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POST UTME COVENANT UNIVERSITY 2021 Mathematics | Objective

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Question 1 View Details

Determine 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

A survey of 100 students found that 40 students preferred Mathematics, 30 preferred Science, and 30 preferred both. What is the probability that a randomly selected student prefers Mathematics or Science?

Correct A. 0.7

B. 0.6

C. 0.5

D. 0.4

Correct Answer: A

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Question 3 View Details

In a geometric sequence, the first term is 2 and the common ratio is 3. Find the sum of the first five terms.

Correct A. 2+6+18+54+162

B. 2+6+18+54+162+486

C. 2+6+18+54+162+486+1458

D. 2+6+18+54+162+486+1458+4374

Correct Answer: A

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Question 4 View Details

A right circular cone has a height of 10 cm and a base radius of 5 cm. Find the volume of the cone.

Correct A. 250\pi

B. 500\pi

C. 750\pi

D. 1000\pi

Correct Answer: A

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Question 5 View Details

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

Correct A. \(\frac{8}{3}\)\)

B. \(\frac{16}{3}\)\)

C. \(\frac{32}{3}\)\)

D. \(\frac{64}{3}\)\)

Correct Answer: A

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Question 6 View Details

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

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

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

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

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

Correct Answer: A

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Question 7 View Details

A fair six-sided die is rolled. What is the probability that the number rolled is a multiple of 3?

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

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

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

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

Correct Answer: B

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Question 8 View Details

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

Correct A. \(x = -2\)

B. \(x = 2\)

C. \(x = -1\)

D. \(x = 1\)

Correct Answer: A

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Question 9 View Details

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

Correct A. \(\frac{8}{3}\)

B. \(\frac{16}{3}\)

C. \(\frac{32}{3}\)

D. \(\frac{64}{3}\)

Correct Answer: A

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Question 10 View Details

Find the vector ( mathbf{v} ) such that \(\mathbf{v} \cdot \mathbf{i} = 3\) and \(\mathbf{v} \cdot \mathbf{j} = 4\).

Correct A. \(\mathbf{v} = 3\mathbf{i} + 4\mathbf{j}\)

B. \(\mathbf{v} = 4\mathbf{i} + 3\mathbf{j}\)

C. \(\mathbf{v} = 3\mathbf{i} - 4\mathbf{j}\)

D. \(\mathbf{v} = 4\mathbf{i} - 3\mathbf{j}\)

Correct Answer: A

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Question 11 View Details

Find the determinant of the matrix [ egin{pmatrix} 2 & 3 & 4 \ 5 & 6 & 7 \ 8 & 9 & 10 \end{pmatrix} ].

A. 0

B. -1

Correct C. 1

D. 2

Correct Answer: C

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Question 12 View Details

Solve the system of linear equations [ egin{cases} \(x + 2y - 3z = 7\) \\(2x - 3y + z = -2\)\ \(3x + y + 2z = 5\) \end{cases} ].

Correct A. \begin{pmatrix} 1 \ 2 \ 3 \end{pmatrix}

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

C. \begin{pmatrix} 3 \ 1 \ -2 \end{pmatrix}

D. \begin{pmatrix} 4 \ 2 \ -1 \end{pmatrix}

Correct Answer: A

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Question 13 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. \(\frac{1}{x^2 + 1\) ^2}\)\)

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

Correct Answer: A

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Question 14 View Details

A fair six-sided die is rolled. What is the probability that the number rolled is greater than 4?

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

B. \(\frac{2}{6}\)\)

C. \(\frac{3}{6}\)\)

Correct D. \(\frac{4}{6}\)\)

Correct Answer: D

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Question 15 View Details

Solve the quadratic equation [ \\((x^2 + 5x + 6\)\(= 0\)\) \].

Correct A. \begin{pmatrix} -2 \ -3 \end{pmatrix}

B. \begin{pmatrix} -3 \ -2 \end{pmatrix}

C. \begin{pmatrix} 2 \ 3 \end{pmatrix}

D. \begin{pmatrix} 3 \ 2 \end{pmatrix}

Correct Answer: A

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Question 16 View Details

Determine the value of (x\) in the equation \(2^x + 5^x = 7^x\\((x) in the equation\).

A. 1

B. 2

C. 3

Correct D. 4

Correct Answer: D

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Question 17 View Details

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

A. 10

Correct B. 12

C. 14

D. 16

Correct Answer: B

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Question 18 View Details

A set of 10 numbers has a mean of 20 and a standard deviation of 5. Find the probability that a randomly selected number from the set is greater than 25.

A. 0.05

Correct B. 0.10

C. 0.15

D. 0.20

Correct Answer: B

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Question 19 View Details

Find the volume of the solid formed by revolving the region bounded by the curve (y = \(x^2\)\) and the line \(x = 2\\((y = x^2) and the line\) about the x-axis.

A. 32\pi

Correct B. 64\pi

C. 128\pi

D. 256\pi

Correct Answer: B

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Question 20 View Details

A circle has a diameter of 10 cm. Find 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 21 View Details

A survey of 1000 students revealed that 60% of them preferred Mathematics as their favorite subject, while 40% preferred English Language. If 10% of the students who preferred Mathematics also preferred English Language, what is the probability that a randomly selected student who prefers Mathematics also prefers English Language?

Correct A. 0.1

B. 0.2

C. 0.3

D. 0.4

Correct Answer: A

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Question 22 View Details

A cylindrical \tank has a height of 10m and a radius of 4m. If the \tank is filled with water to a height of 8m, what is the volume of water in the \tank?

A. 2000π

Correct B. 2500π

C. 3000π

D. 3500π

Correct Answer: B

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Question 23 View Details

A polynomial function f(x) = \(ax^3 + bx^2 + cx + d\) has roots at x = -2, \(x = 1\), and (x = 3\). If f\(-1 = 10\\((x = 3). If f\), find the value of f(2).

A. 10

B. 20

Correct C. 30

D. 40

Correct Answer: C

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Question 24 View Details

A histogram of exam scores has a mean of 60 and a standard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected student scored above 70?

A. 0.1

B. 0.2

Correct C. 0.3

D. 0.4

Correct Answer: C

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Question 25 View Details

A circuit consists of a 12V battery, a 4Ω resistor, and a 6Ω resistor connected in series. If the current through the circuit is 2A, what is the voltage across the 6Ω resistor?

A. 8V

Correct B. 10V

C. 12V

D. 14V

Correct Answer: B

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