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In a young's double slit experiment, two narrow vertical slits placed 0.800 mm apart are illuminated by the same source of yelow light of wavelength 589 nm. How far are the adjacent bright bands in the interference pattern observed on a screen 2.00 m away?

Three ammeters $-,1,2$ and $3$ have different internal resistances $r_1,r_2$ and $r_3$ respectively. Internal resistance $r_1$ is known but $r_2$ and $r_3$ are unknown. The angular deflection of pointer in each ammeter is proportional to the current. Initially, the three ammeters were connected in series to a voltage source and deflections for the three ammeters were ${\theta }_1,{\theta }_2$ and ${\theta }_3$ respectively. The three ammeters were then connected in parallel to the same voltage source. This time the deflections were observed to be ${\theta }_1^{\prime },{\theta }_2^{\prime }$ and ${\theta }_3^{\prime }$ respectively. If ${\theta }_2={\theta }_3$ but ${\theta }_3^{\prime }>{\theta }_2^{\prime }$ then

In the adjoining figure, a section of a complicated circuit is shown, in which $E=10\text{V},$ $C_1=2\mu \text{F}$, $C_2=3\mu \text{F}$ and $(V_A-V_B)=10\text{V}.$ The potential on $C_1$ will be

The gravitational potential difference between the surface of a planet and a point 100 m above its surface is $10Jk{g}^{-1}$. If the gravitational field over this range is uniform, then the work done to raise the body of 5 kg from the surface to a height of 40 m is

A marble is to be thrown horizontally from a height of $19.6\text{cm}$ above the ground so that it hits another marble on the ground $2\text{m}$ away. The velocity with which the marble should be thrown is

The least count of the main scale of a vernier callipers is $1\text{mm}$. Its vernier scale is divided into $10$ divisions and coincide with $9$ divisions of the main scale. When jaws are touching each other, the $7^{\text{th}}$ division of vernier scale coincides with a division of main scale and the zero of vernier scale is lying right side of the zero of main scale. When this vernier is used to measure length of a cylinder the zero of the vernier scale between $3.1\text{cm}$ and $3.2\text{cm}$ and $4^{\text{th}}\text{VSD}$ coincides with a main scale division. The length of the cylinder is $(\text{VSD}$ is vernier scale division$)$

A large block of wood of mass $M$ $=5.99\text{kg}$ is hanging from two long massless cords. A bullet of mass $m=10\text{g}$ is fired into the block and gets embedded in it. The (block + bullet) then swing upwards, their centre of mass rising a vertical distance $h=9.8\text{cm}$ before the (block + bullet) pendulum comes momentarily to rest at the end of its arc. The speed of the bullet just before collision is: (take $g=9.8{\text{ms}}^{-2}$)

A uniform magnetic field $\overrightarrow{B}=B_o\hat{k}$ exists in a region . A current carrying wire is placed in $x-y$ plane as shown in the figure. The magnetic force acting on the part $\text{AB}$ of wire is:

A body, constrained to move in Y-direction is subjected to a force F = (– 2i + 15j + 6k)N. What is the work done by this force in moving the body through a distance of 10 m along the Y-axis?

A non-uniform rod $AB$ has a mass $M$ and length $2l$.The mass per unit length of the rod is $mx$ at a point of the rod distant $x$ from $A$. Find the moment of inertia of this rod about an axis perpendicular to the rod through $A$.

If a bar magnet of magnetic moment $M$ is freely suspended in a uniform magnetic field of strength $B$, the work done in rotating the magnet through an angle $\theta$ is

A particle of mass $1\text{g}$ executes an oscillatory motion on the concave surface of a spherical dish placed on a horizontal plane. If the motion of the particle begins from a point on the dish at height $1\text{cm}$ from the horizontal plane and coefficient of friction is $0.01$, find the total distance covered by the particle before it comes to rest (Assume the radius of curvature of the concave surface to be very large).

Sinusoidal carrier voltage of frequency 1.5 $MHz$ and amplitude 50 $V$ is amplitude modulated by sinusoidal voltage of frequency 10 $KHz$ producing 50% modulation . The lower and upper side-band frequencies in $kHz$ are:

A body started with velocity of $12\text{m/s}$ and moving with an acceleration of $2{\text{m/s}}^2$. The distance travelled by the body in the $8^{\text{th}}$ second is

Indicator diagram of an ideal gas is as shown in figure. Find the workdone by the gas in the process $ABCD$.

The position vector of a particle is given as $\overrightarrow{r}=(t^2-4t+6)\hat{i}+\left(t^2\right)\hat{j}.$ The time after which the velocity vector and acceleration vector becomes perpendicular to each other is equal to

Two infinite plane sheets $\text{A}$ and $\text{B}$ carrying current in same direction, and current per unit length are $5\text{A/m}$ and $\lambda \text{A/m}$ respectively. Find the value of $\lambda$ so that magnetic field at point $\text{P}$ is zero.

A
magnetic field of 100 G (1 G = 10⁻⁴
T) is required which is uniform in a region of linear dimension about
10 cm and area of cross-section about 10⁻³
m².
The maximum current-carrying capacity of a given coil of wire is 15 A
and the number of turns per unit length that can be wound round a
core is at most 1000 turns m⁻¹.
Suggest some appropriate design particulars of a solenoid for the
required purpose. Assume the core is not ferromagnetic

When sound wave is refracted from air to water, which of the following will remain unchanged?

A parallel plate capacitor of $1\mu F$ capacity is discharging through a resistor. If its energy reduces to half in one $\text{second}$. The value of resistance will be

If $f\left(x\right)$ is the anti-derivative of $\frac{x+1}{x^2{e}^x}$ and $f\left(x\right)=-x^a{e}^{kx}+C,$ where $a,k\in R$ and $C$ is an integration constant. Then which of the following is(are) correct

A particle of mass m is executing uniform circular motion on a path of radius r. If p is the magnitude of its linear momentum. The radial force acting on the particle is

An electron is moving along positive x - axis. A
uniform electric field exists towards negative y - axis. What should be the
direction of magnetic field of suitable magnitude so that net force on electron
is zero?

The figure shows a conducting loop, being pulled out of a magnetic field, with a uniform speed $v$. Which of the following graph represents the correct graph of power $P$ delivered by the pulling force, as a function of the speed $v$ ?



Assume loop wire has some resistance.

A particle of mass $m$ oscillates between $P_1$ and $P_2$ inside a fixed smooth spherical shell of radius $R$. At any instant the kinetic energy of the particle is $E$. Then the force exerted by the particle on the shell at this instant is:

A system is shown in the figure. The time period for small oscillations of the two blocks will be

A parallel beam of diameter $d$ is incident on the air-glass interface, as shown in figure. The diameter of the refracted light beam is



$(d=3\text{mm},\theta ={45}^{\circ }\text{and}\frac{n_{glass}}{n_{air}}=\frac{3}{2})$

The power factor of the circuit is $\frac{1}{\sqrt{2}}$. The capacitance of the circuit is equal to -