A charged particle accelerated through a potential difference of V volts acquires a speed u. The particle is then made to enter perpendicularly in a uniform magnetic field B. The radius of the circular path followed by the charged particle will be proportional to

The speed of the electron in \(n = 3\) orbit of \(He^+\) ion would be: (Given \(k = 9 × 10^9 \text{ N}⋅­m^2C^{-2}, e = 1.6 × 10^{-19} \text{ C}, h = 6.63 × 10^{-34} \text{ Js}\))

An atom has a positively charged point nucleus of charge Ze surrounded by a uniform density of negative charge up to a radius R. The atom is taken as neutral. The electric field at a distance r < R from the nucleus is given by:

The electric field and magnetic field of a plane electromagnetic wave propagating in vacuum are expressed as
\(E_x=E_0 \sin (k z-\omega t)\)
\(B_y=B_0 \sin (k z-\omega t)\)
Which of the following statements are correct?
(A). The wave is propagating along the z- direction.
(B). The electric field Ex and magnetic field By are perpendicular to each other and perpendicular to the z direction.
(C) The electric and magnetic fields Ex and By are perpendicular to each other, and parallel to the direction of propagation.
(D) k is related to the wave length À of the wave by the usual equation \(k = A / 2 Tt\)
Choose the correct answer from the options given below:

Photo electric effect reveals the:

A polaroid sheet \(P _2\) is rotated by an angle \(\theta\) (angle between pass axies of \(P _1\) and \(P _2\) ) between two crossed polaroids \(P _1\) and \(P _3\). The intensity of tranamitted light will be maximum for:

The current sensitivity of a galvanometer increases by 10%. If its resistance also increases by 20%, the voltage sensitivity will

The terminal voltages of a cell are found to be 29 V and 28 V when it delivers currents of 1 A and 2 A, respectively. The emf and the internal resistance of the cell are, respectively:

Read the following passage carefully and answer the given questions.
Some strains of Bacillus thuringiensis produce proteins that kill certain insects such as lepidopterans (tobacco budworm, armyworm), coleopterans (beetles) and dipterans (flies, mosquitoes). B. thuringiensis forms protein crystals during a particular phase of their growth. Transgenic animals that produce useful biological products can be created by the introduction of the portion of DNA (or genes) which codes for a particular product such as human protein (a-1-antitrypsin) used to treat emphysema. In 1997, the first transgenic cow, Rosie, produced human protein-enriched milk (2.4 grams per litre). The milk contained the human alpha-lactalbumin and was nutritionally a more balanced product for human babies than natural cow-milk. A nematode Meloidegyne incognitia infects the roots of tobacco plants and causes a great reduction in yield. A novel strategy was adopted to prevent this infestation which was based on the process of RNA interference (RNAi). This method involves silencing of a specific mRNA due to a complementary dsRNA molecule that binds to and prevents translation of the mRNA (silencing). Biopiracy is the term used to refer to the use of bio-resources by multinational companies and other organisations without proper authorisation from the countries and people concerned without compensatory payment. ELISA is based on the principle of antigen-antibody interaction. Infection by pathogen can be detected by the presence of antigens (proteins, glycoproteins, etc.) or by detecting the antibodies synthesised against the pathogen.
In 1997, the first transgenic cow, Rosie, produced human protein-enriched milk (2.4 grams per litre). The milk contained a protein called _______ which was nutritionally a more balanced product for human babies than natural cow-milk.

The value of \(\sin ^{-1}\left(\frac{8}{17}\right)+\sin ^{-1}\left(\frac{3}{5}\right)\) is :

In a compound microscope the focal length of objective lens and eye lens are 4 em and 10 cm respectively. An object is placed at 6 cm from the objective lens. If the final image is formed at the near point of eye, then the magnifying power of microscope is:

In species-area relationships equation - log S = log C + Z log A
'Z' denotes the -

In Young's double slit experiment using monochromatic light of wavelength \(\lambda\), the intensity of light at a point on the screen where path difference is \(\lambda\), is 'T' units. What is the intensity of light at a point where path difference is \(\frac{\lambda}{4}\) ?