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POST UTME UNIBEN 2020 Mathematics | Objective

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Question 1 View Details

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

Correct A. 10

B. 100

C. 1000

D. 10000

Correct Answer: A

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Question 2 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 3 View Details

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

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

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

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

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

Correct Answer: A

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Question 4 View Details

Solve the system of equations \(x + y = 2\) and \(xy = 3\).

Correct A. (1, 3)

B. (3, 1)

C. (2, 2)

D. \(-1, -3\)

Correct Answer: A

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Question 5 View Details

Find the sum of the first 5 terms of the geometric series ( 2, 6, 18, ... ).

Correct A. 62

B. 64

C. 66

D. 68

Correct Answer: A

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Question 6 View Details

A random variable X has a probability distribution given by P\(X = 1 = 0.4\), P\(X = 2 = 0.3\), P\(X = 3 = 0.2\), and P\(X = 4 = 0.1\). If two independent random variables X and Y have the same probability distribution as X, find the probability that X + Y is greater than 5.

A. 0.2

B. 0.3

Correct C. 0.4

D. 0.5

Correct Answer: C

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Question 7 View Details

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

A. 16\pi

B. 32\pi

Correct C. 64\pi

D. 128\pi

Correct Answer: C

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Question 8 View Details

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

Correct A. \(x + y + z = 6\)

B. \(x - y + z = 6\)

C. \(x + y - z = 6\)

D. \(x - y - z = 6\)

Correct Answer: A

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Question 9 View Details

Find the sum of the first 10 terms of the geometric series with first term 2 and common ratio 3.

A. 59048

Correct B. 59049

C. 59050

D. 59051

Correct Answer: B

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Question 10 View Details

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

A. \(x - 2\)^2 + \(y - 3\)^\(2 = 1\)

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

Correct C. \(x - 2\)^2 + \(y - 3\)^\(2 = 9\)

D. \(x - 2\)^2 + \(y - 3\)^\(2 = 16\)

Correct Answer: C

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Question 11 View Details

Determine the value of x in the equation \(2^x + 5^x = 3^x\).

A. 1

Correct B. 2

C. 3

D. 4

Correct Answer: B

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Question 12 View Details

A circle has a radius of 4 cm. Find the area of the circle.

A. 16π

B. 32π

Correct C. 64π

D. 128π

Correct Answer: C

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Question 13 View Details

In a set of 5 numbers, the mean is 10 and the median is 8. If the largest number is 15, find the sum of the remaining 3 numbers.

A. 25

B. 30

Correct C. 35

D. 40

Correct Answer: C

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Question 14 View Details

A binary operation (*\) on the set of real numbers is defined as \(a * b = a^2 + b^2\\((*) on the set of real numbers is defined as\). Find the value of \(2 * 3\).

A. 13

B. 17

Correct C. 19

D. 21

Correct Answer: C

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Question 15 View Details

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

A. 2.5

B. 3.75

Correct C. 4.33

D. 5.00

Correct Answer: C

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Question 16 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 17 View Details

Solve the matrix equation \(egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 3 \ 7 \end{bmatrix}\).

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

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

C. \(x = 3\), \(y = 4\)

D. \(x = 4\), \(y = 3\)

Correct Answer: B

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Question 18 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 - 3 \\)^2 + \(y - 2\)^\(2 = 16\) )

C. \(x - 2 \\)^2 + \(y - 3\)^\(2 = 9\) )

D. \(x - 3 \\)^2 + \(y - 2\)^\(2 = 9\) )

Correct Answer: A

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Question 19 View Details

Find the sum of the first 10 terms of the geometric progression ( 2, 6, 18, ldots ).

Correct A. 59049

B. 59048

C. 59050

D. 59051

Correct Answer: A

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Question 20 View Details

Find the area of the triangle with vertices ( (0, 0), (3, 0), (0, 4) ).

Correct A. 6

B. 8

C. 10

D. 12

Correct Answer: A

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Question 21 View Details

A random variable X has a probability distribution given by P\(X = 1 = 0.3\), P\(X = 2 = 0.4\), and P\(X = 3 = 0.3\). Find the expected value of X.

Correct A. 1.1

B. 1.2

C. 1.3

D. 1.4

Correct Answer: A

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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 A and B contains 2 elements, find the number of elements in the union of A and B.

A. 8

B. 9

Correct C. 10

D. 11

Correct Answer: C

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Question 23 View Details

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

A. 2.5

Correct B. 2.6

C. 2.7

D. 2.8

Correct Answer: B

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Question 24 View Details

A histogram is shown below: \(\begin{array}{|c|c|c|c|} \hline \text{Class} & 0-10 & 10-20 & 20-30 \ \hline \text{Frequency} & 5 & 10 & 15 \ \hline \end{array}\). Find the mean of the data.

A. 20

B. 21

Correct C. 22

D. 23

Correct Answer: C

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Question 25 View Details

A quadratic equation is given by: \(x^2 + 4x + 4 = 0\). Find the roots of the equation.

A. 0

Correct B. -2

C. -1

D. 1

Correct Answer: B

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