POST UTME ELIZADE UNIVERSITY 2023 Mathematics | Objective

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Question 1 View Details
Let ( X ) be a random variable with probability density function ( f(x) = egin{cases} 2x & 0 leq x leq 1 \ 0 & \text{otherwise} \end{cases} ). Find the probability that ( X ) takes a value greater than 0.5.
Correct A. 0.25
B. 0.5
C. 0.75
D. 1

Correct Answer: A

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Question 2 View Details
Solve the inequality \(\frac{x^2 - 4}{x^2 - 9} > 0\).
A. \(-3, -1\) \cup (1, 3)
B. \(-3, -1\) \cup (1, 3) \cup \(4, \infty\)
Correct C. \(-3, -1\) \cup (1, 3) \cup \(-\infty, -4\) \cup \(4, \infty\)
D. \(-3, -1\) \cup (1, 3) \cup \(-\infty, -4\) \cup \(4, \infty\) \cup (0, 1)

Correct Answer: C

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Question 3 View Details
Find the area under the curve \(y = \frac{1}{x^2 + 1}\) from \(x = 0\) to \(x = 1\).
Correct A. \(\frac{\pi}{4}\)\)
B. \(\frac{\pi}{2}\)\)
C. \(\frac{\pi}{3}\)\)
D. \(\frac{\pi}{6}\)\)

Correct Answer: A

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Question 4 View Details
Solve the equation \(x^3 - 6x^2 + 11x - 6 = 0\).
A. 1
B. 2
Correct C. 3
D. 4

Correct Answer: C

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Question 5 View Details
Find the sum of the infinite geometric series \(\sum_{n = 1}^\infty \frac{2}{3^n}\).
A. \(\frac{2}{3}\)\)
Correct B. \(\frac{2}{3}\)\) \cdot \(\frac{1}\){1 - \(\frac{1}{3}\)}\)
C. \(\frac{2}{3}\)\) \cdot \(\frac{1}\){1 - \(\frac{1}{3}\)}\) \cdot \(\frac{1}\){1 - \(\frac{1}{3}\)}\)
D. \(\frac{2}{3}\)\) \cdot \(\frac{1}\){1 - \(\frac{1}{3}\)}\) \cdot \(\frac{1}\){1 - \(\frac{1}{3}\)}\) \cdot \(\frac{1}\){1 - \(\frac{1}{3}\)}\)

Correct Answer: B

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Question 6 View Details
A random variable X has a probability distribution given by P\(X = 1 = 0.4\), P\(X = 2 = 0.3\), P\(X = 3 = 0.2\), and P\(X = 4 = 0.1\). What is the expected value of X?
A. 1.2
Correct B. 1.8
C. 2.4
D. 3.0

Correct Answer: B

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Question 7 View Details
Solve for x in the equation \(2^x + 5^x = 7^x\)
A. \log(7) - \log(5)
Correct B. \log(7) - \log(2)
C. \log(5) - \log(2)
D. \log(7) - \log(2) + \log(5)

Correct Answer: B

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Question 8 View Details
Find the determinant of the matrix \(\begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{bmatrix}\)
Correct A. 0
B. 1
C. 2
D. 3

Correct Answer: A

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Question 9 View Details
A histogram of exam scores has a mean of 60 and a standard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score will be greater than 70?
A. 0.1587
B. 0.3413
C. 0.4772
Correct D. 0.6827

Correct Answer: D

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Question 10 View Details
Solve the quadratic equation \(x^2 + 4x + 4 = 0\)
Correct A. \(x = -2\)
B. \(x = -1\)
C. \(x = 0\)
D. \(x = 1\)

Correct Answer: A

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