The mutual inductance of a pair of coils, each of '$$N$$' turns, is '$$M$$' henry. If a current of '$$I$$' ampere in one of the coils is brought to zero in '$$t$$' second, the e. m. f. induced per turn in the other coil in volt is

To manufacture a solenoid of length $$1 \mathrm{~m}$$ and inductance $$1 \mathrm{~mH}$$, the length of thin wire required is

(cross - sectional diameter of a solenoid is considerably less than the length)

In a radioactive disintegration, the ratio of initial number of atoms to the number of atoms present at time $$t=\frac{1}{2 \lambda}$$ is [$$\lambda=$$ decay constant]

A bullet is fired on a target with velocity '$$\mathrm{V}$$'. Its velocity decreases from '$$\mathrm{V}$$' to '$$\mathrm{V} / 2$$' when it penetrates $$30 \mathrm{~cm}$$ in a target. Through what thickness it will penetrate further in the target before coming to rest?