TN State Board 12th Physics Question Paper 2022

Peacock feather is a classic example of a natural nanomaterial. Its vibrant colors are not due to pigments but due to periodic nanostructures that cause interference of light. A grain of sand is typically macroscopic. Whale skin and beak are biological tissues not characterized primarily as nanomaterials.

The de-Broglie wavelength is given by $\lambda = \frac{h}{\sqrt{2meV}}$. Thus, $\lambda \propto \frac{1}{\sqrt{V}}$. If the voltage $V_1 = 14 \text{ kV}$ is changed to $V_2 = 224 \text{ kV}$, the ratio $\frac{\lambda_2}{\lambda_1} = \sqrt{\frac{V_1}{V_2}} = \sqrt{\frac{14}{224}} = \sqrt{\frac{1}{16}} = \frac{1}{4}$. Therefore, the wavelength decreases by 4 times.

Frequency modulation (FM) is defined as the process where the frequency of the carrier wave is varied in accordance with the instantaneous amplitude of the modulating signal. Amplitude modulation varies amplitude, and phase modulation varies the phase.

The Q factor for a series RLC circuit is defined as $Q = \frac{1}{R}\sqrt{\frac{L}{C}}$. At resonance, $X_L = X_C$, and $Q$ can also be expressed as $\frac{X_L}{R}$ or $\frac{X_C}{R}$. Since the options represent equivalent mathematical forms for this circuit, 'All the above' is correct.

When two spheres are connected, charge flows until both are at the same potential $V = \frac{kQ_1}{r_1} = \frac{kQ_2}{r_2}$. Thus, $\frac{Q_1'}{r_1} = \frac{Q_2'}{r_2}$. Given $r_1 = 1, r_2 = 3$, $Q_2' = 3Q_1'$. Total charge $Q_{total} = -1 + 5 = 4 \times 10^{-2} \text{ C}$. Substituting $Q_2' = 3Q_1'$, we get $Q_1' + 3Q_1' = 4 \times 10^{-2}$, so $Q_1' = 1 \times 10^{-2}$ and $Q_2' = 3 \times 10^{-2} \text{ C}$.