A long wire is bent into a circular coil of one turn and then into a circular coil of smaller radius having n turns. If the same current passes in both the cases, then the ratio of the magnetic fields produced at the centers in two cases will be :

Two cylindrical wires of the same material have their lengths in the ratio 2: 1 and their diameters in the ratio \(1: 3\). The ratio of the resistance of thinner wire to that of thicker wire is:

An \(\alpha\)-particle moves in a circular paths of radius 0.83 cm in the presence of a magnetic field \( 0.25 \text{ Wb/m}^2 \). The de-Broglie wavelength associated with the particle would be approximately :

A current of 5 A is passing through a metallic wire of cross-sectional area \( 5 \times 10^{-6} \text{ m}^2 \).
If the density of the charge carriers in the wire is \( 5 \times 10^{26} \text{ m}^{-3} \), the drift velocity of the electrons is:

Under forward-bias of a p-n diode
(A) p-side of the diode is connected to the positive terminal of the battery and n-side to the
negative terminal
(B) p-side of the diode is connected to the negative terminal of the battery and n-side to the
positive terminal
(C) The direction of the applied voltage (V) is opposite to the built-in potential drop
(D) The direction of the applied voltage (V) is the same as the built-in potential drop
(E) The magnitude of the diode forward current is usually in mA
Choose the correct answer from the options given below :

The expression of the magnetic energy stored in a solenoid in terms of magnetic field B, cross-sectional area A and length l of the solenoid, is:

Two bulbs marked 220 V, 200 W and 220 V, 1000 W, respectively, are connected in series to 220 V mains supply. The ratio of heat generated in them, respectively will be

If a line makes angles \(\alpha, \beta, \gamma\) with the positive directions of \(x\)-axis, \(y\)-axis, \(z\)-axis respectively, then the value of \(\cos 2 \alpha+\cos 2 \beta+\cos 2 \gamma\) is equal to:

Reaction of aniline with conc. \(HNO _3\) and conc. \(H _2 SO _4\) at 298 K will produce \(47 \%\) of:

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.
Some strains of Bacillus thuringiensis produce proteins that do not kill certain arthropods, such as:

The area of region bounded by the curve \(y=\cos x\) and \(x\)-axis between \(x=0\) and \(x=\pi\) is

Answer the question on the basis of passage given below:
Aldehydes are generally more reactive than ketones in nucleophilic addition reactions due to steric and electronic reasons. Sterically, the presence of two relatively large substituents in ketones hinders the approach of nucleophile to carbonyl carbon more than aldehydes having only one such substituent Electronically aldehydes are more reactive than ketones because two alkyl groups reduce the elctrophilicity of the carbonyl more effectively than in former.
4-Hydroxy-4-methylpentan-2-one and 4-methylpent-3-en-2-one are the products obtained from A by aldol
condensation. \(A\) is:

If \(|\vec{a}-\vec{r}|=|\vec{a}|=|\vec{r}|=1\), then angle between \(\vec{a}\) and \(\vec{r}\) is