Potential energy (V) versus distance (x) is given by the graph, Rank various regions as per the magnitudes of the force (F) acting on a particle from high to low.

The velocity of the bullet becomes one third after it penetrates \(4\,cm\) in a wooden block. Assuming that bullet is facing a constant resistance during its motion in the block. The bullet stops completely after travelling at \((4+x)\,cm\) inside the block. The value of \(x\) is\(.....\)

A copper rod of mass \(m\) slides under gravity on two smooth parallel rails, with separation \(l\) and set at an angle of \(\theta\) with the horizontal. At the bottom, rails are joined by a resistance \(R\). There is a uniform magnetic field \(B\) normal to the plane of the rails, as shown in the figure. The terminal speed of the copper rod is

Two radioactive substances \(A\) and \(B\) have decay constants \(5\lambda \) and \(\lambda \) respectively. At \(t = 0\), a sample has the same number of the two nuclei. The time taken for the ratio of the number of nuclei to become \((\frac {1}{e})^2\) will be

Two projectiles are fired with same initial speed from same point on ground at angles of \(\left(45^{\circ}-\alpha\right)\) and \(\left(45^{\circ}+\alpha\right)\), respectively, with the horizontal direction. The ratio of their maximum heights attained is :

A coin is placed on a disc. The coefficient of friction between the coin and the disc is \(\mu\). If the distance of the coin from the center of the disc is \(r\), the maximum angular velocity which can be given to the disc, so that the coin does not slip away, is _______.

\(\mathrm{N}\) moles of a polyatomic gas \((f=6)\) must be mixed with two moles of a monoatomic gas so that the mixture behaves as a diatomic gas. The value of \(\mathrm{N}\) is _______.

The relationship between the magnetic susceptibility \((\chi)\) and the magnetic permeability \((\mu)\) is given by :
(\(\mu_0\) is the permeability of free space and \(\mu_{\mathrm{r}}\) is relative permeability)

A regular polygon of \(6\) sides is formed by bending a wire of length \(4 \pi\) meter. If an electric current of \(4 \pi \sqrt{3} \mathrm{~A}\) is flowing through the sides of the polygon, the magnetic field at the centre of the polygon would be \(x \times 10^{7} \mathrm{~T}\). The value of \(\mathrm{x}\) is ______.

Given are statements for certain thermodynamic variables,
(A) Internal energy, volume (V) and mass (M) are extensive variables.
(B) Pressure (P), temperature (T) and density ( \(\rho\) ) are intensive variables.
(C) Volume (V), temperature (T) and density ( \(\rho\) ) are intensive variables.
(D) Mass (M), temperature (T) and internal energy are extensive variables.

Choose the correct answer from the options given below :

If frequency of electromagnetic wave is \(60 \mathrm{MHz}\) and it travels in air along \(\mathrm{z}\) direction then the corresponding electric and magnetic field vectors will be mutually perpendicular to each other and the wavelength of the wave (in \(\mathrm{m}\) ) is _______.

A parallel plate capacitor with plate area \(A\) and plate separation \(d\) is filled with a dielectric material of dielectric constant \(K =4\). The thickness of the dielectric material is \(x\), where \(x < d\). Let \(C_1\) and \(C_2\) be the capacitance of the system for \(x =\frac{1}{3} d\) and \(x =\frac{2 d }{3}\), respectively. If \(C _1=2 \mu F\) the value of \(C _2\) is \(........... \mu F\)