Electric field at a point due to a uniformly charged infinite plane sheet is

Which of the following is true ?
(A) The equilibrium of a charged particle under the action of coulomb force alone can never be stable.
(B) A hollow metal sphere placed on an insulating stand is charged positively. The electric potential inside is same as on surface
(C) A free electron and a free proton are placed in a uniform field, both will experience same magnitude of the force
(D) A free electron and a free proton are placed in a uniform field, both will experience same acceleration
Choose the correct answer from the options given below :

A wire of resistance 4 \( \Omega \) is used to make a coil of radius 7 cm. The wire has a diameter of 1.4 mm and the resistivity of its material is \( \rho = 2 \times 10^{-7} \, \Omega \, m \). The number of turns in the coil will be

The current through a 4/3 \(\Omega\) external resistance connected to a parallel combination of two cells with emfs of 2 V and 1 V, internal resistances 1 \(\Omega\) and 2 \(\Omega\) respectively, is :

A cylindrical coil of radius \(r\), having \(n\) turns per unit length and carrying a current \(I\) has a magnetic field near its end equal to:

Three concentric metallic spherical shells of radii \( R, 2R \), and \( 3R \) are given charges \( Q_1, Q_2 \) and \( Q_3 \), respectively. It is found that the surface charge densities on the outer surfaces of the shells are equal. Then, the ratio of the charges given to the shells \( Q_1 : Q_2 : Q_3 \) is:

Given that two identical coils, one of copper and another of aluminium are rotated with the same angular speed in an external magnetic field, which of the following statements is true?

Which vector was used to introduce nematode specific gene into the host plant?

Read the passage carefully and answer the given questions.
DNA Fingerprinting
Polymorphism in DNA sequence is the basis of genetic mapping of the human genome as well as of DNA fingerprinting. DNA fingerprinting involves identification of differences in some specific regions in the DNA sequence called repetitive DNA. It works on the principle of polymorphisms in DNA sequences. The repetitive DNA are separated from bulk genomic DNA. The bulk DNA forms a major peak and the other small peaks are referred to as satellite DNA. These repetitive/satellite DNA sequences show a high degree of polymorphisms and form the basis of DNA fingerprinting.
DNA fingerprinting is meant for:

A capacitor charged from a 50 V d.c. supply is found to have a charge of \( 10 \ \mu\text{C} \).The capacitance of the capacitor would be:

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.
The formula which correctly represents Potassium tetra hydroxo zincate (II) is :

Coagulating power of an ion for a colloidal solution depends on :

If \(A=\left[\begin{array}{ll}4 & 5 \\ 2 & 1\end{array}\right]\) and \(I\) is an identity matrix of order \(2\) , then \(A-3 I\) equals :