In an AC circuit, the instantaneous values of emf and current are \( E = 100 \sin(314t) \) V and \( I = \sin(314t + \pi/3) \) A. The average power consumed in the circuit is:

In the depletion region of an unbiased p-n junction diode there are

Six charges each +3q are placed at the corners of a regular hexagon of each side 'a'. The electric field at the center of the hexagon 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:

The core of a transformer is laminated, so as to

The forbidden energy gap for Si is

In the Block diagram of a generalised communication system, the elements are given below. The correct order of elements should be :
(A) Transmitter
(B) Information Source
(C) User of Information
(D) Channel
(E) Receiver
Choose the correct answer from the options given below:

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

Read the following passage carefully and answer the given questions. During anaerobic sludge digestion, bacteria produce a mixture of gases such as methane, hydrogen sulphide and carbon dioxide. These gases form biogas and can be used as source of energy as it is inflammable. The bioactive molecule, cyclosporin A, that is used as an immunosuppressive agent in organ-transplant patients, is produced by the fungus Trichoderma polysporum. You must have noticed that bottled fruit juices bought from the market are clearer as compared to those made at home. This is because the bottled juices are clarified by the use of pectinases and proteases. Statins produced by the yeast Monascus purpureus have been commercialised as blood-cholesterol lowering agents. It acts by competitively inhibiting the enzyme responsible for synthesis of cholesterol. The BOD test measures the rate of uptake of oxygen by microorganisms in a sample of water and thus, indirectly, BOD is a measure of the organic matter present in the water.
BOD is a measure of-

The statement "the limiting molar conductivity of an electrolyte can be represented as the sum of the individual contributions of the anion and cation of the electrolyte" corresponds to the law

What is the path difference for destructive interference (if n is an integer)?

Answer the question on basis of passage given below :
Look at the following chemical reactions and answer the following question :
(A) \(C_7H_8 \xrightarrow{\text{Conc. HNO}_3, 0^\circ C}
(B) \xrightarrow{Sn/HCl}
(C) \xrightarrow{NaNO_2/H_3O^+}
(D) \xrightarrow{H_2O, Heat} (E)\)
(E) \(CH_3I \xrightarrow{KMnO_4/H^+}
(F) \xrightarrow{H_3O^+} (G) \xrightarrow{NaOH} (H)\)
Which of the following compounds will undergo coupling reaction ?

If \(\vec{a}, \vec{b}\) and \(\vec{c}\) are three unit vectors such that \(\vec{a}+2 \vec{b}-3 \vec{c}=\overrightarrow{0}\), then the value of \(2 \vec{a} \cdot \vec{b}-6 \vec{b} \cdot \vec{c}-3 \vec{c} \cdot \vec{a}\) is