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POST UTME MADONNA UNIVERSITY 2024 Mathematics | Objective

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Question 1 View Details

Find the volume of the frustum of a cone with height 15 cm, lower base radius 6 cm, and upper base radius 3 cm.

A. 450\pitext{ cm}^3

Correct B. 600\pitext{ cm}^3

C. 750\pitext{ cm}^3

D. 900\pitext{ cm}^3

Correct Answer: B

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Question 2 View Details

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

A. \(x = 2\)

B. \(x = 3\)

Correct C. \(x = 4\)

D. \(x = 5\)

Correct Answer: C

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Question 3 View Details

Find the equation of the circle passing through the points (2, 3), (4, 5), and (6, 7).

Correct A. \(x - 4\)^2 + \(y - 5\)^\(2 = 9\)

B. \(x - 3\)^2 + \(y - 4\)^\(2 = 16\)

C. \(x - 5\)^2 + \(y - 6\)^\(2 = 25\)

D. \(x - 6\)^2 + \(y - 7\)^\(2 = 36\)

Correct Answer: A

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Question 4 View Details

A right-angled triangle has a hypotenuse of length 10 cm and one of the acute angles is 30°. Find the length of the side opposite the 30° angle.

A. 5\text{ cm}

Correct B. 7.5\text{ cm}

C. 10\text{ cm}

D. 12.5\text{ cm}

Correct Answer: B

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Question 5 View Details

Find the value of \(\log_{10} 2^3\).

Correct A. 3

B. 6

C. 9

D. 12

Correct Answer: A

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Question 6 View Details

In the coordinate plane, the line (y = 2x + 3\) intersects the circle \(x^2 + y - 2\\((y = 2x + 3) intersects the circle\)\\((^(2\) = 4\)\)\) at two points. Find the coordinates of the point where the line is \\\(((2 = 4)\)\tangent to the circle.

Correct A. (1, 5)

B. (2, 7)

C. (3, 9)

D. (4, 11)

Correct Answer: A

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Question 7 View Details

A bag contains 5 red marbles, 4 blue marbles, and 3 green marbles. If a marble is drawn at random, what is the probability that it is not blue?

A. \(1/3\)

Correct B. \(2/3\)

C. \(3/4\)

D. \(4/5\)

Correct Answer: B

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Question 8 View Details

Solve the inequality \(|2x - 1| \geq 3\).

Correct A. \(x \leq -1\) or \(x \geq 2\)

B. \(x \leq -2\) or \(x \geq 1\)

C. \(x \leq -3\) or \(x \geq 2\)

D. \(x \leq -1\) or \(x \geq 3\)

Correct Answer: A

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Question 9 View Details

A right triangle has legs of length 3 and 4. Find the length of the hypotenuse.

A. 5

Correct B. 6

C. 7

D. 8

Correct Answer: B

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Question 10 View Details

Find the value of (x\) in the equation \(2^x + 2^x = 64\\((x) in the equation\).

A. 3

Correct B. 4

C. 5

D. 6

Correct Answer: B

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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. 64\pi \(cm^3\)

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

Correct C. 128\pi \(cm^3\)

D. 192\pi \(cm^3\)

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 not blue?

Correct A. \(\frac{2}{3}\)\)

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

C. \(\frac{4}{5}\)\)

D. \(\frac{5}{6}\)\)

Correct Answer: A

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Question 13 View Details

Solve the equation \(x^2 + 2x - 6 = 0\) using the quadratic formula.

A. \(\frac{-2 \pm \sqrt{4 + 24}\)}{2}\)

Correct B. \(\frac{-2 \pm \sqrt{28}\)}{2}\)

C. \(\frac{-2 \pm \sqrt{4 - 24}\)}{2}\)

D. \(\frac{-2 \pm \sqrt{28 - 4}\)}{2}\)

Correct Answer: B

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Question 14 View Details

Find the surface area of the sphere with radius 5 cm.

A. 100\pi \(cm^2\)

B. 200\pi \(cm^2\)

Correct C. 300\pi \(cm^2\)

D. 400\pi \(cm^2\)

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 days

Correct B. 19 days

C. 20 days

D. 21 days

Correct Answer: B

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Question 16 View Details

Solve for x in the equation \(\sin^2 x \\) + \\(\cos^2(x)\) = 1 ) using the identity \(\sin^2 x \\) + \\(\cos^2(x)\)\(= 1 ).\)

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

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

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

D. \(x =\)\(\frac{7\pi}{4}\)\)

Correct Answer: A

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Question 17 View Details

A bakery sells a total of 480 loaves of bread per day. They sell a combination of whole wheat and white bread. If the ratio of whole wheat to white bread is 5:3, how many loaves of whole wheat bread are sold per day?

A. 120

Correct B. 150

C. 180

D. 200

Correct Answer: B

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Question 18 View Details

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

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

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

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

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

Correct Answer: A

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Question 19 View Details

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

Correct A. x < -1 or x > \(\frac{3}{2}\)\)

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

C. x > -1 or x < \(\frac{3}{2}\)\)

D. x > -1 or x > \(\frac{3}{2}\)\)

Correct Answer: A

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Question 20 View Details

A circle has a radius of 4 cm. Find the area of the circle using the formula \(A = \pi r^2\).

Correct A. 50.24 \(cm^2\)

B. 50.24 \(m^2\)

C. 50.24 \(cm^3\)

D. 50.24 \(m^3\)

Correct Answer: A

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Question 21 View Details

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

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

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

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

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

Correct Answer: A

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Question 22 View Details

Solve the system of linear equations using matrices: \begin{align*} x + y &= 3 \ 2x - 3y &= -5 \end{align*}

Correct A. \begin{pmatrix} 1 \ 2 \end{pmatrix}

B. \begin{pmatrix} -1 \ 2 \end{pmatrix}

C. \begin{pmatrix} 1 \ -2 \end{pmatrix}

D. \begin{pmatrix} -1 \ -2 \end{pmatrix}

Correct Answer: A

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Question 23 View Details

Find the determinant of the matrix \begin{pmatrix} 2 & 1 & 3 \ 4 & 2 & 5 \ 6 & 3 & 7 \end{pmatrix}

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 24 View Details

Solve the quadratic equation \(x^2 + 4x + 4 = 0\) using the quadratic formula.

A. \(\frac{-4 \pm \sqrt{16 - 16}\)}{2}\)

Correct B. \(\frac{-4 \pm \sqrt{16 - 4}\)}{2}\)

C. \(\frac{-4 \pm \sqrt{16 + 4}\)}{2}\)

D. \(\frac{-4 \pm \sqrt{16 - 4}\)}{2}\)

Correct Answer: B

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Question 25 View Details

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

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

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

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

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

Correct Answer: A

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