POST UTME FUTA 2017 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
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.
A. \frac{1}{2}
B. \frac{1}{4}
C. \frac{3}{4}
D. \frac{3}{5}
Question 2
Solve the inequality \( \frac{x}{x-1} > 2 \) for \( x > 1 \).
A. x > 3
B. x > 5
C. x < 3
D. x < 5
Question 3
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].
A. \frac{\pi}{4}
B. \frac{\pi}{2}
C. \frac{\pi}{6}
D. \frac{\pi}{3}
Question 4
Find the value of x in the equation \( x^2 - 7x + 12 = 0 \).
A. 3
B. 4
C. 5
D. 6
Question 5
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. \( 2 + 6 + 18 + ldots + 12288 \)
D. \( 2 + 6 + 18 + ldots + 12288 \)
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
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 8
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 ).
A. 7
B. 9
C. 11
D. 13
Question 9
Find the equation of the circle with center (2, 3) and radius 4.
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 \)
Question 10
Let $f(x) = \frac{1}{x^2 + 1}$. Find the derivative of $f(x)$ u\sing the quotient rule.
A. -\frac{2x}{\( x^2 + 1 \)^2}
B. -\frac{2x}{\( x^2 + 1 \)^3}
C. \frac{2x}{\( x^2 + 1 \)^2}
D. \frac{2x}{\( x^2 + 1 \)^3}
Question 11
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 12
A vector \vec{a} has a magnitude of 5 units and makes an angle of 60\circ with the positive x-axis. Find the x and y components of \vec{a}.
A. 2.5 \hat{i} + 4.33 \hat{j}
B. 3.33 \hat{i} + 2.5 \hat{j}
C. 4.33 \hat{i} + 2.5 \hat{j}
D. 5 \hat{i} + 5 \hat{j}
Question 13
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 14
Solve the inequality \( 2x^2 + 5x - 3 > 0 \) for ( x ).
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 \( x > \frac{3}{2} \)
Question 15
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 )
B. ( 2.5 )
C. ( 3.5 )
D. ( 4.5 )

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