Match List-I with List-II

List-I (Inverse Trigonometric Function)	List-II (Principal Value)
(A) \(\sin ^{-1}\left(-\frac{1}{2}\right)\)	(I) \(\pi / 6\)
(B) \(\cos ^{-1}\left(-\frac{1}{2}\right)\)	(II) \(-\pi / 6\)
(C) \(\tan ^{-1}(-\sqrt{3})\)	(III) \(2 \pi / 3\)
(D) \(\cot ^{-1}(\sqrt{3})\)	(IV) \(-\pi / 3\)

Choose the correct answer from the options given below :

The function \(f(x)=x^4-2 x^2\) is increasing on

match List - I with List - II

List - I (function)	List - II (inceasing on the interval)
(A) f(x) = -\(x^2\) - 2x + 1	(I) \((-\infty,-1)\)
(B) f(x) = \(x^2\) + 1	(II) \((1, \infty)\)
(C) f(x) = \(x^2\) - 2x + 3	(III) \((-\infty, 0)\)
(D) f(x) = \(- x^2\)	(IV) \((0, \infty)\)

Choose the correct answert from the option given below :

Three mangoes and three apples are kept in a box. If two fruits are selected at random from the box, the probability that the selection will contain one mango and one apple is :

In a 10 km race, \(A, B\) and \(C\) each run at uniform speed and get the first, second and third positions respectively.
If \(A\) beats \(B\) by 1 km and \(B\) beats \(C\) by 1 km , then by how much distance does \(A\) beat \(C\) ?

Match List-I with List-II
The function \(f(x)=(x-1)(x+1)^2\) has

List-I	List-II
(A) A local maxima at \(x=\) __________	(I) \(\frac{1}{3}\)
(B) A local minima at x = __________	(II) \(0\)
(C) The local minimum value of \(f(x)=\) __________	(III) \(-1\)
(D) The local maximum value of \(f(x)=\) __________	(IV) \(-\frac{32}{27}\)

Choose the correct answer from the options given below :

A man is known to speak truth 3 out of 4 times. He throws a die and reports that it is four. The probability that it is actually four is :

Read the following paragraph and answer the given questions:
In order to link the alien DNA, the vector needs to have very few, preferably single, recognition sites for the commonly used restriction enzymes. Presence of more than one recognition site in the vector will generate several fragments, which will complicate the gene cloning. In order to link the alien DNA, the vector needs to have very few, preferably single, recognition sites for the commonly used restriction enzymes. Presence of more than one recognition sites within the vector will generate several fragments, which will complicate the gene cloning. The ligation of alien DNA is carried out at a restriction site present in one of the two antibiotic resistance genes. The recombinant plasmids will lose tetracycline resistance due to insertion of foreign DNA but can still be selected out from non-recombinant ones by plating the transformants on tetracycline containing medium.
The recombinants will grow in ampicillin containing medium but not on that containing tetracycline. But, non- recombinants will grow on the medium containing both the antibiotics. In this case, one antibiotic resistance gene helps in selecting the transformants, whereas the other antibiotic resistance gene gets 'inactivated due to insertion' of alien DNA, and helps in selection of recombinants. Origin of replication (ori) is a sequence from where replication starts and any piece of DNA when linked to this sequence can be made to replicate within the host cells. This sequence is also responsible for controlling the copy number of the linked DNA. So, if one wants to recover many copies of the target DNA it should be cloned in a vector whose origin support has high copy number.
In pBR322 'rop' codes for -

Read the following paragraph and answer the given questions.
Repeated amplification is achieved by the use of a thermostable DNA polymerase (isolated from a bacterium, Thermusaquaticus}), which remain active during the high temperature induced denaturation of double stranded DNA. The separated DNA fragments can be visualised only after staining the DNA with a compound known as ethidium bromide followed by exposure to UV radiation. The separated bands of DNA are cut out from the agarose gel and extracted from the gel piece. The convention for naming these enzymes is the first letter of the name comes from the genus and the second two letters come from the species of the prokaryotic cell from which they were isolated, e.g., EcoRI comes from Escherichiacoli} RY 13. In EcoRI, the letter 'R' is derived from the name of strain. Roman numbers following the names indicate the order in which the enzymes were isolated from that strain of bacteria. Stanley Cohen and Herbert Boyer accomplished this in 1972 by isolating the antibiotic resistance gene by cutting out a piece of DNA from a plasmid which was responsible for conferring antibiotic resistance. Since the DNA is enclosed within the membranes, we have to break the cell open to release DNA, RNA, protein, polysaccharides etc. The RNA can be removed by treatment with ribonuclease whereas proteins can be removed by treatment with protease. Other molecules can be removed by appropriate treatments and purified DNA ultimately precipitates out after the addition of chilled ethanol.

In the isolation process of genetic material, the purified DNA can be precipitated out after the addition of:

Three point charges +q, +q and -2q are placed at the corner of an equilateral triangle of side 'a'. The net dipole moment of the system is

Which of the following is a molecular solid?

The particular solution of the differential equation \(x\left(1+y^2\right) d x-y\left(1+x^2\right) d y=0\), given that \(y(0)=1\) is :

Read the passage given below and answer the question.
Phenols and Alcohol have the same function group (-OH) but phenols are stronger acids than alcohol due the resonance stabilization of phenoxide ion than alkoxide ion (-RO\(^{-}\)). Electron withdrawing groups tend to increase the acidic strength while electron releasing groups tend to decrease it.
Which of the following reagent is used to distinguish between phenol and benzoic acid ?