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POST UTME FUTA 2024 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 histogram of exam scores is shown below. If the mean score is 75, and the standard deviation is 10, what is the probability that a randomly selected score will be between 60 and 90?

Correct A. 0.5

B. 0.6

C. 0.7

D. 0.8

Correct Answer: A

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Question 3 View Details

Solve for \(x\): \(\tan(x) = \sqrt{3}\).

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

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

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

D. \(\frac{\pi}{4}\)\)

Correct Answer: A

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Question 4 View Details

A vector \(\vec{a}\) has components \(a_x = 3) and \(a_y = 4\). Find the magnitude of \\() and (a_y = 4\(\vec{a}\).

A. 5

B. \(\sqrt{5}\)

Correct C. \(\sqrt{25}\)

D. \(\sqrt{50}\)

Correct Answer: C

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Question 5 View Details

Two events \(A\) and \(B\) are independent. If \(P(A) = 0.4\) and \(P(B) = 0.6\), what is the probability that both events occur?

Correct A. 0.2

B. 0.4

C. 0.6

D. 0.8

Correct Answer: A

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Question 6 View Details

In a certain number base (b\), the number \(1011_5\\((b), the number\) is equivalent to \(3b^3 + 4b^2 + 2b + 1\) in base \(10\). Find the value of \(b\).

A. 2

Correct B. 3

C. 4

D. 5

Correct Answer: B

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Question 7 View Details

A fair six-sided die is rolled twice. What is the probability that the sum of the two numbers obtained is \(7\)?

A. \(1/6\)

B. \(1/12\)

Correct C. \(1/36\)

D. \(1/18\)

Correct Answer: C

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Question 8 View Details

Let (S\) be the set of all positive integers \(n\\((S) be the set of all positive integers\) such that (n\) is a multiple of \(3\\((n) is a multiple of\) and (n\) is a power of \(2\\((n) is a power of\). Which of the following is the smallest element of \(S\)?

A. 1

B. 2

C. 4

Correct D. 8

Correct Answer: D

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Question 9 View Details

The sequence (a_n\) is defined recursively by \(a_n = 2a_{n-1} + 1\\((a_n) is defined recursively by\) for \(n \ge 2\), with \(a_1 = 3\). Find the value of \(a_{10}\).

Correct A. 1023

B. 1024

C. 1025

D. 1026

Correct Answer: A

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Question 10 View Details

The quadratic equation \(x^2 + bx + c = 0\) has roots \(x = 1\) and (x = -2\). Find the value of \(b\\((x = -2). Find the value of\).

Correct A. -3

B. -2

C. -1

D. 1

Correct Answer: A

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Question 11 View Details

Find the determinant of the matrix [ egin{pmatrix} 2 & 3 & 1 \ 4 & 5 & 2 \ 1 & 2 & 3 \end{pmatrix} ].

Correct A. -2

B. 4

C. 6

D. 8

Correct Answer: A

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Question 12 View Details

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

Correct A. \(x =\)\(\frac{-5 \pm \sqrt{5^2 - 4\) 2) -3 \ }\)}{2(2)}\)

B. \(x =\)\(\frac{-5 \pm \sqrt{5^2 - 4(2)(3)}\)\)}{2(2)}\)

C. \(x =\)\(\frac{-5 \pm \sqrt{5^2 - 4\) 2) -3 \ }\)}{2(2)}\)

D. \(x =\)\(\frac{-5 \pm \sqrt{5^2 - 4(2)(3)}\)\)}{2(2)}\)

Correct Answer: A

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Question 13 View Details

Find the value of [ sin(2x) \] given that [ \\(sin(x) =\)\\(sin(2x) ] given that [ \(\frac{1}{2}\)\) \].

Correct A. \cos(x)

B. \sin(x)

C. \cos(2x)

D. \sin(2x)

Correct Answer: A

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Question 14 View Details

Solve the inequality [ \(2x - 5 > 3\) ].

Correct A. \(x >\)\(\frac{8}{2}\)\)

B. \(x <\)\(\frac{8}{2}\)\)

C. \(x >\)\(\frac{8}{2}\)\)

D. \(x <\)\(\frac{8}{2}\)\)

Correct Answer: A

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Question 15 View Details

Find the value of [ cos(2x) \] given that [ \\(cos(x) =\)\\(cos(2x) ] given that [ \(\frac{1}{2}\)\) \].

A. \cos(x)

B. \sin(x)

Correct C. \cos(2x)

D. \sin(2x)

Correct Answer: C

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Question 16 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 17 View Details

Find the value of [ tan(2x) \] given that [ \\(tan(x) =\)\\(tan(2x) ] given that [ \(\frac{1}{2}\)\) \].

A. \tan(x)

B. \sin(x)

C. \cos(x)

Correct D. \tan(2x)

Correct Answer: D

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Question 18 View Details

Solve the inequality [ \(3x + 2 > 7\) ].

Correct A. \(x >\)\(\frac{5}{3}\)\)

B. \(x <\)\(\frac{5}{3}\)\)

C. \(x >\)\(\frac{5}{3}\)\)

D. \(x <\)\(\frac{5}{3}\)\)

Correct Answer: A

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Question 19 View Details

Find the value of [ sin(2x) \] given that [ \\(sin(x) =\)\\(sin(2x) ] given that [ \(\frac{1}{3}\)\) \].

A. \cos(x)

B. \sin(x)

C. \cos(2x)

Correct D. \sin(2x)

Correct Answer: D

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Question 20 View Details

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

A. 12

Correct B. 16

C. 20

D. 24

Correct Answer: B

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Question 21 View Details

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

Correct A. 1

B. -1

C. -2

D. 2

Correct Answer: A

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Question 22 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. \(x + 2\)^2 + \(y + 3\)^\(2 = 16\)

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

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

Correct Answer: A

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Question 23 View Details

Find the vector projection of vector →\(b =\)→(2, 3) onto vector →\(a =\)→(4, 5).

Correct A. \u2192\(\frac{29}{41}, \frac{50}{41}\)

B. \u2192\(\frac{29}{41}, -\frac{50}{41}\)

C. \u2192\(-\frac{29}{41}, \frac{50}{41}\)

D. \u2192\(-\frac{29}{41}, -\frac{50}{41}\)

Correct Answer: A

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Question 24 View Details

Find the sum of the infinite geometric series \sum_{\(n = 1\)}^\infty \(\frac{1}{2^n}\)\)\).

A. 1

Correct B. \(\frac{1}{2}\)\)

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

D. \(\frac{3}{4}\)\)

Correct Answer: B

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Question 25 View Details

Solve the trigonometric equation \\(\sin^2\) x + \\(\cos^2\) \(x = 1\).

Correct A. \(x =\)\(\frac{\pi}{2}\)\)

B. \(x =\)\(\frac{\pi}{4}\)\)

C. \(x =\)\\(\frac{3\pi}{4}\)\)

D. \(x =\)\\(\frac{5\pi}{4}\)\)

Correct Answer: A

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