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POST UTME UNN 2018 Mathematics | Objective

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Question 1 View Details

Find the volume of the frustum of a cone with a height of 6 cm, a lower base radius of 4 cm, and an upper base radius of 2 cm.

A. 48\pi

B. 64\pi

Correct C. 72\pi

D. 80\pi

Correct Answer: C

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Question 2 View Details

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

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

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

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

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

Correct Answer: A

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Question 3 View Details

A circle is inscribed in a square of side length 10 cm. Find the area of the shaded region.

A. 50\pi

Correct B. 100\pi

C. 200\pi

D. 250\pi

Correct Answer: B

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Question 4 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. \(y = x + 1\)

D. \(y = x - 1\)

Correct Answer: A

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Question 5 View Details

A right triangle has a hypotenuse of length 10 cm and one leg of length 6 cm. Find the length of the other leg.

Correct A. 8\sqrt{3}

B. 6\sqrt{3}

C. 8\sqrt{2}

D. 6\sqrt{2}

Correct Answer: A

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Question 6 View Details

A random variable X has a probability distribution given by P(X) = \(1/2\)^\(X-1\) for \(X = 1\), 2, 3, ... . Find the probability that X is greater than 2.

Correct A. \(1/4\)

B. \(1/2\)

C. \(3/4\)

D. 1

Correct Answer: A

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Question 7 View Details

Solve the matrix equation (AX = B\), where A = \begin{bmatrix} 2 & 1 \\\(((AX = B)\), where A = \\ 1 & 2 \end{bmatrix},\(X =\)\begin{bmatrix} x \\ y \end{bmatrix}, and B = \begin{bmatrix} 3 \\ 4 \end{bmatrix}.

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

B. \begin{bmatrix} 2 \\ 3 \end{bmatrix}

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

D. \begin{bmatrix} 4 \\ 5 \end{bmatrix}

Correct Answer: A

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Question 8 View Details

Find the area under the curve \(y = x\^2\) from \(x = 0\) to \(x = 4\).

Correct A. 16

B. 32

C. 64

D. 128

Correct Answer: A

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Question 9 View Details

Solve the trigonometric equation sin(x) = \cos(x) for \(0 \\(sin(x) = cos(x) for \le x\)\(\le 2\)π.

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

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

C. \(\frac{5\pi}{4}\)\)

D. \(\frac{7\pi}{4}\)\)

Correct Answer: A

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Question 10 View Details

Find the solution to the quadratic equation \\((x^2 + 5x + 6\)\(= 0.\)\)

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

B. \begin{bmatrix} -3 \\ -2 \end{bmatrix}

C. \begin{bmatrix} 2 \\ 3 \end{bmatrix}

D. \begin{bmatrix} 3 \\ 2 \end{bmatrix}

Correct Answer: A

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Question 11 View Details

Determine the mean of the following dataset: {1, 3, 5, 7, 9}.

A. 2

Correct B. 4

C. 6

D. 8

Correct Answer: B

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Question 12 View Details

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

Correct A. \(\frac{4\pi}{3}\)\)

B. \(\frac{8\pi}{3}\)\)

C. \(\frac{16\pi}{3}\)\)

D. \(\frac{32\pi}{3}\)\)

Correct Answer: A

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Question 13 View Details

Solve the differential equation \(\frac{dy}{dx}\)\) = \(\frac{y}{x}\)\) using the chain rule.

Correct A. \(y =\)\ln|x|

B. \(y =\)\ln|\(x^2\)|

C. \(y =\)\ln|\(x^3\)|

D. \(y =\)\ln|\(x^4\)|

Correct Answer: A

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Question 14 View Details

Find the equation of the tangent line to the curve \(y = x\^2\\(tangent line to the curve (y = x\) at the point (1, 1).

Correct A. \(y = 2x - 1\)

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

C. \(y = 3x - 1\)

D. \(y = 3x + 1\)

Correct Answer: A

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Question 15 View Details

Determine the number of solutions to the equation \\((x^2 + 2x + 2\)\(= 0.\)\)

A. 0

Correct B. 1

C. 2

D. 3

Correct Answer: B

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Question 16 View Details

Find the volume of the frustum of a cone with height 6cm, lower base radius 4cm and upper base radius 2cm.

A. 24π\(cm^3\)

Correct B. 48π\(cm^3\)

C. 96π\(cm^3\)

D. 192π\(cm^3\)

Correct Answer: B

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Question 17 View Details

A histogram of exam scores has a mean of 70 and a standard deviation of 10. What is the probability that a randomly selected score is between 60 and 80?

A. 0.5

B. 0.6

Correct C. 0.7

D. 0.8

Correct Answer: C

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Question 18 View Details

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

A. 14

B. 16

Correct C. 18

D. 20

Correct Answer: C

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Question 19 View Details

Solve the equation \\((2x^2 + 5x - 3\)\(= 0\)\) using the quadratic formula.

Correct A. \(x = -1\)± \(√2\)

B. \(x = 1\) ± \(√2\)

C. \(x = -1\)± \(√3\)

D. \(x = 1\) ± \(√3\)

Correct Answer: A

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Question 20 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. \(y = x - 1\)

D. \(y = x + 1\)

Correct Answer: A

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Question 21 View Details

Let X be a random variable with probability density function f(x) = \(\frac{1}{2}e^{-|x|}\) for -∞\(< x\)< ∞. Find the probability that X is greater than 1.

Correct A. 0.5

B. 0.6

C. 0.7

D. 0.8

Correct Answer: A

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Question 22 View Details

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

Correct A. \(-∞, -1\) ∪ (3, ∞)

B. \(-∞, -3\) ∪ (1, ∞)

C. \(-∞, -1\) ∪ (1, ∞)

D. \(-∞, 1\) ∪ (3, ∞)

Correct Answer: A

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Question 23 View Details

Find the value of x in the equation \(x^3 - 2x^2 - 5x + 6 = 0\).

A. 1

Correct B. -1

C. 2

D. -2

Correct Answer: B

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Question 24 View Details

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

A. 0

Correct B. -2

C. 2

D. -4

Correct Answer: B

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Question 25 View Details

Find the value of y in the equation (y = 2x + 3\), given that \(x = 2\\((y = 2x + 3), given that\).

Correct A. 7

B. 5

C. 3

D. 1

Correct Answer: A

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