The truth of the given circuit diagram is _______.

The pitch of the screw gauge is \(1\, mm\) and there are \(100\) divisions on the circular scale. When nothing is put in between the jaws, the zero of the circular scale lies \(8\) divisions below the reference line. When a wire is placed between the jaws, the first linear scale division is clearly visible while \(72^{\text {nd }}\) division on circular scale coincides with the reference line. The radius of the wire is.........\(mm\)

Three equal masses \(m\) are kept at vertices (A, B, C) of an equilateral triangle of side a in free space. At \(t=0\), they are given an initial velocity \(\vec{V}_A=V_0 \overrightarrow{A C}, \vec{V}_B=V_0 \overrightarrow{B A}\) and \(\vec{V}_C=V_0 \overrightarrow{C B}\). Here, \(\overrightarrow{A C}, \overrightarrow{C B}\) and \(\overrightarrow{B A}\) are unit vectors along the edges of the triangle. If the three masses interact gravitationally, then the magnitude of the net angular momentum of the system at the point of collision is :

A galvanometer has a \(50\) \(division\) scale. Battery has no internal resistance. It is found that there is deflection of \(40\) \(divisions\) when \(R = 2400\,\Omega \). Deflection becomes \(20\) \(divisions\) when resistance taken from resistance box is \(4900\,\Omega \) . Then we can conclude

Match the thermodynamic processes taking place in a system with the correct conditions. In the table: \(\Delta Q\) is the heat supplied, \(\Delta W\) is the work done and \(\Delta U\) is change in internal energy of the system

Process	Condition
\((I)\) Adiabatic	\((A)\; \Delta W =0\)
\((II)\) Isothermal	\((B)\; \Delta Q=0\)
\((III)\) Isochoric	\((C)\; \Delta U \neq 0, \Delta W \neq 0 \Delta Q \neq 0\)
\((IV)\) Isobaric	\((D)\; \Delta U =0\)

The equivalent resistance between \(A\) and \(B\) is \(......\)

A source of sound \(A\) emitting waves of frequency \(1800\,Hz\) is falling towards ground with a terminal speed \(v.\) The observer \(B\) on the ground directly beneath the source receives waves of frequency \(2150\,Hz.\) The source \(A\) receives waves, reflected from ground of frequency nearly ..... \(Hz\) (Speed of sound \(= 343\,m/s\) )

The temperature dependence of resistances of \(Cu\) and undoped \(Si\) in the temperature range \(300-400\;K\), is best described by

The charge accumulated on the capacitor connected in the following circuit is________ \(\mu \mathrm{C}\) (Given \(\mathrm{C}=150\  \mu \mathrm{F}\))

A thin smooth rod of length \(L\) and mass \(M\) is rotating freely with angular speed \({\omega _0}\) about an axis perpendicular to the rod and passing through its centre. Two beads of mass \(m\) and negligible size are at the centre of the rod initially. The beads are free to slide along the rod. The angular speed of the system, when the beads reach the opposite ends of the rod will be

In a circuit for finding the resistance of a galvanometer by half deflection method, a  \(6\,V\)  battery and a high resistance of  \(11\,k\Omega \)  are used. The figure of merit of the galvanometer \(60\,\mu A/\)  division. In the absence of shunt resistance, the galvanometer produces a deflection of  \(\theta = 9\)  divisions when current flows in the circuit. The value of the shunt resistance that can cause the deflection of \(\theta /2 ,\)  is closest to ..................  \(\Omega\)

One mole of an ideal gas is taken through an adiabatic process where the temperature rises from \(27^{\circ} {C}\) to \(37^{\circ} {C}\). If the ideal gas is composed of polyatomic molecule that has \(4\) vibrational modes which of the following is true?

Identify the pair of physical quantities that have same dimensions