$\lim _{x \rightarrow 0} \frac{\tan ^3 x-\sin ^3 x}{x^5}$ is equal to

If $f_n(x) = \log \log \log \ldots \log x$ (where $\log$ is repeated $n$ times),then $\int (x f_1(x) f_2(x) \ldots f_n(x))^{-1} dx$ is equal to

$A$ number $n$ is chosen at random from $S=\{1, 2, 3, \ldots, 50\}$. Let $A=\{n \in S: n+\frac{50}{n} > 27\}$,$B=\{n \in S: n \text{ is a prime}\}$ and $C=\{n \in S: n \text{ is a square}\}$. Then,the correct order of their probabilities is

If the bond length and dipole moment of a diatomic molecule are $1.25 \ \mathring{A}$ and $1.0 \ D$ respectively,what is the per cent ionic character of the bond?

The area (in square units) of the circle which touches the lines $4x + 3y = 15$ and $4x + 3y = 5$ is

In which of the following reactions,the concentration of product is higher than the concentration of reactant at equilibrium? $(K = \text{equilibrium constant})$