The phase difference between two points A and B on a given wavefront separated by distance \(\lambda\) is :

If \( \lambda_1 \) and \( \lambda_2 \) are the longest wavelengths of the Lyman and Paschen series respectively, then \( \lambda_1 : \lambda_2 \) is:

In a coil, a current of 0.2 A increases at the rate of \( 0.4 \text{ A s}^{-1} \). If the power flow in the coil is \( 0.6 \text{ J s}^{-1} \) the inductance of the coil is:

Two similar coils of radius R are lying concentrically with their planes perpendicular to each other and carrying current I and 2I respectively. What is the resultant magnetic field at the center?

An ideal battery of 6 V and resistance R are connected in series in the primary circuit of a potentiometer of length 4 m and resistance \( 10 \Omega \). The value of R, to give a potential difference of 10 mV across 20 cm of potentiometer wire is:

The magnetic flux passing perpendicular to the plane of a coil is changing according to the equation \( \Phi = 6t^2 + 7t + 1 \) where \( \Phi \) is in mWb and t is in seconds. The magnitude of induced emf at t = 2 s is:

Which of the following statements are correct?
(A) In dispersion through a prism of glass, the red color ray deviates most.
(B) In simple microscope, to get a magnified image, the object is placed within the focus of a convex lens.
(C) In compound microscope, total magnification is m = (magnification due to eye lens) x (magnification due to objective)
(D) Magnifying power of telescope M = focal length of eye lens / focal length of objective lens
Choose the correct answer from the options given below:

The probability that a student is not a swimmer is \(\frac{1}{5}\). Then, the probability that out of 5 students, 4 are swimmers is

A point charge Q is kept at the midpoint of a face of cube of side L. The electric flux emerging from the cube is

50 g of ethylene glycol \(C_2H_6O_2\) is mixed with 900 g of water. The freezing point of the solution will be\(\left(K_f\right.\) of water \(\left.=1.86 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\right)\)

Bacillus thuringiensis produces proteins (Bt toxin) that kill certain insects. Identify the correct statements.
(A) Bt toxin protein exists as an inactive form (protoxin) in Bacillus thuringiensis.
(B) Bt toxin protein exists as an active form toxin in the insect gut.
(C) The alkaline pH of the gut of an insect solubilize the toxin and converts in an inactive form.
(D) The toxin is coded by a gene crylAc named cry.
Choose the correct answer from the options given below:

Which of the following is connected to the coil of the galvanometer, to protect it from possible damages due to large current?

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.
Resistance to root-borne pathogens, salinity and drought tolerance are introduced into which type of plants?