If $x$ is small,so that $x^2$ and higher powers can be neglected,then the approximate value for $\frac{(1-2 x)^{-1}(1-3 x)^{-2}}{(1-4 x)^{-3}}$ is

$A$ vertical bar magnet is dropped from a position on the axis of a fixed metallic coil as shown in fig-$I$. In fig-$II$,the magnet is fixed and a horizontal coil is dropped. If the acceleration of the magnet and the coil are $a_1$ and $a_2$ respectively,then:

Which one of the following is not a calcination reaction?

If the direction cosines of two lines are given by $l+m+n=0$ and $l^2-5m^2+n^2=0$,then the angle between them is

Yeast is used in the production of

The equation of the circle of radius $3$ that lies in the fourth quadrant and touches the lines $x=0$ and $y=0$ is