Match List-I with List-II (here symbols have their usual meanings)

List-I (Physical Quantity / Law)	List-II (Formula)
(A) Snell's law	(I) \( t/\mu \)
(B) Apparent Shift	(II) \( c/v \)
(C) Refractive Index	(III) \(\frac{\mu_2}{\mu_1}\)
(D) Apparent depth	(IV) \( t(1 - \frac{1}{\mu}) \)

Choose the correct answer from the options given below:

The ratio of the radius of the third orbit to that of the second orbit in a hydrogen atom is

The mutual inductance of a pair of solenoids depends on

The 'stopping potential' in photoelectric emissions

The ratio of energies of photons produced due to the transition of an electron of hydrogen atom from its
i. second permitted energy level to the first level and
ii. the highest permitted energy level to the first energy level is

In a coil of self inductance 10 H, the rate of change of current is \( 4 \text{ A s}^{-1} \). The electromotive force (emf) induced in the coil will be

A flask contains Argon and Chlorine in the ratio of 2:1 by mass. The temperature of the mixture is \( 27^{\circ}\text{C} \). The ratio of root mean square speed of molecules of two gases will be : (atomic mass of Argon = 40 u and molecular mass of Chlorine = 71 u)

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 cloning vector pBR322, the BamH1 site codes for:

\(\int \frac{e^x(1+x) d x}{\cos ^2\left(e^x x\right)}\) is equal to:

A radioactive source is freshly prepared. It is found that it emits radiation of intensity which is 128 times the premissible safe level. The half life of this sample is 3 hours. Find the minimum time after which it would be possible to work safely with this radioactive source.

If a capacitor is connected in an ac circuit, what is the phase relationship between current and potential difference applied across the capacitor ?

The disease phenylketonuria is caused by mutation in the gene that codes for -

The smaller area between the ellipse \(\frac{x^2}{4}+\frac{y^2}{36}=1\) and the line \(\frac{x}{2}+\frac{y}{6}=1\) is given by: