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POST UTME VERITAS UNIVERSITY 2018 Mathematics | Objective

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Question 1 View Details

In a random experiment, two events A and B are independent. If P(A) = 0.4 and P(B) = 0.6, what is the probability that both events occur?

Correct A. 0.24

B. 0.48

C. 0.64

D. 0.76

Correct Answer: A

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Question 2 View Details

Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.

A. 24π \(cm^3\)

Correct B. 48π \(cm^3\)

C. 64π \(cm^3\)

D. 80π \(cm^3\)

Correct Answer: B

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Question 3 View Details

In the diagram below, the circle with center O passes through points A, B, and C. What is the measure of angle AOC?

A. 60°

B. 90°

Correct C. 120°

D. 150°

Correct Answer: C

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Question 4 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 5 View Details

A right triangle has a hypotenuse of length 10 cm and one leg of length 6 cm. What is the length of the other leg?

A. 4 cm

B. 6 cm

Correct C. 8 cm

D. 12 cm

Correct Answer: C

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Question 6 View Details

Find the volume of the frustum of a cone with height 8 cm, lower base radius 4 cm, and upper base radius 2 cm.

A. 256\pi \(cm^3\)

B. 512\pi \(cm^3\)

Correct C. 768\pi \(cm^3\)

D. 1024\pi \(cm^3\)

Correct Answer: C

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Question 7 View Details

Solve the equation \(x^2 + 2x - 6 = 0\) using the quadratic formula.

Correct A. \(x = 2\) \pm \(\sqrt{7}\)

B. \(x = -2\)\pm \(\sqrt{7}\)

C. \(x = 2\) \pm \(\sqrt{5}\)

D. \(x = -2\)\pm \(\sqrt{5}\)

Correct Answer: A

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Question 8 View Details

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

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

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

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

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

Correct Answer: A

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Question 9 View Details

Solve the trigonometric equation (2\\(sin^2\) x + 3\(1x - 1 = 0\) for \\((2sin^2 x + 3\)\(1x - 1 = 0\)\(0 \leq x \leq 2\pi\).

Correct A. \(\frac{\pi}{6}\)\), \(\frac{\pi}{2}\)\), \(\frac{5\pi}{6}\)\)

B. \(\frac{\pi}{6}\)\), \(\frac{\pi}{4}\)\), \(\frac{5\pi}{4}\)\)

C. \(\frac{\pi}{4}\)\), \(\frac{\pi}{2}\)\), \(\frac{3\pi}{4}\)\)

D. \(\frac{\pi}{6}\)\), \(\frac{\pi}{3}\)\), \(\frac{\pi}{2}\)\)

Correct Answer: A

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Question 10 View Details

Find the equation of the line passing through the points \((2, 3)\) and \((4, 5)\).

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

B. \(y = 2x + 1\)

C. \(y = x - 1\)

D. \(y = x + 1\)

Correct Answer: A

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Question 11 View Details

Find the determinant of the matrix [ egin{array}{ccc} 2 & 3 & 1 \ 4 & 5 & 2 \ 1 & 2 & 3 \end{array} ].

Correct A. -1

B. 1

C. 2

D. 3

Correct Answer: A

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Question 12 View Details

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

A. -1

B. 0

Correct C. 1

D. 2

Correct Answer: C

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Question 13 View Details

Find the volume of the solid formed by revolving the region bounded by the curve [ \(y = x\^2\) \] and the line [ \(y = 2x\) \] about the x-axis.

A. 4\pi

B. 8\pi

C. 16\pi

Correct D. 32\pi

Correct Answer: D

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Question 14 View Details

A set of 5 points [ A, B, C, D, E \] are chosen at random from the set of points [ (0,0), (1,0), (2,0), (3,0), (4,0), (5,0), (6,0), (7,0), (8,0), (9,0) \]. What is the probability that the points [ A, B, C, D, E \] are in increasing order?

A. \(\frac{1}{252}\)\)

B. \(\frac{1}{126}\)\)

Correct C. \(\frac{1}{63}\)\)

D. \(\frac{1}{32}\)\)

Correct Answer: C

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Question 15 View Details

Find the surface area of the solid formed by revolving the region bounded by the curve [ \(y = x\^2\) \] and the line [ \(y = 2x\) \] about the x-axis.

A. 16\pi

B. 32\pi

C. 64\pi

Correct D. 128\pi

Correct Answer: D

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Question 16 View Details

Solve the inequality (\(\frac{x}{x-1}\(> 2\)\) for \\((frac{x}{x-1} > 2\(x > 1\)\).

A. \(x > 3\)

B. \(x > 5\)

C. \(x > 2\)

Correct D. \(x > 4\)

Correct Answer: D

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Question 17 View Details

Find the area under the curve \(y = x^2 + 2x - 3\) from \(x = 0\) to \(x = 2\).

A. 4

B. 6

Correct C. 8

D. 10

Correct Answer: C

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Question 18 View Details

A sequence is defined by \(a_n = 2n^2 - 3n + 1\). Find the sum of the first 5 terms of the sequence.

A. 40

B. 50

Correct C. 60

D. 70

Correct Answer: C

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Question 19 View Details

Solve the equation \(x^2 + 4x + 4 = 0\).

Correct A. \(x = -2\)

B. \(x = 0\)

C. \(x = -1\)

D. \(x = 1\)

Correct Answer: A

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Question 20 View Details

Find the value of \(\log_{10} 1000 \\) ).

A. 3

Correct B. 4

C. 5

D. 6

Correct Answer: B

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Question 21 View Details

Solve the quadratic equation \(x^2 + 4x + 4 = 0\) using the quadratic formula. What is the value of ( x )?

A. 0

B. -2

Correct C. 2

D. -1

Correct Answer: C

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Question 22 View Details

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

A. \(1/2\)

B. \(1/3\)

Correct C. \(2/3\)

D. \(1/6\)

Correct Answer: C

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Question 23 View Details

The mean of a set of numbers is 25. If one of the numbers is increased by 5, the mean becomes 26. How many numbers are in the set?

A. 5

Correct B. 10

C. 15

D. 20

Correct Answer: B

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Question 24 View Details

Solve for ( x ) in the equation \(2^x = 16\).

A. 2

Correct B. 3

C. 4

D. 5

Correct Answer: B

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Question 25 View Details

A circle has a radius of 4 cm. What is the area of the circle?

A. 16π

Correct B. 32π

C. 64π

D. 128π

Correct Answer: B

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