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POST UTME ELIZADE UNIVERSITY 2024 Mathematics | Objective

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Question 1 View Details

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

A. 5 cm

Correct B. 7.07 cm

C. 10 cm

D. 15 cm

Correct Answer: B

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Question 2 View Details

Solve for x in the equation \(2^x + 2^x = 2^{x+2}\).

A. \(x = 1\)

Correct B. \(x = 2\)

C. \(x = 3\)

D. \(x = 4\)

Correct Answer: B

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Question 3 View Details

A histogram is shown below. What is the mean of the data set?

A. 10

B. 15

Correct C. 20

D. 25

Correct Answer: C

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Question 4 View Details

Solve the inequality \(x^2 - 4x + 3 > 0\).

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

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

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

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

Correct Answer: A

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Question 5 View Details

A circle has a radius of 5 cm. What is the area of the circle?

A. 25\pi

Correct B. 50\pi

C. 75\pi

D. 100\pi

Correct Answer: B

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Question 6 View Details

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

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

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

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

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

Correct Answer: A

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Question 7 View Details

Solve the equation \(\log_2 x^2-4\)=3\).

A. 4

B. -2

Correct C. 2

D. -4

Correct Answer: C

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Question 8 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 9 View Details

Solve the 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 10 View Details

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

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

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

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

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

Correct Answer: A

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Question 11 View Details

Solve the inequality \(\frac{x}{x-2} > 0\) for ( x in mathbb{R} setminus {2} ).

Correct A. \(-∞, 2\) ∪ (2, ∞)

B. \(-∞, 0\) ∪ (2, ∞)

C. \(-∞, 2\) ∪ (2, ∞)

D. (0, 2) ∪ (2, ∞)

Correct Answer: A

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Question 12 View Details

Find the value of ( k ) such that the quadratic equation \(x^2 + kx + 16 = 0\) has equal roots.

A. 4

Correct B. -4

C. 8

D. -8

Correct Answer: B

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Question 13 View Details

Solve the system of equations \(egin{cases} x + y = 4 \ 2x - y = 3 \end{cases}\).

Correct A. {(1, 3), (2, 2)}

B. {(1, 3), (3, 1)}

C. {(2, 2), (3, 1)}

D. {(1, 3), (2, 2)}

Correct Answer: A

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Question 14 View Details

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

Correct A. 6

B. 8

C. 10

D. 12

Correct Answer: A

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Question 15 View Details

A binary operation ( odot ) on the set ( mathbb{R} ) is defined as \(x odot y = xy + 1\). Find the value of ( x odot (x odot x) ).

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

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

C. \(x^3 + 2x^2 + 2\)

D. \(x^3 + x^2 + 2\)

Correct Answer: A

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Question 16 View Details

Find the volume of the solid formed by rotating the region bounded by the curves \(y = 2x\^2\) and \(y = 4x\) about the x-axis.

A. 64\pi

B. 128\pi

Correct C. 256\pi

D. 512\pi

Correct Answer: C

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Question 17 View Details

Solve the equation \(\log_2 x^2 + 1\) - \log_2 \(x + 1\)\(= 1\)\).

A. 1

Correct B. 2

C. 3

D. 4

Correct Answer: B

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Question 18 View Details

In the diagram below, ABCD is a rectangle with \(AB = 6\) cm and \(BC = 8\) cm. Find the area of triangle ABE.

A. 24

B. 30

Correct C. 36

D. 40

Correct Answer: C

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Question 19 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. \(3/12\)

B. \(5/12\)

Correct C. \(7/12\)

D. \(9/12\)

Correct Answer: C

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Question 20 View Details

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

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

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

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

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

Correct Answer: C

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Question 21 View Details

Find the area under the curve \(y = \frac{1}{2}x^2 + 3x - 4\) from \(x = 0\) to \(x = 2\).

A. 10

B. 12

Correct C. 14

D. 16

Correct Answer: C

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Question 22 View Details

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

A. 1

Correct B. 2

C. 3

D. 4

Correct Answer: B

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Question 23 View Details

Find the sum of the infinite geometric series \(1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + cdots\).

A. 2

Correct B. 4

C. 8

D. 16

Correct Answer: B

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Question 24 View Details

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

Correct A. \left\(x - 2 \right\)^2 + \left\(y - 3 \right\)^\(2 = 16\)

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

C. \left\(x - 4 \right\)^2 + \left\(y - 5 \right\)^\(2 = 16\)

D. \left\(x - 5 \right\)^2 + \left\(y - 4 \right\)^\(2 = 16\)

Correct Answer: A

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Question 25 View Details

Find the value of ( x ) in the equation \(2x^2 + 5x - 3 = 0\).

A. 1

Correct B. 2

C. 3

D. 4

Correct Answer: B

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