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POST UTME DELSU 2018 Mathematics | Objective

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Question 1 View Details

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

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

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

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

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

Correct Answer: B

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Question 2 View Details

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

A. \(x = 2\)

B. \(x = 3\)

Correct C. \(x = 4\)

D. \(x = 5\)

Correct Answer: C

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Question 3 View Details

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

Correct A. \(\frac{64}{3}\)

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

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

D. \(\frac{8}{3}\)

Correct Answer: A

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Question 4 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 5 View Details

Find the determinant of the matrix \(egin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix}\).

Correct A. ( 0 )

B. ( 1 )

C. \(-1\)

D. ( 2 )

Correct Answer: A

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Question 6 View Details

A particle moves in a straight line with a velocity of \(\mathbf{v} = 2t , \mathbf{i} + 3t^2 , \mathbf{j}) \(m/s\), where ( t ) is in seconds. Find the position vector of the particle at time \\() (m/s\(t = 2\) seconds.

Correct A. 8\mathbf{i} + 12\mathbf{j}

B. 4\mathbf{i} + 12\mathbf{j}

C. 8\mathbf{i} + 8\mathbf{j}

D. 4\mathbf{i} + 8\mathbf{j}

Correct Answer: A

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Question 7 View Details

A rectangular box has dimensions ( x ) cm by ( y ) cm by ( z ) cm. If the surface area of the box is 600 \((cm^2\)\), and the volume is 1200 \(cm^3\\((cm^2), and the volume is 1200\), find the value of \(x + y + z\).

A. 20

B. 25

Correct C. 30

D. 35

Correct Answer: C

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Question 8 View Details

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

Correct A. 0.24

B. 0.36

C. 0.48

D. 0.60

Correct Answer: A

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Question 9 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. \(\frac{-2}{x^2 + 1\) ^2}\)\)

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

Correct Answer: A

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Question 10 View Details

A number is represented in base 8 as 1234. What is the value of this number in base 10?

A. 512

B. 1024

Correct C. 1536

D. 2048

Correct Answer: C

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Question 11 View Details

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

A. \(x = -10\)

B. \(x = 6\)

Correct C. \(x = -3\)

D. \(x = 2\)

Correct Answer: C

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Question 12 View Details

A binary operation (*\) on the set of real numbers is defined as \(a * b = ab + 1\\((*) on the set of real numbers is defined as\). Find the value of \(2 * 3\).

Correct A. 7

B. 9

C. 11

D. 13

Correct Answer: A

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Question 13 View Details

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

A. \(1/3\)

B. \(1/2\)

Correct C. \(2/3\)

D. \(1/6\)

Correct Answer: C

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Question 14 View Details

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

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

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

C. \(x < 1\) or \(x > 3\)

D. x < -3 or \(x < 1\)

Correct Answer: A

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Question 15 View Details

A number is divisible by 3 if the sum of its digits is divisible by 3. What is the smallest 3-digit number that is divisible by 3?

A. 100

B. 102

Correct C. 105

D. 108

Correct Answer: C

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Question 16 View Details

Find the value of x in the equation \(2x^2 + 5x - 3 = 0\)

A. 1

Correct B. -1

C. 3

D. -3

Correct Answer: B

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Question 17 View Details

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

Correct A. \(10^4\)

B. \(10^2\)

C. \(10^8\)

D. \(10^6\)

Correct Answer: A

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Question 18 View Details

Find the determinant of the matrix \(\begin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix}\)

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 19 View Details

A sequence is defined by the formula \(a_n = 2n + 1\). Find the sum of the first 5 terms of the sequence.

A. 15

B. 20

Correct C. 25

D. 30

Correct Answer: C

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Question 20 View Details

A vector \(\vec{a} = \begin{bmatrix} 1 \ 2 \ 3 \end{bmatrix}\) is given. Find the magnitude of the vector.

A. 3

B. 4

Correct C. 5

D. 6

Correct Answer: C

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Question 21 View Details

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

A. 10

B. 100

C. 1000

Correct D. 10000

Correct Answer: D

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Question 22 View Details

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

Correct A. \(-∞, -1\) ∪ (3, ∞)

B. \(-∞, -3\) ∪ (1, ∞)

C. \(-∞, 1\) ∪ (3, ∞)

D. \(-∞, -3\) ∪ (1, ∞)

Correct Answer: A

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Question 23 View Details

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

Correct A. 6x - 2

B. 6x + 2

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

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

Correct Answer: A

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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 score is between 50 and 70?

A. 0.5

B. 0.6

Correct C. 0.7

D. 0.8

Correct Answer: C

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Question 25 View Details

Solve the equation \(2^x + 3^x = 5^x\).

A. \(x = 2\)

Correct B. \(x = 3\)

C. \(x = 4\)

D. \(x = 5\)

Correct Answer: B

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