When $10 \ g$ of methane is completely burnt in oxygen,the heat evolved is $560 \ kJ$. What is the heat of combustion (in $kJ \ mol^{-1}$) of methane?

Let $z = a - \frac{i}{2}$,where $a \in R$. Then $|i + z|^2 - |i - z|^2$ is equal to

$A$ uniform meter scale is balanced at the $30 \ cm$ mark on a knife edge,when weights of $60 \ N$ and $10 \ N$ are suspended at the $10 \ cm$ and $80 \ cm$ marks,respectively. The mass of the meter scale is: (in $kg$)

Two bodies of masses $0.1\, kg$ and $0.4\, kg$ move towards each other with the velocities $1\, m/s$ and $0.1\, m/s$ respectively. After collision they stick together. In $10\, s$ the combined mass travels ............... $m$.

$\lim _{x \rightarrow \infty} \left(\frac{x+a}{x+b}\right)^{x}$ is equal to

The wavelengths of light in two liquids '$x$' and '$y$' are $3500 \ \mathring A$ and $7000 \ \mathring A$ respectively. The critical angle of '$x$' with respect to '$y$' will be ...... $^o$.