The absolute configurations of the two chiral centers in the following molecule are:

Two short magnets $AB$ and $CD$ are in the $X-Y$ plane and are parallel to the $X$-axis. The coordinates of their centers are $(0,2)$ and $(2,0)$ respectively. The line joining the north-south poles of $CD$ is opposite to that of $AB$ and lies along the positive $X$-axis. The resultant magnetic field induction due to $AB$ and $CD$ at point $P(2,2)$ is $100 \times 10^{-7} \ T$. When the poles of the magnet $CD$ are reversed,the resultant magnetic field induction is $50 \times 10^{-7} \ T$. The values of the magnetic moments of $AB$ and $CD$ (in $Am^2$) are:

The area (in square units) of the triangle formed by $x+y+1=0$ and the pair of straight lines $x^2-3xy+2y^2=0$ is

In the circuit shown,the current in the $1\,\Omega$ resistor is

If $y = (\cos x^2)^2$,then $\frac{dy}{dx}$ is equal to:

$100$ 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 equal number of cells. The number of rows should be