Sulphuric acid reacts with $PCl_5$ to give

Let $f$ be a differentiable function satisfying $f(x + 2y) = 2yf(x) + xf(y) - 3xy + 1$ for all $x, y \in R$ such that $f'(0) = 1$. Then $f(2)$ is equal to:

The figure shows the variation of the gravitational acceleration $a_g$ of four planets with the radial distance $r$ from the centre of the planet for $r \geq$ radius of the planet. Plots $1$ and $2$ coincide for $r \geq R_2$,and plots $3$ and $4$ coincide for $r \geq R_4$. The sequence of the planets in the descending order of their densities is:

Which of the following statements is not correct?

Silica is added to roasted copper ore during extraction in order to remove

$A$ wheel of mass $m$ has charges $+q$ and $-q$ at diametrically opposite points. It remains in equilibrium on a rough inclined plane in the presence of a uniform vertical electric field $E$. Find the value of $E$.