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Two coherent narrow slits emitting light of wavelength $\lambda$ in the same phase, are placed parallel to each other at a small separation of $3\lambda$. The light is collected on a screen $S$ which is placed at a distance $D(>>\lambda )$ from the slits. The smallest distance $x$ such that the $P$ is a maxima.

In the system as shown, mass of the block is 1kg and spring constant is 25 $\frac{N}{m}$. The maximum kinetic energy of the block is 50J.

In the circuit shown, the switch is shifted from position $1\to 2$ at t = 0. The switch was initially in position 1 since a long time. The graph between charge on capacitor C and time 't' is

The minimum angular momentum of electron of hydrogen atom in stationary orbit is

Region surrounding oscillating electric dipole has which kind of field?

Consider the situation shown in figure (16-E9). The wire which has a mass of 4.00 g oscillates in its second harmonic and sets the air column in the tube into vibrations in its fundamental mode. Assuming that the speed of sound in air is $340m{s}^{-1}$, find the tension in the wire.

Two identical coherent sources are placed on the diameter of a circle of radius $R$ at separation $x=5\lambda (x<<R)$ symmetrically about the centre of the circle. The sources emit identical wavelength $\lambda$ each. The number of points on the circle with maximum intensity is

What is the equivalent capacitance of the system of capacitors between $\text{A}$ and $\text{B}$

In a $\text{YDSE}$ setup shown in diagram a thin mica sheet $(\mu =1.5)$ is placed in front one of the slits. If the central maxima shifts by $0.4\text{cm}$, then what is the thickness of the mica sheet?

Find the magnifying power of the telescope in case of normal adjustment, if the length of the telescope and focal length of the eyepiece is $38\text{cm}$ and $2\text{cm}$ respectively?

Two point charges $q_1$ and $q_2$ are placed at a distance of $50\text{m}$ from each other in air, and interact with a certain force $F$. The same charges are now put in oil whose relative permittivity is $5.0$. Find the new force of interaction between them :

A positively charged particle, having charge q, is accelerated by a potential difference V. This particle, moving along the x-axis, enters a region where a constant electric field E exists. The direction of electric field is along positive y-axis. The electric field E exists in the region bounded by the lines x = 0 and x = a. Beyond the line x = a (i.e., in region x $\ge$ a), there exists a constant magnetic field of strength B, directed along positive y-axis. What is the pitch of helix formed after particle enters the region x $\ge$ a? (mass of the particle is m).

The maximum potential energy that the spring connecting blocks A and B can have, as a consequence of collision of block C with A is $\frac{m{v}_0^2}{n}$.Then the value of $n$ is .(Assume the collision between C and A to be elastic and ignore any friction).

Graph of V vs I is given in figure. Its ln(P) vs ln(I) graph will be

A pulley mass system is shown in the figure.


The pulley and string are massless and all surfaces are frictionless. Find out the acceleration of $COM$ of the system. [Take $g=10{\text{m/s}}^2$ and consider upward direction as positive]

Two coils are at fixed locations. When coil-$1$ has no current and current in the coil-$2$ increases at the rate $15.0{\text{As}}^{-1}.$ The e.m.f. in the coil-$1$ is $25.0\text{mV}$. When coil-$2$ has no current and coil-$1$ has a current of $3.6\text{A}.$, the flux linkage in coil-$2$ is-

Two bodies, $A$ and $B$ with moment of inertia $I_A$ and $I_B(I_B>I_A)$ have equal rotational kinetic energy are rotating about the same axis. If $L_A$ and $L_B$ be their angular momentum respectively then

Four particles of masses $m,2m,3m$ and $4m$ are arranged at the corners of a parallelogram (shown in figure) with each side equal to $a$ and one of the angles between two adjacent sides is ${60}^{\circ }$. The parallelogram lies in the $\text{x- y}$ plane with mass$m$ at the origin and $4m$ on the x - axis. The centre of mass of arrangement will be located at

Which of the following statements are wrong about Galvanic cells?

An object is placed 15cm from a convex mirror of radius of curvature 90cm. Calculate image position and magnification.

The infinitely long charged sheets are placed as shown in figure. The electric field at point $P$ is

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A steel plate, connnected to a fixed channel using three identical bolts $A,B$ and $C$, carries a load of $6kN$as shown in the figure. Considering the effect of direct load and moment,the magnitude of resultant shear force (in kN) on bolt $C$ is

Two thermally insulated vessels $1$ and $2$ are filled with air at temperature ($T_1$, $T_2$), volume ($V_1$, $V_2$) and pressure ($P_1$, $P_2$) respectively. If the value joining the two vessels is opened, the temperature inside the vessel at equilibrium will be