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A copper rod of length $88cm$ and an aluminium rod of unknown length have their increase in length independent of increase in temperature. The length of the aluminium rod is
(${\alpha }_{Cu}=1.7\times {10}^{-5}{K}^{-1}$and ${\alpha }_{Al}=2.2\times {10}^{-5}{K}^{-1}$)

Twelve resistances each of resistance R are connected in the circuit as shown in fig. Net resistance between points A and C would be

When the momentum of a body increases by 100%, its KE increases by

Two circuits have mutual inductance of 0.09 H. Average e.m.f. induced in the secondary by a change of current from 0 to 20 A in 0.006 s in primary will be

Two particles of masses $m$ and $2m$ start moving from origin with same constant speed along $x$ and $y$ axis respectively. The centre of mass of system of particles will move along the line

Assuming the string to be inextensible and pulley and surface to be frictionless, the speed of block B in the pulley block system as shown in figure is

A metre stick swinging in a vertical plane about a fixed horizontal axis passing through its one end undergoes small oscillations of frequency $f_0$. If the bottom half of the stick is cut off and glued to the upper half, then the new frequency for small oscillations is

Two blocks A and B of mass $m$ and $2m$ respectively are connected by a massless spring of force constant $k$. They are placed on a smooth horizontal plane. They are stretched by an amount $x$ and then released. The relative velocity of the blocks when the spring comes to its natural length is

$\frac{d}{dx}\left(cos{x}^0\right)$

A hemisphere of radius r a point charge Q is kept at distance y above the centre such that y is tending towards 0. electric flux through the curved surface is

Two forks $A$ and $B$ produce 3 $\text{beats/s}$. Forks $B$ and $C$ produce 5 $\text{beats/s}$. $A$ and $C$ will produce

For a binary ideal liquid solution, the total pressure of the solution is given as:

If the rms speed of nitrogen molecules is $490m{s}^{-1}$ at 273K, find the rms speed of hydrogen molecules at the same temperature -

The position of the particle is given by $x=3t^3+4$ in $\text{m}$. The average speed of the particle in $3\text{sec}$ is

A particle, which is constrained to move along the x-axis, is subjected to a force in the same direction which varies with the distance x of the particle from the origin as $F\left(x\right)=-kx+a{x}^3$. Here k and a are positive constants. For $x\ge 0$, the functional form of the potential energy U(x) of the particle is

A charge Q is divided into two parts of q and Q-q. If the coulomb repulsion between them when they are separated is to be maximum, the ratio of $\frac{Q}{q}$ should be

An insect crawls up a hemispherical surface very slowly (see the figure). The coefficient of friction between the surface and the insect is $\frac{1}{3}$. If the joining the centre of the hemispherical surface to the insect makes an angle $\alpha$ with the vertical, the maximum possible value of $\alpha$ is given

A prism having an apex angle $4^{\circ }$ and refractive index 1.5 is located in front of a vertical plane mirror as shown in figure. Through what total angle is the ray deviated after reflection from the mirror

A sandbag ballast is dropped from a balloon that is ascending with a velocity of $40ft/s$. If the sandbag reaches the ground in $20s$, how high was the balloon when the bag was dropped? Neglect air resistance.

The Electric Field between the capacitor plates is a constant 5N/C. If the region between the plates has vacuum, what is the energy density for the capacitor?

A source emitting light of wavelengths 480 nm and 600 nm is used in a double slit interference experiment. The separation between the slit is 0.25mm and the interference is observed ona screen placed at 150 cm from the slits. Find th linear separation between the first maximum (next ot the central maximum) corresponding to he two wavelengths.

A vessel A has volume V and a vessel B has volume 2V. Both contain some water which has a constant volume. The pressure in the space above water is $p_a$ for vessel A and $p_b$ for vessel B.

If the excess pressure inside a soap bubble of radius $1\text{cm}$ is balanced by an oil
($\rho =0.8{\text{g/cm}}^3)$ column of height $2\text{mm}$, then the surface tension of soap solution will be
[Take $g=10{\text{m/s}}^2$]

Suppose A nad B in the previous problem change their positions in such a way that tha line joining them becomes perpendicular to the direction of wind while maintaining the separation x. What will be the time lag B finds between seeing and hearing the drum beasting by A ?

Figure 17.5 shows the P - V diagram for a fixed mass of an ideal gas undergoing cyclic process ABCA.AB represents isothermal process. Which of the graphs shown in Fig. 17.6 represents the P - T diagram of the cyclic process ?

Find the acceleration of the system shown in the figure.

When the temperature of a rod increases from $t$ to $t+\Delta t$, the moment of inertia of the rod increases from $I$ to $I+\Delta I$. If the coefficient of linear expansion of the rod is $\alpha$, the ratio $\frac{\Delta I}{I}$ is

A small empty bucket of mass M is attached to a long inextensible cord of length l. The bucket is released from rest when the cord is in a horizontal position. In its lowest position the bucket scoops up a mass m of water, what is the height of the swing above the lowest position?

The general solution of is

[AISSE 1984]

If the volume of the given mass of a gas is increased four times, the temperature is raised from ${27}^{o}C$ to ${127}^{o}C$. The elasticity will become

If the latus rectum of a hyperbola forms an equilateral triangle with the vertex at the centre of the hyperbola, then its eccentricity e =

Write the postulates of Kinetic theory of gases

Two rods of length $L_2$ and coefficient of linear expansion ${\alpha }_2$ are connected freely to a third rod of length $L_1$ of coefficient of linear expansion ${\alpha }_1$ to form an isosceles triangle. The arrangement is supported on the knife edge at the midpoint of $L_1$ which is horizontal. The apex of the isosceles triangle is to remain at a constant distance from the knife edge if

Sir Countinuing from my previous ques which i have asked

I want to know when nothing is mention about tangential acceleration n centripital acceleration i hv asked to find force then what to do

A uranium-238 nucleus,initially at rest,emits an alpha particle with a speed of $1.4\times {10}^7$ $m/s$.Calculate the recoil speed of the residual nucleus thorium-234.Assume that the mass of a nucleus is proportional to the mass number.+

A wooden cylinder of base area $50c{m}^2$ and height $1m$ has mass of $2.5kg$. It is carefully lowered in a cylindrical vessel of water. The vessel has inner area $100c{m}^2$ and height of $1m$. Which of the four figures correctly represents the equilibrium state?

A metal surface of threshold frequency $5.3\times {10}^{14}se{c}^{-1}$ is exposed to a photon of radiation having energy $3.4\times {10}^{-19}J$.

The direction of Mowgali which is at the position $(4,6)$ with respect to Bageera which is at the position $(2,3)$ is

A gun moving at a speed of $30m/s$ fires a bullet (in the same direction gun is moving) at an angle ${30}^o$ with the horizontal and a velocity of $150m/s$ relative to the gun. Find the distance between the gun and the bullet when the bullet hits the ground. (Take $g=10m/s^2$)

Five identical plates are arranged such that each pair is a capacitor of capacitance 2 mF.
The plates are connected to a source of emf 10 V as shown. The charge on the plate C is

PARAGRAPH

In electromagnetic theory, the electric and magnetic phenomena are related to each other. Therefore, the dimensions of electric and magnetic quantities must also be related to each other. In the questions below, $\left[E\right]$ and [𝐵] stand for dimensions of electric and magnetic fields respectively, while $\left[{\epsilon }_0\right]$ and $\left[{\mu }_0\right]$ stand for dimensions of the permittivity and permeability of free space respectively. $\left[L\right]$ and $\left[T\right]$ are dimensions of length and time respectively. All the quantities are given in SI units.





The relation between [𝐸] and [𝐵] is