A particle of mass \(m\) moving with velocity \(v\) collides with a stationary particle of mass \(2m\). After collision, they stick together and continue to move together with velocity ........

Light enters from air into a given medium at an angle of \(45^{\circ}\) with interface of the air-medium surface. After refraction, the light ray is deviated through an angle of \(15^{\circ}\) from its original direction. The refractive index of the medium is.

The velocity of a particle executing SHM varies with displacement \(( x )\) as \(4 v ^2=50- x ^2\). The time period of oscillations is \(\frac{x}{7} s\). The value of \(x\) is \(............\) \(\left(\right.\) Take \(\left.\pi=\frac{22}{7}\right)\)

In a given circuit diagram, a \(5 \,{V}\) zener diode along with a series resistance is connected across a \(50 \,V\) power supply. The minimum value of the resistance required, if the maximum zener current is \(90\, {mA}\) will be \(.....\,\Omega .\)

An electric field \(\overrightarrow{\mathrm{E}}=4 \mathrm{x} \hat{\mathrm{i}}-\left(\mathrm{y}^{2}+1\right) \hat{\mathrm{j}}\; \mathrm{N} / \mathrm{C}\) passes through the box shown in figure. The flux of the electric field through surfaces \(A B C D\) and \(BCGF\) are marked as \(\phi_{I}\) and \(\phi_{\mathrm{II}}\) respectively. The difference between \(\left(\phi_{\mathrm{I}}-\phi_{\mathrm{II}}\right)\) is (in \(\left.\mathrm{Nm}^{2} / \mathrm{C}\right)\)

A heavy iron bar, of weight \(\mathrm{W}\) is having its one end on the ground and the other on the shoulder of a person. The bar makes an angle \(\theta\) with the horizontal. The weight experienced by the person is _______.

The angle between vector \((\overrightarrow{{A}})\) and \((\overrightarrow{{A}}-\overrightarrow{{B}})\) is :

The radius of electron's second stationary orbit in Bohr's atom is \(R\). The radius of the third orbit will be

In a physical balance working on the principle of moments, when \(5\, mg\) weight is placed on the left pan, the beam becomes horizontal. Both the empty pans of the balance are of equal mass. Which of the following statements is correct?

A parallel plate capacitor is made of two circular plates separated by a distance \(5\ mm\) and with a dielectric of dielectric constant \(2.2\) between them. When the electric field in the dielectric is \(3 \times 10^4\) \( Vm^{-1}\) the charge density of the positive plate will be close to

A rod of length \(L\) at room temperature and uniform area of cross section \(A\), is made of a metal having coefficient of linear expansion \(\alpha {/^o}C\). It is observed that an external compressive force \(F\), is applied on each of its ends, prevents any change in the length of the rod, when it temperature rises by \(\Delta \,TK\). Young’s modulus, \(Y\), for this metal is