A prism of refractive index n₁ and another prism of refractive index n₂ are stuck together (as shown in the figure). n₁ and n₂ depend on $$\lambda$$, the wavelength of light, according to the relation

$${n_1} = 1.2 + {{10.8 \times {{10}^{ - 14}}} \over {{\lambda ^2}}}$$ and $${n_2} = 1.45 + {{1.8 \times {{10}^{ - 14}}} \over {{\lambda ^2}}}$$

The wavelength for which rays incident at any angle on the interface BC pass through without bending at that interface will be _____________ nm.

A stone of mass 20 g is projected from a rubber catapult of length 0.1 m and area of cross section 10^$$-$$6 m² stretched by an amount 0.04 m. The velocity of the projected stone is ______________ m/s.

(Young's modulus of rubber = 0.5 $$\times$$ 10⁹ N/m²)

A transistor is connected in common emitter circuit configuration, the collector supply voltage is 10 V and the voltage drop across a resistor of 1000 $$\Omega$$ in the collector circuit is 0.6 V. If the current gain factor ($$\beta$$) is 24, then the base current is _____________ $$\mu$$A. (Round off to the Nearest Integer)

The amplitude of upper and lower side bands of A.M. wave where a carrier signal with frequency 11.21 MHz, peak voltage 15 V is amplitude modulated by a 7.7 kHz sine wave of 5V amplitude are $${a \over {10}}V$$ and $${b \over {10}}V$$ respectively. Then the value of $${a \over b}$$ is ____________.