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POST UTME RHEMA UNIVERSITY 2017 Mathematics | Objective

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Question 1 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 2 View Details

A box contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is not blue?

Correct A. \(\frac{2}{3}\)

B. \(\frac{3}{5}\)

C. \(\frac{1}{3}\)

D. \(\frac{4}{5}\)

Correct Answer: A

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Question 3 View Details

Solve the equation \(2^x + 2^{x+1} = 3 \cdot 2^{x+1}\) for ( x ).

A. \(x = -1\)

Correct B. \(x = 0\)

C. \(x = 1\)

D. \(x = 2\)

Correct Answer: B

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Question 4 View Details

Find the area of the triangle with vertices ( A(0, 0) ), ( B(2, 0) ), and ( C(1, 3) ).

A. ( 3 )

B. ( 6 )

Correct C. ( 9 )

D. ( 12 )

Correct Answer: C

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Question 5 View Details

A circle has a radius of 4 cm. Find the area of the sector with a central angle of 60°.

A. ( 12pi )

Correct B. ( 16pi )

C. ( 20pi )

D. ( 24pi )

Correct Answer: B

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Question 6 View Details

Let S = {x in mathbb{R} : \\((x^2 + 2x + 1\)\(= 0\)\)}. Find lim_{x \to 2} \(\frac{x^2 - 4}{x - 2}\)\)\) if it exists.

A. 4

B. 2

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

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

Correct Answer: D

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Question 7 View Details

A binary operation ( odot ) on the set (\mathbb{R}\) is defined as \\((mathbb{R}\(x odot y = xy + 1\). Find ( (2 odot 3) odot 4 ).

A. 25

Correct B. 29

C. 33

D. 37

Correct Answer: B

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Question 8 View Details

Find the probability that at least one of two independent events ( A ) and ( B ) occurs, given that ( P(A) = \(\frac{1}{2}\)\) ) and ( P(B) = \(\frac{1}{3}\)\) ).

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

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

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

D. \(\frac{7}{12}\)\)

Correct Answer: C

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Question 9 View Details

A vector ( mathbf{a} ) is given by \(\mathbf{a} = 2\mathbf{i} + 3\mathbf{j}\). Find the magnitude of ( mathbf{a} ).

Correct A. \(\sqrt{13}\)

B. \(\sqrt{17}\)

C. \(\sqrt{25}\)

D. \(\sqrt{29}\)

Correct Answer: A

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Question 10 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. \(-\infty, 1\) \cup \(3, \infty\)

Correct Answer: A

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Question 11 View Details

A random sample of 16 students from a university had a mean height of 175.5 cm with a standard deviation of 5.2 cm. If the population standard deviation is unknown, calculate the 95% confidence interval for the population mean.

A. 173.2 cm, 177.8 cm

Correct B. 174.1 cm, 176.9 cm

C. 172.9 cm, 178.1 cm

D. 173.5 cm, 177.5 cm

Correct Answer: B

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Question 12 View Details

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

A. \(10^4\)

Correct B. \(10^8\)

C. \(10^12\)

D. \(10^16\)

Correct Answer: B

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Question 13 View Details

A bakery sells 250 loaves of bread per day at ₦120 per loaf. If the \cost price per loaf is ₦80, calculate the profit per loaf and the total profit per day.

Correct A. ₦40, ₦10,000

B. ₦30, ₦8,000

C. ₦20, ₦6,000

D. ₦10, ₦4,000

Correct Answer: A

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Question 14 View Details

In the circuit below, identify the component labeled A.

Correct A. Resistor

B. Battery

C. Capacitor

D. Inductor

Correct Answer: A

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Question 15 View Details

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

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

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

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

D. \(x = 1\), \(x = 4\)

Correct Answer: A

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Question 16 View Details

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

A. 2

Correct B. -3

C. -2

D. 1

Correct Answer: B

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Question 17 View Details

A set of 10 numbers has a mean of 20. If 5 is added to each number, what is the new mean?

Correct A. 22.5

B. 25

C. 20

D. 22

Correct Answer: A

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Question 18 View Details

Find the sum of the first 5 terms of the geometric series ( 2, 6, 18, ... ).

Correct A. 62

B. 64

C. 60

D. 58

Correct Answer: A

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Question 19 View Details

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

Correct A. 7

B. 6

C. 5

D. 4

Correct Answer: A

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Question 20 View Details

Solve the inequality \(x^2 - 4x - 5 > 0\).

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 21 View Details

Find the value of x in the equation \(\log_{10} x^2 \\)\(= 4 ).\)

A. 10

Correct B. 100

C. 1000

D. 10000

Correct Answer: B

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Question 22 View Details

Solve the matrix equation \(egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 5 \ 6 \end{bmatrix}\).

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

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

C. \(x = 3\), \(y = 4\)

D. \(x = 4\), \(y = 5\)

Correct Answer: A

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Question 23 View Details

A circle has a radius of 5 units. Find the area of the circle.

A. 25π

Correct B. 50π

C. 75π

D. 100π

Correct Answer: B

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Question 24 View Details

Find the value of x in the equation \(x^2 + 4x + 4 = 0\).

Correct A. -2

B. -1

C. 1

D. 2

Correct Answer: A

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Question 25 View Details

A die is rolled. Find the probability that the number obtained is greater than 4.

A. \(1/6\)

B. \(1/3\)

C. \(1/2\)

Correct D. \(2/3\)

Correct Answer: D

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