The ratio of the de-Broglie wavelengths associated with protons accelerated through a potential of 128 V and alpha particles accelerated through a potential of 64 V will be

The magnetic moment of a current loop is \( 2.1 \times 10^{-25} \text{ A m}^{2} \). The magnetic field on the axis of the loop at a distance of 1.0 \( \text{\AA} \) from the loop would be : (Given radius of loop negligible)

A current of 2 A is maintained in a long straight conductor placed in air. Calculate the magnitude of the magnetic field at a distance of 2 m from the conductor.

A transformer with turns ratio \( \frac{N_1}{N_2} = \frac{100}{1} \) is connected to a 240 V ac supply. If the primary and secondary resistance are \( 1.0 \text{ k}\Omega \) and \( 1 \ \Omega \) respectively, then find the output power ?

A proton of charge \(1.6 \times 10^{-19} C\) is moving with a velocity of \(5 \times 10^3 m / s\) in a magnetic field of 4 T. The work done by the magnetic field on the proton is :

Match List-I with List-II

List - I	List - II
(A) E is independent of r	(I) For a point charge
(B) \(E \propto \frac{1}{r}\)	(II) For a short dipole
(C) \(E \propto \frac{1}{r^2}\)	(III) For a linear charge distribution
(D) \(E \propto \frac{1}{r^3}\)	(IV) For a surface charge distribution on an infinite plane sheet

Choose the correct answer from the options given below :

Two particles carrying a charge of q = 2 nC each connected by an insulating string are placed r = 1 m apart on a smooth horizontal surface. The tension in the string is

If the matrix \(A=\left[\begin{array}{lll}0 & b & 1 \\ 2 & 0 & c \\ 3 & 4 & 0\end{array}\right]\) is a symmetric matrix, then the values of \(b\) and \(c\) are:

Two coherent light beams of intensities I and 4 I are superimposed. The maximum and minimum possible intensities in the resulting pattern are :

If \(A=\left[\begin{array}{cc}1 & 2 \\ 4 & -3\end{array}\right]\) and \(f(x)=2 x^2-4 x+5\), then \(f(A)\) is equal to

Read the Passage carefully and answer the questions
When a ligand is bound to a metal ion through a single donor atom, it is said to be a unidentate ligand but when it bind through two donor atoms, then it is said to be didentate ligand and when several donor atoms are present in a single ligand, it is said to be a polydentate ligand. When a di- or polydentate ligand uses its two or more donor atoms simultaneously to bind a single metal ion, it is said to be a chelate ligand. The number of such ligating groups is called the denticity of the ligand. ligand which has two different donor atoms and either of the two ligetes in the complex is called ambidentate ligands. The number of ligand donor atoms to which the metal is directly bonded, is called coordination number of the metal ion in the complex. Complexes in which a metal is bound to only one kind of donor groups are known as homoleptic and in which a metal is bound to more than one kind of donor groups are known as heteroleptic complexes.
Which of the following molecule/ion is not expected to behave as a ligand?

In the equation \( P = \frac{E}{c} \), where \( P \) is momentum, \( E \) is energy and \( c \) is the speed of light, this equation is valid in which of the following cases:

The probability that it will rain on any particular day is \(50 \%\). The probability that it rains only on the first 4 days of the week is :