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POST UTME ELIZADE UNIVERSITY 2022 Mathematics | Objective

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Question 1 View Details

Solve for x in the equation \(\frac{1}{2}x^2 + 5x - 3 = 0\).

A. \(x = -10\)

Correct B. \(x = 3\)

C. \(x = -3\)

D. \(x = 10\)

Correct Answer: B

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Question 2 View Details

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

A. ( 2 )

B. ( 4 )

Correct C. ( 6 )

D. ( 8 )

Correct Answer: C

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Question 3 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 4 View Details

Find the derivative of the function ( f(x) = \(x^3 - 2x^2 + 5x - 1\) ) using the chain rule.

Correct A. ( f'\((x) =\)\(3x^2 - 4x + 5\) )

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

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

D. ( f'\((x) =\)\(3x^2 - 4x - 5\) )

Correct Answer: A

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Question 5 View Details

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

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

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

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

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

Correct Answer: A

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Question 6 View Details

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

A. 64

B. 80

Correct C. 96

D. 112

Correct Answer: C

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Question 7 View Details

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

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 8 View Details

Find the equation of the circle with center ( (3, 4) ) and radius ( 5 ).

Correct A. \(x - 3\)^2 + \(y - 4\)^\(2 = 25\)

B. \(x - 4\)^2 + \(y - 3\)^\(2 = 25\)

C. \(x - 3\)^2 + \(y - 4\)^\(2 = 30\)

D. \(x - 4\)^2 + \(y - 3\)^\(2 = 30\)

Correct Answer: A

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Question 9 View Details

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

A. \(x < -1\)

Correct B. \(x > -1\)

C. \(x < 3\)

D. \(x > 3\)

Correct Answer: B

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Question 10 View Details

Find the value of ( x ) in the equation \(x^3 - 6x^2 + 11x - 6 = 0\).

A. \(x = 1\)

B. \(x = 2\)

Correct C. \(x = 3\)

D. \(x = 4\)

Correct Answer: C

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Question 11 View Details

A random variable X has a probability distribution given by P\(X = 1 = 0.3\), P\(X = 2 = 0.4\), and P(X = 3 = 0.3\). If two independent random variables X and Y are defined on the same probability space, and Y has a probability distribution given by P\(Y = 1 = 0.4\\((X = 3 = 0.3). If two independent random variables X and Y are defined on the same probability space, and Y has a probability distribution given by P\), P\(Y = 2 = 0.3\), and P\(Y = 3 = 0.3\), what is the probability that \(X + Y = 4\)?

A. 0.1

B. 0.2

Correct C. 0.3

D. 0.4

Correct Answer: C

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Question 12 View Details

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

Correct A. \(x = \frac{-5 \pm \sqrt{109}}{4}\)

B. \(x = \frac{-5 \pm \sqrt{121}}{4}\)

C. \(x = \frac{-5 \pm \sqrt{169}}{4}\)

D. \(x = \frac{-5 \pm \sqrt{225}}{4}\)

Correct Answer: A

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Question 13 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.

Correct A. \(\frac{32\pi}{5}\)

B. \(\frac{64\pi}{5}\)

C. \(\frac{128\pi}{5}\)

D. \(\frac{256\pi}{5}\)

Correct Answer: A

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Question 14 View Details

Solve the system of equations \(\begin{cases} 2x + 3y = 7 \ 4x - 2y = -3 \end{cases}\) using matrices.

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

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

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

Correct Answer: A

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Question 16 View Details

A random sample of 25 students from a university had a mean height of 175.5 cm with a standard deviation of 5.2 cm. If the population standard deviation is 6.1 cm, calculate the 95% confidence interval for the population mean.

A. 168.3 cm, 182.7 cm

Correct B. 170.1 cm, 180.9 cm

C. 172.9 cm, 178.1 cm

D. 169.5 cm, 181.5 cm

Correct Answer: B

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Question 17 View Details

Solve for x in 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 18 View Details

A binary number 1101 is converted to decimal. What is the decimal equivalent?

A. 13

Correct B. 15

C. 17

D. 19

Correct Answer: B

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Question 19 View Details

Two events A and B are independent. If P(A) = 0.4 and P(B) = 0.6, find P(A and B).

Correct A. 0.24

B. 0.36

C. 0.48

D. 0.60

Correct Answer: A

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Question 20 View Details

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

Correct A. \(x \leq -1.5\) or \(x \geq 1.5\)

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

C. \(x \leq 0\) or \(x \geq 2\)

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

Correct Answer: A

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Question 21 View Details

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

A. 64

B. 80

Correct C. 96

D. 112

Correct Answer: C

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Question 22 View Details

A solid cylinder has a height of 10 cm and a radius of 4 cm. Find the volume of the cylinder.

A. 800\pi

Correct B. 1000\pi

C. 1200\pi

D. 1600\pi

Correct Answer: B

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Question 23 View Details

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

Correct A. \cos 2x

B. \sin 2x

C. \cos x

D. \sin x

Correct Answer: A

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Question 24 View Details

Solve the system of equations using matrices: \begin{align*} 2x + 3y &= 7 \ 4x - 2y &= -3 \end{align*}

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

B. \begin{bmatrix} 2 \ 1 \end{bmatrix}

C. \begin{bmatrix} 3 \ 4 \end{bmatrix}

D. \begin{bmatrix} 4 \ 3 \end{bmatrix}

Correct Answer: A

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Question 25 View Details

Simplify the expression \(\frac{2^3 \cdot 3^2}{2^2 \cdot 3^4}\).

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

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

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

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

Correct Answer: A

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