The shortest wavelength in the Balmer series of hydrogen atom would be (Given R = \( 1.1 \times 10^7 \, m^{-1} \))

A spherical metallic conductor of radius \(6 . 0 ~ c m\) is held in air. The maximum charge it can hold if
dielectric strength of air is \(20 kV / cm\) will be :
\(\left(\text { Take } \frac{1}{4 \pi \epsilon_0}=9 \times 10^9 N m^2 C^{-2}\right)\)

The angular momentum of an electron moving in the circular path of diameter D in a uniform magnetic field \( B_0 \) is:

Which of the following will increase the mobility of charge carriers?

What is the particle X in the fusion reaction shown below ?
\({ }_1^2 H +{ }_1^2 H \rightarrow{ }_2^3 He + X +3.27 MeV\)

Identify the correct statements.
(A) Neutrons penetrate the nucleus more readily as compared to protons.
(B) It is easier to release an orbital electron, but quite difficult to release a nucleon.
(C) Nuclear density is not the same for all nuclei.
(D) The radius of the nucleus is directly proportional to the cube root of the mass number.
Choose the correct answer from the options given below:

If 'n' identical resistors, each of value 'R' are first connected in series to a battery of emf 'E' and internal resistance 'R', the current drawn is 'I'. Now if they are connected in parallel, then the current drawn is '5 I'. The value of n is

Which factors are responsible for making fluorine the strongest oxidising agent ?
(A) \quad Highest electronegativity
(B) \quad High electron gain enthalpy
(C) \quad High bond dissociation enthalpy
(D) \quad Small size of flourine
Choose the correct answer from the options given below :

If \(A\) and \(B\) are square matrices of the same order 3 , such that \(\operatorname{det}(A)=3\) and \(A B=3 I\), where \(I\) is an identity matrix of order 3. Then the value of \(\operatorname{det}(B)\) is :

A part of an infinitely long current carrying wire is bent into a circular shape as shown in the diagram. The magnetic field at the centre of the circle is

Let \(\vec{a}\) and \(\vec{b}\) be two unit vectors and \(\theta\) is the angle between them. If \(\vec{a}+\vec{b}\) is a unit vector, then \(\theta\) is:

Answer the question on basis of passage given below :
Adsorption is surface phenomenon and it differs from absorption which occurs throughout the body of the substance which absorbs. In physisorption the attractive forces are mainly van der Waal forces while in chemisorption actual bonding occurs between the particles of adsorbent and adsorbed more easily on the surface of a solid as compared to the gases which are liquified with difficulty. Adsorption increases with the increases in pressure and decreases as temperature is increased.
The ease with which the gases \(H _2, CH _4, CO _2 \backslash \& NH _3\) are adsorbed on the surface of charcoal is -

\(60 \%\) members of a committee favour a certain proposal and \(40 \%\) members oppose the proposal.
A member is selected and let the random variable \(X=0\) if he opposes and \(X=1\) if he is in favour.
Then the variance of the random variable \(X\) is