A radar has a power of $$1kW$$ and is operating at a frequency of $$10$$ $$GHz.$$ It is located on a mountain top of height $$500$$ $$m.$$ The maximum distance upto which it can detect object located on the surface of the earth (Radius of earth $$ = 6.4 \times {10^6}m$$) is :

Assume that a neutron breaks into a proton and an electron. The energy released during this process is : (mass of neutron $$ = 1.6725 \times {10^{ - 27}}kg,$$ mass of proton $$ = 1.6725 \times {10^{ - 27}}\,kg,$$ mass of electron $$ = 9 \times {10^{ - 31}}\,kg$$ ).

A diatomic molecule is made of two masses $${m_1}$$ and $${m_2}$$ which are separated by a distance $$r.$$ If we calculate its rotational energy by applying Bohr's rule of angular momentum quantization, its energy will be given by: ($$n$$ is an integer)

Truth table for system of four $$NAND$$ gates as shown in figure is: