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The radiation force experienced by body exposed to radiation of intensity $I$, assuming surface of body to be perfectly absorbing is

A coil of inductance $L=2\mu \text{H}$ and resistance $R_1=1\Omega$ is connected to a source of constant emf $E=3\text{V}$. A resistance of $R_2=2\Omega$ is connected in parallel with the coil. Find the amount of heat generated in the coil after the switch is disconnected. The internal resistance of the source is negligible,

The transition from the state n = 5 to n = 1 in a hydrogen atom results in UV radiation. Infrared radiation will be obtained in the transition

In common emitter amplifier, the current gain is $20.$ The collector resistance and input resistance are $4k\Omega$ and $800\Omega$ respectively. If the input voltage is $0.01\text{V}.$ The output voltage is

Current flowing in a Zener diode as shown in circuit is:



(Given diode is an ideal and $V_Z=4\text{V})$

In a double slit experiment, the two slits are 1 mm apart and the screen is placed 1m away. A monochromatic light of wave length 500 nm is used. What will be the width of each slit for obtaining ten maxima of double slit within the central maxima of single slit pattern?

In the circuit shown, the initial voltages across the capacitors $C_1$and$C_2$ are 1 V and 3 V respectively. The switch is closed at time t = 0. The total energy dissipated (in Joules) in the resistor R until steady state is reached, is .

1. 1.5

A uniformly tapering vessel is filled with a liquid of density $900{\text{kg/m}}^3$. The force that acts on the base of the vessel due to the liquid (excluding atmospheric force) is : [Take $g=10{\text{m/s}}^2$]

Find the equivalent capacitance between $A$ and $B$ in the circuit shown in the figure. Given $C=5\mu \text{F}$

A block of mass m, attached to a fixed position O on a smooth inclined wedge of mass M, oscillates with
amplitude A and linear frequency f . The wedge is located on a rough horizontal surface. If the angle of the
wedge is 60⁰, then the force of friction acting on the wedge is given by (coefficient of static friction $=\mu$

A steel plate of upper face area $2{\text{cm}}^2$ and thickness $6\text{cm}$ is fixed rigidly at the lower surface. A tangential force $F=20\text{kN}$ is applied on the upper surface as shown in the figure. The lateral displacement $x$ of upper surface w.r.t the lower surface is (Take modulus of rigidity for steel is $8\times {10}^{11}{\text{N/m}}^2$).

The latent heat of vaporization of water is $2240\text{J/g}$. If the work done in the process of expansion of $1\text{g}$ is $168\text{J}$, then increase in internal energy is

The pulley shown in the figure has a radius of 20 cm and moment of inertia 0.2 kg-$m^2$. The string going over it is attached at one end to a vertical spring of spring constant 50 N/m fixed from below, and supports a 1 kg mass at the other end. The system is released from rest with the spring at its natural length. Find the speed of the block when it has descended through 10 cm. Take g = 10 $m/s^2$

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Find the net electric field due to a finite wire of linear charge density $+\lambda \text{C/m}$ at a point $\text{P}$ located at a perpendicular distance $d$ as shown in the figure.



$[K=\frac{1}{4\pi {\epsilon }_0}]$

The graph below shows the relationship between the number of people and profits earned (in ₹).





The equation of the above graph is .

Which of the following graphs represents the distance-time variation of a body released from the top of a building?

Two particles A and B are thrown vertically upward with velocity, 5 m/s and 10 m/s respectively ($g=10m/s^2$). Find separation between them after one second. (Use relative motion approach)

If $U_1,U_2,U_3$ represents the potential energy of mass $m$ moving from A to B along three different paths $1$,$2$ & $3$ (as shown in the figure) in the gravitational field, then

An observer in a speeding car sees a traffic jam ahead of him. He slows down to $36\text{km/hour}$. He finds that traffic has eased. A car moving ahead of him at $18\text{km/hour}$ is honking at a frequency of $1392\text{Hz}$. If the speed of sound is $343\text{m/s}$, the frequency of the honk as heard by him will be

Two particles of medium disturbed by the wave propagation are at $x_1=0and{x}_2=1cm$. The respective displacements (in cm) of the particles can be given by the equations: $y_1=2sin3\pi t,y_2=2sin(3\pi t-\frac{\pi }{8})$. The wave velocity is

A cylindrical bar with $200mm$ diameter is being turned with a tool having geometry $0^o-9^o-7^o-8^o-{15}^o-{30}^o-0.05inch$ (Coordinate system, ASA) resulting in a cutting force $F_{c1}$. If the tool geometry is changed to $0^o-9^o-7^o-8^o-{15}^o-0^o-0.05inch$ (Coordinate system, ASA) and all other parameters remain unchanged, the cutting force changes to $F_{c2}$. Specific cutting energy (in $J/m{m}^3$) is $U_c=U_0(t_1{)}^{-0.4}$, where $U_o$ is the specific energy coefficient, and $t_1$ the uncut thickness in $mm$. The value of percentage change in cutting force $F_{c2}$. i.e., $\left(\frac{F_{c2}-F_{c1}}{F_{c1}}\right)\times 100,$, is

(round off to one decimal place).

A particle moves in the $x-y$ plane under the action of a force $\overrightarrow{F}$ such that the value of its linear momentum $\overrightarrow{p}$ at any instant is $\overrightarrow{p}=2(\cos t\hat{i}+\sin t\hat{j})$. The angle $\theta$ between $\overrightarrow{F}$ and $\overrightarrow{p}$ is

Two particles $\text{P}$ and $\text{Q}$ are moving with velocities of $(\hat{i}+\hat{j})$ and $(-\hat{i}+2\hat{j})$ respectively. At time $t=0$, $\text{P}$ is at origin and $\text{Q}$ is at a point with position vector $(2\hat{i}+\hat{j})$. The equation of the path of $\text{Q}$ with respect to $\text{P}$ is $x+2y=C$. Find the value of $C$.

The displacement-time graph of a moving object is shown in figure. Which of the following velocity-time graphs could represent the motion of the same body?

Three elements A,B and C crystalize in a cubic lattice with A atoms at the corners, B atoms at the cube center and C atoms at the centre of the face of the cube.The simplest formula for the compound will be:

Standing waves of frequency 5.0 kHz are produced in a tube filled with oxygen at 300 K. The separation between the consecutive modes is 3.3 cm. Calculate the specific heat capacities $C_p$ and $C_v$ of the gas

The bob of a pendulum at rest is given an impulse to impart a horizontal velocity $\sqrt{gl}\text{m/s}$ where $l$ is the length of the pendulum. Find the tangential acceleration at the point where velocity of the bob is zero.

Activities of three radioactive substance $\text{A, B}$ and $\text{C}$ are represented by the curves $\text{A, B}$ and $\text{C}$, in the figure. Then their half gives $T_{1/2}\left(A\right):T_{1/2}\left(B\right):T_{1/2}\left(C\right)$ are in the ratio

A
closely wound solenoid of 2000 turns and area of cross-section
1.6 ×
10⁻⁴
m²,
carrying a current of 4.0 A, is suspended through its centre allowing
it to turn in a horizontal plane.

(a)
What is the magnetic moment associated with the solenoid?

(b) What is the
force and torque on the solenoid if a uniform horizontal magnetic
field of 7.5 × 10⁻²
T is set up at an angle of 30º with the axis of the solenoid?

Radioactive isotopes are produced in a nuclear physics experiment at a constant rate. An inductor of inductance $100\text{mH},$ a resistor of resistance $100\Omega$ and a battery are connected to form a series circuit. The circuit is switched on at the instant the production of radioactive isotope starts. It is found that $\frac{i}{N}$ remains constant in time, where $i$ is the current in the circuit at time $t$ and $N$ is the number of active nuclei at time $t$. Find the half-life of the isotope.

If a ball strikes the ground with a force of $3N$, the force exerted by the ground on the ball is

The mass of a planet is six times that of the earth. The radius of the planet is twice that of the earth. If the escape velocity from the earth is $v$, then the escape velocity from the planet is :

A hollow sphere of mass $M$ and radius $R$ is initially at rest on a horizontal rough surface. It moves under the action of a constant horizontal force $F$ as shown in figure.


The linear acceleration $\left(a\right)$ of the sphere is :