(\frac{5}{6}\)\)

D. \(\frac{7}{8}\)\)

Correct Answer: B

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Question 8 View Details

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

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

B. \begin{bmatrix} 2 \\ 1 \end{bmatrix}

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

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

Correct Answer: A

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Question 9 View Details

Find the volume of the solid formed by revolving the region bounded by the curves \(y = x\^2\) and \(y = 2x - 1\) about the x-axis.

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

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

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

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

Correct Answer: B

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Question 10 View Details

Find the area under the curve \(y = x\^3 - 6x^2 + 9x + 2\) from \(x = 0\) to \(x = 2\).

A. \(\frac{28}{3}\)\)

Correct B. \(\frac{32}{3}\)\)

C. \(\frac{36}{3}\)\)

D. \(\frac{40}{3}\)\)

Correct Answer: B

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