A \(9\, V\) battery with internal resistance of \(0.5\,\Omega \) is connected across an infinite network as shown in the figure. All ammeters \(A_1 , A_2, A_3\) and voltmeter \(V\) are ideal. Choose correct statement

An \(AC\) source rated \(220\, V , 50\, Hz\) is connected to a resistor. The time taken by the current to change from its maximum to the rms value is

Two vectors \(\overrightarrow{{X}}\) and \(\overrightarrow{{Y}}\) have equal magnitude. The magnitude of \((\overrightarrow{{X}}-\overrightarrow{{Y}})\) is \({n}\) times the magnitude of \((\overrightarrow{{X}}+\overrightarrow{{Y}})\). The angle between \(\overrightarrow{{X}}\) and \(\overrightarrow{{Y}}\) is -

A physical quantity \(y\) is represented by the formula \(y=m^{2}\, r^{-4}\, g^{x}\,l^{-\frac{3}{2}}\). If the percentage error found in \(y, m, r, l\) and \(g\) are \(18,1,0.5,4\) and \(p\) respectively, then find the value of \(x\) and \(p\).

In a series \(L R\) circuit \(X_{L}=R\) and power factor of the circuit is \(P _{1}\). When capacitor with capacitance \(C\) such that \(X _{ L }= X _{ C }\) is put in series, the power factor becomes \(P_{2}\). The ratio \(\frac{ P _{1}}{ P _{2}}\) is

A cone of base radius \(R\) and height \(h\) is located in a uniform electric field \(\vec E\) parallel to its base. The electric flux entering the cone is

At very high frequencies, the effective impendance of the given circuit will be \(....\Omega\)

\(1\,g\) of a liquid is converted to vapour at \(3 \times 10^5\,Pa\) pressure. If \(10 \%\) of the heat supplied is used for increasing the volume by \(1600\,cm ^3\) during this phase change, then the increase in internal energy in the process will be \(............\,J\)

Two magnetic dipoles \(X\) and \(Y\) are placed at a separation \(d\), with their axes perpendicular to each other. The dipole moment of \(Y\) is twice that of \(X\). A particle of charge \(q\) is passing through their mid-point \(P\), at angle \(\theta  = 45^o\) with the horizontal line as shown in the figure. What would be the magnitude of force on the particle at that instant ? (\(d\) is much larger than the dimensions of the dipole)

A uniform rod of length \('l'\) is pivoted at one of its ends on a vertical shaft of negligible radius When the shaft rotates at angular speed \(\omega\) the rod makes an angle \(\theta\) with it (see figure). To find \(\theta\) equate the rate of change of angular momentum (direction going into the paper ) \(\frac{ m \ell^{2}}{12} \omega^{2} \sin \theta \cos \theta\) about the centre of mass \((CM)\) to the torque provided by the horizontal and vertical forces \(F_{H}\) and \(F_{V}\) about the CM. The value of \(\theta\) is then such that: