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A particle of specific charge $\alpha$ starts moving from the origin under the action of an electric field $\overrightarrow{E}=E_0\hat{i}$ and magnetic field $\overrightarrow{B}=B_0\hat{k}$. Its velocity at $(x_0,y_0,0)$ is $(4\hat{i}+3\hat{j})$. The value of $x_0$ is:

A carrier signal $C\left(t\right)=25\sin (2.512\times {10}^{10}t)$ is amplitude modulated by a message signal $m\left(t\right)=5\sin (1.57\times {10}^{8}t)$ and transmitted through an antenna. What will be bandwidth of the modulated signal?

A proton with 1 MeV kinetic energy is moving in a circular path of radius R in a uniform magnetic field. What should be the energy of an α - particle to describe a circle of same radius in the same magnetic field?

A curved road of radius $50m$ is banked at correct angle for a given speed. If the speed is to be doubled keeping the same banking angle, the radius of curvature of the road should be changed to

Block $A$ of mass $m$ placed on a smooth inclined plane is connected by a string to another block $B$ of mass $M$ as shown in the figure. If the system is in equilibrium , express $M$ in terms of $m$

Electric field in a certain region is acting radially outward and variation of electric field with distance from origin of field is represented below. Slope of the straight line given in the graph is $\text{A}$.





The charge contained in a sphere of radius $a$ centred at the origin of field will be given by

A small particle is placed at the pole of a concave mirror and then moved along the principal axis to a large distance. During the motion, the distance between the pole of the mirror and the image is measured. The procedure is then repeated with a convex mirror, a concave lens and a convex lens. The graph is plotted between image distance versus object distance. Match the curves shown in the graph with the mirror or lens that is corresponding to it. (Curve 1 has two segments) [Click and drag to move]

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$\begin{array}{cccccc}& \text{Column 1}& & \text{Column 2 (Graph)}& & \text{Column 3 (Power)}\\ \text{(I)}& \text{Convex lens}& \text{(i)}& 1& \text{(P)}& \text{Positive}\\ \text{(II)}& \text{Convex mirror}& \text{(ii)}& \text{2}& \text{(Q)}& \text{Zero}\\ \text{(III)}& \text{Concave lens}& \text{(iii)}& 3& \text{(R)}& \text{Infinite}\\ \text{(IV)}& \text{Concave mirror}& \text{(iv)}& 5& \text{(S)}& \text{Negative}\end{array}$

Which of the option correctly matches with convex mirror?

The minimum and maximum distances of a palnet revolving around the sun are $x_1$ and $x_2$. If the minimum spped of the planet on its trajectory is $v_0$ then is maximum speed will be :

A small sphere is given vertical velocity of magnitude $v_0=5{\text{ms}}^{-1}$ and it swings in a vertical plane about the end of a massless string. The angle $\theta$ with the vertical at which the string will break, given that it can withstand a maximum tension equal to twice the weight of the sphere, is

One end of a uniform wire of length $L$ and of weight $W$ is attached rigidly to a point in the roof and a weight $W_1$ is suspended from its lower end. If $S$ is the area of cross-section of the wire, the stress in the wire at a height $\frac{3L}{4}$ from its lower end is

1. 40.95

Monochromatic light of
wavelength 589 nm is incident from air on a water surface. What are
the wavelength, frequency and speed of (a) reflected, and (b)
refracted light? Refractive index of water is 1.33.

Two capacitors $C_1$ and $C_2$ are charged to $120\text{V}$ and $200\text{V}$, respectively. It is found that by connecting them together, the potential difference across each one can be made zero. Then:

A geostationary satellite is orbiting the earth at a height of 6R above the surface of the earth; R being the radius of the earth. What will be the time period of another satellite at a height 2.5 R from the surface of the earth?

If $\overrightarrow{A}$ = 3 $\hat{i}$ + 4 $\hat{j}$ and $\overrightarrow{B}$ = 7 $\hat{i}$ + 24 $\hat{j}$ , find a vector having the same magnitude as $\overrightarrow{B}$ and parallel to $\overrightarrow{A}$

The angle which a vector $\hat{i}-\hat{j}+\sqrt{2}\hat{k}$ makes with y - axis is

A parallel beam of light of wavelength 560 nm falls on a thin film of oil (refractive index = 1.4). What shoul be the minimum thickness of the film so that it strongly reflects the light?

A heat engine receives $50\text{kcal}$ of heat from the source per cycle, and operates with an efficiency of $20\%$. Find the heat rejected to the sink per cycle.

Two capacitors of capacities $1\mu \text{F}$ and $C\mu \text{F}$ are connected in series and this combination is charged to a potential difference of $120\text{V}$. If the charge on the $1\mu \text{F}$ capacitor is $80\mu \text{C}$, then the energy stored in the capacitor $C$ (in micro joule) is

In interference of two waves, two individual amplitudes are $A_0$ each and the intensity is $I_0$ each. The resultant amplitude at a point where phase difference between two waves is ${60}^{\circ }$ is

If $\overrightarrow{C}=\overrightarrow{A}+\overrightarrow{B}$, then the magnitude of $\overrightarrow{B}$ is

A particle moves under the influence of a force F = CX from X = 0 to $X=X_1$. The work done in this process will be

The potential variation with distance for a uniformly charged ring having radius $R$ and carrying charge $Q$ is:

In
the adjacent diagram, CP represents a wavefront and AO & BP, the
corresponding two rays. Find the condition on q for constructive
interference at P between the ray BP and reflected ray OP

A body of mass $m$ dropped from a certain height strikes a light vertical fixed spring of stiffness $k$. The height of its fall before touching the spring if the maximum compression of the spring is equal to $\frac{3mg}{k}$ is

A uniform electric field $\left(\overrightarrow{E}\right)$ and magnetic field $\left({\overrightarrow{B}}_0\right)$ exist in a region as shown in figure. Both the fields are mutually perpendicular.



A positively charged particle having charge $q$ and mass $m$ is projected vertically upward, and it's crossed the line $\text{AB}$ after time $t_0$. Find the speed of projection, if the particle moves with constant velocity after time $t_0$.

$($Given, $g$ is acceleration due to gravity, and $qE=mg)$ $($ Here, the electric field and gravity exist everywhere but the magnetic field starts only after crossing the line $AB)$

A cubical wooden box of side $L$ is placed on a horizontal rough surface and the coefficient of static friction between them is $\mu$. Another cubical box of the same wood but of side $2L$ is placed on the same surface. Then the coefficient of static friction is

A square metal wire loop of side $10cm$ is moved with a constant velocity $v$ in a uniform magnetic field $B=2Wb{m}^{-2}$ as shown in figure. The magnetic field lines are perpendicular to the plane of the loop and directed into the plane. The loop is connected to the network of resistances, each of value $3\Omega$. The resistance of the other wires are negligible. The speed of the loop so as to have a steady current of $1mA$ in the loop is

In the figure shown below, $W_{AB}$ and $W_{CD}$ are workdone during process $AB$ and $CD$. Which of the following options is correct?