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The equation of a transverse wave on a stretched string is given by $y=0.05\sin 2\pi (\frac{t}{0.002}-\frac{x}{0.1})$, where $x$ and $y$ are expressed in metre and $t$ in second. The speed of the wave is

A tape measures the length of a copper rod as $90\text{cm}$ at ${10}^{\circ }C$. What would the tape read for the length of the rod at ${30}^{\circ }C$?
Given, ${\alpha }_{\text{Cu}}=1.7\times {{10}^{-5}}^{\circ }{C}^{-1}$

A particle executes linear $\text{SHM}$ with a time period of $10\text{s}$. Find the time taken by the particle to go directly from its mean position (at $t=0)$ to $\frac{1}{2}$ of its amplitude.

Is there some way of producing high voltage on your body without getting a shock?

A boat which has a speed of $5\text{km/h}$ in still water crosses a river of width $1\text{km}$ along the shortest possible path in $15\text{min}$. The magnitude of velocity of the river water in $\text{km/h}$ is

A grasshopper can jump a maximum distance $1.6m$. It spends negligible time on the ground. How far can it go in $10s$?
(Take $g=10m/s^2$)

Two discs are rotating about their axes, normal to the plane of the discs and passing through the centre of the discs. Disc $D$ has $2\text{kg}$ mass and $0.2\text{m}$ radius and initial angular velocity of $50\text{rad/s}$. Disc $D_2$ has $4\text{kg}$ mass, $0.1\text{m}$ radius and initial angular velocity of $200\text{rad/s}$. The two discs are brought in contact face to face with their axes of rotation coincident. The final angular velocity (in $\text{rad/s}$) of the system is

If difference of pressure between inside and outside of the spherical drop is $70{\text{N/m}}^2$, then what is the radius of spherical drop ?
Given: Surface tension of water is $70\times {10}^{-3}\text{N/m}$.

For intensity I of a light of wavelength $5000\stackrel{\circ }{A}$ the photoelectron saturation current is 0.40 $\mu A$ and stopping potential is 1.36 V, the work function of metal is

The property of a liquid that increases with a increase in temperature is:

The velocity of heat radiation in vacuum is

The equation of a progressive wave is given by $y=2sin(\pi t–0.5\pi t)$ where x and y are in metre and t is in second. The velocity of the particle at t = 1 second and x = 1 m is

The left block in figure collides in-elastically with the right block and sticks to it. Find the amplitude of the resulting simple harmonic motion.

A cyclotron’s oscillator frequency is 10 MHz. the operating magnetic field for the cyclotron to accelerate the proton is ( mass of proton $=1.67\times {10}^{-27}kg$

One mole of $O_2$ gas having a volume equal to $22.4$ litres at $0^{\circ }C$ and 1 atmospheric pressure is compressed isothermally so that its volume reduces to $11.2$ litres. The work done in this process is

A hot air balloon is rising vertically upwards at a constant velocity of $10{\text{ms}}^{-1}$. When it is at a height of $45\text{m}$ from the ground, a man bails out from it. After $3\text{s}$ he opens his parachute and decelerates at a constant rate of $5{\text{ms}}^{-2}$. After how long does the parachutist takes to hit the ground after his exit from the balloon?

How many different wavelengths may be observed in the spectrum from a hydrogen sample if the atoms are excited to states with principal quantum number $n$ ?

If $y=1/x^4$ then, $\frac{dy}{dx}$ will be

An infinite long straight wire is bent into a semicircle of radius R, as shown in the figure. A current I is sent through the conductor. The magnetic field at the center of the semicircle is:

An aluminium plate fixed in a horizontal position has a hole of diameter 2.000 cm. A steel sphere of diameter 2.005 cm rests on this hole. All the lengths refer to a temperature of ${10}^{\circ }C$. The temperature of the entire system is slowly increased. At what temperature will the ball fall down ? Coefficient of linear expansion of aluminium is $23\times {10}^{-6}{}^{\circ }{C}^{-1}$ and that of steel is $11\times {10}^{-6}{}^{\circ }{C}^{-1}$.

Starting from rest a particle is first accelerated for time $t_1$ with constant acceleration $a_1$ and then stops in time $t_2$ with constant retardation $a_2.$ Let $v_1$ be the average velocity in this case and $s_1$ the total displacement.
In the second case, it is accelerated for the same time $t_1$ with constant acceleration $2a_1$ and comes to rest with constant retardation $a_2$ in time $t_3.$ If $v_2$ is the average velocity in this case and $s_2$ the total displacement, then:

Find the value of m so that the vector 3$\hat{i}-2\hat{j}+\hat{k}$ may be perpendicular to the vector $2\hat{i}+6\hat{j}+m\hat{k}$.

Find all the angles between $0^{\circ }$ and ${360}^{\circ }$, which satisfy the equation $si{n}^2\theta =\frac{3}{4}$. Suppose a student substituted $\theta ={60}^{\circ }$ and checked that it is true. He concluded statement is always true. What type of quality he should acquire to reach at correct result?

A projectile is fired from the surface of earth of radius R with a speed $k{v}_e$ in radially outward direction (where $v_e$ is escape velocity and k < 1). Neglecting air resistance, the maximum height from the centre of the earth is:

A lift of mass 1000kg , which is moving with an acceleration of 1 m/s² in upward direction has tension developed in its string equal to:

An electric charge ${10}^{-3}\mu C$ is placed at the origin (0, 0) of X - Y co-ordinate system. Two points A and B are situated at $(\sqrt{2},\sqrt{2})$ and (2, 0) respectively. The potential difference between the points A and B will be

Figure shows a liquid flowing through a tube at the rate of $0.1m^3/s$. The tube is branched into two semi-circular tubes of cross-sectional area $\frac{A}{3}$ and $\frac{2A}{3}$ of sections P and Q respectively. The velocity of liquid at Q is (the cross section of the main tube is $A={10}^{-2}{m}^2$ and $V_P=20m/s$)

An inductor of inductance L = 400 mH and resistors of resistance $R_1=2\Omega$ and $R_2=2\Omega$ areconnected to a battery of emf 12 V as shown in the figure. Theinternal resistance of the battery is negligible. The switch S is closed at t = 0. The potential drop across L as a function of time is

Two wires having different mass densities are soldered together end to end, then stretched under tension $T$. The wave speed in the first wire is twice that in the second wire and the amplitude of incident wave is $a$. Assuming no energy losses in the wire, find the fraction of the incident power that is reflected.

Two springs A and B have force constants $k_{1}and{k}_2$ respectively. The ratio of the work done on A to that done on B in increasing their length by the same amount is

A battery of internal resistance $4\Omega$ is connected to the network of resistance as shown. In order to deliver the maximum power to the network, the value of R in ohm should be:

A conducting rod of length $l$ falls vertically under gravity in a region of uniform magnetic field $B$. The field vectors are inclined at an angle $\theta$ with the horizontal as shown in figure. If the instantaneous velocity of the rod is $v$, the induced emf in the rod $ab$ is

A straight rope of length 'L' is kept on a frictionless horizontal surface and a force 'F' is applied to one end of the rope in the direction of its length and away from that end. The tension in the rope at a distance 'l' from that end is

Figure shows the temperature variation when heat is added continuously to a specimen of ice $\left(10\text{g}\right)$ at $-{40}^{\circ }\text{C}$ at constant rate. (Specific heat of ice $=0.53{\text{cal/g}}^{\circ }\text{C}$ and $L_{\text{ice}}=80\text{cal/g},L_{\text{water}}=540\text{cal/g)}$

$\begin{array}{cc}\text{Column - I}& \text{Column - II}\\ \left(A\right)\text{Value of}{Q}_1\text{(in cal)}& \left(P\right)800\\ \left(B\right)\text{Value of}{Q}_2\text{(in cal)}& \left(Q\right)1000\\ \left(C\right)\text{Value of}{Q}_3\text{(in cal)}& \left(R\right)5400\\ \left(D\right)\text{Value of}{Q}_4\text{(in cal)}& \left(S\right)212\\ & \left(T\right)900\end{array}$

Please list out all the derivations in Electromagnetic Induction.

A spring balance hanging in steady state inside a train moving on a straight track shows a reading of double the actual mass of an object. Calculate the acceleration of the train.

A solid sphere of mass ‘m’ and radius R rolls on a horizontal rough surface without slipping due to a horizontal force ‘F’ acting at the top of the sphere. Then the frictional force acting between the body and the surface is

Two sources P and Q produces notes of frequency $990\text{Hz}$ each. A listener moves from P to Q with a speed of $1{\text{ms}}^{-1}$. If the speed of sound is $330\text{m/s}$, then the number of beats heard by the listener per second is

Using differentials, find the approximate value of the following up to 3 places of decimal.
$(401{)}^{\frac{1}{2}}$

A closed system receives $200kJ$ of heat at constant volume. It then rejects $100kJ$ of heat while it has $50kJ$ of work done on it at constant pressure. If an adiabatic process can be found which will restore the system to its initial state, the work done by the system during this process is

The acceleration of a car moving in positive $x-$direction with an initial velocity of $6m/s$ is $4m/s^2$. Its velocity at $t=5sec$ is

As shown in the figure, pressure acting on the two limbs of a $U-$tube are $P\&P_0$ respectively. Then, identify the correct relation between $P\&P_0$:

What is acceleration due to gravity?