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If characteristic gas constant of a given gas is one fourth of universal gas constant, the given gas could be

How oil in transformer helps in insulation

The value of $C_v$ for one mole of neon gas is

The Rolle's Theorem states

Given equation of the curve is $y=sinx$.



Using definite integral, find the area of the region between the given curve and the x-axis in the interval of $[0,\pi ]$.

What is the acceleration (in ${\text{m/s}}^2)$ of the block of mass $m$ relative to the wedge of mass $M$ for the figure shown? Assume all surfaces to be smooth. Take $g=10{\text{m/s}}^2$.

A stone falls from a balloon that is descending at a uniform rate of 12 m/s. The magnitude of the displacement of the stone from the point of release after 10 sec is

Consider the situation shown in the figure. The capacitor $\text{A}$ has a charge $q$ on it where capacitor $\text{B}$ is uncharged. The charge appearing on the capacitor $\text{B}$ a long time after the switch is closed is

Electric field $\overrightarrow{E}=4t\hat{i}$ exists in space. Displacement current associated with a square of side a = 2cm with its plane perpendicular to $\overrightarrow{\epsilon }$ at t = 2 sec will be

An aeroplane moving with 150 m/s drops a bomb from a height of 80 m so as to hit a target. What is the distance between the target and the point where the bomb is dropped? (given $g=10m/s^2$)

A system of coordinates is drawn in a medium whose refractive index varies as $\mu =\frac{2}{1+y^2}$, where $0\le y\le 1$. A ray of light is incident at origin at an angle ${60}^{\circ }$ with $y$ -axis as shown in the figure. At point P ray becomes parallel to $x-axis$. The value of $H$ is

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

A fan at a rock concert is 30 m from the stage, and at this point the sound intensity level is 110 dB.How much energy is transferred to her eardrums each second? (Assume eardrum to be circular with a radius of 10mm)

1. 9

If velocity of particle is given by $v=2t^4$, then its acceleration $\frac{dv}{dt}$ at any time $t$ will be given by

A small ball of mass $m$ starts from rest from point $A(b,c)$ on a smooth slope which is a parabola. The normal force that the ground exerts at the instant, the ball arrives at lowest point $(0,0)$ is

Answer the following
questions:

(a) In a single slit diffraction experiment, the width of the
slit is made double the original width. How does this affect the size
and intensity of the central diffraction band?

(b) In what way is diffraction from each slit related to the
interference pattern in a double-slit experiment?

(c) When a tiny circular obstacle is placed in the path of
light from a distant source, a bright spot is seen at the centre of
the shadow of the obstacle. Explain why?

(d) Two students are separated by a 7 m partition wall in a
room 10 m high. If both light and sound waves can bend around
obstacles, how is it that the
students are unable to see each other even though they can converse
easily.

(e) Ray
optics is based on the assumption that light travels in a straight
line. Diffraction effects (observed when light propagates through
small apertures/slits or around small obstacles) disprove this
assumption. Yet the ray optics assumption is so commonly used in
understanding location and several other properties of images in
optical instruments. What is the justification?

The area of cross-section of the wider tube shown in figure is $800{\text{cm}}^2$. If a mass of $12\text{kg}$ is placed on the massless piston, the difference in heights in the level of water in the two tubes is:

A loop is formed by joining two semicircular wires of radii $R_1$ and $R_2$ carrying a current as shown in the figure. The current in the loop is $I$ and is placed in the uniform magnetic field $B$ which is parallel to the plane of loop. What will be the torque acting on the loop.

A bullet is fired vertically upwards with a velocity $v$ from the surface planet when it reaches its maximum height, its acceleration due to the planet's gravity is $1/4$th of its value at the surface of the planet. If the escape velocity from the planet is $v_{esc}=v\sqrt{N}$, then the value of $N$ is (ignore energy loss due to atmosphere)

A projectile is thrown into space so as to have maximum horizontal range R. Taking the point of projection as origin, the co-ordinates of the point where the speed of the particle is minimum are

The $n$ row each containing $m$ cells in series are joined in parallel. Maximum current is taken from this combination across an external resistance of $3\Omega$ resistance. If the total number of cells used are $24$ and internal resistance of each cell is $0.5$ $\Omega$, then

The adjacent graph shows the extension $\left(\Delta l\right)$ of a wire fo length I m suspended from the top of a roof at one end and load w connected to the other end. If the cross-sectional area of the wire is ${10}^{-6}{m}^2$, calculate from the graph Young's modulus of the material of the wire.

A sample of $\text{HCl}$ gas is placed in an electric field of $2.5\times {10}^4\text{N/C}$. The dipole moment of each $\text{HCl}$ molecule is $3.4\times {10}^{-30}\text{C-m}$. Find the maximum torque that can act on a molecule.

Two particles of masses $m_1$ and $m_2$ are located at $x=0\text{m}$ and $x=6\text{m}$. If the position of their centre of mass is at $x=4\text{m}$, then the ratio of their masses $\frac{m_2}{m_1}$ is

A monkey of mass 40 kg climbs on a rope (Fig. 5.20) which can stand a maximum tension of 600 N. In which of the following cases will the rope break: the monkey

(a) climbs up with an acceleration of 6 m s^–2

(b) climbs down with an acceleration of 4 m s^–2

(c) climbs up with a uniform speed of 5 m s^–1

(d) falls down the rope nearly freely under gravity?

(Ignore the mass of the rope).

Fig. 5.20

A uniform horizontal rod of length 40 cm and mass 1.2 kg is supported by two identical wires as shown in figure (15 - E9). Where should a mass of 4.8 kg be placed on the rod so that the same tuning fork may excite the wire on left into its fundamental vibrations and that on right into its first overtone ? Take $g=10m{s}^{-2}$

One end of a steel wire is fixed to the ceiling of an elevator moving up with an acceleration $2{\text{m/s}}^2$ and a load of $10\text{kg}$ hangs from other end. Area of cross -section of the wire is $2{\text{cm}}^2$. The longitudinal strain in the wire is $(g=10{\text{m/s}}^2$ and $Y=2\times {10}^{11}{\text{Nm}}^{-2})$

A planet of mass $m$ moves around the Sun of mass $M$ in an elliptical orbit. The maximum and minimum distances of the planet from the sun are $r_1$ and $r_2$ respectively. The time period of the planet is proportional to

Three identical metallic plates are kept at small separations as shown. Initially charge -2Q, +6Q and +Q are given to the plates A, B and C respectively. Now both the switches $S_1$ and $S_2$ are closed simultaneously, then

The acceleration due to gravity above earth's surface ___ as the altitude increases.