In a Young's double slit experiment 15 fringes are observed on a small portion of the screen when light of wavelength 500 nm is used. Ten fringes are observed on the same section of the screen when another light source of wavelength $$\lambda $$ is used. Then the value of $$\lambda $$ is (in nm) __________.

The circuit shown below is working as a 8 V dc regulated voltage source. When 12 V is used as input, the power dissipated (in mW) in each diode is; (considering both zener diodes are identical) _________.

Starting at temperature 300 K, one mole of an
ideal diatomic gas ($$\gamma $$ = 1.4) is first compressed
adiabatically from volume V₁ to V₂ = $${{{V_1}} \over {16}}$$. It is
then allowed to expand isobarically to volume 2V₂. If all the processes are the quasi-static then
the final temperature of the gas (in ^oK) is (to the nearest integer) _____.

An electron of mass m and magnitude of charge |e| initially at rest gets accelerated by a constant electric field E. The rate of change of de-Broglie wavelength of this electron at time t ignoring relativistic effects is :