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A non-conducting ring of radius 0.5m carries a total charge of $1.11\times {10}^{-10}C$ distributed non-uniformly on its circumference producing an electric field $\overrightarrow{E}$ every where in space. The value of the line integral ${\int }_{l-0}^{l-\infty }-\overrightarrow{E}.d\overrightarrow{l}$ ($l-0$ being centre of the ring) in volts is

Two springs of force constant $100N/m$ and $150N/m$ are in series as shown. The block is pulled by a distance of $2.5cm$ to the right from equilibrium position. What is the ratio of work done by the spring $1$ to the work done by the spring $2$?

For a cell, a graph is plotted between the potential difference V across the terminals of the cell and the current I drawn from the cell. The e.m.f and the internal resistance of the cell are E and r, respectively. Then

If in a p-n junction, a square input signal of 10 V is applied as shown, then the output across RL will be :

The mass of the sphere is $3.2\times {10}^{-14}kg$ and it carries a net charge equal to that of 10 electrons. If the electronic charge is $-1.6\times {10}^{-19}C$ and the acceleration of free fall is $10m{s}^{-2}$ the field required to keep the sphere stationary is

The minimum distance between an object and its real image formed by a thin convex lens of focal length f is Kf. Find the value of K.

A uniform chain of mass 6 kg and length 10 m is placed on a frictionless horizontal table. Due to a small jerk, chain starts to slide down from edge of table. Find the speed of chain when chain is slips off completely. [Height of table is greater than 10m]

A disc of mass m and charge Q is rotating with angular velocity $\omega$ about its own axis as shown in the region of magnetic field B which is directed upwards in the plane of disc. The magnetic force experienced by disc is

An $n–p–n$ transistor circuit has $\alpha =0.985$. If Collector current $I_c=2mA$, then value of base current $I_b$ is____.

A player catches a ball of mass $150\text{gm}$ moving at a speed of $20\text{m/s}$. If the process of catching has to be completed in $0.1\text{sec}$, what is magnitude of the impulsive force imparted by the ball to the hands of the player?

Trajectories are shown in figure for three footballs. Initially vertical and horizontal velocity components are $u_y$ and $u_x$ respectively. Ignoring air resistance, choose the correct statements from List-II for the value of variable in List-I

$\begin{array}{cccc}& \text{List-I}& & \text{List-II}\\ \text{(I)}& \text{Time of flight}& \text{(P)}& \text{greater for A only}\\ \text{(II)}& \frac{u_y}{u_x}& \text{(Q)}& \text{greater for C only}\\ \text{(III)}& u_x& \text{(R)}& \text{Equal for A and B}\\ \text{(IV)}& u_x{u}_y& \text{(S)}& \text{Equal for B and C}\end{array}$

A diffraction pattern is produced by a single slit of width $0.5\text{mm}$ with the help of a convex lens of focal length $40\text{cm}$. If the wavelength of light used is $5896\AA$, then the distance of first dark fringe from the axis will be

A stone that is thrown upwards is caught by the thrower himself after 10 seconds. What is the total distance travelled by the ball? (Neglect air friction and take $g=10m/s^2$)

A $4\text{kg}$ ball moving to the right at $6\text{m/s}$ collides with a $5\text{kg}$ ball ahead of it and moving to the right at speed $2\text{m/s}$ . Find the magnitude of final velocity of the $4\text{kg}$ and $5\text{kg}$ balls respectively, if coefficient of restitution is $0.5$.

Some springs are combined in series and parallel arrangement as shown in the figure and a mass $m$ is suspended from them. The ratio of their frequencies will be

In the following figure the masses of the blocks $A$ and $B$ are the same and each equal to $m$. The tensions in the strings $OA$ and $AB$ are $T_2$ and $T_1$ respectively. The system is in equilibrium with a constant horizontal force $mg$ on $B$. Then $T_2$ is:

The original area of a metal plate is $110{\text{cm}}^2$ at $20{}^{\circ }\text{C}$. If $\beta$ for the metal is $0.000036{/}^{\circ }\text{C},$ then find the area of the plate at ${200}^{\circ }\text{C}$.

Calculate the ratio of the speed of sound in neon to that in water vapour at any given temperature.
[molecular weight of neon $=2.02\times {10}^{-2}\text{kg/mol}$ and of water vapour $=1.8\times {10}^{-2}\text{kg/mol}$. Given that water vapour is triatomic]

A riffle of mass $25\text{kg}$ fires at the rate of 6 bullets per second. If the mass of each bullet is $30\text{g}$ and the velocity of the bullet when it leaves the gun is $1080\text{km/h}$, find the magnitude of average force required to hold the gun while firing (neglect recoil speed of riffle).

Two cars $A$ and $B$ move on a straight road with constant velocity. When they move in same direction, they come close by $8\text{m}$ in $10\text{s}$ and when they move in opposite direction towards each other, they come close by $20\text{m in 1 s}$. The speed of the cars A and B (in $m/s$) respectively are

An electron and proton are accelerated through the same potential. Which one of the two has a greater value of de-Broglie wavelength associated with it and less momentum?

Two miscible fluids of densities 1.2 gm/cm³ and 1.4 gm/cm³ are mixed with a proportion of their volumes equal to 3:5. Assuming both fluids to be perfectly miscible, what is the density of resulting liquid?

If a change in current of 0.01 A in one coil produces a change in magnetic flux of $2\times {10}^{-2}$ Wb in the other coil, then the mutual inductance (in henry) of the two coils is

A typical dorm room or bedroom contains about 2500 moles of air. Find the change in the internal energy of this much air when it is cooled from ${35.0}^{\circ }C$ to ${26.0}^{\circ }C$ at a constant pressure of 1.00 atm. Treat the air as an ideal gas with $\gamma =1.400$.

Find the integral of the given function w.r.t x

$y=cos(8x+6)+cose{c}^2(7x+5)+6secxtanx$

A saturn year is 29.5 times the earth's year. How far is the saturn from the sun if the earth is 1.50*10^8 km away from the sun?

A body starts from rest under constant acceleration and let $S_1$ be the displacement in the first $(p-1)$ seconds and $S_2$ be the displacement in the first $p$ seconds. The displacement in $(p^2-p+1{)}^{th}$ second will be

Block B has a mass m and is released from rest when it is on top of wedge A, which has a mass 3 m. Determine the tension in cord CD needed to hold the wedge from moving while B is sliding down A. Neglect friction

If an antenna radiates electromagnetic waves from a height h, then the range d upto which the signal can be detected is given by ( R is the radius of the earth)

A stone is projected from the ground with a velocity of 25 m/s. Two seconds later, it just clears a pole of 5m height. The angle of projection is

A small mass starts sliding down a fixed inclined plane of inclination ${45}^{\circ }$ with the horizontal. The coefficient of friction is $\mu ={\mu }_{0}x$ where $x$ is the distance through which the mass slides down and ${\mu }_0$ is a constant. Find the heat produced during half the distance travelled by the particle before it stops.

From above fromula we can say, magnetic field due to a current carrying toroidal solenoid is independent of its radius.The magnetic field at the ends of a solenoid is

Who among the following sits exactly between G and C?

Graph between log $\frac{X}{m}$ and log P is a straight line inclined at an angle $\theta ={45}^{\circ }$. When pressure is 0.5 atm and log k = 0.699, the amount of solute adsorbed per g of adsorbent will be:

A particle is resting on a smooth horizontal floor. At $t=0$, a horizontal force starts acting on it. Magnitude of the force increases with time according to law $F=\alpha t$, where $\alpha$ is a constant. For the figure shown which of the following statement is wrong?

A bar marget is demagnetized by placing it inside a solenoid of length $20cm$, $500$ turns & carrying current of $4.8A$. The coercivity of bar magnet material is

How energy and pressure have the same dimension?

Torques of equal magnitude are applied to a hollow cylinder and a solid sphere, both having the same mass and radius. The cylinder is free to rotate about its standard axis of symmetry, and the sphere is free to rotate about an axis passing through its centre. Which of the two will acquire a greater angular speed after a given time?

The work done per unit volume to stretch the length of area of cross-section $2{\text{mm}}^2$ by $2\%$ will be
Take the young's modulus of material as $[Y=8\times {10}^{10}{\text{N/m}}^2]$

If the sum of two unit vectors is a unit vector, then magnitude of difference is

In an experiment on photo electric effect, light of wavelength 400 nm is incident on a cesium plate at the rate of 5.0 W. The potential of the collector plate is made sufficiently positive with respect to the emitter so that the current reaches its saturation value. Assuming that on the average one out of every ${10}^6$ photons is able to eject a photo electron, find the photo current in the circuit.

A projectile is projected with velocity of 50m/s at an angle of 60^° with the horizontal from the ground. The time after which is velocity will make an angle of 45^° with the horizontal is

1)2.5s

2)1.83s

3)2.37s

4)3.72s

Two particles of masses $m_1$ & $m_2$ and velocities $u_1$ and $\left(\alpha u_1\right)(\alpha \ne 0)$ make an elastic head on collision. If the initial kinetic energies of the two particles are equal and $m_1$ comes to rest after collision, then