Match List I with List II

LIST I	LIST II
A. \(\int_{1}^{2} \frac{\sqrt{x}}{\sqrt{3-x} + \sqrt{x}} dx\)	I. -\(\frac{1}{2}\log 3\)
B. \(\int_{1}^{2} x^2 dx\)	II. \(\frac{7}{3}\)
C. \(\int_{-4}^{-1} \frac{1}{x} dx\)	III. \(\frac{1}{2}\)
D. \(\int_{0}^{1} \frac{1}{2x-3} dx\)	IV. -\(\log 4\)

Choose the correct answer from the options given below:

If P and Q are non-singular square matrices of the same order, then \(\left(P Q^{-1}\right)^{-1}\) equals

\(\int \frac{1 - \sin x}{\cos^2 x} dx\) is equal to:

\(\int \frac{x+\sqrt{x}}{2 \sqrt{x}} d x=\)

Area bounded between the parabola \(y=x^2-2\) and the line \(y=x\) in square units is:

The solution set of the inequality \(\frac{2 x+3}{x-1}<0\) is:

The value of the integral \(\int \frac{e^x(1+x)}{\cos ^2\left(x e^x\right)} d x\) 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.
Choose the free living, nitrogen-fixing bacteria from the following.

An ammeter and a Voltmeter are to be connected in a circuit. Which of the following statements are correct?
(A) Ammeter has negligible resistance.
(B) Ammeter is always connected in series in the circuit.
(C) Voltmeter should have negligible resistance.
(D) Voltmeter should be connected in parallel so that the whole current may pass through it.
Choose the correct answer from the options given below:

A heater boils \( x \) amount of water in time \( t_{1} \) and another heater boils the same water in time \( t_{2} \) having resistances \( R_{1} \) and \( R_{2} \) respectively. The ratio \( \frac{t_{1}}{t_{2}} \) will be:

Arrange the following alkyl halides in increasing order of reactivity towards \(SN ^2\) reaction?
(A)\(CH _3- Cl\)
(B)\(CH _3- Br\)
(C)\(CH _3- F\)
(D)\(CH _3- I\)
Choose the correct answer from the options given below:

Match List I with List II

List - I	List - II
(A) Convergent evolution	(I) Speciation
(B) Divergent evolution	(II) Analogous organs
(C) Adaptive radiation	(III) Homologous organs
(D) Natural selection	(IV) Australian marsupials

Choose the correct answer from the options given below:

The amount of urea required to make a 500 mL solution of 0.25 molarity is
(Molar mass of Urea \(=60 g mol ^{-1}\) )