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Two narrow organ pipes, one open (length $l_1$) and the other closed (length $l_2$) are sounded in the respective fundamental modes. The beat frequency heard is 5 Hz. If now the pipes are sounded in the first overtones, then also the beat frequency heard 5 Hz. Then

The speed of sound in oxygen $\left(O_2\right)$ at a certain temperature is $460m/s$. The speed in helium $\left(He\right)$ at the same temperature will be [assume both gases to be ideal]

In Bohr's atom, energy is absorbed or radiated when an electron makes a transition between two stationary states. If $f$ is the frequency of emitted radiation and $E_1$ and $E_2$ are the energies of electron in two states, then practically which is correct for a hydrogen like atom for the transition as shown in the figure.

Two plane mirrors are placed at an angle of ${120}^{\circ }$ and a man combing his hair is standing at an asymmetric position. How many images will he see?

In the following circuit of PN junction diodes $D_1,D_{2}and{D}_3$ are ideal then i is
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1. (A) – (q); (B) – (r); (C) – (s); (D) – (p)

The position vectors of four points A,B,C and D are$\hat{i}+\hat{j}+\hat{k},2\hat{i}+5\hat{j},3\hat{i}+2\hat{j}-3\hat{k},\hat{i}-6\hat{j}-\hat{k}$ respectively. Then select the correct relation.

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:

In an $L–R$ series circuit $(L=\frac{175}{11}mHandR=12\Omega )$, a variable emf source $(V=V_{0}sin\omega t)$ of $V_{rms}=130\sqrt{2}V$ and frequency $50Hz$ is applied. The current amplitude in the circuit and phase of current with respect to voltage are respectively $(\text{use}\pi =\frac{22}{7})$.

One end of a steel wire is fixed to the ceiling of a moving elevator. A load of $20\text{kg}$ hangs from the other end. If the elevator is moving up with an acceleration $1{\text{m/s}}^2$ and Area of cross- section of wire is $2{\text{cm}}^2$ then find the longitudnal strain in the wire.
[Take $g=10{\text{ms}}^{-2},Y=2\times {10}^{11}{\text{Nm}}^{-2}$ ]

A road is banked such that a vehicle can go in the middle of it with a constant velocity of 40 m/s. What will happen if the velocity is decreased and why?
Imagine friction is not present

Three liquids of densities $d,2d$ and $3d$ are mixed in equal volumes. Then the density of the mixture is

An object moves along the grid through points A,B,C,D,E and F as shown in the figure. Find the distance covered by the moving object?

A body having a mass of $100\text{gm}$ is allowed to fall freely (from a very large height) under the action of gravity. Work done by gravity during first $10\text{s}$ of journey is (Take $g=10{\text{m/s}}^2$)

A small particle of mass $0.36\text{g}$ rests on a horizontal turntable at a distance $25\text{cm}$ from the axis of the spindle. The turntable is accelerated at a rate of $\alpha =\frac{1}{3}{\text{rad s}}^{-2}$. The frictional force that the table exerts on the particle $2\text{s}$ after the startup is

A Light source that radiates 10 Joules of energy per second is kept at the centre of a hemisphere. How much energy will the hemisphere receive?

Energy (in Joules) =

In a photo electric experiment 4 electrons with varying kinetic energy come out.

$E1=1.6\times {10}^{-19}JE2=2.1\times {10}^{-19}JE3=3.2\times {10}^{-19}JE1=1.2\times {10}^{-19}J$

The stopping potential , given this data will be __ Volt

A body falls from rest under gravity and travels half of its total path in the last second. Find the time of fall. (Take $g=10m{s}^{-2}$)

The position of centre of mass of a system consisting of two particles of masses $m_1$ and $m_2$ separated by a distance L apart, from $m_1$ will be

There is hole of area $a$ at the bottom of a cylindrical container of cross-sectional area $A$. Water is filled upto a height of $H$ and all the water flows out in time $t$. If water is filled upto a height of $4H$, all the water will flow out in time -

The displacement x of a particle moving in one dimension is related to time t by the equation $t=\sqrt{x}+3$ where x is in metres and t in seconds. The displacement of the particle when its velocity is zero is

What will be the total resistance offered to the flow of water by the system of pipe $1$, pipe $2$, pipe $3$ and pipe ignoring the joints? If all the pipes are of length $3\text{m}$ and radius $2\text{m}$ and '$\eta$' is viscosity of water. (Assume $\pi =3$)

Two rods A and B of different materials are welded together as shown in the figure. If their thermal conductivities are $k_1$ and $k_2$, the thermal conductivity of the composite rod will be

In which of the following cases light bends towards the normal?

Water rises to a height of 10cm in a capillary tube and mercury falls to a depth of 3.42 cm in the same capillary tube. If the density of mercury is 13.6g/cc and the angle of contact of mercury and water are ${135}^o$ and $0^o$ respectively, the ratio of surface tension of water and mercury is

A small block of super dense material has a mass of $3\times {10}^{24}$ kg.it is situated at a height h (much smaller than the earth's radius) from where it falls on the earth's surface.Find its speed when its height from the earth's surface has reduced to $\frac{h}{2}$.The mass of the earth is $6\times {10}^{24}$ kg.

Two parallel plane sheets 1 and 2 carry uniform charge densities ${\sigma }_1$ and ${\sigma }_2$ (see Fig. 20.8). The electric field in the region marked I is $({\sigma }_1>{\sigma }_2)$. (Consider the right direction as the positive direction)

In a uniform electric field, the potential is $10V$ at the origin of coordinates, and $8V$ at each of the points $(1,0,0),(0,1,0)$ and $(0,0,1)$. The potential at the point $(1,1,1)$ will be

If the speed of a particle is given as $v=3t^2+5\text{m/s}$, the speed of the particle at $4\text{sec}$ and the average speed in $4\text{sec}$ respectively is

Eight equal drops of water are falling through air with a steady velocity of $5\text{cm/sec}$. If smaller drops combine to form a single large drop, then the terminal velocity (in $\text{cm/sec}$) of this large drop is

A car of mass $800\text{kg}$ moves on a horizontal circular track of radius $40\text{m}$. If the coefficient of static friction (${\mu }_s$) is $0.5$, then the maximum velocity with which the car can move will be

Obtain a relation for the distance travelled by an object moving with uniform acceleration in the Interval between 4^th and 5^th seconds.

What is the acceleration of a train travelling at 30 m/s as it goes round a curve of 120 m radius?

A river flows due south with a speed of 2.0 m/s. A man steers a motorboat across the river; his velocity relative to the water is 4 m/s due east. The river is 800 m wide. What is his velocity relative to the earth? Assume North as positive y-direction.

The kinetic energy of an electron in the second Bohr orbit of a hydrogen atom is [$a_0$ is Bohr radius]:

Two balls are thrown from an inclined plane at angle of projection $\alpha$ with the plane, one up the incline and other down the incline as shown in figure (t stands for total time of flight):