A single slit of width $a$ is illuminated by a monochromatic light of wavelength $600\mathrm{nm}$. The value of ' $a$ ' for which first minimum appears at $\theta =30^{\circ }$ on the screen will be :

In a Young's double slits experiment, the ratio of amplitude of light coming from slits is $$2:1$$. The ratio of the maximum to minimum intensity in the interference pattern is:

The ratio of intensities at two points $$\mathrm{P}$$ and $$\mathrm{Q}$$ on the screen in a Young's double slit experiment where phase difference between two waves of same amplitude are $$\pi /3$$ and $$\pi /2$$, respectively are

The width of fringe is $$2\mathrm{mm}$$ on the screen in a double slits experiment for the light of wavelength of $$400\mathrm{nm}$$. The width of the fringe for the light of wavelength 600 $$\mathrm{nm}$$ will be:

Given below are two statements: One is labeled as Assertion A and the other is labeled as Reason R. Assertion A : Two metallic spheres are charged to the same potential. One of them is hollow and another is solid, and both have the same radii. Solid sphere will have lower charge than the hollow one. Reason R : Capacitance of metallic spheres depend on the radii of spheres In light of the above statements, choose the correct answer from the options given below.

A parallel plate capacitor has plate area 40 cm$${}^2$$ and plates separation 2 mm. The space between the plates is filled with a dielectric medium of a thickness 1 mm and dielectric constant 5. The capacitance of the system is :

In the network shown below, the charge accumulated in the capacitor in steady state will be:

A capacitor of capacitance $$\mathrm{C}$$ is charged to a potential V. The flux of the electric field through a closed surface enclosing the positive plate of the capacitor is :

A parallel plate capacitor of capacitance $$2\mathrm{F}$$ is charged to a potential $$\mathrm{V}$$, The energy stored in the capacitor is $$E_1$$. The capacitor is now connected to another uncharged identical capacitor in parallel combination. The energy stored in the combination is $${\mathrm{E}}_2$$. The ratio $${\mathrm{E}}_2/{\mathrm{E}}_1$$ is :

The distance between two plates of a capacitor is $$\mathrm{d}$$ and its capacitance is $${\mathrm{C}}_1$$, when air is the medium between the plates. If a metal sheet of thickness $$\frac{2d}{3}$$ and of the same area as plate is introduced between the plates, the capacitance of the capacitor becomes $${\mathrm{C}}_2$$. The ratio $$\frac{{\mathrm{C}}_2}{{\mathrm{C}}_1}$$ is

The equivalent capacitance of the combination shown is :

In this figure the resistance of the coil of galvanometer G is $$2\Omega$$. The emf of the cell is $$4\mathrm{V}$$. The ratio of potential difference across $${\mathrm{C}}_1$$ and $${\mathrm{C}}_2$$ is:

A steel wire with mass per unit length $$7.0\times 10^{-3}\mathrm{kg}{\mathrm{m}}^{-1}$$ is under tension of $$70\mathrm{N}$$. The speed of transverse waves in the wire will be:

A person observes two moving trains, 'A' reaching the station and 'B' leaving the station with equal speed of $$30\mathrm{m}/\mathrm{s}$$. If both trains emit sounds with frequency $$300\mathrm{Hz}$$, (Speed of sound: $$330\mathrm{m}/\mathrm{s}$$) approximate difference of frequencies heard by the person will be:

A travelling wave is described by the equation $$y(x,t)=[0.05\sin (8x-4t)]$$ m The velocity of the wave is : [all the quantities are in SI unit]

A car P travelling at $$20{\mathrm{ms}}^{-1}$$ sounds its horn at a frequency of $$400\mathrm{Hz}$$. Another car $$\mathrm{Q}$$ is travelling behind the first car in the same direction with a velocity $$40{\mathrm{ms}}^{-1}$$. The frequency heard by the passenger of the car $$\mathrm{Q}$$ is approximately [Take, velocity of sound $$=360{\mathrm{ms}}^{-1}$$ ]

For a periodic motion represented by the equation $$y=\sin \omega \mathrm{t}+\cos \omega \mathrm{t}$$ the amplitude of the motion is

The engine of a train moving with speed $$10{\mathrm{ms}}^{-1}$$ towards a platform sounds a whistle at frequency $$400\mathrm{Hz}$$. The frequency heard by a passenger inside the train is: (neglect air speed. Speed of sound in air $$=330{\mathrm{ms}}^{-1}$$ )

As shown in the figure, a long straight conductor with semicircular arc of radius $$\frac{\pi }{10}$$m is carrying current $$\mathrm{I}=3A$$. The magnitude of the magnetic field, at the center O of the arc is : (The permeability of the vacuum $$=4\pi \times 10^{-7}{\mathrm{NA}}^{-2}$$)

A long conducting wire having a current I flowing through it, is bent into a circular coil of $\mathrm{N}$ turns. Then it is bent into a circular coil of $\mathrm{n}$ turns. The magnetic field is calculated at the centre of coils in both the cases. The ratio of the magnetic field in first case to that of second case is :