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A balloon is moving vertically upward with a velocity of $5\text{m/s}$. When it is at a height of $h$, a body is gently released from it. If it reaches the ground in $3\text{s}$, the height of the balloon when the body is released is (Take $g=10{\text{m/s}}^2$)

The wavelength of the first spectral line in the Balmer series of hydrogen atom is $6561\stackrel{\circ }{A}$. The wavelength of the second spectral line in the Balmer series of singly-ionized helium atom is

The electric field $\overrightarrow{E}=(20\hat{i}+30\hat{j})\text{N/C}$ exists in space. If the potential at origin in taken to be zero, find the potential at $P(3,2)$.

A block of mass $1\text{kg}$ slides down on an inclined plane of inclination ${30}^{\circ }$. Find the work done by the block's weight as it slides through $50\text{cm}$.

A body moves a distance of $10\text{m}$ along a straight line under the action of a force $5\text{N}$. If the work done is $25\text{joule}$, the angle which the force makes with the direction of motion of body is:

Find the equivalent resistance of the circuits shown in figure (32-E17)between the points a and b. Each resistor has a resistance r.

Figure 32-E17

In an atom, the two electrons move round the nucleus in circular orbits of radii R and 4R. The ratio of the time taken by them to complete one revolution is

In the circuit shown in the figure, a $12\text{volt}$ battery has been connected across the points $\text{X}$ and $\text{Y}$. The work done by battery will be:

A copper wire is stretched to make it $0.5\%$ longer. The percentage change in its electrical resistance if its volume remains unchanged is:

A potential barrier of 0.5 V exists across a pn-junction having depletion region (0.8 $\mu$m wide). An electron approaches from n-side with K.E 0.6 eV. Find E in depletion region and K.E of electron when it enters p-side.

1. 400

In the following common emitter circuit if $\beta =100,V_{CE}=7V,V_{BE}$ = Negligible $R_C=2k\Omega$ then $I_B$ = ?

A spring is compressed between two blocks of masses $m_1$ and $m_2$ placed on a horizontal frictionless surface as shown in the figure. When the blocks are released, they have initial velocity of $v_1$ and $v_2$ as shown. The blocks travel distances $x_1$ and $x_2$ respectively before coming to rest.

The ratio $\left(\frac{x_1}{x_2}\right)$ is

Let there be a spherically symmetric charge distribution with charge density varying as $\rho \left(r\right)={\rho }_o(\frac{5}{4}-\frac{r}{R})$ where $r$ is the distance from the origin. The electric field at a distance $r(r<R)$ from the origin is given by

The gravitational
attraction between electron and proton in a hydrogen atom is weaker
than the coulomb attraction by a factor of about 10⁻⁴⁰.
An alternative way of looking at this fact is to estimate the radius
of the first Bohr orbit of a hydrogen atom if the electron and proton
were bound by gravitational attraction. You will find the answer
interesting.

The angular position of a rotating disc is given as $\theta =6t^2+5t-4$ where $\theta$ is in radians, $t$ is in seconds. What is the average angular velocity for the first time interval from $t=0\text{(s)}$ to $t=4\text{(s)}$?

Two conducting plates of surface area $5{\text{m}}^2$ are placed parallel to each other at a distance $0.885\text{cm}$. If the charge on one plate is $60\mu \text{C}$ and on the other is $20\mu \text{C}$, find the potential difference between the plates.

The dynamic plate resistance of a triode valve is $10k\Omega$ Find the change in the plate current if the plate voltage is changed from 200 V and to 220 V.

In the circuit shown in the figure, the total charge is $750\mu \text{C}$ and the voltage across capacitor $C_2$ is $20\text{V}$. Then the charge on capacitor $C_2$ is-

A long metal rod of length $l$ and relative density $\sigma$ is held vertically with its lower end just touching the surface of water. The speed of the rod when it just sinks in water is given by

If potential (in volts) in a region is expressed as $V(x,y,z)=6xy-y+2yz$, the electric field (in $N/C$) at point $(1,1,0)$is

If the arcs of the same length in two circles subtend angles ${45}^{\circ }$ and ${135}^{\circ }$ at the centre, find the ratio of their radii.

The pointer of a dead-beat galvanometer gives a steady deflection because [MP PMT 1994]

A metal bar of length $1\text{m}$ and area of cross-section $1{\text{mm}}^2$ is clamped between two rigid supports. For the material of rod, its Young's modulus is $Y={10}^{11}{\text{N/m}}^2$ and coefficient of linear expansion is $\alpha =1.8\times {10}^{-5}{}^{\circ }{C}^{-1}$. If the temperature of the rod is decreased by $\Delta T={10}^{\circ }C$, the force exerted by the rod on the supports is

A conducting square frame of side ‘a’ and along straight wire carrying current I are located in the same plane a shown in the figure. The fame moves to the right with constant velocity ‘v’. The emf induced in the frame will be proportional to:

Find the integration of $\int \frac{e^{{\sin }^{-1}x}}{\sqrt{1-x^2}}.dx$

A
short bar magnet of magnetic moment 5.25 × 10⁻²
J T⁻¹
is placed with its axis perpendicular to the earth’s field
direction. At what distance from the centre of the magnet, the
resultant field is inclined at 45º with earth’s field on

(a)
its normal bisector and (b) its axis. Magnitude of the earth’s
field at the place is given to be 0.42 G. Ignore the length of the
magnet in comparison to the distances involved.

A device uses hall effect to measure magnetic fields. When in a magnetic field of $200\text{G},$ it gives a hall voltage of $16\mu \text{V}.$ If with the same current and orientation, it gives a hall voltage of $23\mu \text{V}$ in an unknown field, then the magnitude of unknown field is

the magnitude of change in velocity of a particle having speed v is, v during a time interval △ t while moving in a uniform circular motion.The magnitude of average force on the particle is proportional to:

An $220\text{V}$ $\text{AC}$ voltage at a frequency of $100\text{Hz}$ is applied to a circuit containing a pure inductance of $0.01\text{H}$ and a pure resistance of $6.28\Omega$ in series. Calculate the phase angle between current and voltage.

Current $I$ flow through a long conducting wire bent at right angles as shown in the figure. The magnetic field at a point $\text{P}$ on the right bisector at a distance $r$ from $\text{O}$ is-