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POST UTME COAL CITY UNIVERSITY 2020 Mathematics | Objective

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Question 1 View Details

Let ( f(x) = \(\frac{1}{x^2 + 1}\)\)) ). Find \(int_{-\frac{\\() ). Find (int_{-\pi}{2}}^{\frac{\pi}{2}} f x \\) , dx ).

A. 0

B. 1

Correct C. π

D. 2π

Correct Answer: C

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Question 2 View Details

Solve the system of equations: \(egin{cases} x + y + z = 6 \ 2x + 3y + z = 12 \ x + 2y + 3z = 9 \end{cases}\).

Correct A. [1, 2, 3]

B. [2, 1, 3]

C. [1, 3, 2]

D. [3, 2, 1]

Correct Answer: A

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Question 3 View Details

A fair six-sided die is rolled twice. What is the probability that the sum of the two rolls is 7?

A. \(1/6\)

Correct B. \(1/12\)

C. \(1/2\)

D. \(5/6\)

Correct Answer: B

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Question 4 View Details

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

Correct A. 16

B. 32

C. 64

D. 128

Correct Answer: A

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Question 5 View Details

Solve the equation \(x^3 - 6x^2 + 11x - 6 = 0\).

A. 1

B. 2

Correct C. 3

D. 4

Correct Answer: C

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Question 6 View Details

In a certain number base, the value of the digit 5 is represented as \(\overline{1011}_b\). If the base is denoted as ( b ), find the value of ( b ) in base 10.

A. 2

Correct B. 3

C. 4

D. 5

Correct Answer: B

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Question 7 View Details

A polynomial ( P(x) ) is defined as ( P(x) = \((ax^3 + bx^2 + cx + d\)\) ). If ( P(1) = 4 ),\(( P(2) = 12 )\), and ( P(3) = 24 ), find the value of \(a + b + c + d\\((ax^3 + bx^2 + cx + d) ). If ( P(1) = 4 ), ( P(2) = 12 ), and ( P(3) = 24 ), find the value of\).

A. 10

B. 12

Correct C. 14

D. 16

Correct Answer: C

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Question 8 View Details

Two events, ( A ) and ( B ), are independent. If ( P(A) = 0.4 ) and ( P(B) = 0.6 ), find the probability that both events occur.

A. 0.2

Correct B. 0.24

C. 0.28

D. 0.32

Correct Answer: B

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Question 9 View Details

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

Correct A. -1

B. 1

C. 3

D. 5

Correct Answer: A

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Question 10 View Details

A rectangular prism has a length of 6 cm, a width of 4 cm, and a height of 3 cm. Find its volume.

Correct A. 72

B. 80

C. 84

D. 90

Correct Answer: A

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Question 11 View Details

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

A. 48\pi \(cm^3\)

B. 64\pi \(cm^3\)

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

D. 96\pi \(cm^3\)

Correct Answer: C

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Question 12 View Details

A histogram of exam scores is shown below. Find the mean score.

A. 60

B. 70

Correct C. 80

D. 90

Correct Answer: C

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Question 13 View Details

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

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

Correct B. \(x < 1\) or \(x > 2\)

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

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

Correct Answer: B

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Question 14 View Details

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

A. 18

B. 20

Correct C. 22

D. 24

Correct Answer: C

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Question 15 View Details

A snail is at the bottom of a 20-foot well. Each day, it climbs up 3 feet, but at night, it slips back 2 feet. How many days will it take for the snail to reach the top of the well?

A. 18

B. 20

Correct C. 22

D. 24

Correct Answer: C

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Question 16 View Details

Find the value of \(\frac{d}{dx} \left \frac{1}{x^2 + 1} \right\)\) using the quotient rule.

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

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

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

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

Correct Answer: A

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Question 17 View Details

Solve the inequality \(|x - 2| > 3\).

Correct A. \(-∞, -1\) ∪ (4, ∞)

B. \(-∞, 1\) ∪ (4, ∞)

C. \(-∞, -1\) ∪ (1, 4)

D. \(-∞, 1\) ∪ (1, 4)

Correct Answer: A

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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. \(x - 2\)^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 19 View Details

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

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 20 View Details

Find the value of \(\int_0^1 x^2 dx\).

Correct A. \(1/3\)

B. \(1/2\)

C. \(2/3\)

D. 1

Correct Answer: A

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Question 21 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 22 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 23 View Details

Find the sum of the first 10 terms of the geometric series \(2 + 6 + 18 + ldots\).

A. 1950

Correct B. 1960

C. 1970

D. 1980

Correct Answer: B

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Question 24 View Details

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

A. \(1/2\)

B. \(1/3\)

Correct C. \(2/5\)

D. \(3/8\)

Correct Answer: C

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Question 25 View Details

Find the derivative of the function ( f(x) = \(3x^2 + 2x - 5\) ).

Correct A. 6x + 2

B. 6x - 2

C. 3x + 2

D. 3x - 2

Correct Answer: A

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