A wire when connected to $$220$$ $$V$$ mains supply has power dissipation $${P_1}.$$ Now the wire is cut into two equal pieces which are connected in parallel to the same supply. Power dissipation in this case is $${P_2}.$$ Then $${P_2}:{P_1}$$ is

1 mole of a gas with $$\gamma = 7/5$$ is mixed with $$1$$ mole of a gas with $$\gamma = 5/3,$$ then the value of $$\gamma $$ for the resulting mixture is

A spring of force constant $$800$$ $$N/m$$ has an extension of $$5$$ $$cm.$$ The work done in extending it from $$5$$ $$cm$$ to $$15$$ $$cm$$ is

Infrared radiation is detected by