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Which of the following options represent a travelling wave? Here, $y$ is the displacement of the particle, $x$ is the position of the particle from origin and $t$ is time.

Magnetic field $\overrightarrow{B}=3x\hat{i}$ exists in space. Energy stored in a cylinderical region of length 1m along x-axis with one end at origin is [Radius of the cylinder is 2m]

A wire of length $L$ and mass per unit length $6.0\times {10}^{-3}{\text{kgm}}^{-1}$ is put under tension of $540\text{N}$. Two consecutive frequencies that resonates with it are : $420\text{Hz}$ and $490\text{Hz}$. Then the value of $L$ (in meters) is:

A point charge $q$ is surrounded by eight fixed identical point charges at the same distance $r$ as shown in figure. How much work will be done by external force to remove point charge $q$ from centre $O$ to infinity very slowly?

A battery having emf $E_1=100\text{V}$ and internal resistance $r=0.5\Omega$ is connected to a storage battery of emf $E_2=90\text{V}$ and external resistance $R$ as shown in figure. For what value of $R$ no current will pass through storage battery $E_2$?

The deflection in a galvanometer falls from $50$ divisions to $20$ divisions, when a $12\Omega$ shunt (resistance connected in parallel to galvanometer) is applied. The galvanometer resistance is

The diagram shows a scalene triangle, $ABC$, with vectors $\overrightarrow{AB}=\hat{a}$ and $\overrightarrow{AC}=2\hat{b}$. The point $D$ is positioned on the line $BC$ such that $BD:DC=3:2$. The point $E$ is positioned on the line $AD$ such that $AE:ED=1:2$. The expression for the vector $\overrightarrow{AE}$ in terms of $\hat{a}$ and $\hat{b}$ is

For the following circuit diagram, what is the equivalent capacitance between points $A$ and $B$?







$[$0.77 Mark$]$

An insulated box containing a diatomic gas of molecular mass $M$ is moving with velocity $v$. If the box is suddenly stopped, the resulting change in temperature is ($R$ is the gas constant)

There are two identical small holes on the opposite sides of a tank containing a liquid. The tank is open at the top. The difference in height between the two holes is $h$. As the liquid comes out of the two holes, the tank will experience a net horizontal force proportional to -

Which of the following relations is true

Water flows through the tube shown in figure. The areas of cross section of the wide and the narrow portions of the tube are 5 $c{m}^2$ and 2 $c{m}^2$ respectively. The rate of flow of water through the tube is 500 $c{m}^3$ $s^{-1}$. Find the difference of mercury levels in the U-tube.

The constant $\gamma$ for oxygen as well as for hydrogen is $1.40$. If the speed of the sound in oxygen is $470{\text{ms}}^{-1}$, what will be the speed in hydrogen at the same temperature and pressure ?

A charged particle having charge $q$, accelerated through a potential difference of
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$V\text{volt}$ enters a transverse magnetic field region in which it experiences a force $F$. If $V$ is increased to $5V$, the particle will experience a force.

If the area of the plate $A=10{\text{cm}}^2$, then equivalent capacitance across the two ends $\text{A}$ and $\text{B}$ is

One of the lines in the emission spectrum of ${\text{Li}}^{2+}$ has the same wavelength as that of $2^{nd}$ line of Balmer series in hydrogen spectrum. The electronic transition corresponding to this line is :-

Given the numbers: $161\text{cm},0.161\text{cm},0.0161\text{cm}$. The number of significant figures for the three numbers is:

The boiling point of NH3 H2O and HF are exceptionally higher explain

A machine gun is mounted on a 2000 kg car on a horizontal frictionless surface. At some instant the gun fires bullets of mass 10 gm with a velocity of 500m/ s with respect to the car . The number of bullets fired per second is ten. The average thrust on the system is ??

When do we use .U= 1/2(C1+C2)V^2 And U=1/2 (C1C2/C1+C2) *V^2

The approximate wave number of the spectral line of the shortest wavelength in Balmer series of atomic hydrogen will be:

(Rydberg constant $\left(R_H\right)=109678{\text{cm}}^{-1}$)

If $\overrightarrow{E}$ = 2i +3j +4k and $\overrightarrow{A}$ = 3i +2j +4k. What is the flux of the given $\overrightarrow{E}$ through the area?

An observer moves towards a stationary source of sound with a speed ${\frac{1}{4}}^{th}$ of the speed of sound. The wavelength and frequency of the source emitted are $\lambda$ and f respectively. The apparent frequency and wavelength recorded by the observer are respectively.

In the figure given below, the position-time graph of a particle of mass 0.1 Kg is shown. The impulse at t = 2 sec is

A tank is filled with water of density 1 g per $c{m}^3$ and oil of density 0.9 g $c{m}^{-3}$. The height of water layer is 100 cm and of the oil layer is 400 cm. If
g = 980 $c{m}^{-2}$ then the velocity of efflux from an opening in the bottom of the tank is

Two objects are placed on the principal axis of a thin converging lens. One is $10cm$ from the lens and the other is on the other side of the lens at a distance of $40cm$ from the lens. The image of both objects are in the same place. The focal length of the lens is (in $cm$).

A rectangular wire frame ABCD that contains a soap bubble is suspended vertically as shown in the figure. The side BC is of length and is movable. It is attached to a mass less plate FG as shown in figure. If particles continuously fall on the plate at the rate of n particles per second and each particle has a momentum of ‘p’. Find the surface tension, if the system is in equilibrium given the particles have a perfectly elastic collision .

The temperature difference between a hot body suspended inside a room (which is maintained at a constant temperature) and the room's temperature becomes half the original value in a time interval $t_0$. In how much time will the temperature difference between the body and the surrounding becomes $\frac{1}{3}$rd of the original value?