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Four particles each of mass $1\text{kg}$ are placed at the four corners of a square $ABCD$ with a side of length $2\text{m}$. What is the moment of inertia of the system about an axis passing through the mid-points of sides $AB$ and $CD$?

A long solid cylindrical current carring conductor is placed along the $z-$ aixs, carrying current $I$ in the negative $z$ direction. The magnetic field $\overrightarrow{B}$ at a point having coordinate $(x,y)$ on the $z=0$ plane is

A thin rod of length ${}^{\prime }{L}^{\prime }$ is lying along the x-axis with its ends at $x=0$ and $x=L$. Its linear density $\left(\frac{\text{mass}}{\text{length}}\right)$

varies with $x$ as $k{\left(\frac{x}{L}\right)}^n$, where $n$ can be zero or any positive number. If the position $x_{cm}$ of the center of mass of the rod is plotted against ${}^{\prime }{n}^{\prime }$ which of the following graphs best approximates the dependence of $x_{cm}$ on $n$?

In Young's double slit experiment, the fringe pattern is observed on a screen placed at a distance $D$. The slits are illuminated by light of wavelength $\lambda$. The distance from the central point where the intensity falls to half the maximum is

In Young's double slit experiment, two slits $4\text{mm}$ apart, are illuminated by a light of wavelength $600\text{nm}$. What will be the fringe width on a screen placed $2\text{m}$ from the slits?

The ratio of the radii of gyration of a circular disc to that of a circular ring, each of same mass and radius, around their respective axes is

A charged particle of mars $m=1\text{kg}$ and charge $q=2\mu \text{C}$ is thrown from a horizontal ground at an angle of $\theta ={45}^{\circ }$ with speed of $20\text{m/s}$. In space a horizontal electric field $E=2\times {10}^7\text{V/m}$ exists. Find the range on horizontal ground of the projectile thrown.

Assume that gravity is vertical and $g=10{\text{m/s}}^2$

Statement 1 – Electric flux is the flow rate of electric field through a surface.

Statement 2: Electric field due to charges at rest is a time-varying field

In the given circuit, the current through Zener diode is $\frac{5k}{3}\text{mA}$. The value of $k$ is ___

Six identical resistors each of value $1\Omega$ are joined to form a regular hexagon. Further six more resistors of the same value are connected between the six vertices and the centre of the hexagon. The equivalent resistance between any two vertices lying opposite to each other is

Point charge $\left(q\right)$ moves from point $\left(P\right)$ to point $\left(S\right)$ along the path $PQRS$ as shown in fig. in a uniform electric field $E$, pointing parallel to the positive direction of the x-axis. The co-ordinates of the points $P,Q,R$ and $S$ are $(a,b,0),(2a,0,0),(a,-b,0)$ and $(0,0,0)$ respectively. The work done by the field in the above process is given by the expression -

A particle is projected with a velocity $u$, at an angle $\alpha$ with the horizontal. Time at which its vertical component of velocity becomes half of its net speed at the highest point will be

Evaluate the Given limit:

A hundred turns of insulated copper wire are wrapped around an iron cylinder of area ${10}^{-3}{m}^2$ and are connected to a resistor. The total resistance in the circuit is 10 ohms. If the longitudinal magnetic induction in the iron changes from 1 weber $m^{-2}$, in one direction to 1 Weber $m^{-2}$ in the opposite direction, how much charge flows through the circuit?

The value of ${}^{\prime }{a}^{\prime }$ in Van der Waal's equation for the gases $O_2,N_2,N{H}_3$ and $C{H}_4$ are $1.35,1.38,4.16$ and $2.25$ respectively. The gas which can most easily be liquified is

Which of the following are the author's position regarding counter-factualism?
a) Counter-factualism is a world filled with fascination
b) Counter-factualism has been accorded with academic respectability
c) Counter-factualism contains meaningful truth
d) Counter-factualism does not seem to have a human urge

A projectile is fired horizontally with a velocity $98\text{m/s}$ from the top of a hill $490\text{m}$ high. Find the coordinates of the projectile at time $t=10\text{sec}$.

Take origin at the top of hill and vertically downwards as positive $y$-direction, positive $x$-direction along the direction of horizontal projection.$[g=9.8{\text{m/s}}^2]$

A monochromatic beam of light passes from a denser medium into a rarer medium. As a result [CPMT 1972]

Which of the following atom has zero magnetic moment ?

An interference is observed due to two coherent sources $\text{A}\&\text{B}$ having zero phase difference separated by a distance $4\lambda$ along the $y-$axis where $\lambda$ is the wavelength of the source. A detector $\text{D}$ is moving on the positive $x-$axis. The number of points on the $x-$axis including the points $x=0$ & $x=\infty$ at which maxima will be deserved is-

The length of wire, when $M_1$ is hung from it is $l_1$ and is $l_2$ with both $M_1$ and $M_2$ hanging. The natural length of wire is

A sample of ${}_{19}{K}^{40}$ disintegrates into two nuclei Ca and Ar with decay constant ${\lambda }_{ca}=4.5\times {10}^{-10}{s}^{-1}$ and ${\lambda }_{Ar}=0.5\times {10}^{-10}{s}^{-1}$ respectively. The time after which $99\%$ of ${}_{19}{K}^{40}$ get decayed is

A stone is dropped into a well in which the level of water is $h$ below the top of the well. If $v$ is speed of sound in the air, the time $T$ after which the splash is heard is given by

A long solenoid of diameter $0.1m$ has $2\times {10}^4$ turns per meter. At the centre of the solenoid, a coil of $100$turns and radius $0.01m$ is placed with its axis coinciding with the solenoid axis. The current in the solenoid reduces at a constant rate to$0A$ from $4A$ in $0.05s$. If the resistance of the coil is $10{\pi }^2\Omega$, the total charge flowing through the coil during this time is

Which of the following statement (s) is /are correct

A circular wire loop of radius $R$ is placed in the $XY-$plane, centered at the origin $O$. A square loop of side $a$ $(a<<R)$ having two turns is placed with its center at $Z=\sqrt{3}R$ along the axis of the circular wire loop as shown in figure. The plane of the square loop makes an angle of ${45}^{\circ }$ with respect to the $Z-$axis. If the mutual inductance between the loops is given by $\frac{{\mu }_0{a}^2}{2^{P/2}R}$, then the value of $P$ is -

Net electric potential at point P due to three point charges as shown in figure is



चित्रानुसार तीन बिंदु आवेशों के कारण बिन्दु P पर नेट विद्युत विभव है

When a block of mass $M$ is suspended by a long wire of length $L$, the length of the wire becomes $\left(L+l\right)$. The elastic potential energy stored in the extended wire is

A graph of mass ejected vs time is shown in the figure below. [Given $\ln \left(\frac{50}{49}\right)=0.02$]


Find the velocity of the rocket after $5\text{s}$, if initial launch velocity is $200\text{m/s}$ and velocity of ejected fuel w.r.t the rocket is $20\text{m/s}$. [Take $g=10{\text{m/s}}^2$ and initial mass of the rocket is $500\text{kg}$ ].

Two coils $\text{P}$ and $\text{Q}$ are separated by some distance. When a current of $3\text{A}$ flows through coil $\text{P}$, a magnetic flux of ${10}^{-3}\text{Wb}$ passes through $\text{Q}$. No current is passed through $\text{Q}.$ When no current passes through $\text{P}$ and a current of $2\text{A}$ passes through $\text{Q}.$ The flux through $\text{P}$ is-