When a bucket is half full,the weight of the bucket and the water is $10 \ kg$. When the bucket is two-thirds full,the total weight is $11 \ kg$. What is the total weight (in $kg$),when the bucket is completely full?

An ideal gas expands isothermally from volume $V_1$ to volume $V_2$. It is then compressed to the original volume $V_1$ adiabatically. If $p_1$ and $p_2$ represent the initial pressure and final pressure respectively,and $W$ represents the net work done by the gas during the entire process,then:

In majority of higher animals and plants, . . . . . . and . . . . . . are mutually exclusive events.

At a certain place,the horizontal component of the Earth's magnetic field is $B_0$ and the angle of dip is $45^o$. The total intensity of the field at that place will be:

If $\sin ^{-1}\left(\frac{x}{13}\right)+\operatorname{cosec}^{-1}\left(\frac{13}{12}\right)=\frac{\pi}{2}$,then the value of $x$ is

The conjugate acid of $NH_2^-$ is