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Find the MOI of four identical solid spheres about axis $X{X}^{\prime }$ placed in horizontal plane each of mass $M$ and radius $R$ as shown in figure. Line $X{X}^{\prime }$ touches two spheres (3 and 4) and passes through diameter of other two spheres (1 and 2).

If ${\lambda }_v,{\lambda }_x,{\lambda }_m$ represent the wavelengths of visible light, $X$-rays and microwaves respectively, then

A particle is projected vertically upward and it reaches a point 25m hieght at instant. After 4 seconds from this instant particle reaches again that point in downward journey.What will be the initial velocity.(g=10m/s^{​​​​​​2}).?

The focal length of a lens of dispersive power $0.45$ which should be placed in contact with a convex lens of focal length $84\text{cm}$ and dispersive power $0.21$ to make the achromatic combination from the two lenses (in cm) is

There are two frictionless conducting rails placed in a transverse uniform magnetic field $B$ as shown in the figure. The rails are connected by a fixed capacitive arm $AB$ and a movable conducting rod $PQ$ is also placed as shown. If the rod $PQ$ is given a rightward initial velocity $V$ then the graph that best represents variation of speed of rod as a function of time

In a physics lab, we took two readings of dip angle by dip circle, in two readings planes of dip circle are mutually perpendicular, then ratio of vertical & horizontal component of field the to earth in lab is (reading 1 = ${45}^0$ reading 2 = ${60}^0$)

A car is moving with a speed of $30{\text{ms}}^{-1}$ on a circular path of radius $225\text{m}$. If its speed is increasing at the rate of $3{\text{ms}}^{-2}$, the net acceleration of the car is

A boat can row with a speed of $10km/hr$ in still water. The river flows steadily at $5km/hr$ and the width of the river is $2km$. If the boat man cross the river with reference to minimum distance of approach then time elapsed in rowing the boat will be

The equivalent capacitance of the infinite ladder shown in the figure between points $\text{A}$ & $\text{B}$ will be

A simple pendulum with a solid metal bob has a period $T$. The metal bob is now immersed in a liquid of density one tenth that of the bob. The liquid is non-viscous. Now the period of the same pendulum with its bob remaining all the time in the liquid will be

The ratio of the tentions $T$ to $T_1$ is $8:p$. The value of $p$ is

1. 0.9

1. 8

A paramagnetic sample shows a net magnetisation of $6\text{A/m}$, when it is placed in an external magnetic field of $0.4\text{T}$, at a temperature of $4\text{K}$. When the sample is placed in an external magnetic field of $0.3\text{T}$ at a temperature of $24\text{K}$, then the magnetisation will be :

A closed pipe has length 0.6m. The air inside the pipe is maintained at temperature ${27}^{\circ }C$. Calculate the fundamental frequency and the frequency of the next two overtones.

(given velocity of sound in air at $0^{\circ }C=330m{s}^{-1}$)

Two particles of equal mass have coordinates $(2\text{m},4\text{m},6\text{m})$ and $(6\text{m},2\text{m},8\text{m})$. Of these one particle has a velocity $\overrightarrow{v_1}=\left(2\hat{i}\right)\text{m/s}$ and another particle has velocity $\overrightarrow{v_2}=\left(2\hat{j}\right)\text{m/s}$ at time $t=0$. The coordinate of their centre of mass at time $t=1\text{s}$ will be

If $E$ is the energy of electron in $n^{th}$ orbit of hydrogen atom, then the energy of electron in $n^{th}$ orbit of ${\text{He}}^{+}$ will be

A body is thrown with a velocity of $20m{s}^{-1}$ from a building of height $15m$. If the angle of projection is ${30}^{\circ }$ above the horizontal, the time of flight and the range of the projectile are respectively.

(Take $g=10m/s^2$)

(Take $g=10{\text{ms}}^{-2}$)

Express $\frac{16}{25}$ as a percentage.

A vessel of volume $1000{\text{cm}}^3$ contains $0.2\text{mol}$ of oxygen and $0.3\text{mol}$ of carbon dioxide. If the temperature of the mixture is ${27}^{\circ }\text{C}$, find its pressure.

Potential energy of a satellite having mass ‘m’ and rotating at a height of $6.4\times {10}^6$ from the earth centre is

Ratio of the longest wavelengths corresponding to the Lyman and Balmer series in the hydrogen spectrum is

The equivalent capacitance in the circuit between $\text{A}$ and $\text{B}$ is

A laser beam has intensity $2.5\times {10}^{14}{\text{Wm}}^{-2}$. The amplitudes of electric and magnetic fields in the beam are,

Two trains are moving on parallel tracks in opposite directions at the speeds of $20\text{m/s}$ and $15\text{m/s}$ respectively. If both the trains are of equal length $140\text{m}$ each, then how much time will they take to cross each other?

An ideal gas is taken from state $A$ to the state $B$, as shown in the $P-V$ diagram. The work done in the process is