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POST UTME BOWEN UNIVERSITY 2019 Mathematics | Objective

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Question 1 View Details

Find the determinant of the matrix [ egin{pmatrix} 2 & 3 & 1 \ 4 & 5 & 2 \ 1 & 2 & 3 \end{pmatrix} ].

Correct A. 13

B. 15

C. 17

D. 19

Correct Answer: A

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Question 2 View Details

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

Correct A. -2

B. -1

C. 1

D. 2

Correct Answer: A

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Question 3 View Details

Find the sum of the first 5 terms of the geometric progression [ 2, 6, 18, 54, ... ].

Correct A. 728

B. 7280

C. 72800

D. 728000

Correct Answer: A

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Question 4 View Details

In the circuit below, find the current through the 2-ohm resistor.

A. 1 A

Correct B. 2 A

C. 3 A

D. 4 A

Correct Answer: B

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Question 5 View Details

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

Correct A. 6x + 2

B. 6x - 2

C. \(3x^2 + 2\)

D. \(3x^2 - 2\)

Correct Answer: A

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Question 6 View Details

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

Correct A. \(\frac{y - 3}{x - 2}\)\) = \(\frac{5 - 3}{4 - 2}\)\)

B. \(\frac{y - 2}{x - 3}\)\) = \(\frac{5 - 3}{4 - 2}\)\)

C. \(\frac{y - 3}{x - 4}\)\) = \(\frac{5 - 3}{4 - 2}\)\)

D. \(\frac{y - 2}{x - 4}\)\) = \(\frac{5 - 3}{4 - 2}\)\)

Correct Answer: A

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Question 7 View Details

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

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

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

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

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

Correct Answer: B

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Question 8 View Details

Simplify the expression \(\sqrt{\(\frac{16}{25}\)\)}\).

Correct A. \(\frac{4}{5}\)\)

B. \(\frac{2}{5}\)\)

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

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

Correct Answer: A

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Question 9 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. \(x - 4\)^2 + \(y - 3\)^\(2 = 16\)

D. \(x - 3\)^2 + \(y - 4\)^\(2 = 16\)

Correct Answer: A

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Question 10 View Details

Find the sum of the first 5 terms of the geometric series with first term 2 and common ratio 3.

Correct A. 2 + 6 + 18 + 54 + 162

B. 2 + 6 + 18 + 54 + 162 + 486

C. 2 + 6 + 18 + 54 + 162 + 486 + 1458

D. 2 + 6 + 18 + 54 + 162 + 486 + 1458 + 4374

Correct Answer: A

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Question 11 View Details

A cylindrical water \tank has a height of 10m and a radius of 4m. If the water level is 6m, find the volume of water in the \tank.

A. 1000\pi

Correct B. 1200\pi

C. 1500\pi

D. 1800\pi

Correct Answer: B

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Question 12 View Details

A histogram of exam scores has a mean of 75 and a standard deviation of 10. If the scores are normally distributed, find 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 13 View Details

In a game of chance, two events A and B are independent. If the probability of event A occurring is 0.4 and the probability of event B occurring is 0.6, find the probability that both events occur.

A. 0.2

Correct B. 0.24

C. 0.28

D. 0.32

Correct Answer: B

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Question 14 View Details

Solve the equation \(x^2 + 4x - 5 = 0\) using the quadratic formula.

Correct A. \(x = -5, 1\)

B. \(x = -1, 5\)

C. \(x = 1, -5\)

D. \(x = -1, -5\)

Correct Answer: A

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Question 15 View Details

A cone has a height of 8cm and a radius of 4cm. If the volume of the cone is 256\pi cubic cm, find the height of the cone.

A. 2cm

B. 4cm

Correct C. 6cm

D. 8cm

Correct Answer: C

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Question 16 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. 48\pi

B. 64\pi

Correct C. 72\pi

D. 80\pi

Correct Answer: C

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Question 17 View Details

A die is rolled twice. What is the probability that the sum of the two numbers shown is 7?

Correct A. \(1/6\)

B. \(1/12\)

C. \(1/36\)

D. \(1/24\)

Correct Answer: A

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Question 18 View Details

Solve the inequality \(\frac{x-2}{x+1}\)\\() > 0.\)

Correct A. x < -1 or \(x > 2\)

B. x > -1 or \(x < 2\)

C. \(x < 2\) or x > -1

D. \(x > 2\) or x < -1

Correct Answer: A

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Question 19 View Details

Find the value of sin 2x if \\(cos x =\)\(\\(sin 2x if cos x = \frac{3}{5}\)\) and \\(sin x =\)\(\frac{4}{5}\)\).

Correct A. \(\frac{24}{25}\)\)

B. \(\frac{16}{25}\)\)

C. \(\frac{20}{25}\)\)

D. \(\frac{12}{25}\)\)

Correct Answer: A

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Question 20 View Details

Simplify the expression \(\frac{\sqrt{12}}{\sqrt{3}}\).

Correct A. 2\sqrt{3}

B. \(\sqrt{3}\)

C. 2

D. \(\sqrt{12}\)

Correct Answer: A

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Question 21 View Details

Find the equation of the circle passing through the points (1, 2), (3, 4), and (5, 6).

Correct A. \boxed{\(x^2\) + \\((y^2 - 12x - 8y + 36\)\(= 0\)\)}

B. \(x^2\) + \\((y^2 - 10x - 6y + 20\)\(= 0\)\)

C. \(x^2\) + \\((y^2 - 14x - 10y + 40\)\(= 0\)\)

D. \(x^2\) + \\((y^2 - 16x - 12y + 48\)\(= 0\)\)

Correct Answer: A

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Question 22 View Details

Solve the equation \(\sin^2 x + \cos^2 x - \(1x\)\(1x = 0\)\) for x.

Correct A. \boxed{\(x =\)\(\frac{\pi}{4}\)\) + 2kpi}

B. \(x =\)\(\frac{3\pi}{4}\)\) + 2kpi

C. \(x =\)\(\frac{5\pi}{4}\)\) + 2kpi

D. \(x =\)\(\frac{7\pi}{4}\)\) + 2kpi

Correct Answer: A

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Question 23 View Details

Find the derivative of the function \(f(x) = \frac{x^2 + 3x + 2}{x^2 - 4x + 3}\) using the quotient rule.

Correct A. \boxed{\(\frac{2x^2 + 5x + 4}{\) \(x^2 - 4x + 3\) ^2}\)\)}

B. \(\frac{2x^2 + 3x + 2}{\) \(x^2 - 4x + 3\) ^2}\)\)

C. \(\frac{2x^2 + 5x + 4}{\) \(x^2 - 4x + 3\) ^2}\)\)

D. \(\frac{2x^2 + 3x + 2}{\) \(x^2 - 4x + 3\) ^2}\)\)

Correct Answer: A

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Question 24 View Details

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

Correct A. \boxed{x \leq -\(\frac{3}{2}\)\) \text{ or } x \geq \(\frac{1}{2}\)\)}

B. x \leq -\(\frac{3}{2}\)\) \text{ or } x \geq -\(\frac{1}{2}\)\)

C. x \leq -\(\frac{1}{2}\)\) \text{ or } x \geq \(\frac{3}{2}\)\)

D. x \leq -\(\frac{1}{2}\)\) \text{ or } x \geq -\(\frac{3}{2}\)\)

Correct Answer: A

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Question 25 View Details

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

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

B. \(y =\)\(\frac{2}{3}\)\) x + \(\frac{1}{3}\)\)

C. \(y =\)\(\frac{2}{4}\)\) x + \(\frac{1}{4}\)\)

D. \(y =\)\(\frac{2}{5}\)\) x + \(\frac{1}{5}\)\)

Correct Answer: A

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