To project a body of mass \(m\) from earth's surface to infinity, the required kinetic energy is _______. (assume, the radius of earth is \(R_E, g=\) acceleration due to gravity on the surface of earth)

Given below are two statements: Statement \(I:\) For diamagnetic substance \(-1 \leq \chi < 0\), where \(\chi\) is the magneticsusceptibility. Statement \(II:\) Diamagnetic substances when placed in an external magnetic field, tend to move from stronger to weaker part of the field. In the light of the above statements, choose the correct answer from the options given below.

10 mole of an ideal gas is undergoing the process shown in the figure. The heat involved in the process from \(P _1\) to \(P _2\) is \(\alpha\) Joule \(\left( P _1=21.7 Pa\right.\) and \(\left.P _2=30 Pa, C _{ v }=21 J / K . mol , R=8.3 J / mol . K \right)\). The value of \(\alpha\) is _________ .

There are two vessels filled with an ideal gas where volume of one is double the volume of other. The large vessel contains the gas at 8 kPa at 1000 K while the smaller vessel contains the gas at 7 kPa at 500 K. If the vessels are connected to each other by a thin tube allowing the gas to flow and the temperature of both vessels is maintained at 600 K , at steady state the pressure in the vessels will be (in kPa).

A zener diode with 5 V zener voltage is used to regulate an unregulated dc voltage input of 25 V. For a \(400 \Omega\) resistor connected in series, the zener current is found to be 4 times load current. The load current \(\left(I_L\right)\) and load resistance \(\left(R_{\mathrm{L}}\right)\) are :

A travelling microscope has \(20\) divisions per \(cm\) on the main scale while its Vernier scale has total \(50\) divisions and \(25\) Vernier scale divisions are equal to \(24\) main scale divisions, what is the least count of the travelling microscope \(..........\,cm\)

A proton, a deuteron and an \(\alpha-\)particle with same kinetic energy enter into a uniform magnetic field at right angle to magnetic field. The ratio of the radii of their respective circular paths is

Let \(\sigma\) be the uniform surface charge density of two infinite thin plane sheets shown in figure. Then the electric fields in three different region \(E_{ I }, E_{ II }\) and \(E_{III}\) are

The minimum energy required by a hydrogen atom in ground state to emit radiation in Balmer series is nearly _______.

Match List\(-I\) with List\(-II\)

List\(-I\)	List\(-II\)
\((a)\) \(h\) (Planck's constant)	\((i)\) \(\left[ M L T ^{-1}\right]\)
\((b)\) \(E\) (kinetic energy)	\((ii)\) \(\left[ M L ^{2} T ^{-1}\right]\)
\((c)\) \(V\) (electric potential)	\((iii)\) \(\left[ M L ^{2} T ^{-2}\right]\)
\((d)\) \(P\) (linear momentum)	\(( iv )\left[ M L ^{2} I ^{-1} T ^{-3}\right]\)

Choose the correct answer from the options given below

A voltage regulating circuit consisting of Zener diode, having break-down voltage of 10 V and maximum power dissipation of 0.4 W , is operated at 15 V . The approximate value of protective resistance in this circuit is _________ \(\Omega\).

An massless equilateral triangle \(EFG\) of side \('a'\) (As shown in figure) has three particles of mass \(m\) situated at its vertices. The moment of intertia of the system about the line \(EX\) perpendicular to \(EG\) in the plane of \(EFG\) is \(\frac{ N }{20}\, ma ^{2}\) where \(N\) is an integer. The value of \(N\) is

A metal sample carrying a current along \(X-\) axis with density \(J_x\) is subjected to a magnetic field \(B_z\) ( along \(z-\) axis ). The electric field \(E_y\) developed along \(Y-\) axis is directly proportional io \(J_x\) as well as \(B_z\) . The constant of proportionality has \(SI\, unit\).