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POST UTME UNILORIN 2019 Mathematics | Objective

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Question 1 View Details

Determine the volume of the solid formed by revolving the region bounded by the curves \(y = x\^2\) and \(y = 4 - x\^2\) about the x-axis.

Correct A. \(\frac{16\pi}{3}\)\)

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

C. \(\frac{64\pi}{3}\)\)

D. \(\frac{128\pi}{3}\)\)

Correct Answer: A

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Question 2 View Details

Find the mean deviation about the median for the data set: 2, 4, 6, 8, 10.

A. 2

Correct B. 4

C. 6

D. 8

Correct Answer: B

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Question 3 View Details

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

Correct A. \(-\infty, 0\) \cup \(1, \infty\)

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

C. \(-\infty, 0\) \cup (0, 1)

D. (0, 1)

Correct Answer: A

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Question 4 View Details

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

Correct A. 12

B. 16

C. 20

D. 24

Correct Answer: A

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Question 5 View Details

A solid is formed by revolving the region bounded by the curves \(y = x\^2\) and \(y = 4 - x\^2\) about the x-axis. Find the volume of the solid.

Correct A. \(\frac{16\pi}{3}\)\)

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

C. \(\frac{64\pi}{3}\)\)

D. \(\frac{128\pi}{3}\)\)

Correct Answer: A

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Question 6 View Details

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

Correct A. 13

B. 14

C. 15

D. 16

Correct Answer: A

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Question 7 View Details

Solve the system of equations using matrices: \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 5 \\ 6 \end{bmatrix}.

Correct A. \begin{bmatrix} 1 \\\\ 2 \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 volume of the solid formed by revolving the region bounded by \(y = x\^2\), \(y = 0\), and \(x = 2\) about the x-axis.

Correct A. \(\frac{32\pi}{5}\)\)

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

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

D. \(\frac{64\pi}{5}\)\)

Correct Answer: A

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Question 9 View Details

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

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

B. \(-\infty, -3\) \cup \(1, \infty\)

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

D. \(-\infty, -4\) \cup \(4, \infty\)

Correct Answer: A

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Question 10 View Details

Find the surface area of the solid formed by revolving the region bounded by \(y = x\^2\), \(y = 0\), and \(x = 2\) about the x-axis.

Correct A. 16\pi

B. 32\pi

C. 64\pi

D. 128\pi

Correct Answer: A

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Question 11 View Details

Solve the system of equations using matrices: \begin{bmatrix} 2 & 1 \\ 1 & 2 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 3 \\ 4 \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 12 View Details

Find the volume of the solid formed by revolving the region bounded by \(y = x\^3\), \(y = 0\), and \(x = 2\) about the x-axis.

Correct A. \(\frac{64\pi}{7}\)\)

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

C. \(\frac{64\pi}{5}\)\)

D. \(\frac{128\pi}{7}\)\)

Correct Answer: A

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Question 13 View Details

Solve the inequality \\((x^2 - 4x + 3\)\(> 0.\)\)

A. (1, 3)

B. \(-\infty, 1\) \cup \(3, \infty\)

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

D. \(-\infty, -3\) \cup \(3, \infty\)

Correct Answer: VIEW ANSWER

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Question 14 View Details

In a random sample of 100 students, the mean height is 175 cm with a standard deviation of 5 cm. If the distribution of heights is approximately normal, what is the probability that a randomly selected student will be taller than 180 cm?

Correct A. 0.1587

B. 0.3413

C. 0.4772

D. 0.6179

Correct Answer: A

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Question 15 View Details

A circle has a radius of 4 cm. If a chord of the circle subtends an angle of 60° at the center, what is the length of the chord?

A. 4 cm

Correct B. 6 cm

C. 8 cm

D. 10 cm

Correct Answer: B

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Question 16 View Details

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

A. 2

B. 4

Correct C. 8

D. 16

Correct Answer: C

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Question 17 View Details

A histogram of exam scores has a mean of 75 and a standard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score will be between 60 and 90?

A. 0.8413

Correct B. 0.9772

C. 0.9986

D. 0.9999

Correct Answer: B

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Question 18 View Details

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

A. 32

B. 64

Correct C. 128

D. 256

Correct Answer: C

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Question 19 View Details

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

Correct A. \(\frac{-x}{x^2 + 1 \\)^{\(3/2\)}} )

B. \(\frac{x}{x^2 + 1 \\)^{\(3/2\)}} )

C. \(\frac{1}{x^2 + 1 \\)^{\(3/2\)}} )

D. \(\frac{-1}{x^2 + 1 \\)^{\(3/2\)}} )

Correct Answer: A

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Question 20 View Details

A histogram of exam scores has a mean of 75 and a standard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 60 and 90?

Correct A. 0.8413

B. 0.6915

C. 0.8413

D. 0.6915

Correct Answer: A

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Question 21 View Details

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

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 22 View Details

Solve the system of linear equations \(egin{cases} 2x + 3y = 7 \ x - 2y = -3 \end{cases}\).

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

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

C. \(x = 2, y = 2\)

D. \(x = 1, y = 1\)

Correct Answer: A

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Question 23 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 + \(y - 3\)^\(2 = 4\) )

C. \(x - 2 \\)^2 + \(y - 3\)^\(2 = 9\) )

D. \(x - 2 \\)^2 + \(y - 3\)^\(2 = 25\) )

Correct Answer: A

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Question 24 View Details

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

A. 13

Correct B. 25

C. 5

D. 9

Correct Answer: B

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Question 25 View Details

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

Correct A. \(x = -2, x = -3\)

B. \(x = 2, x = 3\)

C. \(x = -1, x = -6\)

D. \(x = 1, x = 6\)

Correct Answer: A

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