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You are in a lift moving from the 3^rd floor to the 12^th floor, through a height H. If the elevator moves at a constant speed without stopping, what is the work performed on you by the elevator? Take your body mass as M.

The weight of an object in a coal mine, at sea level, and at top of moutain are $W_1,W_2$ and $W_3$ respectively, then

Suppose that the electromagnetic wave in vacuum is
$\overrightarrow{E}=\{\left(3.1\frac{N}{C}\right)\cos \left[(1.8\frac{rad}{m}\right)y+(5.4\times {10}^6\frac{rad}{s})t]\hat{i}$
What is the frequency?

Do you see an intersection of time and space in the story?

A stone of mass 1 kg tied to a light in extensible string of length $L=\frac{10}{3}m$ is whirling in a circular path of radius L in a vertical plane. The ratio of the maximum tension in the string to the minimum tension in the string is 4 and if g is taken to be $10\frac{m}{s^2}.$ The speed of stone at the highest point of the circle is

The minimum horizontal acceleration of the container so that the pressure at point A of the container becomes atmospheric is (the tank is of sufficient height)

When the momentum of a proton is changed by an amount $P_0$, the corresponding change in the de-Broglie wavelength is found to be $0.25\%$. Then, the original momentum of the proton was

The value of $\int \frac{x^2-1}{(x^2+1)\sqrt{1+x^4}}dx$ is (where $C$ is integration constant)

A sphere of radius 1m has an equation of the form $x^2+y^2+z^2=r^2$

Statement 1: For its surface, only 6 distinct numbers of normal vectors are possible.

Statement 2: At every point of its surface intersecting with the coordinate Axis, there will a normal vector along the direction of coordinate axis at those points.

Let $T_1$ and $T_2$ be the time period of oscillation of two springs $A$ and $B$ when a mass $m$ is suspended from them separately. Now both the springs are connected in parallel and the same mass $m$ is suspended with them. If $T$ is time period of the parallel system, then

A composite rod is made of copper $\alpha =1.8\times {10}^{-5}{K}^{-1}$ and steel $1.2\times {10}^{-5}{K}^{-1}$ as shown in figure, is heated up, then it

Which of the following graphs best represents the variation of photo current with respect to intensity of radiation?

A moving coil galvanometer of resistance $20\Omega$ gives a full scale deflection when a current of $1\text{mA}$ is passed through it. It is to be converted into an ammeter reading $20\text{A}$ on full scale. But the shunt of $0.005\Omega$ only is available. What resistance should be connnected in series with the galvanometer coil?

A spring of spring constant $5\times {10}^3\text{N/m}$ is stretched initially by $5\text{cm}$ from the unstretched position. The work required to further stretch the spring by another $5\text{cm}$ is:

What will be the rotation under the left load for the beam shown below:

The diameter and height of a cylinder are measured by a meter scale to be $12.6\pm 0.1\text{cm}\text{and}34.2\pm 0.1\text{cm}$ respectively. What will be the value of its volume in appropriate significant figures ?

Two blocks $B_1$ and $B_2$ of masses $m_1$ and $m_2$ respectively are connected with the help of a pulley and string as shown. Upper surface of vehicle is smooth but vertical surface is rough.





Given $a=\frac{g}{7}$ and $m_1=7.5m_2$. If $B_1$ and $B_2$ are at rest wrt vehicle, coefficient of friction between block $B_2$ and side of vehicle is

The energy of a photon of light has what kind of proportionality to its frequency and its wavelength?

The acceleration-displacement graph of a particle executing SHM is shown in given figure. The time period of its oscillation in seconds is

A particle is simultaneously acted by two forces equal to 4 N and 3 N. The net force on the particle is

A ray of light passes through an equilateral prism $(\mu =1.5)$ such that the angle of incidence is equal to the angle of emergence & the either is equal to $\frac{3}{4}th$ of the angle of prism. Calculate angle of deviation.

The rms speed of oxygen at room temperature is about $500\text{m/s}$. The rms speed of hydrogen at the same temperature is about

A rod made of glass, refractive index $1.5$ and of square cross section, is bent into the shape shown in figure. A parallel beam of light falls normally on the plane flat surface $A$. Referring to the diagram, $d$ is the width of a side and $R$ is the radius of inner semicircle. Find the maximum value of ratio $\frac{d}{R}$ so that all light entering the glass through surface $A$ emerges from the glass through surface $B$.

The relation between current in a conductor and time is shown in the figure.



$\left(ii\right)$ Write the expression of current in terms of time.



​​​​​​​$[$1 Mark$]$

A projectile thrown at an angle of ${30}^{\circ }$ with the horizontal has a range $R_1$. Another projectile thrown, with the same velocity, at an angle ${30}^{\circ }$ with the vertical, has a range $R_2$. The relation between $R_1$ and $R_2$ is

A thin sheet of metal of uniform thickness is cut into the shape bounded by the line $x=a$ and $y=\pm k{x}^2$ as shown.

Find the coordinates of the centre of mass.

[Here, $a\&k$ are positive constant]

In the given diagram, force acting on the conductor $\text{OA}$, aligned along the body digonal of the cube, is:

( Given, side of the cube is $2\text{m},I=2\text{A},\overrightarrow{B}=3\hat{k}\text{T}$ )

The force on a particle of mass $10\text{g}$ is $(10\hat{i}+5\hat{j})$. If it starts from rest from origin, what would be its position at time $\text{t}=5\text{s}?$

Current
in a circuit falls from 5.0 A to 0.0 A in 0.1 s. If an average emf of
200 V induced, give an estimate of the self-inductance of the
circuit.