The initial speed of a bullet fired from a rifle is \(630\, m/s\). The rifle is fired at the centre of a target \(700\, m\) away at the same level as the target. How far above the center of the target (in \(m\)) the rifle must be aimed in order to hit the target? (Take \(g=10 \;m/s^2\))

A capillary tube is immersed vertically in water and the height of the water column is \(x\). When this arrangement is taken into a mine of depth \(d\), the height of the water column is \(y\). If \(R\) is the radius of earth, the ratio \(\frac{x}{y}\) is

Given that \(1\,g\) of water in liquid phase has volume \(1\,cm^3\) and in vapour phase \(1671\, cm^3\) at atmospheric pressure and the latent heat of vaporization of water is \(2256\,J/g;\) the change in the internal energy in joules for \(1\,g\) of water at \(373\,K\) when it changes from liquid phase to vapour phase at the same temperature is ....... \(J\)

The figure represents a voltage regulator circuit using a Zener diode. The breakdown voltage of the Zener diode is \(6\,V\) and the load resistance is \(R_L= 4\,k\Omega .\) The series resistance of the circuit is \(R_i = 1\,k\Omega .\) If the battery voltage \(V_B\) varies from \(8\,V\) to \(16\,V,\) what are the minimum and maximum values of the current through Zener diode?

A point source of light \(S\), placed at a distance \(60 \,cm\) infront of the centre of a plane mirror of width \(50 \,cm\), hangs vertically on a wall. A man walks infront of the mirror along a line parallel to the mirror at a distance \(1.2\, m\) from it (see in the \(figure\)). The distance between the extreme points where he can see the image of the light source in the mirror is \(\ldots \ldots \ldots\, cm.\)

Consider a modified Bernoulli equation.
\(\left( P +\frac{ A }{ Bt ^2}\right)+\rho g ( h + Bt )+\frac{1}{2} \rho V^2=\) constant
If \(t\) has the dimension of time then the dimensions of A and B are _________ , _________ respectively.

The magnetic potential due to a magnetic dipole at a point on its axis situated at a distance of \(20 \mathrm{~cm}\) from its center is \(1.5 \times 10^{-5} \  \mathrm{Tm}\). The magnetic moment of the dipole is _______ \(\mathrm{Am}^2\). (Given : \(\frac{\mu_0}{4 \pi}=10^{-7} \  \mathrm{TmA}^{-1}\) )

A capacitor P with capacitance \( 10\times10^{-6} F \) is fully charged with a potential difference of 6.0 V and disconnected from the battery. The charged capacitor P is connected across another capacitor Q with capacitance \( 20\times10^{-6} F \). The charge on capacitor Q when equilibrium is established will be \( \alpha\times10^{-5} C \).(assume capacitor \(Q\) does not have any charge initially),The value of \( \alpha \) is __________ .

A uniform electric field of \(10\,N / C\) is created between two parallel charged plates (as shown in figure). An electron enters the field symmetrically between the plates with a kinetic energy \(0.5\,eV\). The length of each plate is \(10\,cm\). The angle \((\theta)\) of deviation of the path of electron as it comes out of the field is  \(.........\)(in degree).

A beam of light travelling along \(X\)-axis is described by the electric field \(E _{ y }=900 \sin \omega( t - x / c )\). The ratio of electric force to magnetic force on a charge \(q\) moving along \(Y\)-axis with a speed of \(3 \times 10^{7}\,ms ^{-1}\) will be. [Given speed of light \(=3 \times 10^{8}\,ms ^{-1}\) ]

A concave mirror has radius of curvature of \(40\, cm\). It is at the bottom of a glass that has water filled up to \(5\, cm\) (see figure). If a small particle is floating on the surface of water, its image as seen, from directly above the glass, is at a distance \(d\) from the surface of water. The value of \(d\) is close to ......\(cm\) (Refractive index of water \(= 1.33\))

An infinitely long straight wire carrying current \(I\) is bent in a planer shape as shown in the diagram. The radius of the circular part is r . The magnetic field at the centre O of the circular loop is :