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For the given situation shown below,find the angle from horizontal the mirror must be rotated in order to get a vertical reflected ray

A current $i\text{A}$ flows in a circular arc of wire whose radius is $R$ and it subtends an angle $\frac{3\pi }{2}\text{radian}$ at its centre. The magnetic field at the centre is

Find the current through $25\text{V}$ in the figure shown.

A man wants to swim across a river from A to B and back from B to A always following line AB. The distance S between points A and B is S. The velocity of the river current v is constant over the entire width of the river. The line AB makes an angle $\alpha$ with the direction of current. Let the man travel with velocity u and at angle $\beta$ to the line AB. Find time 't' by which he will be back.

Two seconds after projection a projectile is travelling in a direction inclined at ${30}^{\circ }$ to the horizontal after one more sec, it is travelling horizontally, the magnitude and direction of its initial velocity are-

The magnetic intensity $H$ at the centre of a long solenoid carrying a current of $2.0\text{A}$, is found to be $1500{\text{Am}}^{-1}$. Find the number of turns per metre of the solenoid.

A rod of length $L$ is placed along the $x-$ axis between $x=0$ and $x=L$. The linear density (mass/length) $\lambda$ of the rod varies with the distance $x$ from the origin as $\lambda =k{x}^2$. Here $k$ is a positive constant. Find the position of the centre of mass of this rod.

At relatively high pressure, van der Waals equation reduces to

A body is vertically thrown upward at 55m/s. $g=10m/s^2$. Calculate the distance in the 6th second. Plz explain

If $15\text{g}$ mass of nitrogen gas is enclosed in a vessel at a temperature ${27}^{\circ }\text{C}$. Amount of heat transfered to the gas, so that rms velocity of molecules is doubled is about

[Take $R=8.3\text{J/K mole}$]

Two masses are in the ratio 5:1. What is ratio of their inertia?

A parallel plate capacitor with plate area A and initial separation d is connected to battery of EMF \(V_0\). Work done by external force to increase separation of plates from d to 2d slowly is

[Battery remains connected]

1. 103.2

Two particles are projected from ground with a speed of $40\text{m/s}$ at complimentary angles. If the difference in the maximum height of the particles is $50\text{m}$, then the height of the individual particles is

Find equivalent capacitance across $\text{AB}$ (all capacitance are in $\mu \text{F})$.

Determine expression for the output for the circuit of figure shown below:

A small coil is introduced between the poles of an electromagnet so that its axis coincides with the magnetic field direction. The number of turns is $n$ and the cross sectional area of the coil is $A$. When the coil turns through $180°$about its diameter, the charge flowing through the coil is $Q$. The total resistance of the circuit is $R$. What is the magnitude of the magnetic induction?

A liquid is compressed in a cylinder from a volume of 0.0113$m^3$ at $6.87\times {10}^{6}N/m^2$ pressure to $0.0112m^3$ at $13.73\times {10}^{6}N/m^2$. The compressibility of the liquid is

A car is moving along a straight horizontal road with speed $v_0$. If the coefficient of friction between the tyres and the road is $\mu$, the shortest distance in which the car can be stopped is

A proton is moving in a gravity free space having a uniform electric field $E$ of unknown magnitude and direction. There is a uniform magnetic field of $0.01\text{T}$ pointing in the $y$ - direction. The proton moves in the $x$ - direction at a constant velocity of $10\text{km/s}$ . All directions are with respect to the usual right handed $x-y-z$ coordinate system. Which of the following is /are correct ?

If $x=a{\cos }^3\theta ,y=a{\sin }^3\theta$, then $1+{\left(\frac{dy}{dx}\right)}^2$ is

1. 155

If $x=5t^4$ and $y=2t^2+1,$ then $\frac{dy}{dx}$ at $t=1$ is equal to



[2 marks]

What is the de-Brogile wavelength of fullerene $\left(C_{60}\right)$, if it is moving with $4\times {10}^5\text{m/s}$?

$(N_A=6\times {10}^{23})$

One end of a string of length l is connected to a particle of mass m and the other to a small peg on a smooth horizontal table. If the particle moves in a circle with speed v the net force on the particle (directed towards the centre) is:
(i) T,
(ii) $T-\frac{m{v}^2}{l}$
(iii) $T+\frac{m{v}^2}{l}$
(iv) 0
T is the tension in the string. [Choose the correct alternative].

A body moves a distance of $5\text{m}$ along a straight line under the action of a force of $15\text{N}$. If work done by this force is $45\text{J}$, the angle which the force makes with the direction of motion with the horizontal is

A capacitor of capacitance $C$ has a reactance $X$. If capacitance and frequency are tripled in value, then reactance will be

The figure shows a ray incident at incidence angle ($i$) $\pi /3$. The plot drawn shows the variation of $|r-i|$ versus $({\mu }_1/{\mu }_2=k$), where $r$ = 'angle of refraction'.
The ray is going from ${\mu }_2$ to ${\mu }_1$. Choose possible correct options.

Which of the following cases, a rigid body, necessarily has an angular acceleration.

Consider the figure. Each capacitor has capacitance C.
The equivalent capacitance between 4 and 5 is