In the given figure, the face $$A C$$ of the equilateral prism is immersed in a liquid of refractive index '$$n$$'. For incident angle $$60^{\circ}$$ at the side $$A C$$, the refractive light beam just grazes along face $$A C$$. The refractive index of the liquid $$n=\frac{\sqrt{x}}{4}$$. The value of $$x$$ is ____________.
(Given refractive index of glass $$=1.5$$ )
Two lighter nuclei combine to form a comparatively heavier nucleus by the relation given below :
$${ }_{1}^{2} X+{ }_{1}^{2} X={ }_{2}^{4} Y$$
The binding energies per nucleon for $$\frac{2}{1} X$$ and $${ }_{2}^{4} Y$$ are $$1.1 \,\mathrm{MeV}$$ and $$7.6 \,\mathrm{MeV}$$ respectively. The energy released in this process is _______________ $$\mathrm{MeV}$$.
A uniform heavy rod of mass $$20 \mathrm{~kg}$$, cross sectional area $$0.4 \mathrm{~m}^{2}$$ and length $$20 \mathrm{~m}$$ is hanging from a fixed support. Neglecting the lateral contraction, the elongation in the rod due to its own weight is $$x \times 10^{-9} \mathrm{~m}$$. The value of $$x$$ is _______________.
(Given, young modulus Y = 2 $$\times$$ 1011 Nm$$-$$2 and g = 10 ms$$-$$2)
The typical transfer characteristics of a transistor in CE configuration is shown in figure. A load resistor of $$2 \,k \Omega$$ is connected in the collector branch of the circuit used. The input resistance of the transistor is $$0.50 \,\mathrm{k} \Omega$$. The voltage gain of the transistor is ______________.