Electrostatics deals with the study of forces, fields and potential arising from static charges. Which of the following statements are correct ?
(A) Electrostatic force is a conservative force
(B) Charge is quantized because only integral number of electrons can be transferred from one body to the other
(C) In a uniform electric field E , an electric dipole experiences a torque \(\tau\) and a net force F .
(D) The electric field lines start from positive charges and end at negative charges. If there is a single charge, these may start or end at infinity.
(E) If the uniform surface charge density of an infinite plane sheet is positive, the electric field is directed away from the plate.
Choose the correct answer from the options given below :

A non conducting solid sphere of radius R is uniformly charged. The magnitude of the electric field due to the sphere at a distance r from its center :
A. decreases as r increases, for 0 < r < \(\infty\)
B. increases as r increases, for r < R
C. becomes zero.
D. decreases as r increases, for R < r < \(\infty\)
Choose the correct answer from the options given below:

Two charges \( q_1 = 4 \times 10^{-7} \text{ C} \) and \( q_2 = -6 \times 10^{-7} \text{ C} \) are located 3 m apart. At what point on the line joining the two charges is the electric potential zero? (Consider potential zero at infinity.)

Kirchhoff's junction rule and loop rule are based on which of the following conservation laws respectively ?

A beam of electrons move horizontally from South to North in the region of the magnetic field acting vertically downward. The force acting on the electron due to the magnetic field is :

Electric field intensity at a point varies as \( \frac{1}{r^3} \) due to:

In an AC circuit, the current leads the voltage by \(\pi/2\). The circuit is :

The elucidation of the lac operon was the result of close association between the geneticist _________ and the biochemist _________.

Read the passage carefully and answer
When a metal is placed in a solution of its ions, the metal can lose electron and can go in the solution as ion or the metal ion in the solution can take electron from the electrode and get deposited as metal. Thus, the electrode acquires either positive or negative charge with respect to the solution leading to the development of a potential difference between the metal electrode and the solution. This potential difference is called the electrode potential of the metal. The electrode potential of a metal is a measure of relative tendency to undergo oxidation (loss of electron) or reduction (gain of electron). When the concentration of the ions in the solution is unity, the electrode potential is called standard electrode potential. The magni of potential depends upon the nature of electrode, concentration of ions in solution and the temperature. In a galvanic cell, the electrode at which oxidation occurs is known as anodic half-cell and the electrode at which reduction occurs is known as cathodic half cell. The emf of the cell in terms of standard reduction potential is given by \(E_{\text {cell }}^{\circ}=E_{\text {cathode }}^{\circ}-E_{\text {anode. }}^{\circ}\).The standard free energy change of the redox reaction taking place in the cell is related to \(E_{\text {cell }}^{\circ}\) by \(\Delta G^{\circ}=-n F E^{\circ}\). A redox reaction would occur spontaneously if the free energy change is negative. The equilibrium constant of the reaction is related to the standard free energy change by \(\Delta G^{\circ}=-R T \ln K\).
The half call reaction is the one that

A bulb and a capacitor are connected in series to an a.c. source. A dielectric slab is now introduced between the plates of the capacitor. The intensity of the bulb will be:

The system of equations \(2 x+\lambda y=8, \lambda x+8 y=3\) has a unique solution if the value of \(\lambda\) is (are):

Given that the function \(f(x)\) is continuous on \(R\). Match \(List - I\) with \(List - II\) .

\(List - I\)	\(List - II\)
(A) \(f(x)=\left\{\begin{array}{ll}k x^2, & x<3 \\ 3, & x \geq 3\end{array}\right.\)	(I) \(k=\frac{5}{4}\)
(B) \(f(x)=\left\{\begin{array}{ll}k x+1, & x \geq 4 \\ x+2, & x<4\end{array}\right.\)	(II) \(k=-1\)
(C) \(f(x)=\left\{\begin{array}{ll}\frac{5+x}{2}, & x \neq 0 \\ 3 k, & x=0\end{array}\right.\)	(III) \(k=\frac{1}{3}\)
(D) \(f(x)=\left\{\begin{array}{ll}x+k, & x>-2 \\ -3, & x \leq-2\end{array}\right.\)	(III) \(k=\frac{5}{8}\)

Choose the correct answer from the options given below:

Identify, which is not the example of homology in evolution.