Three charges +2q. +3q and -4q are situated at (0,-3a), (2a, 0) and (-2a,0) respectively in the xy plane. The resultant dipole moment about origin is _________

Two cars are approaching each other at an equal speed of \(7.2\, km / hr\). When they see each other, both blow horns having frequency of \(676\, Hz\). The beat frequency heard by each driver will be \(.....\, Hz\). [Velocity of sound in air is \(340\,m / s .]\)

When a gas filled in a closed vessel is heated by raising the temperature by \(1^{\circ} C\), its pressure increase by \(0.4 \%\). The initial temperature of the gas is ..........\(K\)

If \({V}_{{A}}\) and \({V}_{{B}}\) are the input voltages (either \(5\, {V}\) or \(0\, {V}\) ) and \({V}_{0}\) is the output voltage then the two gates represented in the following circuit \((A)\) and \((B)\) are:- \((A)\quad\quad\quad\quad(B)\)

An engine approaches a hill with a constant speed. When it is at a distance of \(0.9\, km\), it blows a whistle whose echo is heard by the driver after \(5\, seconds\). If the speed of sound in air is \(330\, m/s\), then the speed of the engine is .... \(m/s\)

Consider two physical quantities A and B related to each other as \(E=\frac{B-x^2}{A t}\) where \(E, x\) and \(t\) have dimensions of energy, length and time respectively. The dimension of \(A B\) is _______.

A sinusoidal voltage \(V(t)=210\,\sin 3000 t\) volt is applied to a series \(LCR\) circuit in which \(L =10\) \(mH , C =25 \mu F\) and \(R =100 \Omega\). The phase difference \((\Phi)\) between the applied voltage and resultant current will be

If \({q}_{{f}}\) is the free charge on the capacitor plates and \({q}_{{b}}\) is the bound charge on the dielectric slab of dielectric constant \(k\) placed between the capacitor plates, then bound charge \(q_{b}\) can be expressed as 

Angle of minimum deviation is equal to the half of the angle of prism in an equilateral prism. The refractive index of the prism is __________.

A Young's doublc\(-\)slit experiment is performed using monochromatic light of wavelength \(\lambda\). The intensity of light at a point on the screen, where the path difference is \(\lambda,\) is \(K\) units. The intensity of light at a point where the path difference is A \(\frac{\lambda}{6}\) is given by \(\frac{n K}{12},\) where \(n\) is an integer. The value of \(n\) is\(......\)

In an adiabatic process, the density of a diatomic gas becomes \(32\) times its initial value. The final pressure of the gas is found to be \(n\) times the initial pressure. The value of \(n\) is

A small rigid spherical ball of mass M is dropped in a long vertical tube containing glycerine. The velocity of the ball becomes constant after some time. If the density of glycerine is half of the density of the ball, then the viscous force acting on the ball will be (consider g as acceleration due to gravity)