$A$ wire of length $l$ is bent into a circular loop of radius $R$ and carries a current $I$. The magnetic field at the centre of the loop is $B$. The same wire is now bent into a double loop of equal radii. If both loops carry the same current $I$ and it is in the same direction,the magnetic field at the centre of the double loop will be

The equation of the locus of $z$ such that $\left|\frac{z-i}{z+i}\right|=2$,where $z=x+iy$ is a complex number,is

In a $\triangle ABC$,the expression $\frac{\cos C+\cos A}{c+a}+\frac{\cos B}{b}$ is equal to

$A$ cubical block of side '$a$' and density '$\rho$' slides over a fixed inclined plane with constant velocity '$v$'. There is a thin film of viscous fluid of thickness '$t$' between the plane and the block. If the angle of inclination is $37^{\circ}$,then the coefficient of viscosity of the thin film will be:

Vegetative propagation in $Pistia$ occurs by:

Two cylinders $A$ and $B$ fitted with pistons,contain equal number of moles of an ideal monoatomic gas at $400 ~K$. The piston of $A$ is free to move while that of $B$ is held fixed. Same amount of heat energy is given to the gas in each cylinder. If the rise in temperature of the gas in $A$ is $42 ~K$,the rise in temperature of the gas in $B$ is $(\gamma = 5/3)$. (in $~K$)