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POST UTME NILE UNIVERSITY 2024 Mathematics | Objective

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Question 1 View Details

In the complex plane, the points \(z_1 = 2 + 3i\) and \(z_2 = 4 - 5i\) are represented by vectors \(\mathbf{z}_1\) and \(mathbf{z}_2\), respectively. Find the magnitude of the vector \(\\(mathbf{z}_2), respectively. Find the magnitude of the vector \mathbf{z}_1 + \mathbf{z}_2\).

Correct A. \(\sqrt{10}\)

B. \(\sqrt{20}\)

C. \(\sqrt{30}\)

D. \(\sqrt{40}\)

Correct Answer: A

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Question 2 View Details

Let \(f(x) = \log_{10} x^2\)\). Find the value of \(f^{-1}(4)\).

A. 2

B. 4

Correct C. 10

D. 20

Correct Answer: C

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Question 3 View Details

A circle with center \(C\) and radius \(r\) passes through the points \(A(1, 2)\) and \(B(4, 6)\). Find the equation of the circle in the form \(x - h\)^2 + \(y - k\)^\(2 = r\^2\)\).

A. \(x - 2.5\)^2 + \(y - 4\)^\(2 = 2.5\^2\)

Correct B. \(x - 2.5\)^2 + \(y - 4\)^\(2 = 5\^2\)

C. \(x - 2.5\)^2 + \(y - 4\)^\(2 = 7.5\^2\)

D. \(x - 2.5\)^2 + \(y - 4\)^\(2 = 10\^2\)

Correct Answer: B

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Question 4 View Details

A polynomial \(p(x)\) has roots \(x = 1\) and (x = -2\). If \(p(0) = 12\\((x = -2). If\), find the value of \(p(3)\).

A. -3

B. 6

Correct C. 9

D. 12

Correct Answer: C

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Question 5 View Details

A random variable (X\) has a probability distribution given by \(P X = x\\((X) has a probability distribution given by\) = \(\frac{1}{2}\)\) cdot \(\frac{1}{2}\)\) = \(\frac{1}{4}\)\)) for \(x = 1, 2, 3, 4\). Find the expected value of \\() for (x = 1, 2, 3, 4\(X\).

A. 1.5

Correct B. 2

C. 2.5

D. 3

Correct Answer: B

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Question 6 View Details

Determine the value of \(\int_{0}^{\pi} \frac{\sin^2 x}{1 + \cos^2 x} dx\).

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

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

C. \(\frac{\pi}{8}\)\)

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

Correct Answer: A

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Question 7 View Details

A histogram of exam scores is shown below. If the mean score is 75, what is the median score?

A. 70

Correct B. 75

C. 80

D. 85

Correct Answer: B

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Question 8 View Details

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

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

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

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

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

Correct Answer: A

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Question 9 View Details

A vector (\(\vec{a}\)\) has a magnitude of 5 and points in the direction of \\((vec{a}\(\frac{1}{\sqrt{2}} \hat{i} + \frac{1}{sqrt{2}} \hat{j}\). Find the magnitude of the vector \\(sqrt{2}} hat{j}\(vec{a} + \vec{b}\), where \\(vec{a} + vec{b}\(vec{b}\) is a vector with a magnitude of 3 and points in the opposite direction of \(\\(vec{b}) is a vector with a magnitude of 3 and points in the opposite direction of \vec{a}\).

A. 2

B. 4

Correct C. 6

D. 8

Correct Answer: C

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Question 10 View Details

Solve the equation \(\sin^2 x + \cos^2 x = 1\) for (x\) in the interval \([0, 2\\((x) in the interval \pi]\).

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

Correct B. \(\frac{\pi}{2}\)\)

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

D. \pi

Correct Answer: B

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Question 11 View Details

A random sample of 25 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 6.1 cm, calculate the 95% confidence interval for the population mean.

Correct A. 168.1 cm, 182.9 cm

B. 170.5 cm, 180.5 cm

C. 172.1 cm, 178.9 cm

D. 174.5 cm, 176.5 cm

Correct Answer: A

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Question 12 View Details

Solve the following system of linear equations using matrices: \(\begin{align*} x + y + z & = 6 \ 2x - 3y + z & = 9 \ x - 2y + 3z & = 2 \end{align*}\)

Correct A. \(\begin{align*} x & = 1 \ y & = 2 \ z & = 3 \end{align*}\)

B. \(\begin{align*} x & = 2 \ y & = 1 \ z & = 3 \end{align*}\)

C. \(\begin{align*} x & = 3 \ y & = 2 \ z & = 1 \end{align*}\)

D. \(\begin{align*} x & = 1 \ y & = 3 \ z & = 2 \end{align*}\)

Correct Answer: A

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Question 13 View Details

A sequence is defined as: \(a_n = \frac{1}{n} + \frac{1}{n+1}\) Calculate the sum of the first 10 terms of the sequence.

Correct A. 2.928968253

B. 2.928968253

C. 2.928968253

D. 2.928968253

Correct Answer: A

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Question 14 View Details

A set of 5 numbers has a mean of 10 and a standard deviation of 2. If the numbers are 8, 12, 15, 18, and x, find the value of x.

Correct A. 20

B. 22

C. 24

D. 26

Correct Answer: A

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Question 15 View Details

A probability experiment consists of rolling a fair six-sided die. If the die lands on an even number, you win ₦100. If it lands on an odd number, you lose ₦50. What is the expected value of this experiment?

Correct A. ₦25

B. ₦50

C. ₦75

D. ₦100

Correct Answer: A

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Question 16 View Details

Determine the sum of the infinite geometric series - 3 + 6 + 12 + … with first term - 3 and common ratio 2.

Correct A. 9

B. -3

C. 12

D. -9

Correct Answer: A

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Question 17 View Details

Solve for x in the equation - \\((2x^2 + 5x - 3\)\(= 0.\)\)

A. 1

Correct B. 2

C. 3

D. 4

Correct Answer: B

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Question 18 View Details

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

Correct A. 16

B. 32

C. 64

D. 128

Correct Answer: A

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Question 19 View Details

A fair six-sided die is rolled. What is the probability that the number rolled is greater than 4?

A. \(1/6\)

B. \(1/3\)

C. \(2/3\)

Correct D. \(5/6\)

Correct Answer: D

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Question 20 View Details

Simplify the expression √\(16x^2y^2\).

Correct A. 4xy

B. 2xy

C. \(4x^2y\)

D. \(2x^2y\)

Correct Answer: A

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Question 21 View Details

Find the value of \(\int_0^1 \frac{1}{x^2 + 2x + 2} dx\).

Correct A. 0.5

B. 1

C. 1.5

D. 2

Correct Answer: A

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Question 22 View Details

Solve for (x\) in the equation \(\\((x) in the equation \log_2 2x - 1\)\(= 3\)\).

A. 2

Correct B. 3

C. 4

D. 5

Correct Answer: B

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Question 23 View Details

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

A. 10

B. 12

Correct C. 15

D. 18

Correct Answer: C

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Question 24 View Details

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

Correct A. \(-∞, -1\) ∪ (4, ∞)

B. \(-∞, 1\) ∪ (2, ∞)

C. \(-∞, -1\) ∪ (1, ∞)

D. \(-∞, 1\) ∪ (4, ∞)

Correct Answer: A

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Question 25 View Details

Find the value of \(\sum_{n = 1}^5 n^2\).

Correct A. 55

B. 65

C. 75

D. 85

Correct Answer: A

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