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POST UTME MOUNTAIN TOP UNIVERSITY 2018 Mathematics | Objective

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Question 1 View Details

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

Correct A. \(x > 3 \\)

B. \(x < 3 \\)

C. \(x = 3 \\)

D. \(x = 2 \\)

Correct Answer: A

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Question 2 View Details

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

Correct A. \(\frac{64}{3} \\)

B. \(16 \\)

C. \(32 \\)

D. \(64 \\)

Correct Answer: A

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Question 3 View Details

Solve the system of equations \(\begin{cases} x + y = 4 \ x - 2y = -2 \end{cases}\).

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 4 View Details

Find the volume of the solid formed by rotating the region bounded by the curves \(y = x^2\) and \(y = x\) about the x-axis.

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

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

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

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

Correct Answer: A

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Question 5 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 = 3, y = 4 \\)

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

Correct Answer: A

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Question 6 View Details

A random variable X has a probability distribution given by P\(X = 1 = 0.3\), P\(X = 2 = 0.4\),\(P(X = 3\)= 0.3\). If Y is an independent random variable with P\(Y = 1 = 0.5\\((X = 3 = 0.3). If Y is an independent random variable with P\),\(P(Y = 2\)= 0.5\), find the probability that \(X + Y = 3\\((Y = 2 = 0.5), find the probability that\).

A. 0.35

B. 0.45

Correct C. 0.55

D. 0.65

Correct Answer: C

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Question 7 View Details

Find the equation of the circle with center (2, 3) and radius 4.

Correct A. text{Equation of circle: } \(x - 2\)^2 + \\(text{Equation of circle:} (x - 2\(y - 3\)^\(2 = 4\^2\)

B. text{Equation of circle: } \(x + 2\)^2 + \\(text{Equation of circle:} (x + 2\(y - 3\)^\(2 = 4\^2\)

C. text{Equation of circle: } \(x - 2\)^2 + \\(text{Equation of circle:} (x - 2\(y + 3\)^\(2 = 4\^2\)

D. text{Equation of circle: } \(x + 2\)^2 + \\(text{Equation of circle:} (x + 2\(y + 3\)^\(2 = 4\^2\)

Correct Answer: A

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Question 8 View Details

Solve the equation \(\frac{x^2 - 4}{x + 2}\)\)\\() = 2.\)

A. \(x = 0\)

Correct B. \(x = 2\)

C. \(x = -2\)

D. \(x = 4\)

Correct Answer: B

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Question 9 View Details

Find the determinant of the matrix \begin{bmatrix} 2 & 3 & 1 \ 4 & 1 & 2 \ 3 & 2 & 1 \end{bmatrix}.

Correct A. 0

B. 2

C. 4

D. 6

Correct Answer: A

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Question 10 View Details

Solve the trigonometric equation \\(\sin^2\) x + \\(\cos^2\) \(x = 1\).

A. \(x =\)\(\frac{\pi}{2}\)\)

Correct B. \(x =\)\(\frac{\pi}{4}\)\)

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

D. \(x =\)\(\frac{5\pi}{4}\)\)

Correct Answer: B

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Question 11 View Details

Let \(A = egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix}\) and \(B = egin{bmatrix} 5 & 6 \ 7 & 8 \end{bmatrix}\). Find the determinant of the matrix ( AB ) if it exists.

A. 0

B. 1

Correct C. 2

D. 3

Correct Answer: C

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Question 12 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?

Correct A. \(1/2\)

B. \(2/5\)

C. \(3/8\)

D. \(1/4\)

Correct Answer: A

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Question 13 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 + \(y - 3\)^\(2 = 25\)

C. \(x - 2\)^2 + \(y - 3\)^\(2 = 36\)

D. \(x - 2\)^2 + \(y - 3\)^\(2 = 49\)

Correct Answer: A

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Question 14 View Details

Let \(S = \{1, 2, 3, 4, 5 \}\). Find the number of subsets of ( S ) that contain exactly 3 elements.

A. 5

B. 10

Correct C. 15

D. 20

Correct Answer: C

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Question 15 View Details

Find the sum of the first 5 terms of the geometric progression ( 2, 6, 18, 54, ... ).

Correct A. 120

B. 130

C. 140

D. 150

Correct Answer: A

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Question 16 View Details

Let ( f(x) = \(\frac{x^2 - 4}{x - 2}\)\)\) ). Find the derivative of ( f(x) ) using the quotient rule.

A. \(\frac{2x x - 2 - x^2 - 4\) }{ x - 2 ^2}\)\)

B. \(\frac{2x x - 2 + x^2 - 4\) }{ x - 2 ^2}\)\)

Correct C. \(\frac{2x x - 2 - x^2 - 4\) }{ x - 2 ^2}\)\)

D. \(\frac{2x x - 2 + x^2 - 4\) }{ x - 2 ^2}\)\)

Correct Answer: C

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Question 17 View Details

Solve the equation \(2^x + 3^x = 5^x\) for ( x ).

A. \(x = 2\)

Correct B. \(x = 3\)

C. \(x = 4\)

D. \(x = 5\)

Correct Answer: B

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Question 18 View Details

Find the area of the triangle with vertices ( A(0, 0) ), ( B(3, 0) ), and ( C(0, 4) ).

Correct A. 6

B. 8

C. 10

D. 12

Correct Answer: A

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Question 19 View Details

Find the derivative of ( f(x) = \(x^2\) \sin x ) using the product rule.

A. \(x^2\) \cos x + 2x \sin x

B. \(x^2\) \cos x - 2x \sin x

Correct C. \(x^2\) \cos x + 2x \sin x

D. \(x^2\) \cos x - 2x \sin x

Correct Answer: C

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Question 20 View Details

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

Correct A. \(x < -3\)

B. \(x > -3\)

C. \(x < 3\)

D. \(x > 3\)

Correct Answer: A

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Question 21 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 + \(y - 3\)^\(2 = 4\)

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

D. \(x - 2\)^2 + \(y - 3\)^\(2 = 25\)

Correct Answer: A

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Question 22 View Details

Find the derivative of ( f(x) = \sin (2x) ) using the chain rule.

A. 2 \cos (2x)

B. 2 \sin (2x)

Correct C. 2 \cos (2x)

D. 2 \sin (2x)

Correct Answer: C

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Question 23 View Details

Solve the system of equations \(x + y = 4\) and \(x - y = 2\).

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

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

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

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

Correct Answer: VIEW ANSWER

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Question 24 View Details

Let X and Y be independent events with P(X) = 0.4 and P(Y) = 0.6. What is the probability that both events occur?

Correct A. 0.24

B. 0.36

C. 0.48

D. 0.64

Correct Answer: A

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Question 25 View Details

Find the sum of the first 10 terms of the geometric series 2 + 6 + 18 + ...

A. 3120

B. 3240

Correct C. 3360

D. 3480

Correct Answer: C

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