If $(2+\sin x) \frac{dy}{dx} + (y+1) \cos x = 0$ and $y(0) = 1$,then $y\left(\frac{\pi}{2}\right)$ is

The electrochemical equivalent of a metal is $x \ g \ C^{-1}$. The equivalent weight of the metal is:

With a standard rectangular bar magnet of length $l$,breadth $b$ $(b \ll l)$,and magnetic moment $M$,the time period of the magnet in a vibration magnetometer is $4 \ s$. If the magnet is cut normal to its length into four equal pieces,the time period (in seconds) with one of the pieces is:

$A$ fully charged capacitor $C$ with initial charge $q_0$ is connected to a coil of self-inductance $L$ at $t = 0$. The time at which the energy is stored equally between the electric and the magnetic fields is

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 $~K$)

If $x^3 + y^3 - 3axy = 0$,then $\frac{dy}{dx}$ equals