Two wavelengths of sodium light \(590 \mathrm{~nm}\) and \(596 \mathrm{~nm}\) are used one after another to study diffraction due to single slit of aperture \(2 \times 10^{-6} \mathrm{~m}\). The distance between the slit and the screen is \(1.5 \mathrm{~m}\). The separation between the positions of first maximum of the diffraction pattern obtained in the two cases is

A solid sphere and thin walled hollow sphere have same mass and same material. Which of them have greater moment of inertia about their diameter?
[ \(\mathrm{I}_{\mathrm{h}}=\) moment of inertia of hollow sphere about an axis coinciding with its diameter, \(\mathrm{I}_{\mathrm{s}}=\) moment of inertia of solid sphere about an axis coinciding with its diameter]

Two loops ' \(A\) ' and ' \(B\) ' of radii ' \(R_1\) ' and ' \(R_2\) ' are made from uniform wire. If moment of inertia of ' \(A\) ' is ' \(I_A\) ' and that ' \(B\) ' is ' \(\mathrm{B}_{\mathrm{B}}\) ', then \(R_2 / R_1\) is \(\left[\frac{I_A}{I_B}=27\right]\)

The height above the earth's surface at which the acceleration due to gravity becomes \(\left(\frac{1}{n}\right)\) times the value at the surface is ( \(R=\) radius of earth)

In LCR series circuit, \(\mathrm{R}=18 \Omega\) and impedance \(33 \Omega\). An r.m.s. voltage of 220 V is applied across the circuit. The true power consumed in a.c. circuit is

Moving coil galvanometers \(\mathrm{M}_{1}\) and \(\mathrm{M}_{2}\) have resistance, number of turns, area of coil and magnetic field as follows.
\(\mathrm{R}_{1}=10 \Omega, \mathrm{R}_{2}=14 \Omega, \mathrm{N}_{1}=30, \mathrm{~N}_{2}=42\)
\(\mathrm{A}_{1}=3 \cdot 6 \times 10^{-3} \mathrm{~m}^{2}, \mathrm{~A}_{2}=1 \cdot 8 \times 10^{-2} \mathrm{~m}^{2},\) \(\mathrm{~B}_{1}=0 \cdot 25 \mathrm{~T}, \mathrm{~B}_{2}=0 \cdot 50 \mathrm{~T}\)
(Spring constants are same for both materials)
The ratio of (i) current sensitivity and (ii) voltage sensitivity for galvanometer
\(\left(\mathrm{M}_{2}\right.\) to \(\left.\mathrm{M}_{1}\right)\) is respectively

If an alternating voltage is applied across a p-n junction diode in series with a load then

Given below are two statements.
Statement I - Smaller the food chain, more is the available energy at each trophic level.
Statement II - Pyramid of energy can also be sometimes inverted.
In the light of above statements, Select the correct option given below:

The integral \(\int_{\frac{\pi}{6}}^{\frac{\pi}{3}} \sec ^{\frac{2}{3}} x \operatorname{cosec}^{\frac{4}{3}} x \mathrm{~d} x\) is equal to

If \(y=\sec \left(\tan ^{-1} x\right)\), then \(\frac{\mathrm{d} y}{\mathrm{~d} x}\) at \(x=1\) is equal to

Let \(\mathrm{f}: \mathbb{R}-\{2\} \rightarrow \mathbb{R}-\{1\}\) defined by \(\mathrm{f}(x)=\frac{x-3}{x-2}\) and \(\mathrm{g}: \mathbb{R} \rightarrow \mathbb{R}\) defined by \(\mathrm{g}(x)=3 \mathrm{x}-2\), then sum of all values of \(x\) for which \(\mathrm{f}^{-1}(x)+\mathrm{g}^{-1}(x)=\frac{19}{6}\) is

The logic gate combination circuit shown in the figure performs the logic function of

A capacitor is made of a flat plate of area ' \(A\) ' and the second plate has staircase like structure. Width of each stair is ' \(a\) ' and its height is ' \(b\) '. The capacity of the capacitor is