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POST UTME COAL CITY UNIVERSITY 2021 Mathematics | Objective

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Question 1 View Details

Evaluate the definite integral \(int_{0}^{1} x^2 \sqrt{1-x^2} , dx\).

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

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

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

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

Correct Answer: A

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Question 2 View Details

Find the equation of the circle with center \(-2, 3 \\) ) and radius ( 5 ).

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

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

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

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

Correct Answer: A

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Question 3 View Details

Solve the system of linear equations \(egin{cases} 2x + 3y = 7 \ 4x - 2y = -3 \end{cases}\).

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

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

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

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

Correct Answer: A

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Question 4 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'\((x) =\)\(\frac{-x}{x^2 + 1\) ^2}\)\) )

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

Correct Answer: A

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Question 5 View Details

Solve the inequality \(|x - 2| > 3\).

Correct A. \(x < -1\) or \(x > 5\)

B. \(x > -1\) or \(x < 5\)

C. \(x < 1\) or \(x > 5\)

D. \(x > 1\) or \(x < 5\)

Correct Answer: A

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Question 6 View Details

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

A. 24\pi \(cm^3\)

B. 48\pi \(cm^3\)

Correct C. 96\pi \(cm^3\)

D. 192\pi \(cm^3\)

Correct Answer: C

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Question 7 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?

A. 0.5

B. 0.6

Correct C. 0.7

D. 0.8

Correct Answer: C

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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

Find the derivative of the function f(x) = \(3x^2 + 2x - 5\).

Correct A. 6x + 2

B. 6x - 2

C. 3x + 2

D. 3x - 2

Correct Answer: A

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Question 10 View Details

Find the sum of the first 10 terms of the arithmetic progression 2, 5, 8, ...

Correct A. 155

B. 165

C. 175

D. 185

Correct Answer: A

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Question 11 View Details

A random sample of 25 students from a university had a mean height of 175 cm with a standard deviation of 5 cm. If the population standard deviation is 6 cm, calculate the standard error of the mean.

A. 2.5 cm

Correct B. 3.5 cm

C. 4.5 cm

D. 5.5 cm

Correct Answer: B

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Question 12 View Details

Find the volume of the frustum of a cone with radii 6 cm and 4 cm and height 10 cm.

A. 1000\pi \(cm^3\)

B. 1200\pi \(cm^3\)

Correct C. 1500\pi \(cm^3\)

D. 1800\pi \(cm^3\)

Correct Answer: C

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Question 13 View Details

If the matrix A = \begin{bmatrix} 2 & 1 \\ 4 & 3 \end{bmatrix} and B = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}, find the product AB.

Correct A. \begin{bmatrix} 5 & 8 \\ 11 & 16 \end{bmatrix}

B. \begin{bmatrix} 7 & 10 \\ 13 & 18 \end{bmatrix}

C. \begin{bmatrix} 9 & 12 \\ 15 & 20 \end{bmatrix}

D. \begin{bmatrix} 11 & 14 \\ 17 & 22 \end{bmatrix}

Correct Answer: A

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Question 14 View Details

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

A. 64

B. 80

Correct C. 96

D. 112

Correct Answer: C

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Question 15 View Details

A sequence is defined as \(a_1 = 2\), \(a_2 = 4\), a_\(n = a\)_{n-1} + 2. Find the 10th term of the sequence.

A. 20

B. 22

Correct C. 24

D. 26

Correct Answer: C

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Question 16 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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Question 17 View Details

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

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

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

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

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

Correct Answer: A

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Question 18 View Details

A die is rolled 5 times. Find the probability that exactly 3 of the rolls result in an even number.

Correct A. \(\frac{125}{512}\)\)

B. \(\frac{1}{32}\)\)

C. \(\frac{5}{32}\)\)

D. \(\frac{1}{16}\)\)

Correct Answer: A

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Question 19 View Details

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

A. 4

Correct B. 5

C. 6

D. 7

Correct Answer: B

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Question 20 View Details

Solve the system of linear equations \begin{align*} x + y &= 2 \ x - 2y &= -3 \end{align*}

Correct A. \left\(-1, \frac{5}{2} \right\)

B. \left\(1, -1 \right\)

C. \left\(-1, -1 \right\)

D. \left\(1, \frac{5}{2} \right\)

Correct Answer: A

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Question 21 View Details

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

A. 64\pi

B. 128\pi

Correct C. 256\pi

D. 512\pi

Correct Answer: C

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Question 22 View Details

A particle moves along the curve (y = x\^3 - \(6x^2 + 9x + 2\)\). Find the equation of the \\((y = x^3 - 6x^2 + 9x + 2\tangent line at the point where \(x = 1\).

Correct A. \(y = 3x - 5\)

B. \(y = 3x - 7\)

C. \(y = 3x - 9\)

D. \(y = 3x - 11\)

Correct Answer: A

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Question 23 View Details

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

A. 7

B. 9

Correct C. 11

D. 13

Correct Answer: C

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Question 24 View Details

A force of 3N is applied to an object at an angle of 30° to the horizontal. Find the horizontal and vertical components of the force.

Correct A. \(F_x = 2.6N\), \(F_y = 1.5N\)

B. \(F_x = 1.5N\), \(F_y = 2.6N\)

C. \(F_x = 2.6N\), \(F_y = 2.6N\)

D. \(F_x = 1.5N\), \(F_y = 1.5N\)

Correct Answer: A

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

Correct Answer: A

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