Two long straight wires \(P\) and \(Q\) carrying equal current \(10\,A\) each were kept parallel to each other at \(5\,cm\) distance. Magnitude of magnetic force experienced by \(10\,cm\) length of wire \(P\) is \(F_1\). If distance between wires is halved and currents on them are doubled, force \(F_2\) on \(10\,cm\) length of wire \(P\) will be :

The logic operations performed by the given digital circuit is equivalent to:

A solid sphere and a solid cylinder of same mass and radius are rolling on a horizontal surface without slipping. The ratio of their radius of gyrations respectively \(\left( k _{\text {sph }}: k _{ cyl }\right)\) is \(2: \sqrt{ x }\), then value of \(x\) is .............

A coin placed on a rotating table just slips when it is placed at a distance of \(1\,cm\) from the center. If the angular velocity of the table in halved, it will just slip when placed at a distance of from the centre \(............\,cm\)

A circular disc of radius \(b\) has a hole of radius \(a\) at its centre (see figure). If the mass per unit area of the disc varies as \(\left( {\frac{{{\sigma _0}}}{r}} \right)\), then the radius of gyration of the disc about its axis passing through the centre is

Find the truth table for the function \(Y\) and \(A\) and \(B\) represented in the following figure.

A proton of mass \(m\) collides elastically with a particle of unknown mass at rest. After the collision, the proton and the unknown particle are seen moving at an angle of \(90^o\) with respect to each other. The mass of unknown particle is

For a given gas at \(1\,atm\) pressure, \(rms\) speed of the molecules is \(200\,m/s\) at \(127\,^oC.\) At \(2\,atm\) pressure and at \(227\,^oC,\) the \(rms\) speed of the molecules will be

A wire of resistance \(R\) is bent into a triangular pyramid as shown in figure with each segment having same length. The resistance between points \(A\) and \(B\) is \(R / n\). The value of \(n\) is :

Two p-n junction diodes \(D _1\) and \(D _2\) are connected as shown in figure. A and B are input signals and C is the output. The given circuit will function as a ___________.

In a simple pendulum experiment for determination of acceleration due to gravity \((g)\), time taken for \(20\) oscillations is measured by using a watch of \(1\, second\) least count. The mean value of time taken comes out to be \(30\,s\). The length of pendulum is measured by using a meter scale of least count \(1\, mm\) and the value obtained is \(55.0\, cm\). The percentage error in the determination of \(g\) is close to  ........... \(\%\)

A straight wire \(AB\) of mass \(40\,g\) and length \(50\,cm\) is suspended by a pair of flexible leads in uniform magnetic field of magnitude \(0.40\,T\) as shown in the figure. The magnitude of the current required in the wire to remove the tension in the supporting leads is ...........\(A\). (Take \(g=10\,ms ^{-2}\) ).