Motion of a charged particle having velocity v in a uniform magnetic field B is circular, if v is

Velocity of light in diamond, glass and water decreases in the following order :

A conducting ring of radius r in a magnetic field varying at rate x has electric field intensity at any ring point as :

An electromagnetic wave travels in a medium at a speed of \( 2 \times 10^8 \text{ m/s} \). If the relative permeability (\( \mu_r \)) of the medium is 1.0, then the relative permittivity (\( \varepsilon_r \)) of the medium is equal to

A beam of light of wavelength 500 nm from a distant source falls on a single slit of width \( 10^{-4} \, \text{m} \), and the resulting diffraction pattern is observed on a screen 2 m away. The width of the central bright fringe is:

\( (1/16) \)th of the initial amount of a certain radio-active isotope remains undecayed after two hours. The half life of the isotope would be :

An electric dipole with dipole moment \( 3 \times 10^{-9} \, \text{C m} \) is aligned at \( 30^\circ \) with the direction of uniform electric field of magnitude \( 6 \times 10^4 \, \text{N C}^{-1} \). What will be the magnitude of torque?

Van't Hoff factor (i) is given by

Which of the properties are shown by d block elements ?
(A) Complex formation
(B) Chelating agents
(C) Bleaching agents
(D) Catalytic properties
(E) Alloy formation
Choose the correct answer from the options given below :

A hollow metal sphere of radius 10 cm is uniformly charged such that the electric potential at a distance of 20 cm from the center is 10 V. The electric potential at a distance of 5 cm from the center of the sphere will be

Let \(A=\left[\begin{array}{ccc}2 & -1 & 3 \\ 1 & 2 & -1 \\ 4 & 1 & 2\end{array}\right]\). \(M_{i j}\) and \(A_{i j}\) respectively denote the minor and cofactor of an element \(a_{i j}\) of matrix \(A=\left[a_{i j}\right]\).
(A) \(M_{23}=6\)
(B) \(A_{22}=-8\)
(C) \(A_{13}=7\)
(D) \(M_{32}=-5\)
Choose the correct answer from the options given below:

Which of the following are not involved in intra uterine devices?
(A) Lippes Loop
(B) LNG-20
(C) Saheli
(D) Implants
Choose the correct answer from the options given below:

Read the following passage carefully and answer the given questions.
During anaerobic sludge digestion, bacteria produce a mixture of gases such as methane, hydrogen sulphide and carbon dioxide. These gases form biogas and can be used as source of energy as it is inflammable. The bioactive molecule, cyclosporin A, that is used as an immunosuppressive agent in organ-transplant patients, is produced by the fungus Trichoderma polysporum. You must have noticed that bottled fruit juices bought from the market are clearer as compared to those made at home. This is because the bottled juices are clarified by the use of pectinases and proteases. Statins produced by the yeast Monascus purpureus have been commercialised as blood-cholesterol lowering agents. It acts by competitively inhibiting the enzyme responsible for synthesis of cholesterol. The BOD test measures the rate of uptake of oxygen by micro-organisms in a sample of water and thus, indirectly, BOD is a measure of the organic matter present in the water.
Cyclosporin A, that is used as an immunosuppressive agent in organ-transplant patients, is produced by -