A stationary source is emitting sound at a fixed frequency f₀, which is reflected by two cars approaching the source. The difference between the frequencies of sound reflected from the cars is 1.2% of f₀. What is the difference in the speeds of the cars (in km per hour) to the nearest integer? The cars are moving at constant speeds much smaller than the speed of sound which is 330 ms^$$-$$1.

The focal length of a thin biconvex lens is 20 cm. When an object is moved from a distance of 25 cm in front of it to 50 cm, the magnification of its image changes from m₂₅ to m₅₀. The ratio $${{{m_{25}}} \over {{m_{50}}}}$$ is __________.

An $$\alpha$$-particle and a proton are accelerated from the rest by a potential difference of 100 V. After this, their de Broglie wavelengths are $$\lambda$$_$$\alpha$$ and $$\lambda$$_p, respectively. The ratio $${{{\lambda _p}} \over {{\lambda _\alpha }}}$$, to the nearest integer, is _____________.

When two identical batteries of internal resistance 1 $$\Omega$$ each are connected in series across a resistor R, the rate of heat produced in R is J₁. When the same batteries are connected in parallel across R, the rate is J₂. If J₁ = 2.25 J₂, then the value of R in $$\Omega$$ is __________.