A current is uniformly distributed across the cross-section of cylindrical wire of radius R = 4 mm with current density \( J = 2.5 \times 10^5 \text{ Am}^{-2} \). The amount of current flowing through the outer portion of the wire between radial distance R/2 and R is

The electric field amplitude of an electromagnetic wave is \(100 N C ^{-1}\) and its frequency is 50 MHz . What is the magnitude of wave vector \(k\), (given speed of electromagnetic wave is \(3 \times 10^8 m s ^{-1}\) )

Match List I with List - II.

List I	List II
(A) Zener diode	(I) operates under forward bias
(B) LED	(II) operates under reverse bias
(C) Solar cell	(III) operates under reverse bias in break down region
(D) Photo diode	(IV) no biasing is applied

Choose the correct answer from the options given below :

The magnetic flux linked with a coil at any instant t is given by \( \Phi = (4t^3 - 3t^2 + 2t + 5) \text{ Wb} \). The emf induced in the coil at \( t = 3 \text{ s} \) is

The average emf induced in a coil is 2 V when current is changed in 0.4 s.
(A) from 5 A to 2 A and the self-inductance of the coil is 0.266 mH
(B) from 4 A to 4 A in the opposite direction, the self-inductance of the coil is 0.10 mH

Which of the following is not based on total internal reflection?

The energy of a Hydrogen atom in its first excited state is

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 dior 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 is a chelate complex?

Match List - I with List - II.

List - I	List - II
(A) Opioids	(I) Erythroxylum coca
(B) Heroin	(II) Tobacco
(C) Cocaine	(III) Papaver somniferum
(D) Nicotine	(IV) Diacetyl morphine

Choose the correct answer from the options given below :

A solution of \(CuSO_4\) is electrolysed for \(10\ min\) with a current of \(1.5\ A\).
What is the mass of copper deposited at the cathode?
(Molar mass of \(Cu = 63\ g\ mol^{-1}\), \(1F = 96487\ C\))

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

The area (in sq. units) of the region bounded by the parabola \(y^2=8 x\) and the line \(x=2\) is

Which one of the following genotypes represents a similar skin color?