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POST UTME VERITAS UNIVERSITY 2022 Mathematics | Objective

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Question 1 View Details

Find the determinant of the matrix \(egin{bmatrix} 2 & 3 \ 4 & 5 \end{bmatrix}\).

Correct A. 1

B. 2

C. 3

D. 4

Correct Answer: A

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Question 2 View Details

A sequence is defined by the recurrence relation \(a_n = 2a_{n-1} + 3\) with initial term \(a_1 = 2\). Find the sum of the first 5 terms of the sequence.

A. 33

Correct B. 35

C. 37

D. 39

Correct Answer: B

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Question 3 View Details

The equation of a circle is given by \(x^2 + y^2 - 6x + 4y + 4 = 0\). Find the coordinates of the center of the circle.

Correct A. \(3, -2\)

B. (2, 3)

C. \(4, -1\)

D. (1, 2)

Correct Answer: A

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Question 4 View Details

A histogram is shown below. Find the mean of the data.

A. 10

Correct B. 12

C. 15

D. 18

Correct Answer: B

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Question 5 View Details

A polynomial function is defined by ( f(x) = \((x^3 - 2x^2 + 3x - 1\)\) ). Find the value of \(f -1 \\((x^3 - 2x^2 + 3x - 1) ). Find the value of \\) ).

Correct A. -1

B. 0

C. 1

D. 2

Correct Answer: A

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Question 6 View Details

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

A. 40

B. 50

Correct C. 60

D. 70

Correct Answer: C

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Question 7 View Details

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

Correct A. x < -1 or \(x > 3/2\)\)

B. \(x < 1\) or x > \(-3/2\)

C. \(x <\)\(-3/2\) or \(x > 1\)

D. \(x < 3/2\)\) or x > -1

Correct Answer: A

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Question 8 View Details

Find the sum of the first 5 terms of the geometric series \(2x + 3x^2 + 4x^3 + ..\)..

Correct A. 2x + \(3x^2 + 4x^3 + 5x^4 + 6x^5\)

B. 2x + \(3x^2 + 4x^3 + 5x^4 + 6x^5 + 7x^6\)

C. 2x + \(3x^2 + 4x^3 + 5x^4 + 6x^5 + 7x^6 + 8x^7\)

D. 2x + \(3x^2 + 4x^3 + 5x^4 + 6x^5 + 7x^6 + 8x^7 + 9x^8\)

Correct Answer: A

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Question 9 View Details

In the diagram below, ( ABC ) is a triangle with \(AB = 5\) cm and \(BC = 6\) cm. Find the length of ( AC ).

A. 7

B. 8

Correct C. 9

D. 10

Correct Answer: C

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Question 10 View Details

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

Correct A. \(x = -2\)

B. \(x = -1\)

C. \(x = 1\)

D. \(x = 2\)

Correct Answer: A

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Question 11 View Details

Find the value of x in the equation \(\log_{10} x^2 \\)\(= 4 ).\)

A. 10

B. 100

C. 1000

Correct D. 10000

Correct Answer: D

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Question 12 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 13 View Details

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

A. 4

B. 8

Correct C. 16

D. 32

Correct Answer: C

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Question 14 View Details

A set A contains the elements {1, 2, 3, 4, 5}. Find the number of subsets of A.

A. 5

B. 10

C. 15

Correct D. 20

Correct Answer: D

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Question 15 View Details

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

A. 15

B. 25

C. 35

Correct D. 45

Correct Answer: D

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Question 16 View Details

Find the equation of the circle passing through the points (1, 2), (3, 4), and (5, 6).

Correct A. \(x^2\) + \\((y^2 + 4x - 8y + 5\)\(= 0\)\)

B. \(x^2\) + \\((y^2 - 4x + 8y + 5\)\(= 0\)\)

C. \(x^2\) + \\((y^2 + 2x - 4y + 5\)\(= 0\)\)

D. \(x^2\) + \\((y^2 - 2x + 4y + 5\)\(= 0\)\)

Correct Answer: A

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Question 17 View Details

Solve the matrix equation (AX = B\), where A = egin{bmatrix} 1 & 2 \ 3 & 4 \\\(((AX = B)\), where A = egin{bmatrix} 1 & 2 \end{bmatrix},\(X =\)egin{bmatrix} x \ y \end{bmatrix}, and B = egin{bmatrix} 5 \ 6 \end{bmatrix}.

Correct A. \(X =\)egin{bmatrix} 1 \ 2 \end{bmatrix}

B. \(X =\)egin{bmatrix} 2 \ 1 \end{bmatrix}

C. \(X =\)egin{bmatrix} 3 \ 4 \end{bmatrix}

D. \(X =\)egin{bmatrix} 4 \ 3 \end{bmatrix}

Correct Answer: A

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Question 18 View Details

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

Correct A. 10

B. 12

C. 15

D. 20

Correct Answer: A

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Question 19 View Details

Solve the system of equations: \(x + y = 4\) and \(xy = 6\).

Correct A. \(x = 2\), \(y = 2\)

B. \(x = 3\), \(y = 1\)

C. \(x = 1\), \(y = 3\)

D. \(x = 4\), \(y = 0\)

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).

Correct A. \(y = x + 1\)

B. \(y = x - 1\)

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

D. \(y = x - 2\)

Correct Answer: A

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Question 21 View Details

A random variable X has a probability distribution given by P\(X = 1 = 0.4\), P\(X = 2 = 0.3\),\(P(X = 3\)= 0.3\). If two independent random variables X and Y have the same probability distribution, find the probability that \(X + Y = 5\\((X = 3 = 0.3). If two independent random variables X and Y have the same probability distribution, find the probability that\).

A. 0.1

B. 0.2

Correct C. 0.3

D. 0.4

Correct Answer: C

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Question 22 View Details

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

A. 16\pi

Correct B. 32\pi

C. 64\pi

D. 128\pi

Correct Answer: B

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Question 23 View Details

Solve the equation \\(\sin^2\) x + \\(\cos^2\) \(x = 1\) for x in the interval [0, 2\pi].

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

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

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

Correct D. \pi

Correct Answer: D

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Question 24 View Details

Find the equation of the line passing through the points (1, 2) and (3, 4).

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

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

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

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

Correct Answer: A

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Question 25 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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