Let $f$ be a non-zero real-valued continuous function satisfying $f(x+y)=f(x) \cdot f(y)$ for all $x, y \in R$. If $f(2)=9$,then $f(6)$ is equal to

An ideal gas is expanding such that $PT^2 = \text{constant}$. The coefficient of volume expansion of the gas is: (in $/T$)

The angle between the lines $ab(x^2 - y^2) + (a^2 - b^2)xy = 0$ is

Which one of the following statements is correct with respect to basic character?

If $\sin ^{-1}\left(\frac{x}{13}\right)+\operatorname{cosec}^{-1}\left(\frac{13}{12}\right)=\frac{\pi}{2}$,then the value of $x$ is

The mass of a spaceship is $1000\,kg$. It is to be launched from the earth's surface out into free space. The values of $g$ and $R$ (radius of earth) are $10\,m/s^2$ and $6400\,km$ respectively. The required energy for this work will be: