If the circle $x^2 + y^2 + 2gx + 2fy + c = 0$ touches the $x$-axis,then:

Water is considered to be polluted if the dissolved oxygen $(D.O.)$ content is less than ... $ppm$ :

Amongst $LiCl, RbCl, BeCl_2$ and $MgCl_2$,the compounds with the greatest and least ionic character respectively are:

The time period of a simple pendulum is $T$. When the length is increased by $10 \ cm$,its period is $T_1$. When the length is decreased by $10 \ cm$,its period is $T_2$. Then,the relation between $T, T_1$ and $T_2$ is

If $l$ and $m$ are the degree and the order respectively of the differential equation of the family of all circles in the $XY$ plane with radius $5$ units,then $2l + 3m =$

$A$ child is standing at one end of a long trolley moving with a speed $v$ on a smooth horizontal floor. If the child starts running towards the other end of the trolley with a speed $u$,the centre of mass of the system (trolley + child) will move with a speed.