The magnetic field lines are completely expelled from a material when ( \(\chi\) is the susceptibility and \(\mu_r\) is relative permeability)

Carbon, silicon and germanium have four valence electrons each. Their valence and conduction bands are separated by energy gap \( E_g \). If we represent \( (E_g)_C, (E_g)_{Si} \) and \( (E_g)_{Ge} \) as their respective energy gaps, then which of the following is true

A metal foil of neglible thickness is introduced between two parallel plates of a capacitor at the centre. The new capacitance of the capacitor would be :

A wire of length \( L \) meters, carrying a current \( I \) ampere is bent in the form of a circle. The magnitude of its magnetic moment, in SI units, is:

A common emitter amplifier has a current gain 75. The collector resistance is 4 \( k\Omega \) and the input resistance is 500 \( \Omega \). The voltage gain of amplifier is:

A proton and a deuteron execute circular orbits having same radii of 0.5 m in a plane perpendicular to a uniform magnetic field B. If the kinetic energy of the deuteron is 50 keV, the K.E. of the proton will be

Two conducting spheres of radii 5 cm and 10 cm are given a charge of 15 \(\mu\)C each. If the two spheres are now joined by a conducting wire, the charge on the smaller sphere will be :

The number of free electrons per 100 mm of ordinary copper wire is 2 \(\times 10^{21}\). The average drift speed of electrons is 0.25 mm/s. The amount of current flowing would be : (e = 1.6 \(\times 10^{-19}\) C)

Arrange the following compounds in increasing order of their acidity :
(A) Phenol
(B) 4 -methylphenol
(C) 3-nitrophenol
(D) 4-nitrophenol
Choose the correct answer from the options given below :

Trivalent lanthanoid ions which do not show any colour are:

Read the passage carefully and answer the Questions
Alcohols and phenols are obtained when a hydrogen atom in aliphatic and aromatic hydrocarbons respectively, is replaced by \(OH\) group. These compounds find wide applications in industry as well as in our daily life. You may notice that ordinary spirit is used for polishing wooden furniture which is chiefly a compound containing hydroxyl group. An alcohol contains one or more hydroxyl \((OH)\) group(s) directly attached to carbon atom(s), of an aliphatic system \((CH_3OH)\) while a phenol contains \(OH\) group(s) directly attached to carbon atom(s) of an aromatic system \((C_6H_5OH)\). Alcohols are prepared by the hydration of alkenes, fermentation of glucose, and reduction of carbonyl compounds. Alcohols produce alkenes upon dehydration whereas alkenes on acid catalyzed hydration convert into alcohols.
Which of the following compounds lacks phenolic group?

Three pipes A, B and C are installed to fill a tank. Pipes A and B opened together can fill the tank in the same time in which \(C\) can alone fill the tank. If pipe \(B\) can fill the tank 15 minutes faster than pipe \(A\) and 5 minutes slower than pipe \(C\), then the time required by pipe \(A\) to fill the tank alone is:

The value of \(\cos \left(2 \cos ^{-1} x+\sin ^{-1} x\right)\) at \(x=\frac{1}{5}\) is