The area of the region bounded by the parabola \(y^2=x\) and the straight line 2y = x is

If the system of equations \(2 x+5 y=7,6 x+\lambda y=28\) is inconsistent, then

Match List-l with List-ll
Where \(R\) is set of real numbers

List-l	List-ll
(A) \(f: R \rightarrow R\) s.t \(f(x)=x^4\) is	(I) one-one, Into
(B) \(f: R \rightarrow[0, \infty)\) s.t \(f(x)=x^4\) is	(II) many-one, into
(C) \(f:[0, \infty) \rightarrow R\) s.t \(f(x)=x^4\) is	(III) one-one, onto
(D) \(f:[0, \infty) \rightarrow[0, \infty)\) s.t \(f(x)=x^4\) is	(IV) many-one, onto

Choose the correct answer from the options given below :

The probability distribution of number of aces when two cards are drawn without replacement from a pack of 52 cards is:

Two infinitely long parallel conductors carrying currents I 1 and I 2 are at distance d apart. The force \(F\) on length \(L\) of one conductor due to the other is :

The plane \(2 x-(1+\lambda) y+3 \lambda z=0, \lambda \in R\) passes through the intersection of planes :

Let \(f: R \rightarrow R\) defined by \(f(x)=2 x^3-7\) for \(x \in R\). Then :
(A) \(f\) is one-one function
(B) \(f\) is many to one function
(C) \(f\) is bijective function
(D) \(f\) is into function
Choose the correct answer from the options given below:

The following reaction is given :
\[CH_3-CH(Br)-CH(Br)-CH_3 \xrightarrow[\Delta]{2 NaNH_2} A\]
Identify \(A\) from the following:

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.
Which one of the followings is not a symbiotic microbe?

An infinitely long line charge distribution produces an electric field of \( 9 \times 10^4 \text{ N/C} \) at a distance of 2 cm. The linear charge density of the distribution is :

Arrange the following ligands in increasing order of their field strength:
(A) SCN-
(B) F-
(C) H2O
(D) CO
Choose the correct answer from the options given below :

At some instant, the current in the circuit shown below is 1 A, and it is decreasing at a rate of \( 10^2 \text{ A/s} \). The value of the potential difference \( (V_P - V_Q) \) at that instant is:

A current of 2 A is maintained in a long straight conductor placed in air. Calculate the magnitude of the magnetic field at a distance of 2 m from the conductor.