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In an $LC$ circuit, $L=40\text{mH}$ and $C=100$$\mu F$. If a voltage $V\left(t\right)=10\sin \left(314t\right)$ is applied across the circuit, the current flowing through it is given as:

How
much charge is required for the following reductions:

(i)
1 mol of Al³⁺
to Al.

(ii)
1 mol of Cu²⁺
to Cu.

(iii)
1 mol of

to Mn²⁺.

A particle of mass 0.01 kg travels along a curve with velocity given by $4\hat{i}+16\hat{k}m{s}^{-1}$. After some time, its velocity becomes $8\hat{i}+20\hat{j}m{s}^{-1}$ due to the action of a conservative force. The work done on particle during this interval of time is

An electric field of magnitude $1000\text{N/C}$ is produced between two parallel plates having a separation of $2.0\text{cm}$ as shown in figure. With what minimum speed should an electron be projected from the lower plate in the direction of the field so that it may just reach the upper plate ?

(Assume gravity free space)

(Charge on electron is $-1.6\times {10}^{-19}\text{C}$ and mass of electron is $9.1\times {10}^{-31}\text{kg}$)

A river flows $3{\text{km h}}^{-1}$ and a man is capable of swimming $2{\text{km h}}^{-1}$. He wishes to cross it such that displacement parallel to river is minimum. In which direction will he swim?

The image of the moon is focused by a converging lens of focal length $50\text{cm}$ on a plane screen. The image is seen by an unaided eye from a distance of $2.5\text{cm}$. Find the angular magnification achieved due to the converging lens.

A truck travelled the first one-third of the distance $d$ at a speed of $10{\text{kmh}}^{-1}$, the second one-third of the distance at a speed of $12{\text{kmh}}^{-1}$ and the last one-third of the distance at a speed of $20{\text{kmh}}^{-1}$. The average speed of the truck is approximately equal to (in ${\text{kmh}}^{-1}$)

A solenoid of length $1\text{m}$ with $100$ turns per unit length having area of the loop $1{\text{cm}}^2$ is kept in an external magnetic field of $1\text{T}$ as shown in the figure. If $100\text{mJ}$ of work has to be done to rotate the magnet by ${90}^{\circ }$ in anti-clockwise, then how much current must be flowing through the solenoid ?

A copper disc of radius 0.1 m rotates about its centre with 10 revolutions per second in a uniform magnetic field of 0.1 Tesla. The emf induced across the radius of the disc is

If the operating potential in an X-ray tube is increased by 1 %, by what percentage does the cutoff wavelength decrease ?

The resultant of two vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ is perpendicular to $\overrightarrow{A}$. Magnitude of resultant $\overrightarrow{R}$ is equal to $\frac{\sqrt{3}}{2}$ times of the magnitude of $\overrightarrow{B}$. Find the angle between $\overrightarrow{A}$ and $\overrightarrow{B}.$

Two solids A and B of mass $1\text{k}g$ and $2\text{k}g$ respectively are moving with equal linear momentum. The ratio of their kinetic energies $(K.E.{)}_{\text{A}}$ : $(K.E.{)}_{\text{B}}$ will be $\frac{A}{1}$. So the value of $A$ will be .

A stone is thrown at an angle $\theta$ to the horizontal reaches a maximum height $H$, then the time of flight of stone will be

A particle of charge $-q$ and mass $m$ moves in a circle of radius $r$ around an infinitely long line charge of linear charge density $+\lambda$. The speed of particle is

If an alternating voltage is given by the equation, $E=500\sin \left(100\pi t\right)\text{V}$, then calculate the time taken to reach from zero $($at $t=0)$ to its first maximum value.

Maximum value of electric field at a point at a distance of 2 m from the light source of power 60 watt is

Abhishek decides he knows enough about how stuff works to fix his TV. He then proceeds to turn the switch on and put his finger in the socket. Before the resulting electric shock causes any serious consequential damage, Himanshu decides to violently smash Abhishek’s hand away to save his life. Which of the following objects must he use to ensure he doesn't put himself in any kind of danger while maximizing Abhishek's chances of surviving?

Find the net angle of deviation produced by the system of a prism and a plane mirror as shown in the figure. The prism being very thin has a refracting angle of $4^{\circ }$ and the incident ray is parallel to the base of the prism as shown in the figure below.

A triangle is constructed using the wires $AB,BC\&CA$ of same material and of resistance $\alpha ,2\alpha$ & 3$\alpha$ respectively. Another wire of resistance $\alpha /3$ from $A$ can make a sliding contact with wire $BC$. Find the maximum resistance of the network between point $A$ and the point of contact of the sliding wire with $BC$.

The current through the coil of the ammeter is (Coil resistance: 1k$\Omega$, shunt resistance: 1$\Omega$, incoming current: 1A).

A system consists of three masses $m_1,m_2$ and $m_3$ connected by a string passing over a pulley $P$. The mass $m_1$ hangs freely and $m_2$ and $m_3$ are on a rough horizontal table (the coefficient of friction $=\mu$). The pulley is frictionless and of negligible mass. The downward acceleration of mass $m_1$ is (Assume $m_1=m_2=m_3=m$)

Considering an ideal refrigerator, heat from its inside at a temperature of $277\text{K}$ is transferred to a room at temperature of $300\text{K}$. Find the amount of heat extracted for each Joule of electrical energy consumed by refrigerator.

A body is having a charge of 10 C. When it comes in contact with an charged body then it loses-1.6C of charge. Find the number of electrons lost.

If in a photoelectric experiment, the wavelength of incident radiation is reduced from 6000 $A^{\circ }$ to 4000 $A^{\circ }$ then