\(C_1\) and \(C_2\) are two hollow concentric cubes enclosing charges \(2 Q\) and \(3 Q\) respectively as shown in figure. The ratio of electric flux passing through \(C_1\) and \(C_2\) is _______.

A rocket has to be launched from each in such a way that it never returns. If \(E\) is the minimum energy delivered by the rocket launcher, what should be the minimum energy that the launcher should have if the same rocket is to be launched from the surface of the moon ? Assume that the density of the earth and the moon are equal and that the earth’s volume is \(64\) times the volume of the moon.

In a system two particles of masses \(m_1=3 \mathrm{~kg}\) and \(\mathrm{m}_2=2 \mathrm{~kg}\) are placed at certain distance from each other. The particle of mass \(m_1\) is moved towards the center of mass of the system through a distance \(2 \mathrm{~cm}\). In order to keep the center of mass of the system at the original position, the particle of mass \(\mathrm{m}_2\) should move towards the center of mass by the distance _______\(\mathrm{cm}\).

\(M\) grams of steam at \(100^{\circ} \mathrm{C}\) is mixed with \(200\; \mathrm{g}\) of ice at its melting point in a thermally insulated container. If it produces liquid water at \(40^{\circ} \mathrm{C}\) [heat of vaporization of water is \(540 \;cal/\mathrm{g}\) and heat of fusion of ice is \(80 \;\text { cal/g }]\) the value of \(\mathrm{M}\) is

A person observes two moving trains, '\(A\)' reaching the station and '\(B\)' leaving the station with equal speed of \(30\,m / s\). If both trains emit sounds with frequency \(300\,Hz\), (Speed of sound : \(330\,m / s\) ) approximate difference of frequencies heard by the person will be \(..........Hz\)

On the \(x-\)axis and a dsitance \(x\) from the origin, the gravitational field due to a mass distribution is given by \(\frac{A x}{\left(x^{2}+a^{2}\right)^{3 / 2}}\) in the \(x-\)direction. The magnitude of gravitational potential on the \(x-\)axis at a distance \(x,\) taking its value to be zero at infinity, is

In the circuit, the logical value of \(A =1\) or \(B =1\) when potential at \(A\) or \(B\) is \(5\,V\) and the logical value of \(A=0\) or \(B=0\) when potential at \(A\) or \(B\) is \(0\,V\). The truth table of the given circuit will be :

Given below are two statements : one is labelled as Assertion \(A\) and the other is labelled as Reason \(R\) Assertion \(A :\) Photodiodes are preferably operated in reverse bias condition for light intensity measurement. Reason \(R\) : The current in the forward bias is more than the current in the reverse bias for a \(p - n\) junction diode. In the light of the above statement, choose the correct answer from the options given below :

\(AC\) alternating emf \(\mathrm{E}=110 \sqrt{2} \sin 100 \mathrm{t}\) volt is applied to a capacitor of \(2 \mu \mathrm{F}\), the rms value of current in the circuit is _______ \(\mathrm{mA}\).

Figure shows a rod \({AB}\), which is bent in a \(120^{\circ}\) circular arc of radius \(R\). A charge \((-Q)\) is uniformly distributed over rod \({AB}\). What is the electric field \(\overrightarrow{{E}}\) at the centre of curvature \({O}\) ?

A \(5 \,V\) battery is connected across the points \(X\) and \(Y\). Assume \(D_{1}\) and \(D_{2}\) to be normal silicon diodes. Find the current (in \(A\)) supplied by the battery if the \(+ve\) terminal of the battery is connected to point \(X\)

If force \(\vec{F}=3 \hat{i}+4 \hat{j}-2 \hat{k}\) acts on a particle having position vector \(2 \hat{i}+\hat{j}+2 \hat{k}\) then, the torque about the origin will be