$\begin{aligned} & \frac{x^2+x+1}{(x-1)(x-2)(x-3)}=\frac{A}{x-1}+\frac{B}{x-2}+\frac{C}{x-3} \\ & \Rightarrow A+C= \end{aligned}$

What is the minimum energy required to launch a satellite of mass $m$ from the surface of a planet of mass $M$ and radius $R$ into a circular orbit at an altitude of $2R$?

What are $X$ and $Y$ respectively in the following reaction?
$Z$-product $\stackrel{Y}{\longleftarrow} 2$-butyne $\stackrel{X}{\longrightarrow} E$-product

$A$ $10 \ kW$ transmitter emits radio waves of wavelength $500 \ m$. The number of photons emitted per second by the transmitter is of the order of:

If $\omega$ is a complex cube root of unity,then $\sin \left\{\left(\omega^{10}+\omega^{23}\right) \pi-\frac{\pi}{4}\right\}$ is equal to

When a satellite moves around the earth in a certain orbit,the quantity which remains constant is .........