The inverse of the proposition $(p \wedge \sim q) \Rightarrow r$ is

Which one of the following reactions is an example of oxidative decarboxylation?

The value of ${81^{(1/{\log_5}3)}} + {27^{\log_9 36}} + {3^{4/{\log_7}9}}$ is equal to

If $\int \sqrt{\frac{x}{a^3-x^3}} \, dx = g(x) + c$, then $g(x)$ is equal to:

The intensity of radiation emitted by the Sun has its maximum value at a wavelength of $510 \ nm$ and that emitted by the North Star has the maximum value at $350 \ nm$. If these stars behave like black bodies,then the ratio of the surface temperature of the Sun and the North Star is

$y=e^{a \sin ^{-1} x} \Rightarrow (1-x^2) y_{n+2}-(2 n+1) x y_{n+1}$ is equal to