In the hydrogen atom, an electron revolves around the nucleus in a circular orbit of radius \( 5.11 \times 10^{-11} \text{ m} \) with a frequency of \( 6.8 \times 10^{15} \text{ Hz} \). The magnetic field at the centre of the orbit is :

The potential of a charged spherical conductor of radius r is 20V. The potential at a point r/4 from its center is:

As the frequency of an ac circuit increases, the current first increases till it becomes maximum at resonance and then decreases. Which one of the following combinations of circuit elements are likely to comprise the circuit ?

A 200-turn coil of self-inductance 20 mH carries a current of 4 mA. The magnetic flux linked with each turn of the coil is:

A region has a uniform magnetic field in it. A proton enters the region with a velocity, making an angle of \( 45^\circ \) with the direction of the magnetic field. In this region the proton will move in :

If 100 J of work is done to move electric charge equal to 4 C from a place where potential difference is \( -10 \text{ V} \) to another place where potential is V volt, then the value of V would be:

In a series combination of capacitors connected across a battery

The direction ratios of the perpendicular from the point \((1,0,1)\) to the plane \(x-y+z=0\) are :

\(\int \frac{1}{x\left(x^5-1\right)} d x\) is equal to

DNA recombinant technology involves the use of restriction endonucleases. After having cloned the gene of interest and having optimised the conditions to induce the expression of the target protein, one has to consider producing it on a large scale. The cells harbouring cloned genes of interest may be grown on a small scale in the laboratory. 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. In Biolistics or gene gun method cells are bombarded with high velocity micro particles of gold or tungsten coated with DNA. The ligation of alien DNA is carried out at a restriction site present in one of the two antibiotic resistance genes. For example, you can ligate a foreign DNA at the BamH I site of tetracycline resistance gene in the vector pBR322. Since the DNA is enclosed within the membranes, we have to break the cell open to release DNA along with other macromolecules such as RNA, proteins, polysaccharides and also lipids. 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.
If any protein encoding gene is expressed in a heterologous host, it is called as

Arrange the following steps involved in Recombinant DNA Technology in correct sequence.
(A) Insertion of recombinant DNA into host cell/organism
(B) Cutting of source DNA as well as vector DNA at specific location and their joining
(C) Isolation of the genetic material (DNA)
(D) Obtaining the foreign gene product
(E) Culturing transformed host cells at large scale
Choose the correct answer from the options given below :

A short solenoid of radius a and \( n_{1} \) number of turns per unit length and length L is kept coaxially inside a very long solenoid of radius b and \( n_{2} \) number of turns per unit length. What is the mutual inductance of the system.

Where are IUDs placed in the human female reproductive sytem for contraception?