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For the given set of data, calculate the percentile rank and quartile rank for observation 6.
5, 6, 6, 9, 11, 13, 15, 18, 20
5, 6, 6, 9, 11, 13, 15, 18, 20
If $(2 a+b, a-b)=(8,3)$, find $a$ and $b$.
→A die is rolled. If $E=\{1,3,5\}, F=\{2,3\}$ and $G=$ $\{2,3,4,5\}$, find (a) $P((E \cup F) / G)$, (b) $P((E \cap F) / G)$
→If $\bar{x}$ is the mean and $\sigma^2$ is the variance of $n$ observations $x_1, x_2, x_3, \ldots, x_n$, then prove that the mean and variance of the observations $a x_1, a x_2, \ldots$, $a x_n$ are $a \bar{x}$ and $a^2 \sigma^2$ respectively $(a \neq 0)$.
→If $f(x)=\frac{4 x+3}{6 x-4}, x \neq \frac{2}{3}$, then show that $(f o f)(x)=x$ for all $x \neq \frac{2}{3}$. What is the inverse of $f$.
→$A \cap(B-C)=(A \cap B)-(A \cap C)$
→Check whether the following statement is true or not; "If $x$ and $y$ are odd integers, then $x y$ is an odd integer" by (i) Direct method (ii) Contrapositive method.
→Find the domain and range of the real function \[f(x)=\frac{x^2-9}{x-3}\]
Simplify : $\left[1-\left\{1-\left(1-x^2\right)^{-1}\right\}^{-1}\right]^{-1 / 2}$
→If $f(x)=x-\frac{1}{x}$, prove that
$[f(x)]^3=f(x)^3+3 f\left(\frac{1}{x}\right)$
→$[f(x)]^3=f(x)^3+3 f\left(\frac{1}{x}\right)$