An electric motor is driven by d.c. supply of emf \( V_0 \) and internal resistance r. The current when output power is maximum will be

A pendulum of length 'l' having a bob of mass 'm' carrying charge 'q' is suspended from a stationary rigid support in a region of uniform electric field 'E' as shown in the figure. If the system is in equilibrium, the nature and magnitude of 'q' will be :

Conditions for obtaining a interference pattern of light are
(A) Two waves should be coherent
(B) The distance of the screen from the slits should be small
(C) The separation between slits should be small
(D) Two coherent waves should have nearly the same amplitude
Choose the correct answer from the options given below:

Wavelength of matter wave is independent of :

If the kinetic energy of the particle is increased to 16 times its previous value. The percentage change in de Broglie wavelength of the particle is:

A pair of adjacent coils has a mutual inductance of 2.0 H . If the current in one coil changes from 0 to 30 A in 0.5 s, the change of the magnetic flux linked with the other coil would be

The frequency of an input signal is 50 Hz. The frequencies of an output signal for a half wave rectifier and a full wave rectifier will be respectively :

Which of the following compounds will be repelled when placed in an external magnetic field?

The probability distribution of a random variable \(X\) is given by
\(\begin{array}{lcllll}x & 0 & 1 & 2 & 3 & 4 \\ p(x) & 0.1 & k & 2 k & 2 k & k \end{array} \)
The value of \(k\) is:

Werner was the first to describe the bonding features in coordination compounds. But his theory could not answer basic questions like :
(i) Why only certain elements possess the remarkable property of forming coordination compounds ?
(ii) Why the bonds in coordination compounds have directional properties?
(iii) Why coordination compounds have characteristics magnetic and optical properties ?
Many approaches have been put forth to explain the nature of bonding in coordination compounds viz. Valence Bond Theory (VBT), Crystal Field Theory (CFT), Ligand Field Theory (LFT) and Molecular Orbital Theory (MOT).
We shall focus our attention on elementary treatment of the application of VBT and CFT to coordination compounds.
According to this theory, the metal atom or ion under the influence of ligands can use its ( \(n -1) d , ns np\) or ns, np, nd orbitals for hybridisation
to yield a set of equivalent orbitals of definite geometry such as octahedral, tetrahedral, square planar and so on.
These hybridised orbitals are allowed to overlap with ligand orbitals that can donate electron pairs for bonding.
\(CoCl _3 \cdot 6 NH _3\) gives 3 moles of AgCl on reacting with \(AgNO _3\).
The correct formula for this compound is :

Forward bias applied to a p-n junction diode

Which one of the following correctly represents the concentration term 'ppm'?

Homologous structures have :