If the coefficient of $x$ in the expansion of $\left(x^2+\frac{k}{x}\right)^5$ is $270$,then $k$ is equal to

$A$ light wave enters from medium $1$ to medium $2$. Its velocity in the $2^{nd}$ medium is double that of the $1^{st}$ medium. For total internal reflection to occur,the angle of incidence must be greater than which of the following values?

The angle between the curves $y=\sin x$ and $y=\cos x$ is

If $\alpha$ and $\beta$ are imaginary cube roots of unity,then the value of $\alpha^4 + \beta^{28} + \frac{1}{\alpha\beta}$ is:

Among the following,the least stable resonance structure is

$A$ man wants to reach a certain destination. One-sixth of the total distance is muddy while half the distance is tar road. For the remaining distance,he takes a boat. His speed of travelling in mud,in water,and on tar road is in the ratio $3:4:5$. The ratio of the durations he requires to cross the patch of mud,stream,and tar road is