A 100 m long antenna is mounted on a 25 m tall building. The complex can become a transmission tower for waves with wavelength nearly equal to :

The electric field intensity at a distance of 20 cm from the centre of a small conducting sphere is \(1.5 \times 10^3 \text{ N}⋅­­C^{-1}\) and is directed towards the sphere. The charge on the sphere is:

Match List-I with List-II

List-I	List-II
A. Impedance of a series LCR circuit at resonance	(I) Voltage across L and C are 180 degree out of phase
B. For a series LC Circuit	(II) Current in L and C are 180 degree out of phase
C. For a parallel LC circuit	(III) Minimum
D. Reactance of a capacitor in a DC circuit	(IV) Infinite

Choose the correct answer from the options given below:

An equiconvex lens has a focal length of 20 cm and its radius of curvature is 30 cm . Its refractive index is

In the given figure, a diode D is connected to an external resistance R = 100 \( \Omega \) and an emf of 2.5 V. During forward bias, if the barrier potential developed across the diode is 0.6 V, the current in the circuit will be

Many features of the nuclear binding force are summarised below : Choose the correct statement.
(A) Coulomb force acting between two protons inside the nucleus is much weaker than Nuclear force between them
(B) Between proton-proton inside nucleus gravitational force is stronger than nuclear force
(C) Nuclear force between two nucleons falls rapidly to zero as their distance is more than a few femtometer
(D) Nuclear forces between proton-proton, neutron - proton and neutron-neutron is approximately same when distance between them is same.
Choose the correct answer from the options given below :

The force of attraction between two charges separated by a distance in air is F. If the medium air is replaced by a dielectric medium of dielectric constant K, the force of attraction between the charges will become:

Which among the following are correctly matched?
A. \(C_6H_5OCH_2CH_3\) - Phenetole
B. \(C_6H_5O(CH_2)_6CH_3\) - Heptyl phenyl ether
C. \(C_6H_5OCH_3\) - Dimethyl ether
D. \(C_2H_5OCH_2CH_3\) - Methyl ethyl ether
Choose the correct answer from the options given below:

The integral \(\int \frac{2 d x}{e^{2 x}-1}\) is equal to:

Read the following passage carefully and answer the given questions.
Biofertilisers
Biofertilisers are organisms that enrich the nutrient quality of the soil and their main sources are bacteria, fungi and cyanobacteria. You have studied about the nodules on the roots of leguminous plants formed by the symbiotic association of Rhizobium. These bacteria can fix atmospheric nitrogen into organic forms. Other bacteria can also fix atmospheric nitrogen while free-living in the soil (examples Azospirillum and Azotobacter). Fungi are also known to form symbiotic associations with plants (mycorrhiza). Many members of the genus Glomus form mycorrhiza. Plants having such associations show other benefits also, such as resistance to root-borne pathogens, tolerance to salinity and drought, and an overall increase in plant growth and development. Cyanobacteria are autotrophic microbes widely distributed in aquatic and terrestrial environments many of which can fix atmospheric nitrogen, e.g. Anabaena, Nostoc, Oscillatoria, etc. In paddy fields, cyanobacteria serve as an important biofertiliser. Blue green algae also add organic matter in to the soil and increase its fertility. Currently, in our country, a number of biofertilisers are available commercially in the market and farmers use these regularly in their fields to replenish soil nutrients and to reduce dependence on chemical fertilisers.
Nostoc is an example of :

Match List-I with List-II

List-I	List-II
(A) NBA sin\(\omega\)t	(I) Blv
(B) Joule's loss of heat	(II) Mutual Inductance
(C) Motional emf	(III) \(\frac{B^2l^2v^2}{R}\)
(D) \(\mu_r\) \(\mu_0 n_1 n_2 \pi r^2 l\)	(IV) A.C. Generator

Choose the correct answer from the options given below:

Estradiol hormone is responsible for:

Match List - I with List - II.

List - I	List - II
(A) Resolving power of an astronomical telescope	(I) \( 1.22\lambda/D \)
(B) Limit of resolution of an astronomical telescope	(II) \( \mu \sin \theta \)
(C) Numerical aperture	(III) \( D/1.22\lambda \)
(D) Fresnel distance	(IV) \( a^2/\lambda \)

Choose the correct answer from the options given below: