POST UTME UNILAG 2017 Mathematics | Objective

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Question 1 View Details
Find the volume of the frustum of a cone with height 8cm, lower base radius 4cm, and upper base radius 2cm. Given that the slant height is 6cm. Express your answer in terms of π.
Correct A. \(\frac{1}{3} \pi 4^2 + 2^2 + 4 \times 4 \times 2 \\) )
B. \(\frac{1}{3} \pi 4^2 + 2^2 - 4 \times 4 \times 2 \\) )
C. \(\frac{1}{3} \pi 4^2 + 2^2 + 4 \times 4 \times 6 \\) )
D. \(\frac{1}{3} \pi 4^2 + 2^2 - 4 \times 4 \times 6 \\) )

Correct Answer: A

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Question 2 View Details
Solve the inequality \(2x^2 + 5x - 3 > 0\). Express your answer in interval notation.
Correct A. \(-\infty, -\frac{3}{2} \\) cup \(\frac{3}{2}, \infty\) )
B. \(-\infty, \frac{3}{2} \\) cup \(\infty, -\frac{3}{2}\) )
C. \(-\infty, -\frac{3}{2} \\) cup \(\frac{3}{2}, \infty\) )
D. \(-\infty, \frac{3}{2} \\) cup \(\infty, -\frac{3}{2}\) )

Correct Answer: A

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Question 3 View Details
Find the equation of the circle with center (-2, 3 \\) ) and radius 4. Express your answer in the standard form \\((-2, 3 \(x - h \\)^2 + \(y - k\)^\(2 = r\^2\) ).
Correct A. \(x + 2 \\)^2 + \(y - 3\)^\(2 = 16\) )
B. \(x - 2 \\)^2 + \(y + 3\)^\(2 = 16\) )
C. \(x + 2 \\)^2 + \(y + 3\)^\(2 = 16\) )
D. \(x - 2 \\)^2 + \(y - 3\)^\(2 = 16\) )

Correct Answer: A

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Question 4 View Details
A die is rolled twice. What is the probability that the sum of the two numbers is 7?
A. \(\frac{1}{6}\)
B. \(\frac{1}{12}\)
Correct C. \(\frac{1}{36}\)
D. \(\frac{1}{24}\)

Correct Answer: C

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Question 5 View Details
A water \tank is in the shape of a cone with height 10m and radius 5m. If the water level is at 4m, what is the volume of the water in the \tank?
Correct A. \(\frac{1}{3} \pi 5^2 \\) \(10 - 4\) )
B. \(\frac{1}{3} \pi 5^2 \\) \(10 + 4\) )
C. \(\frac{1}{3} \pi 5^2 \\) \(10 \times 4\) )
D. \(\frac{1}{3} \pi 5^2 \\) \(10 - 4\)^2 )

Correct Answer: A

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