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A monochromatic beam of light falls on YDSE apparatus at some angle (say $\theta$ ) as shown in the figure. A thin sheet of glass is inserted in front of the lower slit $S_2.$ The central bright fringe (path difference $=0$) will be obtained is-

The blocks $B$ and $C$ in the figure have mass $m$ each. The strings $AB$ and $BC$ are light, having tensions $T_1$ and $T_2$ respectively. The system is in equilibrium with a constant horizontal force $mg$ acting on $C$. Then

A body dropped from the top of a tower covers the distance $7x$ in the last second of its journey, where $x$ is the distance covered in $1\text{st}$ sec. How much time does it take to reach the ground ?

Three conducting spherical shells have charges $q,-2q$ and $3q$ as shown in figure. Electric potential at point $\text{P}$ is

$\overrightarrow{F}=3\hat{i}+6\hat{j}-8\hat{k}$

$\overrightarrow{s}=-2\hat{i}+5\hat{j}+2\hat{k}$

If W =$\overrightarrow{F}.\overrightarrow{s}$ find W.

A coil of inductance $5\text{mH}$ and negligible resistance is connected to an oscillator giving an output voltage $E=10\sin \omega t$. The peak currents in the circuit for $\omega =10{\text{s}}^{-1},$$100{\text{s}}^{-1}$ and $500{\text{s}}^{-1}$ are $I_1,I_2$ and $I_3$ respectively. Then the ratio $I_1:I_2:I_3$ is:

The velocity – time graph of a stone thrown vertically upward with an initial velocity of $30{\text{ms}}^{-1}$ is shown in the figure below. The velocity in the upward direction is taken as positive and that in downward direction as negative. What is the maximum height to which the stone rises?

When light falls on a photo diode, its conductivity increases. Experimentally, it is found that the conductivity changes only when the wavelength of the incident light is less than $620\text{nm}$. The band gap of the diode is-

A charge of $10\mu C$ is distributed uniformly over the circumference of a ring of radius $3\text{m}$ placed on the $x-y$ plane with the axis at origin. Find electric potential at point $P(0,0,4\text{m})$

A tumbler, made purely of iron, can be filled with 500 ml ($\sim 500c{m}^3$) of water during a spring temperature of ${20}^{\circ }C$. How much water (in volume) can you store in the tumbler in autumn, if the temperature drops to $8^{\circ }C$? ($\gamma Fe$ = $33.3$${/}^{\circ }C$).

A ball is rotating in circle of radius $r$ with constant speed $u\text{m/s}$ as shown in figure. When ball is at point $a$, find the magnitude of torque acting on ball about point $b$.

The position of a particles varies with time as $\overrightarrow{r}=\alpha t^2\hat{i}-\beta t\hat{j}$ where $\alpha =10m{s}^{-2}$ and $\beta =5m{s}^{-1}$. The torque acting on the particle at t = 1s in N m is: (mass of the particle m = 0.1 kg)

A food packet is dropped from a plane going at an altitude of 100 m. What is the path of the packet as seen from the plane?

If $\int \frac{3\cos x+2\sin x}{4\sin x+5\cos x}dx=ax+b\ln |4\sin x+5\cos x|+C$, then which of the following is/are correct?

(where $a,b$ are fixed constants and $C$ is integration constant)

Ten charges are placed on the circumference of a circle of radius $R$ with constant angular separation between successive charges. Alternate charges $1,3,5,7,9$ have charge $(+q)$ each, while $2,4,6,8,10$ have charge $(-q)$ each. The potential $V$ and the electric field $E$ at the centre of the circle are respectively :

(Take $V=0$ at infinity)

The coercivity of a magnet is $3\times {10}^3{\text{Am}}^{-1}$. What current should be passed through a solenoid, of length $10\text{cm}$ and number of turns $50$, so that the magnet is completely demagnetized, when inserted in it ?

A mixture of ideal gases has 2 moles of Helium, 4 moles of Oxygen and 1 mole of Ozone at absolute temperature $T$. The internal energy of mixture is

An ideal horizontal flow settling basin is 3 m deep having surface area 900 $m^2$. Water flows at the rate of 8000 $m^3/d$, at water temperature ${20}^{\circ }C(m={10}^{-3}kg/m.sand\rho =1000kg/m^3)$ . Assuming Stoke's law to be valid, the proportion (percentage) of spherical sand particles (0.01 mm in diameter with specific gravity 2.65), that will be removed, is

A stone is dropped into a well in which the level of water is $h$ below the top of the well. If $v$ is speed of sound in the air, the time $T$ after which the splash is heard is given by

What is the angle between $\overrightarrow{P}$ and the resultant of $(\overrightarrow{P}+\overrightarrow{Q})$ and $(\overrightarrow{P}-\overrightarrow{Q})$

The work done in placing a charge of $8\times {10}^{-18}$ coulomb on a condenser of capacity 100 micro-Farad is:

[AIEEE-2003]

Five persons $A,B,C,D$ and $E$ are pulling a cart of mass $100\text{kg}$ on a smooth surface and cart is moving with acceleration $3{\text{m/s}}^2$ in east direction. When person $A$ stops pulling, it moves with acceleration $1{\text{m/s}}^2$ in the west direction. When person $B$ stops pulling, it moves with acceleration $24{\text{m/s}}^2$ in the north direction. The magnitude of acceleration of the cart when only $A$ and $B$ pull the cart keeping their directions same as the old directions, is

A hollow disk of inner radius R and outer radius 2R is uniformly charged to charge Q and is rotating at angular velocity $\omega$ as shown in figure. Magnitude of magnetic dipole moment is

A bob of mass ${}^{\prime }{m}^{\prime }$ is attached to ceiling of a lift with the help of string as shown. Calculate tension in string in equilibrium position, when lift is accelerated forward with acceleration ${}^{\prime }{a}^{\prime }$.

The amount of heat require to raise the temperature of mass M of a substance through ∆T is

A convex mirror will form a real image for a virtual object

Calculate the magnetic dipole moment corresp onding to the motion of the electron in the ground state of a hydogen atom.

An electron is projected into a uniform magnetic field of
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$3\text{T}$ and moves along a helical path of radius
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$1\text{cm}$ with pitch $2\pi \text{cm}$. Find the angle of projection of the electron with the magnetic filed.