During Searle's experiment, zero of the Vernier scale lies between 3.20 $$ \times $$ 10^-2 m and 3.25 $$ \times $$ 10^-2 m of the main scale. The 20^th division of the Vernier scale exactly coincides with one of the main scale divisions. When an additional load of 2 kg is applied to the wire, the zero of the Vernier scale still lies between 3.20 $$ \times $$ 10^-2 m and 3.25 $$ \times $$ 10^-2 m of the main scale but now the 45^th division of Vernier scale coincides with one of the main scale divisions. The length of the thin metallic wire is 2 m and its cross-sectional area is 8 $$ \times $$ 10^-7 m². The least count of the Vernier scale is 1.0 $$ \times $$ 10^-5 m. The maximum percentage error in the Young's modulus of the wire is

To find the distance d over which a signal can be seen clearly in foggy conditions, a railways engineer uses dimensional analysis and assumes that the distance depends on the mass density $$\rho $$ of the fog, intensity (power/area) S of the light from the signal and its frequency f. The engineer finds that d is proportional to S^1/n. The value of n is

At time t = 0, terminal A in the circuit shown in the figure is connected to B by a key and an alternating current I(t) = I₀ cos ($$\omega$$t), with I₀ = 1 A and $$\omega$$ = 500 rad s^-1 starts flowing in it with the initial direction shown in the figure. At $$t = {{7\pi } \over {6\omega }}$$, the key is switched from B to D. Now onwards only A and D are connected. A total charge Q flows from the battery to charge the capacitor fully. If C = 20 $$\mu$$F, R = 10 $$\Omega$$ and the battery is ideal with emf of 50 V, identify the correct statement(s).

A light source, width emits two wavelengths $$\lambda$$₁ = 400 nm and $$\lambda$$₂ = 600 nm, is used in a Young's double-slit experiment. If recorded fringe widths for $$\lambda$$₁ and $$\lambda$$₂ are $$\beta$$₁ and $$\beta$$₂ and the number of fringes for them within a distance y on one side of the central maximum are m₁ and m₂, respectively, then