If the ionic product of water $(K_w)$ is $1.96 \times 10^{-14}$ at $35^{\circ} C$,what is its value at $10^{\circ} C$?

Two ions having masses in the ratio $1: 1$ and charges $1: 2$ are projected into a uniform magnetic field perpendicular to the field with speeds in the ratio $2: 3$. The ratio of the radii of circular paths along which the two particles move is :

$\lim _{x \rightarrow 0} \frac{4^x-9^x}{x(4^x+9^x)}$ is equal to

The maximum tension a rope can withstand is $60 ~kg-wt$. The ratio of maximum acceleration with which two boys of masses $20 ~kg$ and $30 ~kg$ can climb up the rope at the same time is

The angle between the lines represented by $y^2 \sin^2 \theta - xy \sin^2 \theta + x^2(\cos^2 \theta - 1) = 0$ is

The point of intersection of the diagonals of a square is at the origin,and the coordinate axes are drawn along the diagonals. If the side length of the square is $a$,which of the following is $NOT$ a vertex of the square?