POST UTME ACHIEVERS UNIVERSITY 2020 Mathematics | Objective

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Question 1 View Details
Determine the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.
A. 24\pi \(cm^3\)
Correct B. 48\pi \(cm^3\)
C. 96\pi \(cm^3\)
D. 192\pi \(cm^3\)

Correct Answer: B

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Question 2 View Details
Find the mean deviation about the median of the data set: 2, 4, 6, 8, 10.
A. 2
B. 4
Correct C. 6
D. 8

Correct Answer: C

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Question 3 View Details
Solve for x in the equation: \(x^2 + 4x + 4 = 0\).
Correct A. -2
B. -1
C. 1
D. 2

Correct Answer: A

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Question 4 View Details
A binary operation (*\) on the set of integers is defined as: \(a * b = a^2 + b^2\\((*) on the set of integers is defined as:\). Find the value of \(2 * 3\).
Correct A. 13
B. 17
C. 19
D. 25

Correct Answer: A

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Question 5 View Details
Find the surface area of the sphere with radius 5 cm.
A. 100\pi \(cm^2\)
B. 200\pi \(cm^2\)
Correct C. 300\pi \(cm^2\)
D. 400\pi \(cm^2\)

Correct Answer: C

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Question 6 View Details
Find the value of ( k ) in the equation \((2x^2 + 7x + k\) = 0\) if the sum of the roots is \(-\\((2x^2 + 7x + k = 0) if the sum of the roots is \frac{7}{2}) and the product of the roots is \(-\frac{3}{4}\\() and the product of the roots is (-\).
A. 1
B. 2
Correct C. 3
D. 4

Correct Answer: C

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Question 7 View Details
A histogram of exam scores is shown below. If the mean score is ( 60 ) and the standard deviation is ( 10 ), what is the value of ( x ) in the interval ( [40, 80] ) where the frequency is maximum?
A. 40
B. 50
Correct C. 60
D. 70

Correct Answer: C

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Question 8 View Details
Solve the equation \(\sin^2 x + \cos^2 x = 1\) for ( x ) in the interval ( [0, 2pi] ).
A. 0
Correct B. \(\frac{\pi}{4}\)\)
C. \(\frac{\pi}{2}\)\)
D. pi

Correct Answer: B

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Question 9 View Details
Find the value of ( x ) in the equation \((x^3 - 6x^2 + 11x - 6\) = 0\) if the sum of the roots is ( 6 ) and the product of the roots is \(-6\\((x^3 - 6x^2 + 11x - 6 = 0) if the sum of the roots is ( 6 ) and the product of the roots is\).
A. 1
B. 2
Correct C. 3
D. 4

Correct Answer: C

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Question 10 View Details
A matrix ( A ) is given by \(A = egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix}\). Find the value of ( x ) in the equation \(A^2 = xA\).
A. 1
B. 2
Correct C. 3
D. 4

Correct Answer: C

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Question 11 View Details
Solve for 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
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 13 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 14 View Details
Find the value of \(\frac{d}{dx} x^3 - 2x^2 + x - 1 \\) ).
Correct A. \(3x^2 - 4x + 1\)
B. \(x^2 - 2x - 1\)
C. \(3x^2 - 4x + 2\)
D. \(x^2 - 2x + 1\)

Correct Answer: A

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Question 15 View Details
Solve the system of equations \(x + y = 4\) and \(x - y = 2\).
Correct A. \(x = 3, y = 1\)
B. \(x = 1, y = 3\)
C. \(x = 2, y = 2\)
D. \(x = 4, y = 0\)

Correct Answer: A

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Question 16 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. \(y = x + 2\)
D. \(y = x - 2\)

Correct Answer: A

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Question 17 View Details
Solve the quadratic equation \(x^2 + 4x + 4 = 0\).
Correct A. \(x = -2\)
B. \(x = -1\)
C. \(x = 0\)
D. \(x = 1\)

Correct Answer: A

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Question 18 View Details
Find the value of \(\frac{d^2}{dx^2} x^3 - 2x^2 + x - 1 \\) ).
Correct A. ( 6x )
B. ( 2x )
C. \(x^2\)
D. ( x )

Correct Answer: A

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Question 19 View Details
Find the volume of the solid generated by revolving the region bounded by the curves \(y = x\^2\), \(y = 0\), and \(x = 2\) about the x-axis.
A. 32\pi
B. 64\pi
Correct C. 128\pi
D. 256\pi

Correct Answer: C

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Question 20 View Details
Solve the inequality |\(x^2 - 4\)|\(> 5.\)
Correct A. x < -3 or \(x > 4\)
B. x < -2 or \(x > 5\)
C. x < -1 or \(x > 6\)
D. \(x < 0\) or \(x > 7\)

Correct Answer: A

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Question 21 View Details
Find the area of the region bounded by the curves \(y = x\^2 + 1\), \(y = 0\), and \(x = 2\).
A. 9
Correct B. 18
C. 27
D. 36

Correct Answer: B

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Question 22 View Details
Solve the equation \(x^3\) - \\((6x^2 + 11x - 6\)\(= 0.\)\)
A. \(x = 1\)
B. \(x = 2\)
Correct C. \(x = 3\)
D. \(x = 4\)

Correct Answer: C

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Question 23 View Details
Find the volume of the solid generated by revolving the region bounded by the curves \(y = x\^2\), \(y = 0\), and \(x = 2\) about the y-axis.
A. 32\pi
B. 64\pi
Correct C. 128\pi
D. 256\pi

Correct Answer: C

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Question 24 View Details
Solve the inequality |\(x^2 - 4\)|\(< 5.\)
A. x < -1 or \(x > 4\)
Correct B. \(x < 0\) or \(x > 5\)
C. \(x < 1\) or \(x > 6\)
D. \(x < 2\) or \(x > 7\)

Correct Answer: B

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Question 25 View Details
Find the area of the region bounded by the curves \(y = x\^2 + 1\), \(y = 0\), and \(x = 2\).
A. 9
Correct B. 18
C. 27
D. 36

Correct Answer: B

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