POST UTME FUTA 2017 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
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.
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 )
Question 2
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
B. 0.75
C. 0.875
D. 1
Question 3
Solve for x in the equation \( \log_{2} \( x^2 \ \) = 4 ).
A. 16
B. 32
C. 64
D. 128
Question 4
Determine the value of the determinant of the matrix \( egin{bmatrix} 2 & 3 \ 4 & 5 \end{bmatrix} \).
A. -1
B. 1
C. 2
D. 3
Question 5
Let $X$ and $Y$ be indep\endent random variables with probability density functions $f_X(x) = egin{cases} 2x & 0 leq x leq 1 \ 0 & \text{otherwise} \end{cases}$ and $f_Y(y) = egin{cases} 3y^2 & 0 leq y leq 1 \ 0 & \text{otherwise} \end{cases}$. Find the probability that $X + Y leq 1$.
A. \frac{1}{2}
B. \frac{1}{3}
C. \frac{2}{3}
D. \frac{3}{4}
Question 6
A geometric sequence has first term \( a = 2 \) and common ratio \( r = 3 \). Find the sum of the first 5 terms.
A. 305
B. 315
C. 325
D. 335
Question 7
Find the sum of the infinite geometric series \( sum_{n=1}^{infty} \frac{2}{3^n} \).
A. 1
B. 1.5
C. 2
D. 3
Question 8
Solve for x in the equation \( x^2 + 2x - 6 = 0 \).
A. -3
B. -2
C. 1
D. 3
Question 9
Find the area under the curve \( y = x^2 \) from \( x = 0 \) to \( x = 4 \).
A. 32
B. 64
C. 96
D. 128
Question 10
A binary operation \ast is defined as a \ast b = ab + 2. Find the value of 3 \ast 4.
A. 10
B. 12
C. 14
D. 16
Question 11
A rec\tangular prism has a length of 6 cm, a width of 4 cm, and a height of 3 cm. Find the volume of the prism u\sing the formula V = lwh.
A. 48
B. 72
C. 96
D. 120
Question 12
Convert the number 1234 from base 8 to base 10.
A. 1000
B. 1001
C. 1002
D. 1003
Question 13
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.
A. 40
B. 50
C. 60
D. 70
Question 14
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
B. 11
C. 12
D. 13
Question 15
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. \( \frac{1}{2} \)
B. \( \frac{3}{5} \)
C. \( \frac{2}{3} \)
D. \( \frac{4}{5} \)

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