A stone is dropped from a height \(h\). It hits the ground with a certain momentum ' \(p\) '. If the same stone is dropped from a different height h' such that percentage change in momentum is \(41.4 \%\), then the height from which the stone is dropped is \(\mathrm{h}^\prime=x \mathrm{~h}\), where \(x\) is:

A proton is moving along negative X axis. If a uniform magnetic field is applied parallel to the positive Z axis, then choose the correct answer from the following options;
1. The proton will experience magnetic force along positive Y direction and will move along a circular path in the XY plane
2. The proton will experience magnetic force along negative Y direction and will move along a circular path in the XY plane
3. The proton will experience magnetic force along positive Y direction and will move along a circular path in the XZ plane
4. The proton will experience magnetic force along negative Y direction and will move along a circular path in the XZ plane

If \(M\) is the atomic mass and \(A\) is the mass number, packing fraction is given by

In a single slit Fraunhofer diffraction pattern obtained at normal incidence, at the angular position of the first diffraction minimum the phase difference (in radian) between the waves from the opposite edges of the slit is

The normal magnetic flux passing through a coil changes with time according to the equation \(\phi=6 t^{2}-5 t+1\). What is the magnitude of the induced current at \(t=0.253 \mathrm{~s}\) and resistance \(10 \Omega\) ?

A bullet, fired into a door gets embedded exactly at it's centre, causing the door to rotate about it's vertical axis, practically without friction, with an angular velocity of \(0.625\ rads^{-1}\). The door is 1.0 m wide and weighs 12 kg. If the mass of the bullet is 10g, find the speed with which it was fired. (Hint: The moment of inertia of the door about the vertical axis at one end is \(\dfrac{ML^2}{3}\)).

The relative permeability of iron is 6000 . Its magnetic susceptibility is

For an adiabatic change in a system, the condition which is applicable will be

Consider a thin spherical shell of radius \(R\) consisting of uniform surface charge density \(s\). The electric field at a point of distance \(x\) from its centre and outside the shell is

A straight line makes positive intercepts on the coordinate axes whose sum is 5 . If the line passes through the point \(P(-3,4)\) then the equation of a line is

Which one of the following condition will increase the voltage of the cell represented by the equation.
\(\mathrm{Cu}(s)+2 \mathrm{Ag}^{+}(a q) \rightleftharpoons \mathrm{Cu}^{2+}(a q)+2 \mathrm{Ag}(s)\)

Which of the following hexoses will form the same osazone when treated with excess phenyl hydrazine?

If \(U_{n+1}=3 U_n-2 U_{n-1}\) and \(U_0=2, U_1=3\), then \(U_n\) is equal to