If $l, m, n$ are in arithmetic progression,then the straight line $lx + my + n = 0$ will always pass through the point:

If the length of a stretched string is shortened by $x \%$ and the tension is increased by $44 \%$,then the ratio of the final and initial fundamental frequencies is $2:1$. The value of $x$ is:

The point on the curve $y^{2}=2(x-3)$ at which the normal is parallel to the line $y-2x+1=0$ is

$\sinh ^{-1} 2 + \sinh ^{-1} 3 = x \Rightarrow \cosh x$ is equal to

$A$ particle is projected vertically upwards from a point $A$ on the ground. It takes $t_1$ time to reach a point $B$ but it still continues to move up. If it takes further $t_2$ time to reach the ground from point $B$,then the height of point $B$ from the ground is:

$A$ charge $Q$ is divided into two charges $q$ and $Q-q$. The value of $q$ such that the force between them is maximum,is