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A gas follows $P{V}^{\frac{1}{2}}=\text{constant}$ as shown in figure. If $V_2=2V_1$, then $\frac{T_2}{T_1}$ is

A
closely wound solenoid 80 cm long has 5 layers of windings of 400
turns each. The diameter of the solenoid is 1.8 cm. If the current
carried is 8.0 A, estimate the magnitude of B
inside the solenoid near
its centre.

A soap bubble of diameter $8\text{mm}$ is formed in air. If the surface tension of liquid is $30\text{dyne/cm}$, then excess pressure inside the soap bubble is

A particle starts from $x=0$ and moves along a straight line such that its velocity $v$ depends on position $x$ as $v=x+4$. For the first four seconds, average velocity of the particle (in $m/s$) is

From a lift moving upward with a uniform acceleration $a$, a man throws a ball vertically upwards with a velocity $v$ relative to the lift. The ball comes back to the man after time $t$. Which relation is correct ?

For the figure given below, the total magnetic induction at point O (due to curved and straight portion) will be

When the radius of a circular current carrying coil is doubled and current in it is halved, the magnetic dipole moment of coil originally $4\text{unit}$, now it becomes

A composite tube is made by striking a thin steel tube on a brass tube. If $A_S$ and $A_B$ are the respective sectional areas of the steel and brass tubes and $Y_S$ and $Y_B$ are their Young's moduli. Find the Young's modulus of a single tube of the same length and total sectional area, which would behave in the same fashion as that of the composite tube.

A spherical black body with a radius of $12\text{cm}$ radiates $450\text{W}$ power at $500\text{K}$. If the radius were halved and the temperature doubled, the power radiated in $\text{W}$ would be

An antenna is mounted on a 400 m all building. What will be the wavelength of signal that can be radiated effectively by the transmission tower upto a range of 44 km?

Which of these is a wave/pulse equation?

A railway track (made of iron) is laid in winter when the average temperature is ${18}^{\circ }C$. The track consists of sections of 12.0 m placed one after the other. How much gap should be left between two such sections so that there is no compression during summer when the maximum temperature goes to ${48}^{\circ }C$ ? Coefficient of linear expansion of iron = $11\times {10}^{-6}{}^{\circ }{C}^{-1}$

Which of the following sets of forces acting simultaneously on a particle keep it in equilibrium?

1.3 N,4 N,5 N

2.4 N,7 N, 12 N

3.2 N,6 N,5 N

4.5 N,8 N,1 N

A sphere of radius $0.1\text{m}$ and mass $8\pi \text{kg}$ is attached to the lower end of a steel wire of length $5.0\text{m}$ and diameter ${10}^{-3}\text{m}$. The wire is suspended from $5.22\text{m}$ high celling of a room. When the sphere is made to swing as a simple pendulum, it just grazes the floor at its lowest point. Calculate the velocity of the sphere at the lowest position.



$(Y_{\text{steel}}=1.994\times {10}^{11}{\text{N/m}}^2)$

An observer $O$ is moving with the velocity $3\text{m/s}$ in the direction as shown in the figure. Find the time till the observer will be able to see his image in the plane mirror placed at an angle of ${60}^{\circ }$ with the horizontal.

A bar of varying square cross-section is loaded symmetrically as shown in the figure. Loads shown are placed on one of the axes of symmetry of cross-section. Ignoring self weight, the maximum tensile stress in $N/m{m}^2$ anywhere is

In nuclear reactions, we have the conservation of

A thin symmetrical double convex lens of power $P$ is cut into three part, as shown in the figure. Power of $A$ is :

Two litres of water at initial temperature of ${27}^{\circ }\text{C}$ is heated by a heater of power $1\text{kW}$ in a kettle. If the lid of the kettle is open, then heat energy is lost at a constant rate of $160\text{J/s}$. The time in which the temperature will rise from ${27}^{\circ }\text{C}$ to ${77}^{\circ }\text{C}$ is (specific heat of water $=4.2\text{kJ/kg}$).

Magnetic field of magnitude $B_0$ exist in the region above the line as shown in figure. A charged particle of mass m and charge q moving at speed 'u' enters magnetic field region. Find time interval for which particle remains in magnetic field.

In a step up transformer the turn ratio is $1:3.$ A Daniel cell of emf $1.5\text{V}$ is connected across the primary, the voltage across the secondary is-

A soil has liquid limit and plastic limit of 47% and 33% respectively. The volumetric shrinkage at the liquid limit and plastic limit are 50% and 30% respectively. If the volume of sample at liquid limit is 150 ml then volume of sample at plastic limit is

A particle starts with initial speed U and retardation a to come to rest in time T. The time taken to cover first half of the total path travelled is? ( answer must be in terms of T)

If surface tension of liquid is $0.03\text{N/m}$, then work done in formation of liquid drop of radius $1\text{cm}$ is

Which of the following is a correct graph for molar heat capacity (at constant pressure) versus temperature for an ideal di-atomic gas ?

If the number of turns of a solenoid is doubled keeping other factors constant, how does the self inductance of the soleniod change?

A particle of mass m moving eastward with a speed v collides with another particle of the same mass moving northward with the same speed v. The two particles coalesce on collision. The new particle of mass 2m will move in the north-easterly direction with a velocity