A long wire with a small current element of length 1 cm is placed at the origin and carries a current of 10 A along the x-axis. The magnitude of the magnetic field, due to the element, on the y-axis at a distance \( r = 0.5 \, m \) from it, would be

In n-type semiconductors, A are the majority charge carriers and B are the minority charge carriers. Here A and B are :

Two nuclei have mass numbers 125 and 27, respectively. The mass density ratio of their nuclei will be

The current and voltage in an ac circuit are given by \( I = 5 \sin(100t - \pi/2) \text{ A} \) and \( V = 200 \sin(100t) \text{ V} \). The power dissipated in the circuit is

The main causes of energy loss in transformers are
1. Hysteresis loss
2. Flux leakage
3. Eddy current
4. Damping
Choose the correct answer from the options given below :

The ratio of the de-Broglie wavelengths associated with protons accelerated through a potential of 128 V and alpha particles accelerated through a potential of 64 V will be

Which of the following combinations should be used for better tuning of an LCR circuit used for communication?

An electron enters a crossed electrical and magnetic field region with a speed of \( 100 \text{ m s}^{-1} \) along \( +x \)-axis and passes undeviated. The strength of magnetic field is 5.0 T and it acts along \( +z \)-axis. Give the electrical field in vector notations indicating its magnitude as well as direction :

In visible light, orange differs from violet as they have

Let A be a non-singular square matrix of order 3 and |adj A| = 5 then |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.
Some strains of Bacillus thuringiensis produce proteins that do not kill certain arthropods, such as:

Photoelectric current depends on
(A) the intensity of incident light
(B) the potential difference applied between the two electrodes
(C) the nature of the emitter material
(D) the conductivity of the emitter material
Choose the correct answer from the options given below:

The area of a triangle whose vertices are (-3,0), (3, 0) and (0, k) is 6. Then the value (or the values) of k will be: