What is the power factor of an ac circuit having resistance R and inductance L connected in series? (\( \omega \) is the angular frequency )

Match List I with List - II.,

List - I	List - II
(A) TV Transmission	(I) Short wave bands
(B) Long distance radio broadcasts	(II) Microwave
(C) RADAR	(III) Infrared rays
(D) TV Remote	(IV) Satellite

Choose the correct answer from the options given below :

An infinite line of charge has a linear charge density of \(10^{-7} \text{ C m}^{-1}\). The magnitude of the force acting on a charge \(6.4 \times 10^{-19} \text{ C}\) kept at a distance of 8 cm from the line of charge is

The maximum and minimum amplitudes of a modulated carrier wave are 1000 mV and 200 mV respectively, the modulation index is

A zener diode is :

If the wave length of 1st line of Balmer series of hydrogen is 6561A, the wavelength of the 2nd line of series will be:

Width of two slits in Young's double slits experiment are in the ratio 9:4.
The ratio of the amplitudes of light waves through them would be:

Identify the incorrect statement(s) among the following:
(A) Two electric field lines of force never intersect.
(B) Two opposite charges, each of \( 10 \times 10^{-9} \, \text{C} \), separated by 5 mm. The magnitude of the dipole moment is \( 5 \times 10^{-11} \, \text{C-m} \).
(C) Electric field intensity due to a single charge varies as the square of the distance from the charge, whereas electric field intensity due to an electric dipole varies inversely as the cube of the distance of the point.
(D) Electric field intensity due to an electric dipole has spherical symmetry around it in space.
Choose the correct answer from the options given below:

A conductor is placed along z-axis carrying current in z direction in uniform magnetic field directed along y-axis. The magnetic force acting on the conductor is directed along:

Match List - I with List - II.

List - I	List - II
(A) Genetic diversity	(I) Mangroves and Coral reef
(B) Species diversity	(II) Rauwolfia vomitoria in different Himalayan ranges
(C) Ecological diversity	(III) Amphibians in Western Ghats
(D) Biodiversity loss	(IV) Dodo in Mauritius

Choose the correct answer from the options given below:

Excess of Lead from human body can be removed by using which of the following chelating agents?

Components of Time Series are :
(A) Secular Trend Component
(B) Seasonal Component
(C) Moving Average Component
(D) Cyclical Component
Choose the correct answer from the options given below :

Read the passage carefully and answer the questions
The resistance ( \(R\) ) of an object is given by the expression \(R=\rho \frac{l}{A}\).
The inverse of \(R\) is called conductance and the inverse of \(\rho\) is called conductivity or specific conductance represented by \(\kappa\).
The conductivity depends upon the nature of the material (insulator, semiconductor or conductor) and the temperature of the substance.
Similarly, the conductance due to the ions present in the solution (ionic conductance) depends upon the nature of the electrolyte, size of ions, the nature of the solvent and the temperature.
Molar conductivity ( \(\Lambda_m\) ) of a solution at a given concentration is the conductance of volume \(V\) containing one mole of electrolyte kept between two electrodes of area \(A\) and unit distance apart. It is given by the expression \(\Lambda_m=\kappa V\).
Molar conductivity increases with decrease in concentration and when concentration approaches zero, it is called limiting molar conductivity.
The decrease is linear for a strong electrolyte. However, for a weak electrolyte the change is gradual at higher concentrations and sharp near zero concentration.
Using limiting molar conductivity values of strong electrolytes we can calculate the limiting molar conductivity of weak electrolytes using Kohlrausch law of independent migration of ions.
From molar conductivity and limiting molar conductivity we can determine the degree of dissociation \(\left(\frac{\Lambda_m}{\Lambda_m^0}\right)\) and the ionization constant of a weak acid.
Which of the following is an insulator?