In a plane electromagnetic wave, the electric field oscillates sinusoidally at a frequency of \( 3 \times 10^{10} \text{ Hz} \) and its amplitude is 30 V/m. The amplitude of the oscillating magnetic field is:

The magnetic moment of a current loop is \( 2.1 \times 10^{-25} \text{ A m}^{2} \). The magnetic field on the axis of the loop at a distance of 1.0 \( \text{\AA} \) from the loop would be : (Given radius of loop negligible)

In a series RLC circuit at resonance
(A) Impedance is maximum
(B) \( X_c = X_L \)
(C) Z = R
(D) \( \omega = \frac{1}{\sqrt{LC}} \)
Choose the correct answer from the options given below:

A sample of radioactive nuclei has a half life of 5.5 years. The fraction of sample remaining undecayed after 22 years is

Match List-I with List-II

List-I	List-II
(A) Intrinsic semiconductor	(I) Number of conduction electrons >> number of holes
(B) n-type semiconductor	(II) Number of conduction electrons << number of holes
(C) p-type semiconductor	(III) Net current is zero
(D) p-n junction under equilibrium	(IV) Number of conduction electrons = number of holes

Choose the correct answer from the options given below:

A diver at a depth of 1.2 m in clear water (n = 4/3) sees the sky in a cone of semi-vertical angle :

The distance between an object and its virtual image of magnification \( \frac{1}{2} \) as produced by a lens is 20 cm.
The focal length of the lens is

If \(A=\left[\begin{array}{ccc}0 & 0 & \sqrt{3} \\ 0 & \sqrt{3} & 0 \\ \sqrt{3} & 0 & 0\end{array}\right]\), then \(|\operatorname{adj} A|\) is equal to:

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.
ELISA is based on the principle of:

The derivative of \(f(\cot x)\) with respect to \(g(cosec x)\) at \(x=\frac{\pi}{4}\) (where \(\left.f^{\prime}(1)=2, g^{\prime}(\sqrt{2})=4\right)\) is:

If \(A\) is an invertible matrix of order 2 , then \(\operatorname{det}\left((\operatorname{adj} A)^{-1}\right)\) is equal to

Identify the species which is not invasive:

The value of \(\int \tan ^2 x d x\) is :
where \(C\) is the constant of integration.