The shortest wavelength of the spectral lines emitted in Balmer Series is : [Rydberg constant \( = 10^7 \text{ m}^{-1} \)]

Monochromatic lights of wavelengths \(6 2 0 ~ n m\) and \(6 2 6 ~ n m\), respectively are used to study diffraction at a single slit of aperture \(0 . 7 ~ m m\). The distance between the slit and the screen is 1.8 m . The separation between the positions of the first maxima of the diffraction pattern obtained in the two cases is

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 :

If charge is moving perpendicular to uniform magnetic field then its time period of revolution is:

A cell of emf \( \mathcal{E} = 10 \text{ V} \) and internal resistance \( r = 3 \Omega \) is connected to a uniform wire of length \( L = 500 \text{ cm} \) and resistance \( R = 3 \Omega \). The drop of potential with length in the wire is:

A metal plate is getting heated: It can be because
A. a direct current is passing through the plate
B. it is placed in a time varying magnetic field
C. it is placed in space varying magnetic field, but doesn't vary with time.
D. an alternating current passing through the plate
E. it is placed between the pole pieces of a magnet
Choose the correct answer from the options given below:

Two waves of amplitudes 3 m and 2 m, respectively superimpose at a point in the same phase. The resultant amplitude would be

The matrix \(\left[\begin{array}{lll}0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{array}\right]\) is a
(A) Null matrix
(B) Unit matrix
(C) Symmetric matrix
(D) Skew-symmetric matrix
Choose the correct answer from the options given below:

Arrange the following alcohols in decreasing order of acidity :

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In an AC generator, a 100 turns coil of area \(0.10 \text{ m}^2\) rotates at 50 Hz in a uniform magnetic field of 0.01 T. The maximum voltage generated in the coil is

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

Consider the differential equation \(\frac{d y}{d x}+y \tan x=\sec x\), then which of the following statements are correct?
(A) It is homogeneous
(B) It has \(\sec x\) as its integrating factor
(C) Its general solution is \(y \sec x=\tan x+c\), where \(c\) is an arbitrary constant.
(D) Its degree is not defined
Choose the correct answer from the options given below :

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.
When \(KMnO _4\) is added to oxalic acid solution, the decolourisation is slow in the beginning but becomes faster after some time because