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In a YDSE performed with wavelength $\lambda =5890\dot{A}$, the angular fringe width is ${0.40}^{\circ }$. What is the angular fringe width if the entire set - up is immersed in water ? $(\mu =\frac{4}{3})$

Two sinusoidal waves produced by two vibrating sources $A$ and $B$ of equal frequencies, are propagating to the point $P$ along a straight line. The amplitude of every wave at $P$ is ${}^{\prime }{a}^{\prime }$ and the phase of $A$ is ahead by $\frac{\pi }{3}$ than that of $B$. The distance $AP$ is greater than $BP$ by $50\text{cm}$. If the wavelength is $1\text{m},$ then the resultant amplitude at the point $P$ will be

Two rectangular blocks, having identical dimensions, can be arranged either in configuration I or II as shown in the figure. One of the blocks has thermal conductivity $K$ and the other, $2K$. The temperature difference between the ends along the $x$-axis is the same in both the configuarations. It takes $9\text{s}$ to transport a certain amount of heat from the hot end to the cold end in configuration I. The time to transport the same amount of heat in the configuration II is:-

An isolated particle of mass $m$ is moving in horizontal plane $x-y$, along the x-axis, at a certain height above ground. It suddenly explodes into two fragments of masses $\frac{m}{4}$ and $\frac{3m}{4}$ . An instant later, the smaller fragment is at $y=+15\text{cm}$. The larger fragment at this instant is at

Find the torque by the force, $\overrightarrow{F}=2\hat{i}+3\hat{j}+5\hat{k}$ acting at the point $\overrightarrow{r_1}=5\hat{i}+2\hat{j}-\hat{k}$ about the point $\overrightarrow{r_2}=6\hat{i}-4\hat{j}+\hat{k}$.

A pendulum bob has a speed $3\text{m/s}$ while passing through its lowest position . The length of the pendulum is $0.5\text{m}$. The speed of the bob when it makes an angle of ${60}^{\circ }$ with the vertical is (Take $g=10\text{m}/s^2$)

An isosceles right angled triangle of side $5\text{cm}$ is cut from a circular disc of radius $5\text{cm}$ as shown in the figure. What will be the coordinates of the centre of mass of the remaining disc? Origin is taken at the centre of the circular disc. Consider the material to be of uniform density.

The condition such that the potential difference, $V_A-V_B=0$ is.

An electromagnetic wave of frequency v = 3 MHz passes from vacuum into dielectric medium with permittivity $ϵ=4.0$ Then

An ideal gas has a molar heat capacity at constant volume $C_V$. Find the molar heat capacity of this gas as a function of its volume $V$, if it undergoes a process $T=T_o{e}^{\alpha V^2}$, where $T_o$ and $\alpha$ are constants.

In the figure shown, find the tension $T_1$ in the string. Take $g=10m/s^2$

The rms value of the electric field of the light coming from sun is 720 N/C. The average energy density of the EM wave is

Which of the following is/are a valid configuration for an electric field?

flux only for an area

Statement 1: The flux of a point charge ‘q’ located at origin, is positive through a point p (1, 2, 4)

Statement 2: The flux of a point charge ‘q’ located at origin is negative through a point P (1,2,4)

Magnetic field inside long solenoid changes from $2\times {10}^{-3}T$ to $1T$ when it is filled with some ferromagnetic material. Susceptibility of this material is

In a forward biased $\mathrm{p-}n$ junction diode, the potential barrier in the depletion region is of the form

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

$y=e^{2x}+\frac{1}{x^2}$

Which of the options is correct if the degree of dissociation of A and A' are $\alpha$ and ${\alpha }^{{}^{\prime }}$ respectively ($P^{{}^{\prime }}$=partial pressure at equilibrium) ?
$A\left(s\right)\rightleftharpoons 2B\left(g\right)+C\left(g\right)$; $K_{P_1}=8\times {10}^{-2}$
$A^{{}^{\prime }}\left(s\right)\rightleftharpoons 2B\left(g\right)+D\left(g\right)$; $K_{P_2}=2\times {10}^{-2}$

In the arrangements shown in figure,masses of each ball are 1 kg and mass of trolley is 4 kg. In the figure shell of mass 1 kg moving horizontally with velocity v = 6 m/sec collides with the ball and get stuck to it .It's maximum deflection of the thread (length 1.5 m) with vertical is:

Vector A has magnitude of 3 units and makes an angle of ${30}^{\circ }$ with the positive x-axis.

Vector B has magnitude of 4 units and makes an angle of ${120}^{\circ }$ with the positive x-axis.

Find the magnitude of the resultant and the angle that it makes with the positive x-axis.

$\left[ta{n}^{-1}\right(\frac{4}{3})={53}^{\circ }]$

The wavelength of a red night lamp that I use in my house (not that I am scared of monsters under my bed, it is just a habit) is 700 nm. Find the energy contained in each photon of light.

What is the acceleration of the ball at the highest point?

A wooden block of 100 kg is about to be published on a floor of coefficient of friction 0.4. What is the magnitude of force of friction on wooden block when it is just pushed?

Illustration: The mass of a box is 2.3 kg. Two marbles of masses 2.15 g and 12.39 g are added to it. Find the total mass of the box to the correct number of significant figures.

What is N capright hand thumb rule

A battery of 15V and of negligible internal resistance is connected to a rheostat XZ of 1 $k\Omega$. The resistance of YZ part is $500\Omega$. The reading of the ammeter will be

A particle moves in a circular path of radius R with an angular velocity $\omega =a–bt$ where a and b are positive constants and t is time. The magnitude of the acceleration of the particle after time $\frac{2a}{b}$ is

The wavelength of the $K_{\alpha }$ line for an element of atomic number 57 is $\lambda$. The wavelength of the
$K_{\alpha }$ line for the element of atomic number 29 is…

In the figure shown, there is no relative motion between the two blocks. Force of friction acting on 1 kg block is

A beam of light is incident on a glass plate at an angle of incidence ${60}^{\circ }$. The reflected ray is polarized. The angle of refraction when the angle of incidence is ${45}^{\circ }$ is

In a photoelectric experiment, the potential difference V that must be maintained between the illuminated surface and the collector so as just prevent any electron from reaching the collector is determined at different frequencies f of the incident illumination. Graph obtained is shown in the figure. The maximum KE of the electrons emitted at frequency $f_1$ is

Two wires are made of the same material and have the same volume. However, wire $1$ has cross - sectional area $A$ and wire-$2$ has cross - sectional area $3A$. If the length of wire $1$ increases by $\Delta x$ on applying force $F$, how much force is needed to stretch wire $2$ by the same amount?

An AC voltage source of variable angular frequency $\omega$ and fixed amplitude V connected in series with a capacitance C and an electric bulb of resistance R (inductance zero). When $\omega$ is increased

According to Joule's law of heating, the heat produced is given by $H=I^{2}Rt,$ where $I$ is current, $R$ is resistance and $t$ is the time. If the errors in the measurement of $I,R$ and $t$ are $3\%$, $4\%$ and $6\%$ respectively, then the error in measurement of $H$ is:

The driver of a train moving with a constant velocity v_{​​​​​1} along a straing track sights another train at a distance d ahrad of him on the same track moving in a same direction with a constant speed V2. He at once applies a brakes and gives his train a constant retardation f. There will be a collosioc of yhe trains if......?

a) v1 > V2 amd (V1 -V2)² /2f < d

b) V1<V2 and (V1+V2)² /2f > d

c) V1 > V2 and ( V1-V2)² /2f > d

d) V1>V2 and (V1^{​​​​​2} - V2^{​​​​​2}​​​​)/2f > d

Two masses $m_1=5kg$ and $m_2=10kg$ connected by an inextensible string over a frictionless pulley, as shown in the figure are moving . The coefficient of friction of horizontal surface is $0.15$. The minimum weight $m$ that should be put on top of $m_2$ to stop the motion is

A bullet of mass $20\text{g}$ strikes a block of mass $180\text{g}$. The bullet remains embedded in the block. Find the amplitude of the resulting SHM (all surfaces are fricitonless]

A block of mass $10\text{kg}$ is kept on a rough inclined plane of inclination ${45}^{\circ }$. A force of $3\text{N}$ is applied on the block down the incline. The coefficient of static friction between the plane and the block is $0.6$. What should be the minimum value of force $F$, such that the block does not move downward? (Take $g=10{\text{ms}}^{-2}$)

Raw and boiled eggs are made to spin on a smooth table by applying the same torque. The egg that spin faster is

A charge q is placed at the center of a cube of side l. What is the electric flux passing through two opposite faces of the cube?

A particle placed on top of a smooth sphere of radius $2\text{m}$ slides through a distance of $\frac{\pi }{3}\text{m}$ and falls off the sphere. What is the velocity of the particle when it is about to drop off the surface of the sphere?

What is permittivity

When temperature of an ideal gas is increased from ${27}^{\circ }\text{C}$ to ${227}^{\circ }\text{C}$ keeping its mass and pressure constant, then volume of the gas will be increased by

Evaluate:
${\log }_{2}8+{\log }_{5}25$