Which of the following statements is NOT correct?

A thin infinite line charge has linear charge density of \( 2.0 \times 10^{-9} \text{ C/m} \). The electric field intensity at a distance of 3 m from the line charge is : (\( \frac{1}{4\pi\epsilon_0} = 9 \times 10^9 \))

An electromagnet has stored 540 J of magnetic energy when a current of 6 A exists in its coil. What is the value of average emf induced, if the current is reduced to zero in 0.54s?

Identify the correct statements among the following.
(A) Electrical appliances in a household are always connected in series.
(B) Electrical appliances in a household are always connected in parallel.
(C) The potential difference across different electrical appliances in households is not equal.
(D) The potential difference across different electrical appliances in households is equal.
Choose the correct answer from the options given below:

Two parallel long wires carry currents, \( i_1 \) and \( i_2 \) with \( i_1 > i_2 \). When the currents are in same direction, the magnetic field at a point midway between them is \( 10 \mu \text{T} \). If the direction of \( i_2 \) is reversed, the field becomes \( 30 \mu \text{T} \). The ratio of \( i_1/i_2 \) is:

A wire of length \( L \) meters, carrying a current \( I \) ampere is bent in the form of a circle. The magnitude of its magnetic moment, in SI units, is:

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

n-Hexane is obtained when glucose is

A slab of material of dielectric constant \( k \), having the same area as the plate of a parallel plate capacitor but has a thickness \( \frac{3}{5} \) of the distance between the plates \( d \), is inserted between the plates of the capacitor. When there is air between the plates, the potential difference is \( V_0 \). What is the potential difference between the plates of the capacitor after inserting the dielectric?

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 micro-organisms in a sample of water and thus, indirectly, BOD is a measure of the organic matter present in the water.
During anaerobic sludge digestion, bacteria produce the biogas. The composition of this biogas is -

Name the particle 'X' emitted in the nuclear reaction given below -
\( {}_{11}^{22}Na \rightarrow {}_{10}^{22}Ne + \nu + X \)

If the matrix \(\left[\begin{array}{ccc}-1 & x-y & 4 \\ 2 & 0 & 5 \\ x+y & z & 6\end{array}\right]\) is symmetric, then \(x+3 y+2 z\) is equal to

The probability distribution of a random discrete variable is given

X	-1	0	1	2	3
P(X)	0.1	p	0.3	q	r

If it is known that \(P(X=1)\) is the mean of \(P(X=0)\) and \(P(X=2)\).Then the value of \(r\) is :