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POST UTME ELIZADE UNIVERSITY 2020 Mathematics | Objective

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Question 1 View Details

Find the volume of the frustum of a cone with height 6cm, lower base radius 4cm, and upper base radius 2cm. Given that the slant height is 10cm.

A. 60\pi \(cm^3\)

Correct B. 80\pi \(cm^3\)

C. 100\pi \(cm^3\)

D. 120\pi \(cm^3\)

Correct Answer: B

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Question 2 View Details

Solve for x in the equation \(\frac{1}{x} + \frac{1}{x+1} = \frac{1}{2} \\) using the method of substitution.

A. -1

B. 1

Correct C. 2

D. 3

Correct Answer: C

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Question 3 View Details

A set A contains 5 elements. If the number of subsets of A is 32, find the number of elements in the power set of A.

A. 5

B. 6

C. 7

Correct D. 8

Correct Answer: D

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Question 4 View Details

Find the sum of the first 10 terms of the arithmetic sequence 2, 5, 8, ...

A. 50

B. 55

C. 60

Correct D. 65

Correct Answer: D

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Question 5 View Details

A circle has an equation of \(x^2 + y^2 - 6x + 4y + 4 = 0\). Find the center and radius of the circle.

Correct A. \(3, -2\), 1

B. (3, 2), 1

C. (2, 3), 1

D. (1, 1), 1

Correct Answer: A

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Question 6 View Details

Determine the value of \(\sin^2 30^circ + \cos^2 30^circ\) using the Pythagorean identity.

Correct A. 1

B. 0

C. 2

D. 3

Correct Answer: A

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Question 7 View Details

A rectangular prism has a length of 10 cm, a width of 5 cm, and a height of 8 cm. Calculate its surface area.

Correct A. 240 \(cm^2\)

B. 200 \(cm^2\)

C. 220 \(cm^2\)

D. 260 \(cm^2\)

Correct Answer: A

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Question 8 View Details

Solve the matrix equation \(egin{bmatrix} 2 & 1 \ 1 & 2 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 3 \ 4 \end{bmatrix}\).

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

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

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

D. \(x = 2, y = 2\)

Correct Answer: A

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Question 9 View Details

Find the area under the curve \(y = x^2\) from \(x = 0\) to \(x = 4\) using integration.

Correct A. 64

B. 32

C. 16

D. 8

Correct Answer: A

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Question 10 View Details

A vector ( mathbf{a} ) has a magnitude of 5 units and makes an angle of 60° with the positive x-axis. Find the x and y components of ( mathbf{a} ).

Correct A. \(x = 2.5, y = 4.33\)

B. \(x = 4.33, y = 2.5\)

C. \(x = 2.5, y = 2.5\)

D. \(x = 4.33, y = 4.33\)

Correct Answer: A

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Question 11 View Details

In a certain number base, the value of the digit 5 is represented as \(\overline{101}_b\). If the base is denoted as ( b ), and the value of the digit 5 is equal to 6 in base 10, find the value of ( b ).

A. 2

Correct B. 3

C. 4

D. 5

Correct Answer: B

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Question 12 View Details

A particle moves along the x-axis with its position given by the equation ( x(t) = 2 sin (3t) + 5 \cos (4t) ). Find the velocity of the particle at time \(t = \\(sin (3t) + 5 cos (4t) ). Find the velocity of the particle at time \frac{\pi}{2}\).

A. \(-6 \sqrt{3}\)

Correct B. \(6 \sqrt{3}\)

C. \(12 \sqrt{3}\)

D. \(-12 \sqrt{3}\)

Correct Answer: B

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Question 13 View Details

A random experiment consists of rolling a fair six-sided die and then flipping a fair coin. If the outcome of the die roll is even, the coin is flipped twice. If the outcome of the die roll is odd, the coin is flipped only once. What is the probability that the number of heads obtained is 2?

Correct A. \(\frac{1}{12}\)

B. \(\frac{1}{6}\)

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

D. \(\frac{1}{3}\)

Correct Answer: A

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Question 14 View Details

Solve the inequality \(\log_2 x^2 + 1 \\)\(> 3 ).\)

A. \(x > -\sqrt{7}\)

Correct B. \(x < \sqrt{7}\)

C. \(x > \sqrt{7}\)

D. \(x < -\sqrt{7}\)

Correct Answer: B

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Question 15 View Details

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

Correct A. \(-\frac{1}{2} x^{-\frac{3}{2}}\)

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

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

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

Correct Answer: A

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Question 16 View Details

Find the determinant of the matrix [ egin{array}{ccc} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{array} ].

A. -120

B. 120

Correct C. 0

D. -60

Correct Answer: C

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Question 17 View Details

A set of 10 numbers has a mean of 20. If 5 is added to each number, what is the new mean?

A. 15

B. 20

C. 25

Correct D. 30

Correct Answer: D

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Question 18 View Details

Find the volume of the frustum of a cone with height 10cm, lower base radius 4cm, and upper base radius 2cm.

A. 100\pi

B. 120\pi

Correct C. 140\pi

D. 160\pi

Correct Answer: C

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Question 19 View Details

In a geometric sequence, the first term is 2 and the common ratio is 3. Find the sum of the first 5 terms.

A. 1210

B. 1230

Correct C. 1250

D. 1270

Correct Answer: C

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Question 20 View Details

A histogram has a mean of 25 and a standard deviation of 5. If the data is normally distributed, what is the probability that a randomly selected value is between 20 and 30?

A. 0.68

B. 0.69

Correct C. 0.70

D. 0.71

Correct Answer: C

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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. -4

Correct Answer: C

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Question 22 View Details

A set A contains 5 elements, and a set B contains 3 elements. If the intersection of sets A and B contains 2 elements, what is the number of elements in the union of sets A and B?

A. 6

Correct B. 7

C. 8

D. 9

Correct Answer: B

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Question 23 View Details

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

A. 15

B. 20

Correct C. 25

D. 30

Correct Answer: C

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Question 24 View Details

A histogram is shown below. What is the mean of the data represented by the histogram?

A. 10

Correct B. 15

C. 20

D. 25

Correct Answer: B

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Question 25 View Details

A geometric shape is shown below. What is the volume of the shape?

A. 8

B. 10

Correct C. 12

D. 15

Correct Answer: C

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