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If $\begin{array}{c}\sin ({\sin }^{-1}\frac{1}{5}+{\cos }^{-1}x)=1\end{array}$, then $x$ is equal to

Difference between -

'Charge is CONSERVED'' and 'Charge is QUANTIZED'.

A plane electromagnetic wave having a frequency $\nu =23.9\text{GHz}$ propagates along the positive z-direction in free space. The peak value of the Electric Field is $60\text{V/m}$. Which among the following is the acceptable magnetic field component in the electromagnetic wave ?

Three identical cars A, B and C are moving at the same speed on three bridges. The car A goes on a plane bridge, B on a bridge convex upward and C goes on a bridge concave upward. Let $F_A,F_{B}and{F}_C$ be the normal forces exerted by the cars on the bridges when they are at the middle of bridges.

A wire carrying a current of $3\text{A}$ is bent in the form of a parabola $y^2=4-x$ as shown in figure, where $x$ and $y$ are in metre. The wire is placed in a uniform magnetic field $\overrightarrow{B}=5\hat{k}\text{T}$. The magnetic force acting on the wire is:

If a particle is moving from its initial position $x=-5\text{m}$ to a position $x=-11\text{m}$ in $2\text{s}$ along a straight line. What will be the average velocity of particle ?

A disc of radius $r$ has linear velocity $V$ and angular velocity $\omega$ as shown in figure. If point $B$ is at a distance $\frac{r}{2}$ from centre, then find the velocity of point $A$ w.r.t point $B$ $\left({\overrightarrow{V}}_{AB}\right)$.

Velocity-time graph for a body of mass $10\text{kg}$ is shown in figure. Work done on the body in the first two seconds of motion is

Suppose the rod in the previous problem has a mass of 1 kg distributed uniformly over its length.

(a) Find the initial angular acceleration of the rod.

(b) Find the tension in the supports to the blocks of mass 2 kg and 5 kg.

An ideal gas is expanding such that $P{T}^2=constant$. The coefficient volume expansion of the gas is

1. 0

A long insulated copper wire is closely wound as a spiral of $10$ turns, the spiral has inner radius $20\text{cm}$ & outer radius $25\text{cm}$. The spiral lies in the $xy-$ plane, & a steady current $2\text{A}$ flows through the wire. The $z-$component of the magnetic field at the centre of the spiral is

(Take $\ln \left(1.25\right)=0.223$)

Two strings are attached to each other as shown in the figure. The linear mass density of the second string is $16$ times that of the first string and the boundary between the two strings is at $x=0$. The incident wave is given by $y=0.01\cos (20x-100t)$. Then, the ratio of amplitude of reflected wave to amplitude of transmitted wave is:
[Assume, tension in both the strings is same]

In a series LCR circuit $V_{L=}{V}_C\ne V_R$.What is the value of power factor?

A point source of light is used in a photoelectric effect. If the source is removed farther from the emitting metal, the stopping potential.

A trolley ($100\text{kg}$) moving forward with acceleration of $1{\text{m/s}}^2$ has block of $1\text{kg}$ mass present on its floor. Find pseudo force acting on block ${}^{\prime }{A}^{\prime }$ with respect to a reference frame attached to trolley

Radiation of wavelength, ${}^{\prime }{\lambda }^{\prime }$ is incident on a photocell. The fastest emitted electron has speed ‘u’. If the wavelength is changed to $\frac{3\lambda }{4}$, the speed of the fastest emitted electron will be

The refracting angle of a prism is $A$, and refractive index of the material of the prism is $\cot \left(A/2\right)$. The angle of minimum deviation is

The height of Mercury column in a simple barometer is h as the tube is inclined with the vertical at an angle a. Find the length L of the mercury column along the length of the tube.

Figure shows a particle starting from point A, travelling upto B with a speed $s$, then upto point C with a speed $2s$ and finally upto A with a speed of $3s$. Find its average speed.

In Fraunhofer diffraction, at the angular position of first diffraction, minimum phase difference (in radian) between wavelengths from the opposite edges of the slit is,

A
straight horizontal conducting rod of length 0.45 m and mass 60 g is
suspended by two vertical wires at its ends. A current of 5.0 A is
set up in the rod through the wires.

(a)
What magnetic field should be set up normal to the conductor in
order that the tension in the wires is zero?

(b)
What will be the total tension in the wires if the direction of
current is reversed keeping the magnetic field same as before?
(Ignore the mass of the wires.) g = 9.8 m s⁻².

Consider two point charges, $\frac{q}{3}$ and $-\frac{2q}{3}$ at point $\text{A}$ and $\text{C}$ respectively as shown in the figure. Take $O$ to be the centre of the circle of radius $R$ and $\angle CAB={60}^{\circ }$. The magnitude of force between the charges is

Prove that NA of fibre does not depend upon the dimension of fibre.

What is the conductivity of a semiconductor (in ${\Omega }^{-1}{\text{m}}^{-1}$) if electron density $5\times {10}^{12}{\text{cm}}^{-3}$ and hole density $8\times {10}^{13}{\text{cm}}^{-3}$

$[{\mu }_e=2.3{\text{m}}^2{\text{V}}^{-1}{\text{s}}^{-1}\text{and}{\mu }_h=0.01{\text{m}}^2{\text{V}}^{-1}{\text{s}}^{-1}]$

When a wave travels in a medium, the particle displacement is given by $y=a\sin 2\pi (bt-cx),$ where $a,b$ and $c$ are constants. The maximum particle velocity will be twice the wave velocity if