The logical statement $[\sim(\sim p \vee q) \vee (p \wedge r)] \wedge (\sim q \wedge r)$ is equivalent to

If $\frac{\cos x}{\cos (x-2y)} = \lambda$,then $\tan (x-y) \tan y$ is equal to

If $z = \sec^{-1}\left(\frac{x^4+y^4-8x^2y^2}{x^2+y^2}\right)$,then $x \frac{\partial z}{\partial x} + y \frac{\partial z}{\partial y}$ is equal to

In which of the following reactions does $H_2O_2$ act as a reducing agent?

Which is $NOT$ an example of a macromolecular colloid?

$A$ bimetallic strip is formed out of two identical strips,one of copper and the other of brass. The coefficients of linear expansion of the two metals are $\alpha_C$ and $\alpha_B$. On heating,the temperature of the strip increases by $\Delta T$ and the strip bends to form an arc of radius $R$. Then $R$ is proportional to