In an electromagnetic wave, the ratio of energy densities of electric and magnetic fields is :

The maximum power drawn out of cell is given by : (E is emf, r is internal resistance)

Identify the correct statements among the following:
(A) Gauss's law is valid for the closed surface only.
(B) It is not possible to derive Gauss's law from Coulomb's law
(C) The electric field inside a uniformly charged thin spherical shell is zero
(D) The flux is contributed by the electric charges outside the closed surface
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A bar magnet of magnetic moment \(M_1\) is axially cut into two equal parts. If these two pieces are arranged perpendicular to each other in the shape of L, the resultant magnetic moment becomes \(M_2\), then the value of \(\frac{ M _1}{ M _2}\) is :

A current I flows in a circular loop of radius R. The magnetic field at a point on its axis at distance r from the center of the loop is

A plane concave lens of glass (\( \mu = 1.5 \)) has a radius of curvature of its curved face 50 cm. The power of the lens is :

The oscillation period of a freely suspended magnetic needle does NOT depend upon :

Identify the commensalism from the following associations:

Read the passage carefully and answer the questions
Sodium dichromate \(Na _2 Cr _2 O _7\) and Potassium dichromate \(K _2 Cr _2 O _7\) are strong oxidizing agents; in acidic solution, its oxidising action can be represented as follows :
\(Cr _2 O _7^{2-}+14 H ^{+}+6 e^{-} \rightarrow 2 Cr ^{3+}+7 H _2 O \left( E ^{\circ}=1.33 V\right)\)
The chromates and dichromates are interconvertible in aqueous solution depending upon pH of the solution.
The chromate ion is tetrahedral whereas the dichromate ion consists of two tetrahedra sharing one corner with \(Cr - O - Cr\) bond angle of \(126^{\circ}\)
Potassium permanganate is prepared by fusion of \(MnO _2\) with an alkali metal hydroxide and an oxidising agent like \(KNO _3\).
This produces the dark green \(K _2 MnO _4\) which disproportionates in a neutral or acidic solution to give permanganate. It is a strong oxidizing agent. Hydrogen ion concentration of the solution plays
an important part in the reduction of permanganate to manganate, manganese dioxide and manganese(II) salt.
Potassium permanganate forms dark purple (almost black) crystals which are isostructural with those of \(KClO _4\).
The salt is not very soluble in water \((6.4 g / 100 g\) of water at 293 K ), but when heated it decomposes at 513 K.
Potassium dichromate is used in the leather industry because of its nature as

Which among the following is not a broad spectrum antibiotic?

Two solenoids of equal number of turns having their lengths and radii in the same ratio \(1: 3\). The ratio of their self inductances \(L _{ 1 }: L _{ 2 }\) will be :

\(\int \frac{x \sin ^{-1} x}{\sqrt{1-x^2}} d x=\)

Match List - I with List - II

List - I	List - II
(A) The degree of the differential equation \(\left(\frac{d^2 y}{d x^2}\right)^2+\left(\frac{d y}{d x}\right)=x \sin \left(\frac{d y}{d x}\right)\)	(I) 4
(B) The degree of differential equation \(\frac{d^2 y}{d x^2}+\left(\frac{d y}{d x}\right)^{1 / 4}+x^{1 / 5}=0\)	(II) 1
(C) The degree of differential equation \(\frac{d^2 y}{d x^2}+\left(\frac{d y}{d x}\right)^3+6 y^5=0\)	(III) Not defined
(D) The degree of differential equation \(1+\left(\frac{d y}{d x}\right)^4=7\left(\frac{d^2 y}{d x^2}\right)^3\)	(IV) 3

Choose the correct answer from the options given below: