POST UTME UNN 2017 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the area of the triangle with vertices \( A(0, 0), B(3, 0), C(0, 4) \).
A. 12
B. 18
C. 24
D. 30
Question 2
Solve the equation \( \log_{10} \( x^2 \ \) = 4 ) for x.
A. 2
B. 4
C. 8
D. 16
Question 3
Find the mean of the set of numbers: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20.
A. 10
B. 12
C. 14
D. 16
Question 4
A set of numbers has a mean of 10 and a s\tandard deviation of 2. Find the probability that a randomly selected number from the set is greater than 12.
A. \( P\( X > 12 \) = 0.25 \)
B. \( P\( X > 12 \) = 0.5 \)
C. \( P\( X > 12 \) = 0.75 \)
D. \( P\( X > 12 \) = 0.9 \)
Question 5
A sequence is defined by the recurrence relation \( a_n = 2a_{n-1} + 3 \) with initial term \( a_1 = 2 \). Find the value of \( a_5 \).
A. 37
B. 41
C. 45
D. 49
Question 6
Solve the quadratic equation: \( x^2 + 4x + 4 = 0 \).
A. \( x = -2 \)
B. \( x = -1 \)
C. \( x = 0 \)
D. \( x = 2 \)
Question 7
Solve for x in the equation \( \sin^2 x + \cos^2 x = 1 \) u\sing the identity \( \sin^2 x + \cos^2 x = 1 \).
A. x = \frac{\pi}{4}
B. x = \frac{3\pi}{4}
C. x = \frac{5\pi}{4}
D. x = \frac{7\pi}{4}
Question 8
A company produces two products, A and B. The profit from product A is $10 per unit, and the profit from product B is $15 per unit. If the company produces 100 units of product A and 50 units of product B, what is the total profit?
A. $1500
B. $2000
C. $2500
D. $3000
Question 9
In the diagram below, ( ABC ) is a right-angled triangle with \( AB = 6 \) cm and \( BC = 8 \) cm. Find the length of the hypotenuse ( AC ).
A. 10
B. 12
C. 14
D. 16
Question 10
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \boxed{\( -\infty, -1 \) \cup \( 3, \infty \)}
B. \( -\infty, 1 \) \cup \( 3, \infty \)
C. \( -\infty, -1 \) \cup \( 1, \infty \)
D. \( -\infty, 1 \) \cup \( -3, \infty \)
Question 11
A histogram of exam scores has a mean of 70 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score will be between 60 and 80?
A. 0.9544
B. 0.8413
C. 0.6915
D. 0.6827
Question 12
Find the surface area of the solid formed by revolving the region bounded by the curve \( y = x^3 \) and the line \( x = 1 \) about the x-axis.
A. 6\sqrt{2}
B. 12\sqrt{2}
C. 24\sqrt{2}
D. 48\sqrt{2}
Question 13
Find the determinant of the matrix [ egin{array}{ccc} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{array} ] u\sing the expansion by minors method.
A. -120
B. 120
C. -60
D. 60
Question 14
Solve the inequality \( \log_2 x > 2 \) for x.
A. x > 4
B. x > 8
C. x > 16
D. x > 32
Question 15
Find the sum of the first 10 terms of the geometric series \( 2 + 6 + 18 + \cdots \).
A. 1023
B. 1024
C. 1025
D. 1026

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