The wavelength of photon emitted by a hydrogen atom when an electron makes a transition from n = 2 to n = 1 state is. (Take the value of the Rydberg constant, \(R = 1.0973 \times 10^7 \text{ m}^{-1}\))

A parallel plate capacitor with air between the plates has a capacitance of 9 pF. What will be the capacitance if the distance between the plates is reduced to half and the space between the plates is filled with a dielectric of dielectric constant 7?

A radioactive substance is emitting β- particles at a certain rate. When it is heated to a high temperature, the rate of emission

An element \( \Delta \vec{l} = 0.5 \hat{j} \text{ cm} \) is placed at the origin and carries a large current \( I = 10 \text{ A} \). The magnetic field at point (50 cm, 0) is

There are two electric charges, \( Q_1 \) and \( Q_2 \), placed in vacuum. Identify the correct statements from the following
1. There will be an electrostatic force between them.
2. If these charges are placed in water, the force between them will increase.
3. The electrostatic force between them is a conservative force.
4. If both of the charges are doubled as \( 2Q_1 \) and \( 2Q_2 \), then the force between them will become 4 times.
Choose the correct answer from the options given below:

The radius of the first orbit in Bohr's hydrogen atom is 0.53\(\text{\AA}\). The radius of fourth orbit of this atom will be:

Match List-I with List-II

List-I (Quantity)	List-II (Variation with distance r)
(A) Electric field intensity (E) due to a single charge	(I) \( \propto \frac{1}{r} \)
(B) Electric field intensity due to electric dipole	(II) \( \propto \frac{1}{r^4} \)
(C) Electric potential (V) due to a single charge	(III) \( \propto \frac{1}{r^3} \)
(D) Electric field intensity due to a quadrupole	(IV) \( \propto \frac{1}{r^2} \)

Choose the correct answer from the options given below:

Two parallel plate capacitors of capacitances \(2 \mu F\) and \(3 \mu F\) are joined in series and connected to a battery of \(V\) volts. The values of potential across the two capacitors V1 and V2 and energy stored in them U1 and U2 are related as :

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.

The convention for naming restriction enzymes is:

Recombinant DNA is directly injected into the nucleus of an animal cell.
This method is known as-

The first isolated restriction endonuclease was:

The total cost \(C(x)\) associated with the production of \(x\) units of an item is given by
\(\ C(x)=0.001 x^3+0.06 x^2+20 x+500\).
The marginal cost when 10 units are produced is:

The negatively charged DNA is wrapped around the positively charged histone octamer and forms a structure, called: