The ratio $\frac{K_p}{K_c}$ for the reaction $CO_{(g)} + \frac{1}{2}O_{2(g)} \rightleftharpoons CO_{2(g)}$ is

The $pH$ of water is $7$. When a substance $Y$ is dissolved in water,the $pH$ becomes $13$. The substance $Y$ is a salt of

For a suitably chosen real constant $a$,let a function $f: R-\{-a\} \rightarrow R$ be defined by $f(x) = \frac{a-x}{a+x}$. Further,suppose that for any real number $x \neq -a$ and $f(x) \neq -a$,$(f \circ f)(x) = x$. Then $f(-\frac{1}{2})$ is equal to

$A$ charge $Q$ is divided into two charges $q$ and $Q-q$. The value of $q$ such that the force between them is maximum,is

$\int \frac{\sin x+8 \cos x}{4 \sin x+6 \cos x} d x$ is equal to

$A$ large open tank has two holes in the wall. One is a square hole of side $L$ at a depth $y$ from the top and the other is a circular hole of radius $R$ at a depth $4y$ from the top. When the tank is completely filled with water,the quantities of water flowing out per second from both holes are the same. Then,$R$ is equal to