Systematics refers to the

$100$ cells each of e.m.f. $5 \ V$ and internal resistance $1 \ \Omega$ are to be arranged so as to produce maximum current in a $25 \ \Omega$ resistance. Each row is to contain an equal number of cells. The number of rows should be

The change in the value of $g$ at a height $h$ above the surface of the earth is the same as at a depth $d$ below the surface of the earth. When both $d$ and $h$ are much smaller than the radius of the earth,then which one of the following is correct?

Which of the following gates will have an output of $1$?

The sum of the infinite series ${\tan ^{ - 1}}\left( {\frac{2}{{1 - {1^2} + {1^4}}}} \right) + {\tan ^{ - 1}}\left( {\frac{4}{{1 - {2^2} + {2^4}}}} \right) + {\tan ^{ - 1}}\left( {\frac{6}{{1 - {3^2} + {3^4}}}} \right) + \dots$ is:

$ABCD$ is a square with side $16$ units and $A$ is the origin. If the equation of the circle circumscribing the square $ABCD$ is $x^2+y^2=4k(x+y)$,then $k=$