A pure inductor of 70 mH is connected to a source of 220 V. The frequency of the source is 50 Hz. The current in the circuit is:

A very long straight wire carries a current (I) directed along positive Y-axis. A point charge +Q moves with velocity (v) along X -axis. The direction of force on the charge at point (5,0,0) m is

A circular conducting loop is placed in a uniform magnetic field with its plane perpendicular to the field. An emf is induced in the loop if:
A. it is displaced in the same plane in magnetic field
B. it is rotated about its axis
C. it is rotated about a diameter
D. it is converted into square loop in the same plane:
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The equivalent resistance of the network shown in figure between the points a and b will be

Rainbow is a phenomenon due to the combined effect of
(A) Interference
(B) Dispersion
(C) Reflection
(D) Refraction
(E) Scattering
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For transistor action, which of the following statements are correct?
A. Base, Emitter and Collector region have similar size and doping concentrations.
B. The base must be very thin and lightly doped.
C. The emitter junction is forward biased and the collector junction is reverse biased.
D. Both emitter and collector junction all forward biased.
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Resistivity of a conductor depends on

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Molar conductivity \(\left(\Lambda_m\right)\) of a solution at a given concentration (c) is the conductance of volume, V of solution, containing one mole of electrolyte kept between the two electrodes with area of cross-section A and at a distance of unit length. It increases with the decrease in concentration and when the concentration approaches zero, the molar conductivity is called limiting molar
conductivity \(\left(\Lambda_m^0\right)\). For a strong electrolyte, \(\Lambda_m\) increases linearly with dilution and is given by \(\Lambda_m=\Lambda_m^0-A c^{1 / 2}\). The value of the constant A for a given solvent depends on the type of electrolyte along with temperature. According to Kohlrausch law, the value of \(\Lambda_m^0\) for an electrolyte is \(\Lambda_m^0=\nu_{+} \lambda_{+}^0+\nu_{-} \lambda_{-}^0\), where \(\nu_{+}\)and \(\nu_{-}\) are the number of cations and anions, respectively, per molecule of the electrolyte and \(\lambda_{+}^0\) and \(\lambda_{-}^0\) are limiting molar conductivities of cation and anion, respectively. Kohlrausch law finds many applications, like determining the solubility of a sparingly soluble salt, determining the degree of dissociation \(\left(\Lambda_m / \Lambda_m^0\right)\), and the dissociation constant of a weak electrolyte.
The plot between \(\Lambda_m\) and \(c^{1 / 2}\) is a straight line with

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.
mRNA silencing through RNA interference (RNAi) refers to the:

A pure silicon crystal has \( 5 \times 10^{28} \text{ atoms m}^{-3} \). It is doped by 2 ppm concentration of pentavalent arsenic. The number of holes are: (Consider \( n_i = 1.5 \times 10^{16} \text{ m}^{-3} \))

If \(\theta\) is the angle between two unit vectors \(\hat{a}\) and \(\hat{b}\) then \(|\hat{a}-\hat{b}|=\)

A plane electromagnetic wave travels in vacuum along y-direction. At the same instant, the direction of Electric and magnetic fields are:

For an AC circuit, a phase diagram shows emf on X-axis, and current I is at angle \( \theta \) to emf. Angle \( \theta \) is phase angle between emf and current. Current I is resolved into two components, \( I \cos \theta \) is along emf on X-axis. \( I \sin \theta \) is along perpendicular direction to emf.
(A) Component \( I \cos \theta \) will draw the power from the source
(B) Component \( I \sin \theta \) will draw the power from the source
(C) \( I \cos \theta \) is called the powerless current
(D) \( I \sin \theta \) is called the powerless current
Choose the correct answer from the options given below: