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

The ratio of minimum wavelengths of Lyman and Balmer series will be

The intercepts on the $x$-axis made by tangents to the curve $y = \int_0^x |t| dt, x \in R$ which are parallel to the line $y = 2x$ are equal to:

If the $x$-coordinate of a point $P$ on the line joining the points $Q(2, 2, 1)$ and $R(5, 1, -2)$ is $4$,then the $z$-coordinate of $P$ is

$A$ car starts from rest and moves with uniform acceleration $a$ on a straight road from time $t = 0$ to $t = T$. After that,a constant deceleration brings it to rest. In this process,the average speed of the car is

Each element in the finite chain of resistors shown in the figure is $1\,\Omega$. $A$ current of $1\,A$ flows through the final element. What is the potential difference $V$ across the input terminals of the chain in $volt$?