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POST UTME OSUSTECH 2024 Mathematics | Objective

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Question 1 View Details

Determine the volume of the frustum of a cone with a height of 6 units, a lower base radius of 4 units, and an upper base radius of 2 units.

Correct A. 24π

B. 48π

C. 96π

D. 192π

Correct Answer: A

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Question 2 View Details

Solve for x in the equation $egin{bmatrix} 2 & 1 \ 1 & 2 \end{bmatrix} egin{bmatrix} x \ 1 \end{bmatrix} = egin{bmatrix} 4 \ 4 \end{bmatrix}$.

A. 1

Correct B. 2

C. 3

D. 4

Correct Answer: B

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Question 3 View Details

A histogram of exam scores has a mean of 75 and a standard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score will be between 60 and 90?

A. 0.5

B. 0.6

Correct C. 0.7

D. 0.8

Correct Answer: C

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Question 4 View Details

Convert the binary number 1010 to decimal.

A. 2

Correct B. 3

C. 4

D. 5

Correct Answer: B

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Question 5 View Details

In the circuit below, what is the equivalent resistance between points A and B?

A. 2Ω

B. 4Ω

Correct C. 6Ω

D. 8Ω

Correct Answer: C

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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 $x = 4$.

Correct A. $\frac{1}{2} \times 4^3 + 3 \times \frac{4^2}{2} - 2 \times 4$

B. $\frac{1}{2} \times 4^2 + 3 \times 4 - 2$

C. $\frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4$

D. $\frac{1}{2} \times 4^2 + 3 \times \frac{4^2}{2} - 2 \times 4$

Correct Answer: A

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Question 7 View Details

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

Correct A. $x = 10^4$

B. $x = 10^2$

C. $x = 10^{-4}$

D. $x = 10^{-2}$

Correct Answer: A

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Question 8 View Details

Find the derivative of the function $y = $12x \$ ) using the chain rule.

Correct A. $\frac{d}{dx} $1(2x \$$) = 2$\cos (2x) )

B. $\frac{d}{dx} $1(2x \$ ) = \cos (2x) )

C. $\frac{d}{dx} $1(2x \$$) = 2$\sin (2x) )

D. $\frac{d}{dx} $1(2x \$ ) = \sin (2x) )

Correct Answer: A

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Question 9 View Details

A set ( A ) contains the elements ( { 1, 2, 3, 4, 5 } ). Find the number of subsets of ( A ) that contain exactly two elements.

Correct A. $inom{5}{2} = 10$

B. $inom{5}{3} = 10$

C. $inom{5}{4} = 5$

D. $inom{5}{1} = 5$

Correct Answer: A

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Question 10 View Details

Find the sum of the first five terms of the geometric series $2x + 3x^2 + 4x^3 + ldots$.

Correct A. $2x + 3x^2 + 4x^3 + 5x^4 + 6x^5$

B. $2x + 3x^2 + 4x^3 + 5x^4 + 6x^5 + 7x^6$

C. $2x + 3x^2 + 4x^3 + 5x^4 + 6x^5 + 7x^6 + 8x^7$

D. $2x + 3x^2 + 4x^3 + 5x^4 + 6x^5 + 7x^6 + 8x^7 + 9x^8$

Correct Answer: A

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Question 11 View Details

Find the sum of the first 10 terms of the geometric series with first term 2 and common ratio 3.

A. 12143

Correct B. 12145

C. 12147

D. 12149

Correct Answer: B

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Question 12 View Details

Solve the system of linear equations using matrices: \begin{align*} x + y + z &= 6 \ 2x + 3y - z &= 2 \ 3x - 2y + z &= 4 \end{align*}

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

B. \begin{pmatrix} 2 \ 3 \ 4 \end{pmatrix}

C. \begin{pmatrix} 3 \ 4 \ 5 \end{pmatrix}

D. \begin{pmatrix} 4 \ 5 \ 6 \end{pmatrix}

Correct Answer: A

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Question 13 View Details

A bag contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is blue?

Correct A. $1/2$

B. $1/3$

C. $2/3$

D. $3/4$

Correct Answer: A

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Question 14 View Details

Solve the quadratic equation $x^2 + 4x + 4 = 0$ using the quadratic formula.

Correct A. $x = -2$

B. $x = -1$

C. $x = 1$

D. $x = 2$

Correct Answer: A

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Question 15 View Details

Find the derivative of the function $f(x) = 3x^2 + 2x - 5$ using the power rule.

Correct A. $f'(x) = 6x + 2$

B. $f'(x) = 3x^2 + 2$

C. $f'(x) = 6x - 2$

D. $f'(x) = 3x^2 - 2$

Correct Answer: A

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Question 16 View Details

Determine the value of x in the equation $\frac{x}{2} + \frac{3}{4} = \frac{5}{8}$.

Correct A. 1

B. 2

C. 3

D. 4

Correct Answer: A

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Question 17 View Details

Find the area under the curve $y = x^2 + 2x - 3$ from $x = 0$ to $x = 2$.

A. 5

Correct B. 6

C. 7

D. 8

Correct Answer: B

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Question 18 View Details

Solve the inequality $2x^2 + 5x - 3 > 0$.

Correct A. $-∞, -1$ ∪ (3, ∞)

B. $-∞, 0$ ∪ (1, ∞)

C. $-∞, -2$ ∪ (2, ∞)

D. $-∞, -3$ ∪ (1, ∞)

Correct Answer: A

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Question 19 View Details

Find the value of ($12\theta$ given that \$($12theta$\(1\theta = \frac{3}{5}$ and 1\$theta =$$\frac{4}{5}$\).

Correct A. $\frac{24}{25}$\)

B. $\frac{16}{25}$\)

C. $\frac{20}{25}$\)

D. $\frac{12}{25}$\)

Correct Answer: A

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Question 20 View Details

A binary operation ( ast ) is defined as $a ast b = ab + 2$. Find the value of ( 3 ast 4 ).

A. 14

Correct B. 16

C. 18

D. 20

Correct Answer: B

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Question 21 View Details

A geometric sequence has a common ratio of 2 and the first term is 3. If the sum of the first four terms is 67, find the sum of the next three terms.

Correct A. 336

B. 337

C. 338

D. 339

Correct Answer: A

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Question 22 View Details

A right circular cone has a height of 10 cm and a base radius of 4 cm. Find the volume of the cone.

Correct A. $\frac{160 \pi}{3}$\)

B. $\frac{160 \pi}{2}$\)

C. $\frac{160 \pi}{1}$\)

D. $\frac{160 \pi}{4}$\)

Correct Answer: A

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Question 23 View Details

A die is rolled twice. What is the probability that the sum of the two numbers is 7?

Correct A. $\frac{1}{6}$\)

B. $\frac{1}{3}$\)

C. $\frac{1}{2}$\)

D. $\frac{2}{3}$\)

Correct Answer: A

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Question 24 View Details

Solve the inequality $\frac{x-2}{x+1}$\$) > 0.$

Correct A. $x > 2$ or x < -1

B. $x > 2$ and x < -1

C. $x < 2$ or x > -1

D. $x < 2$ and x > -1

Correct Answer: A

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Question 25 View Details

Find the mean of the numbers 2, 4, 6, 8, 10.

Correct A. 6

B. 7

C. 8

D. 9

Correct Answer: A

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