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If the amplitude of velocity of a particle acted by a force
$F=F_{0}cos\omega t$ along x-axis is given by
$v_0=\frac{1}{(a{\omega }^2-b\omega +c{)}^{\frac{1}{2}}},where{b}^2>4ac$
The frequency of resonance is :

The phenomenon of flow of solvent molecules through a semi permeable membrane from pure solvent to solution is called

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A galvanometer gives full scale deflection of $1\text{volt}$ when acting like a voltmeter when connected in series with $2\text{k}$$\Omega$ resistance. The same galvanometer gives $500\text{mA}$ full scale deflection when acting like a ammeter when connected with shunt resistance of value $0.2\Omega$ in parallel. Find out the resistance of galvanometer (in $\Omega$).

Some parameters are given in Column - I which are to be matched with their correct answers given in Column - II.
Choose the correct option.
$\begin{array}{cccc}& \text{Column I}& & \text{Column II}\\ \text{a)}& \text{Velocity at}t=0\text{of a particle following}& \text{p)}& \alpha \\ & \text{equation}x=u(t-8)+\alpha (t-2{)}^2& & \\ \text{b)}& \text{Acceleration of a particle moving according to equation}& \text{q)}& 2\alpha \\ & x=4(t-5)+\alpha (t-2{)}^2\text{at}t=0& & \\ \text{c)}& \text{Velocity of the particle moving according to equation}& \text{r)}& u\\ & x=ut+5\alpha t^{2}ln(1+\frac{t}{2})+\alpha t^2\text{at}t=0& & \\ \text{d)}& \text{Acceleration of the particle moving according to the equation}& \text{s)}& u-4\alpha \\ & x=ut+5\alpha t^{2}ln(1+\frac{t}{2})+\alpha t^2\text{at}t=0& & \end{array}$

The work done in moving a positive test charge q_o from infinity to a point P at a distance r from the charge q is

😢😢 how some amount of energy released in the conversion

K to k negatively charge

The $K_{\alpha }$ X-ray emission line of tungsten occurs at $\lambda =0.021$ nm. The energy difference between K and L levels in this atom is about

At a certain point on a screen in a YDSE apparatus, the path difference for the two interfering waves is ${\left(\frac{1}{3}\right)}^{rd}$ of the wavelength. Find the ratio of the intensity at this point to that at the centre of a bright fringe.

It is desirable that the standards of units be easily available, invariable, indestructible and easily reproducible. If we use foot of a person as a standard unit of length, which of the above features are not present?

The reflecting surface of two mirrors make an angle of 90° with each other. If a ray incident of one mirror has an angle of incidents of 30°, draw the ray reflected from the second mirror. What will be its angle of reflection?

A coil has an inductance of $0.7\text{H}$ and is connected in series with a resistor of resistance $220\Omega$. When an alternating emf of $220\text{V}$ at $50\text{cycles/s}$ is applied to it, the wattless component of the current in the circuit is equal to

Derivative of $f\left(x\right)=\sin (x^3+2x+1)$ is

Which of the following relationships is valid only for reversible processes undergone by a closed system of simple compressible substance (neglect changes in kinetic and potential energy)?

A uniform plank of mass $m=1\text{kg}$ and of sufficient length , which is free to move only in the horizontal direction is placed upon the top of a solid cylinder of mass $2m$ and radius $R$. The plank is attached to a fixed wall by means of a light spring of spring constant $k=7\text{N/m}$. Assuming , there is no slipping between cylinder and the plane system, and between cylinder and the ground. Find the Angular frequency of small oscillations of the system.

The internal energy of a gas is given by $U=(2PV+20)\text{J}$. It expands from $100{\text{cm}}^3$ to $200{\text{cm}}^3$ against a constant pressure of $200\text{kPa}$. Calculate the heat absorbed by the gas in the process.

Find the ratio of the lengths of an iron rod and an aluminium rod for which the difference in the lengths is independent of temperature. Coefficients of linear expansion of iron and aluminium are $12\times {10}^{-6}{}^{\circ }{C}^{-1}$ and $23\times {10}^{-6}{}^{\circ }{C}^{-1}$ respectively.

A particle moving in a circle of radius $R$ with a uniform speed takes a time $T$ to complete one revolution. If this particle were projected with the same speed at an angle $\theta$ to the horizontal, the maximum height attained by it is $4R$. The angle of projection, $\theta$ is then given by :

From the displacement time graph of a particle executing SHM, find the maximum velocity of the particle.

Q42) Which of the following cannot be seated at either end?

A power $P=2t^3$ is applied to the particle initially at rest. If the kinetic energy of the particle is $K$ and velocity is $v$ then

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A source of sound and a detector are placed at the same place on ground. At $t=0$ , the source $S$ is projected towards reflector with velocity $v_0$ in vertical upward direction and reflector starts moving down with constant velocity $v_0$. At $t=0$ , the vertical separation between the reflector and source is $H(>\frac{v_0^2}{2g})$. The speed of sound in air is $v(>>v_0)$. Take $f_0$ as the frequency of sound waves emitted by source. Find the frequency of sound received by detector after being reflected by reflector at $t=\frac{v_0}{2g}$.

Find the acceleration (in $m/s^2$) of the body of mass $20kg$ shown in the figure. Take $g=10m/s^2$.

A person is standing at a distance d from a thick plane mirror of thickness t and glass of refractive index $\mu$ as shown in figure. Person will see his image at distance $x$ from him, then $x$ is

When an object is dropped from a height, it accelerates and falls down. The force which accelerates the object is

A particle in a certain consevative force field has a potential energy given by $U=\frac{20xy}{z}$. The force exerted on it is

A capacitor of capacitance C is connected to a battery of emf $\epsilon$ at t = 0 through a resistance R. Find the maximum rate at which energy is stored in the capacitor. When does the rate has this maximum value ?

Temperature of a body is slightly more than the temperature of the surrounding ₀. Its rate of cooling (R) versus temperature of body() is plotted. Its shape would be