$\sinh(ix)$ is equal to

$A$ metallic ring of radius $r$ and cross-sectional area $A$ is fitted into a wooden circular disc of radius $R$ $(R > r)$. If the Young's modulus of the material of the ring is $Y$,the force with which the metal ring expands is

In which of the following complexes is the oxidation state of the metal zero?

If $y = a \sin x + b \cos x$,then $y^2 + \left( \frac{dy}{dx} \right)^2$ is a

An electron in a Hydrogen atom first jumps from the third excited state to the second excited state and then from the second excited state to the first excited state. The ratio of the wavelengths $\lambda_{1} : \lambda_{2}$ emitted in the two cases respectively is:

Total emf produced in a thermocouple does not depend on