The difference in the number of waves when yellow light propagates through air and vacuum columns of the same thickness is one. The thickness of the air column is ___________ mm. [Refractive index of air = 1.0003, wavelength of yellow light in vacuum = 6000 $$\mathop A\limits^o $$]

In the given figure the magnetic flux through the loop increases according to the relation $$\phi$$_B(t) = 10t² + 20t, where $$\phi$$_B is in milliwebers and t is in seconds.

The magnitude of current through R = 2$$\Omega$$ resistor at t = 5 s is ___________ mA.

A particle executes simple harmonic motion represented by displacement function as

x(t) = A sin($$\omega$$t + $$\phi$$)

If the position and velocity of the particle at t = 0 s are 2 cm and 2$$\omega$$ cm s^$$-$$1 respectively, then its amplitude is $$x\sqrt 2 $$ cm where the value of x is _________________.

A swimmer wants to cross a river from point A to point B. Line AB makes an angle of 30$$^\circ$$ with the flow of river. Magnitude of velocity of the swimmer is same as that of the river. The angle $$\theta$$ with the line AB should be _________$$^\circ$$, so that the swimmer reaches point B.