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POST UTME OSUSTECH 2020 Mathematics | Objective

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Question 1 View Details

Solve for x in the equation \(\log_{10} x^2 \\)\(= 4 ).\)

Correct A. 10

B. 100

C. 1000

D. 10000

Correct Answer: A

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Question 2 View Details

Find the volume of the frustum of a cone with height 6cm, lower base radius 4cm, and upper base radius 2cm.

A. 48\pi

B. 64\pi

Correct C. 80\pi

D. 96\pi

Correct Answer: C

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Question 3 View Details

Solve the inequality \(x^2 - 6x + 8 \geq 0\).

Correct A. \(-\infty, 2\) \cup \(4, \infty\)

B. (2, 4)

C. \(-\infty, 2\) \cup \(4, \infty\)

D. (2, 4)

Correct Answer: A

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Question 4 View Details

A particle moves in a circular path with a constant speed of \(5m/s\). If the radius of the circle is 3m, find the magnitude of the acceleration of the particle.

A. 5\pi

B. 10\pi

Correct C. 15\pi

D. 20\pi

Correct Answer: C

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Question 5 View Details

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

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

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

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

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

Correct Answer: A

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Question 6 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. Calculate the coefficient of variation (CV) for the sample.

A. 16.8%

Correct B. 17.4%

C. 18.0%

D. 18.6%

Correct Answer: B

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Question 7 View Details

Solve for x in the equation \(\log_{10} x^2\)\(= 4\)\).

A. \(10^4\)

B. \(10^8\)

Correct C. \(10^12\)

D. \(10^16\)

Correct Answer: C

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Question 8 View Details

A vector (\(\vec{a}\)\) has a magnitude of 5 units and makes an angle of 30° with the positive x-axis. Find the x and y components of \\((vec{a}\(\vec{a}\).

Correct A. 4.33 \hat{i} + 2.5 \hat{j}

B. 4.33 \hat{i} - 2.5 \hat{j}

C. 2.5 \hat{i} + 4.33 \hat{j}

D. 2.5 \hat{i} - 4.33 \hat{j}

Correct Answer: A

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Question 9 View Details

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

A. 32

B. 64

Correct C. 96

D. 128

Correct Answer: C

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Question 10 View Details

A 3x3 matrix (A\) has the following elements: \(A = \\((A) has the following elements: \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 end{bmatrix}\). Find the determinant of \(A\\(end{bmatrix}). Find the determinant of\).

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 11 View Details

Find the determinant of the matrix [ egin{pmatrix} 2 & 3 & 1 \ 4 & 2 & 3 \ 1 & 3 & 2 \end{pmatrix} ].

A. 0

Correct B. 1

C. 2

D. 3

Correct Answer: B

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Question 12 View Details

A rectangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. Find its volume.

Correct A. 30

B. 40

C. 50

D. 60

Correct Answer: A

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Question 13 View Details

Solve the 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 14 View Details

Find the derivative of the function [\(f(x) =\)\(3x^2 + 2x - 5\) ].

Correct A. 6x + 2

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

C. 6x - 2

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

Correct Answer: A

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Question 15 View Details

A circle has a radius of 4 cm. Find its circumference.

A. 8π

Correct B. 16π

C. 32π

D. 64π

Correct Answer: B

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Question 16 View Details

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

A. 40

B. 50

Correct C. 60

D. 70

Correct Answer: C

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Question 17 View Details

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

Correct A. x < -1 or \(x > 3/2\)\)

B. x > -1 or \(x < 3/2\)\)

C. \(x < 3/2\)\) or x > -1

D. \(x > 3/2\)\) or x < -1

Correct Answer: A

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Question 18 View Details

Find the determinant of the matrix \(\begin{bmatrix} 2 & 3 & 4 \ 5 & 6 & 7 \ 8 & 9 & 10 \end{bmatrix}\).

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 19 View Details

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

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

B. \(x = 2\), \(y = 3\)

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

D. \(x = 4\), \(y = 1\)

Correct Answer: A

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Question 20 View Details

Find the vector \(\vec{a} \times \vec{b}) given that \(\vec{a} = \\() given that (\begin{bmatrix} 1 \ 2 \ 3 \end{bmatrix}\) and \(\vec{b} = \begin{bmatrix} 4 \ 5 \ 6 \end{bmatrix}\).

Correct A. \begin{bmatrix} -3 \ 6 \ -3 \end{bmatrix}

B. \begin{bmatrix} 3 \ -6 \ 3 \end{bmatrix}

C. \begin{bmatrix} 6 \ -3 \ 3 \end{bmatrix}

D. \begin{bmatrix} -6 \ 3 \ -3 \end{bmatrix}

Correct Answer: A

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Question 21 View Details

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

Correct A. \(x = -2\)

B. \(x = -1\)

C. \(x = 0\)

D. \(x = 1\)

Correct Answer: A

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Question 22 View Details

Find the \logarithm \(\log_{10} 1000 \\) ).

A. 3

Correct B. 4

C. 5

D. 6

Correct Answer: B

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Question 23 View Details

Solve the inequality \(\frac{x}{2} + 3 > 5\).

Correct A. \(x > 2\)

B. \(x < 2\)

C. \(x > 4\)

D. \(x < 4\)

Correct Answer: A

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Question 24 View Details

Find the value of \(\sqrt{16} + \sqrt{9}\).

A. 7

B. 8

C. 9

D. 10

Correct Answer: VIEW ANSWER

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Question 25 View Details

In a certain number base, the number 1011 is equivalent to 11 in base 10. What is the value of the number base?

A. 5

Correct B. 6

C. 7

D. 8

Correct Answer: B

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