An infinite plane sheet of charge density \(10^{-8} \text{ C m}^{-2}\) is held in air. In this situation, the distance between two equipotential surfaces, whose potential difference is 10 V, will be (Given: Permittivity of vacuum\(\epsilon_0 \approx 8.85 \times 10^{-12} F / m\))

The electric potential due to an electric dipole
(A) depends on r, where r is the magnitude of position vector \( \vec{r} \)
(B) depends on the angle between the position vector \( \vec{r} \) and the dipole moment vector \( \vec{p} \)
(C) falls off at long distances, as \( 1/r^2 \)
(D) does not depend upon the distance separating the charges
Choose the correct answer from the options given below:

An electron, an \( \alpha \)-particle, a proton and a neutron have the same kinetic energy. Which of these particles has the shortest de Broglie wavelength?

A potential difference of 6 V is applied across a conductor of length 12 cm. If the mobility of electrons is \( 5.6 \times 10^{-6} \text{ m}^2/\text{V}\cdot\text{s} \), their drift velocity will be:

An electron is moving at a velocity of 100 m/s along the X-axis in the presence of an electric field of 30 V/m directed along the Y-axis and a magnetic field of 300 G directed along the Z axis. The magnitude and direction of force acting on the electron is (Given: the charge on the electron is "e")

A domestic appliance draws 2.5 A from a 220 V, 50 Hz power supply. The amplitude of current is

A resistor of resistance \( 30 \, \Omega \) and a capacitor of capacitance \( (250 \pi^{-1}) \, \mu\text{F} \) are connected in series to a 220 V, 50 Hz source. The current in the circuit is

Osmotic pressure measurements are less accurate and difficult to carry out. Therefore, this method is not useful for measuring molecular weights. But it is used to find out molecular weights of polymers eg. plastics, proteins and starch having many monomer units. Knowing the value of osmotic pressure of a given solution, molecular weight of the solute can be calculated using Van't Hoff equation.
Determine the Molarity of a solution containing 4g of NaOH in 1L solution

When benzene diazonium chloride reacts with phenol, it results in the formation of an orange colored compound (X); and when benzene diazonium chloride reacts with aniline, it results in the formation of a yellow colored compound ( Y ).
What are \(X\) and \(Y\) ?

For fixed radii of curvature of a lens, power is proportional to :

Select the correct sequence for transport of sperm in the male reproductive
system.
(A) Urethra
(B) Urethra meatus
(C) Ejaculatory duct
(D) Vas deferens
Choose the correct answer from the options given below:

For the L.P.P. Maximize \(z=10 x+6 y\) subjected to
\(3 x+y \leq 12\)
\(2 x+5 y \leq 34\)
\(x, y \geq 0\)
Then the feasible region represented by system of inequalities is

Read the following paragraph carefully and answer the given questions.
In the year 1963 the two enzymes responsible for restricting the growth of bacteriophage in E. coli were isolated. The first restriction endonuclease - Hind II, whose functioning depended on a specific DNA nucleotide sequence was characterized five years later. It was found that Hind II always cut DNA molecules at a particular point by recognizing a specific sequence of six base pairs. This specific base sequence is known as the recognition sequence for Hind II. Besides Hind II, today we know more than 900 restriction enzymes that have been isolated from over 230 strains of bacteria, each of which recognize different recognition sequences.
Hind II is a restriction endonuclease because