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POST UTME ELIZADE UNIVERSITY 2021 Mathematics | Objective

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Question 1 View Details

Find the value of \(\int_{0}^{\pi} \frac{1}{1+\sin^2 x} dx\).

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

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

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

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

Correct Answer: A

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Question 2 View Details

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

Correct A. \(x \leq -1\) or \(x \geq 5\)

B. \(x \leq 1\) or \(x \geq 5\)

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

D. \(x \leq 1\) or \(x \geq 2\)

Correct Answer: A

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Question 3 View Details

A histogram of exam scores for a class of 50 students is shown below. Find the mean score.

A. 40

B. 45

Correct C. 50

D. 55

Correct Answer: C

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Question 4 View Details

Find the area of the region bounded by the curves \(y = x^2\) and \(y = 4 - x^2\).

A. 16\pi

B. 32\pi

Correct C. 48\pi

D. 64\pi

Correct Answer: C

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Question 5 View Details

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

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

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

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

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

Correct Answer: A

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Question 6 View Details

Solve for \(x\): [ \\(\sin^2\) x + \\(\cos^2\) \(x = 1\) ] and [ \\(\tan^2\) \(x + 1 = \sec\^2\) x ].

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

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

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

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

Correct Answer: A

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Question 7 View Details

Find the value of (k\) such that the lines \(2x + 3y = 7\\((k) such that the lines\) and \(kx - 2y = 5\) are parallel.

Correct A. -\(\frac{14}{5}\)\)

B. -\(\frac{7}{5}\)\)

C. \(\frac{7}{5}\)\)

D. \(\frac{14}{5}\)\)

Correct Answer: A

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Question 8 View Details

If (f(x) = \(\frac{1}{\(x^2 + 1}\)\)\), find \\((f(x) = frac{1}{x^2 + 1}\(f'(x)\) using the chain rule.

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

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

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

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

Correct Answer: B

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Question 9 View Details

A circle with center \(C\) and radius \(r\) passes through the points \(A\) and \(B\). If angle \(ACB = 60\)^\\(angle (ACB = 60\circ, find the measure of \(\angle AOB\).

A. 30^\circ

Correct B. 60^\circ

C. 90^\circ

D. 120^\circ

Correct Answer: B

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Question 10 View Details

Two events \(A\) and \(B\) are independent. If \(P(A) = \frac{1}{4}\) and \(P(B) = frac{1}{3}\), find \(P A \\(frac{1}{3}), find \cap B\)\).

Correct A. \(\frac{1}{12}\)\)

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

C. \(\frac{1}{4}\)\)

D. \(\frac{1}{3}\)\)

Correct Answer: A

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Question 11 View Details

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

A. f'\((x) =\)\(\frac{-x}\){ \(x^2 + 1\) \)^{\(3/2\)}}\)

Correct B. f'\((x) =\)\(\frac{x}\){ \(x^2 + 1\) \)^{\(3/2\)}}\)

C. f'\((x) =\)\(\frac{1}\){ \(x^2 + 1\) \)^{\(3/2\)}}\)

D. f'\((x) =\)\(\frac{-1}\){ \(x^2 + 1\) \)^{\(3/2\)}}\)

Correct Answer: B

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Question 12 View Details

Solve the inequality \(2^x > 5\).

Correct A. \(x >\)\log_2(5)

B. \(x <\)\log_2(5)

C. \(x >\)\log_2(5)

D. \(x <\)\log_2(5)

Correct Answer: A

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Question 13 View Details

Find the area under the curve \(y = x^2 + 1\) from \(x = 0\) to \(x = 2\).

A. \(\frac{7}{3}\)\)

Correct B. \(\frac{11}{3}\)\)

C. \(\frac{13}{3}\)\)

D. \(\frac{17}{3}\)\)

Correct Answer: B

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Question 14 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 15 View Details

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

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

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

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

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

Correct Answer: A

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Question 16 View Details

Find the value of ( x ) in the equation \(2^x = 32\).

A. 5

Correct B. 6

C. 7

D. 8

Correct Answer: B

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Question 17 View Details

Find the equation of the line passing through the points ( (1, 2) ) and ( (3, 4) ).

Correct A. \(y = 2x - 1\)

B. \(y = 2x + 1\)

C. \(y = 3x - 2\)

D. \(y = 3x + 2\)

Correct Answer: A

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Question 18 View Details

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

A. \(x < 2\)

Correct B. \(x > 2\)

C. \(x < 1\)

D. \(x > 1\)

Correct Answer: B

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Question 19 View Details

Find the area of the triangle with vertices ( (0, 0) ), ( (3, 0) ), and ( (0, 2) ).

A. 3

B. 4

C. 5

D. 6

Correct Answer: VIEW ANSWER

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Question 20 View Details

Solve for x in the equation \(2x^2 + 5x - 3 = 0\).

Correct A. \(x = -3\)

B. \(x = 1\)

C. \(x = -1\)

D. \(x = 3\)

Correct Answer: A

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Question 21 View Details

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

Correct A. ( 1 )

B. \(-1\)

C. ( 0 )

D. ( 2 )

Correct Answer: A

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Question 22 View Details

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

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 23 View Details

Find the probability of drawing two aces from a standard deck of 52 cards.

A. \(\frac{1}{52}\)

Correct B. \(\frac{1}{26}\)

C. \(\frac{1}{4}\)

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

Correct Answer: B

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Question 24 View Details

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

Correct A. \(x = -2\)

B. \(x = -1\)

C. \(x = 1\)

D. \(x = 2\)

Correct Answer: A

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Question 25 View Details

Find the value of x in the equation \(\log_{10} x^2 \\)\(= 4 ).\)

A. \(x = 10\)

Correct B. \(x = 100\)

C. \(x = 1000\)

D. \(x = 10000\)

Correct Answer: B

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