The length of the $x$-intercept made by the pair of lines $2x^2 + xy - 6y^2 - 2x + 17y - 12 = 0$ is

With a standard rectangular bar magnet,the time period of a vibration magnetometer is $4 ~s$. The bar magnet is cut parallel to its length into four equal pieces. The time period of the vibration magnetometer when one piece is used (in seconds) (bar magnet breadth is small) is

What is $VAM$?

The $EN$ (Electronegativity) of element $A$ is $E_1$ and its $IP$ (Ionization Potential) is $E_2$. Hence,its $EA$ (Electron Affinity) will be:

$P$ is a point on the segment joining the feet of two vertical poles of heights $a$ and $b$. The angles of elevation of the tops of the poles from $P$ are $45^{\circ}$ each. Then,the square of the distance between the tops of the poles is

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 ............. $\mathring{A}$.