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POST UTME VERITAS UNIVERSITY 2024 Mathematics | Objective

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Question 1 View Details

Find the area under the curve \(y = \frac{1}{2}x^2 + 3x - 2\) from \(x = 0\) to \(x = 4\).

A. \(\frac{1}{2}\)

B. ( 3 )

C. \(\frac{1}{2} \times 4^2 + 3 \times 4 - 2\)

Correct D. \(\frac{1}{2} \times 4^2 + 3 \times 4 - 2\)

Correct Answer: D

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Question 2 View Details

Solve the inequality \(2x^2 + 5x - 3 > 0\).

Correct A. \(x < -1\) or \(x > \frac{3}{2}\)

B. \(x < -1\) or \(x < \frac{3}{2}\)

C. \(x > -1\) or \(x < \frac{3}{2}\)

D. \(x > -1\) or \(x > \frac{3}{2}\)

Correct Answer: A

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Question 3 View Details

Find the determinant of the matrix \(egin{bmatrix} 2 & 1 & 3 \ 4 & 2 & 1 \ 1 & 3 & 2 \end{bmatrix}\).

A. ( 2 )

Correct B. \(-1\)

C. ( 1 )

D. ( 0 )

Correct Answer: B

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Question 4 View Details

In the circuit below, find the current flowing through the 5 ohm resistor.

Correct A. ( 1 ) A

B. ( 2 ) A

C. ( 3 ) A

D. ( 4 ) A

Correct Answer: A

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Question 5 View Details

Solve the trigonometric equation \(\sin^2 x + \cos^2 x = 1\).

A. \(x = \frac{\pi}{2}\)

Correct B. \(x = \frac{\pi}{4}\)

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

D. \(x = \frac{5\pi}{4}\)

Correct Answer: B

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Question 6 View Details

Find the volume of the solid formed by revolving the region bounded by the curve (y = \(\frac{1}{2}\\()x^2\)\) about the x-axis, from \\((y = frac{1}{2}x^2\(x = 0\) to \(x = 2\).

Correct A. π/3

B. π/2

C. 2π/3

D. π

Correct Answer: A

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Question 7 View Details

Solve the inequality \(2x^2 - 5x - 3 > 0\).

Correct A. \(-∞, -1\) ∪ (3, ∞)

B. \(-∞, -3\) ∪ (1, ∞)

C. \(-∞, 1\) ∪ (3, ∞)

D. \(-∞, -3\) ∪ (1, ∞)

Correct Answer: A

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Question 8 View Details

Find the area under the curve \(y = 2x^2 - 3x + 1\) from \(x = 0\) to \(x = 2\).

Correct A. \(11/3\)

B. \(13/3\)

C. \(15/3\)

D. \(17/3\)

Correct Answer: A

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Question 9 View Details

Find the sum of the first 5 terms of the arithmetic progression 3, 6, 9, ...

Correct A. 45

B. 50

C. 55

D. 60

Correct Answer: A

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Question 10 View Details

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

Correct A. \(-3, 2\)

B. \(-2, 3\)

C. \(-3, 3\)

D. \(-2, 2\)

Correct Answer: A

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Question 11 View Details

Let ( f(x) = \(x^3 - 6x^2 + 11x - 6\) ). Find the value of ( f(2) ).

Correct A. 10

B. 12

C. 14

D. 16

Correct Answer: A

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Question 12 View Details

A set ( A ) contains the elements ( 1, 2, 3, 4, 5 ). Find the number of subsets of ( A ) that contain exactly two elements.

A. 10

B. 12

Correct C. 15

D. 20

Correct Answer: C

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Question 13 View Details

Find the sum of the infinite geometric series \(1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \cdots \\)

Correct A. 2

B. 4

C. 8

D. 16

Correct Answer: A

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Question 14 View Details

In the diagram below, ( ABC ) is a right-angled triangle with \(AB = 3\) and \(BC = 4\). Find the length of ( AC ).

A. 5

B. 6

Correct C. 7

D. 8

Correct Answer: C

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Question 15 View Details

A bag contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is blue?

A. \(\frac{1}{4}\)\)

B. \(\frac{1}{2}\)\)

Correct C. \(\frac{3}{8}\)\)

D. \(\frac{5}{8}\)\)

Correct Answer: C

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Question 16 View Details

Find the equation of the circle with center \(-2, 3\) and radius 4.

Correct A. \(x^2\) + \\((y^2 + 4x - 6y + 4\)\(= 0\)\)

B. \(x^2\) + \\((y^2 - 4x + 6y + 4\)\(= 0\)\)

C. \(x^2\) + \\((y^2 + 2x - 3y + 4\)\(= 0\)\)

D. \(x^2\) + \\((y^2 - 2x + 3y + 4\)\(= 0\)\)

Correct Answer: A

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Question 17 View Details

Solve for x in the equation: \(\begin{array}{rcl} 2x + 5 & = & 11 \ 3x - 2 & = & 7 \ \hline \end{array}\)

A. \(x = 2\)

Correct B. \(x = 3\)

C. \(x = 4\)

D. \(x = 5\)

Correct Answer: B

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Question 18 View Details

Find the mean of the following data set: 2, 4, 6, 8, 10.

A. 5

B. 6

Correct C. 7

D. 8

Correct Answer: C

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Question 19 View Details

Solve the matrix equation: \(\begin{array}{ccc} 2 & -1 & 3 \ 4 & 2 & -5 \ 1 & 3 & 2 \ \end{array}\) \begin{array}{c} x \ y \ z \ \end{array} = \begin{array}{c} 10 \ 15 \ 20 \ \end{array} \]

Correct A. \(x = 2\), \(y = 3\), \(z = 4\)

B. \(x = 3\), \(y = 4\), \(z = 5\)

C. \(x = 4\), \(y = 5\), \(z = 6\)

D. \(x = 5\), \(y = 6\), \(z = 7\)

Correct Answer: A

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Question 20 View Details

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

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

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

C. \(y = -2x + 1\)

D. \(y = -2x - 1\)

Correct Answer: B

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Question 21 View Details

A right circular cone has a height of 8 cm and a base radius of 4 cm. Find the volume of the cone in cubic centimeters.

A. 256\pi

B. 512\pi

Correct C. 1024\pi

D. 2048\pi

Correct Answer: C

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Question 22 View Details

Solve the inequality \(\frac{x+2}{x-1}\)\\() > 0.\)

Correct A. x < -2 or \(x > 1\)

B. x < -2 or \(x < 1\)

C. x > -2 or \(x > 1\)

D. x < -2 or \(x = 1\)

Correct Answer: A

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Question 23 View Details

A die is rolled twice. Find the probability that the sum of the numbers shown on the two dice is 7.

Correct A. \(\frac{1}{6}\)\)

B. \(\frac{1}{12}\)\)

C. \(\frac{1}{18}\)\)

D. \(\frac{1}{36}\)\)

Correct Answer: A

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Question 24 View Details

Find the equation of the circle with center \(-2, 3\) and radius 4.

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 25 View Details

Find the value of x in the equation \(2^x\) + \\((5^x\)\(= 7\)\\()^x\).

A. \(x = 2\)

Correct B. \(x = 3\)

C. \(x = 4\)

D. \(x = 5\)

Correct Answer: B

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