An element $(X)$ forms compounds of the formula $XCl_3$,$X_2O_5$ and $Ca_3X_2$,but does not form $XCl_5$. Which of the following is the element $X$?

If $f(x)$ is a polynomial of degree $n$ with rational coefficients and $1+2i, 2-\sqrt{3},$ and $5$ are three roots of $f(x)=0$,then the least value of $n$ is

Equivalent conductivity of $Cr_2(SO_4)_3$ is related to molar conductivity by the expression

The angle between the tangents drawn from the point $(1,4)$ to the parabola $y^2=4x$ is

In a system of two particles of masses $m_{1}$ and $m_{2}$,the second particle is moved by a distance $d$ towards the centre of mass. To keep the centre of mass unchanged,the first particle will have to be moved by a distance:

Two large parallel plates are connected to a $100\, V$ power supply. These plates have a fine hole at the centre. An electron having energy $200\, eV$ is directed such that it passes through the holes. When it emerges,its de-Broglie wavelength is ............. $\mathring{A}$.