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POST UTME FUTA 2017 Mathematics | Objective

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Question 1

Determine the value of the determinant of the matrix \( egin{bmatrix} 2 & 3 \ 4 & 5 \end{bmatrix} \).

Correct A. -1

B. 1

C. 2

D. 3

Correct Answer: A

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Question 2

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

Correct A. \( x < -1 \) or \( x > \frac{3}{2} \)

B. \( x < -1 \) or \( x < \frac{3}{2} \)

C. \( x > -1 \) or \( x < \frac{3}{2} \)

D. \( x > -1 \) or \( x > \frac{3}{2} \)

Correct Answer: A

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Question 3

A box contains 5 red balls, 4 blue balls, and 3 green balls. If a ball is drawn at random, what is the probability that it is not blue?

A. \( \frac{1}{2} \)

Correct B. \( \frac{3}{5} \)

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

D. \( \frac{4}{5} \)

Correct Answer: B

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Question 4

Find the sum of the first 10 terms of the geometric series \( 2 + 6 + 18 + ldots \).

A. \( 2 + 6 + 18 + ldots + 12288 \)

B. \( 2 + 6 + 18 + ldots + 12288 \)

C. \( 2 + 6 + 18 + ldots + 12288 \)

Correct D. \( 2 + 6 + 18 + ldots + 12288 \)

Correct Answer: D

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Question 5

A set of 5 integers has a mean of 10. If 10 is added to each of the integers, what is the mean of the new set?

A. 10

Correct B. 11

C. 12

D. 13

Correct Answer: B

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Question 6

A random variable X is uniformly distributed over the interval [0, 1]. Find the probability that X^2 + Y^2 ≤ 1, where Y is an indep\endent random variable uniformly distributed over the interval [0, 1].

Correct A. \frac{\pi}{4}

B. \frac{\pi}{2}

C. \frac{\pi}{6}

D. \frac{\pi}{3}

Correct Answer: A

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Question 7

Solve the equation \( \sin^2 x + \cos^2 x = 1 \) for x in the interval [0, 2\pi].

A. \frac{\pi}{4}

Correct B. \frac{\pi}{2}

C. \pi

D. \frac{3\pi}{2}

Correct Answer: B

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Question 8

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 9

A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. Find the probability that a randomly selected score is between 60 and 90.

Correct A. \frac{1}{2}

B. \frac{1}{4}

C. \frac{3}{4}

D. \frac{3}{5}

Correct Answer: A

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Question 10

Convert the number 1234 from base 8 to base 10.

Correct A. 1000

B. 1001

C. 1002

D. 1003

Correct Answer: A

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Question 11

Let X be a random variable with probability density function (pdf) given by f(x) = \( egin{cases} 2x, & 0 leq x leq 1 \ 0, & \text{otherwise} \end{cases} \). Find the probability that X takes a value greater than 0.5.

A. 0.5

Correct B. 0.75

C. 0.875

D. 1

Correct Answer: B

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Question 12

Solve the inequality \( \frac{x^2 - 4}{x^2 - 9} > 0 \).

A. \( -3, -1 \) cup (1, 3)

Correct B. \( -3, -1 \) cup (1, 3) cup (4, infty)

C. \( -3, -1 \) cup (1, 3) cup (-infty, 4]

D. \( -3, -1 \) cup (1, 3) cup \( -infty, 4 \) cup (4, infty)

Correct Answer: B

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Question 13

Find the sum of the infinite geometric series \( sum_{n=1}^{infty} \frac{2}{3^n} \).

A. 1

Correct B. 1.5

C. 2

D. 3

Correct Answer: B

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Question 14

Solve the equation \( x^2 + 4x - 5 = 0 \).

Correct A. \( -5, 1 \)

B. \( -1, 5 \)

C. \( -5, 1 \) cup (5, infty)

D. \( -1, 5 \) cup (-infty, 5]

Correct Answer: A

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Question 15

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

A. 10

Correct B. 100

C. 1000

D. 10000

Correct Answer: B

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Question 16

In a circle of radius 5 cm, a chord of length 8 cm subt\ends an angle of 60° at the centre. Find the area of the sector.

Correct A. \( \frac{1}{6} pi \( 5 \ \)^2 )

B. \( \frac{1}{6} pi \( 8 \ \)^2 )

C. \( \frac{1}{6} pi \( 5 \ \)^2 - \frac{1}{2} (8)^2 )

D. \( \frac{1}{6} pi \( 5 \ \)^2 + \frac{1}{2} (8)^2 )

Correct Answer: A

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Question 17

A random variable X has a probability distribution given by ( P(X) = egin{cases} 0.2 & \text{if } x = 1 \ 0.3 & \text{if } x = 2 \ 0.5 & \text{if } x = 3 \end{cases} ). Find the expected value of X.

A. ( 1.5 )

Correct B. ( 2.5 )

C. ( 3.5 )

D. ( 4.5 )

Correct Answer: B

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Question 18

In a triangle ABC, the length of side AB is 5 cm, the length of side BC is 6 cm, and the length of side AC is 7 cm. Find the area of the triangle.

A. \( \frac{1}{2} \times 5 \times 6 \)

B. \( \frac{1}{2} \times 6 \times 7 \)

Correct C. \( \frac{1}{2} \times 5 \times 7 \)

D. \( \frac{1}{2} \times 6 \times 5 \)

Correct Answer: C

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Question 19

A population of 1000 people has a mean height of 170 cm. If a sample of 50 people has a mean height of 175 cm, find the s\tandard deviation of the sample.

A. ( 5 )

Correct B. ( 10 )

C. ( 15 )

D. ( 20 )

Correct Answer: B

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Question 20

In a binomial distribution, the probability of success is 0.4 and the number of trials is 10. Find the probability that the number of successes is 4.

Correct A. ( inom{10}{4} (0.4)^4 (0.6)^6 )

B. ( inom{10}{4} (0.4)^5 (0.6)^5 )

C. ( inom{10}{4} (0.4)^6 (0.6)^4 )

D. ( inom{10}{4} (0.4)^7 (0.6)^3 )

Correct Answer: A

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Question 21

Solve the inequality \( \frac{x}{x-1} > 2 \) for \( x > 1 \).

Correct A. x > 3

B. x > 5

C. x < 3

D. x < 5

Correct Answer: A

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Question 22

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

Correct A. 7

B. 9

C. 11

D. 13

Correct Answer: A

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Question 23

A geometric sequence has first term \( a = 2 \) and common ratio \( r = 3 \). Find the sum of the first 5 terms.

Correct A. 305

B. 315

C. 325

D. 335

Correct Answer: A

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Question 24

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

Correct A. 32

B. 64

C. 96

D. 128

Correct Answer: A

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Question 25

A set of 5 numbers has an average of 10. If 2 more numbers are added to the set, the average becomes 12. Find the sum of the original 5 numbers.

Correct A. 40

B. 50

C. 60

D. 70

Correct Answer: A

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