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POST UTME IMS U 2022 Mathematics | Objective

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Question 1 View Details

Let X be a random variable with probability density function ( f(x) = egin{cases} 2x, & 0 leq x leq 1 \ 0, & \text{otherwise} \end{cases} ). Find the probability that X is greater than 0.5.

A. \(\frac{1}{2}\)

Correct B. \(\frac{3}{4}\)

C. \(\frac{5}{8}\)

D. \(\frac{7}{16}\)

Correct Answer: B

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Question 2 View Details

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

A. \(72 \text{cm}^3\)

Correct B. \(96 \text{cm}^3\)

C. \(108 \text{cm}^3\)

D. \(120 \text{cm}^3\)

Correct Answer: B

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Question 3 View Details

Solve the inequality \(\frac{x^2 - 4}{x + 2} > 0\).

Correct A. \(x < -2\)\text{ or } \(x > 2\)

B. \(x < -2\)\text{ or } \(x > 0\)

C. \(x > -2\)\text{ or } \(x < 0\)

D. \(x > -2\)\text{ and } \(x < 0\)

Correct Answer: A

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Question 4 View Details

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

A. \(16 \pi \text{cm}^2\)

B. \(32 \pi \text{cm}^2\)

Correct C. \(64 \pi \text{cm}^2\)

D. \(128 \pi \text{cm}^2\)

Correct Answer: C

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Question 5 View Details

A right triangle has a hypotenuse of length 10 cm and one leg of length 6 cm. Find the length of the other leg.

A. \(8 \text{cm}\)

Correct B. \(12 \text{cm}\)

C. \(14 \text{cm}\)

D. \(16 \text{cm}\)

Correct Answer: B

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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, what is the probability that \(X + Y = 5\)?

A. 0.1

B. 0.2

Correct C. 0.3

D. 0.4

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

Solve the equation \(\frac{x^2 - 4}{x^2 - 2x - 3}\)\)\) = \(\frac{x + 2}{x - 3}\)\).

A. \(x = -1\)

Correct B. \(x = 1\)

C. \(x = 2\)

D. \(x = 3\)

Correct Answer: B

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Question 9 View Details

A set A has 5 elements. If a set B is formed by selecting 3 elements from set A, how many different subsets of B can be formed?

A. 10

Correct B. 15

C. 20

D. 25

Correct Answer: B

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Question 10 View Details

Find the sum of the infinite geometric series \sum_{\(n = 1\)}^\infty \(\frac{2}{3^n}\)\)\).

A. 1

Correct B. 2

C. 3

D. 4

Correct Answer: B

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Question 11 View Details

Find the area under the curve \(y = \frac{1}{x^2}\) from \(x = 1\) to \(x = 2\).

A. 0.5

B. 1

Correct C. 1.5

D. 2

Correct Answer: C

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Question 12 View Details

A circle with center ( C(2, 3) ) and radius \(r = 4\) has a chord ( AB ) of length ( 6 ). Find the distance from the center to the chord.

A. 2

Correct B. 3

C. 4

D. 5

Correct Answer: B

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Question 13 View Details

A histogram with 5 classes has the following frequencies: 2, 3, 5, 7, 8. Find the mean of the data.

A. 4

B. 5

Correct C. 6

D. 7

Correct Answer: C

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Question 14 View Details

Solve the equation \(\sin^2 x + \cos^2 x = 1\) for ( x ) in the interval ( [0, 2pi] ).

A. 0

Correct B. π/2

C. π

D. 3π/2

Correct Answer: B

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Question 15 View Details

A line passes through the points ( (1, 2) ) and ( (3, 4) ). Find the equation of the line in slope-intercept form.

Correct A. \(y = x + 1\)

B. \(y = x - 1\)

C. \(y = -x + 3\)

D. \(y = x - 2\)

Correct Answer: A

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Question 16 View Details

Determine the value of x in the equation \(\(1x \\) = \(\frac{1}\){\(\sqrt{3}\)}\) ) if 1x \\) = \(\frac{1}{2}\)\) ).

Correct A. \(\frac{\pi}{6}\)

B. \(\frac{\pi}{3}\)

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

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

Correct Answer: A

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Question 17 View Details

Find the area under the curve \(y = x^2 - 4x + 3\) from \(x = 1\) to \(x = 3\).

Correct A. ( 4 )

B. ( 6 )

C. ( 8 )

D. ( 10 )

Correct Answer: A

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Question 18 View Details

A die is rolled twice. What is the probability that the sum of the two numbers is 7?

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

Correct B. \(\frac{1}{3}\)

C. \(\frac{1}{2}\)

D. \(\frac{2}{3}\)

Correct Answer: B

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Question 19 View Details

Solve the differential equation \(\frac{dy}{dx} = \frac{y}{x}\) with the initial condition ( y(1) = 2 ).

A. \(y = 2x\)

B. \(y = x^2\)

Correct C. \(y = \frac{2}{x}\)

D. \(y = x^2 + 2\)

Correct Answer: C

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Question 20 View Details

A circle has a radius of 4 cm. What is the area of the circle?

Correct A. ( 16pi )

B. ( 32pi )

C. ( 64pi )

D. ( 128pi )

Correct Answer: A

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Question 21 View Details

Find the value of x in the quadratic equation \(x^2 + 5x + 6 = 0\).

A. 1

Correct B. -2

C. -3

D. 4

Correct Answer: B

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Question 22 View Details

Solve the inequality \(2x^2 + 5x - 3 > 0\).

Correct A. x < -1 or \(x > 3\)

B. \(x < 1\) or x > -3

C. x < -3 or \(x > 1\)

D. \(x < 3\) or x > -1

Correct Answer: A

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Question 23 View Details

Find the derivative of the function ( f(x) = \(x^3 - 2x^2 + 3x - 1\) ).

Correct A. \(3x^2 - 4x + 3\)

B. \(3x^2 - 4x + 1\)

C. \(3x^2 - 4x - 1\)

D. \(3x^2 - 4x - 3\)

Correct Answer: A

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Question 24 View Details

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

A. \(x = 0\)

B. \(x = 90\)

C. \(x = 180\)

Correct D. \(x = 270\)

Correct Answer: D

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Question 25 View Details

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

A. 25

Correct B. 30

C. 35

D. 40

Correct Answer: B

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