A \(\beta\)-particle is moving perpendicular to the uniform electric field created by a potential difference of \( 6 \times 10^3 \text{ V} \) across parallel metal plates separated by a distance of 6 cm. What is the acceleration of the beta particle between the plates? (Mass of electron = \( 9.1 \times 10^{-31} \text{ kg} \))

In an a.c. circuit, a resistor, a capacitor and an inductor are connected in series, in which \( X_C = X_L = R \). The impedance of this circuit will be

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

When a ray of light is incident at an angle \( \theta = 60^{\circ} \) on an air-glass interface, the reflected ray is 100 percent plane polarised. The value of the refractive index of the glass with respect to air (\( ^an_g \)) is given by :

Which of the following phenomenon is responsible for the reddish appearance of sun during sunset or sunrise ?

Stopping potential for photoelectrons :

The work function for a metallic surface is 4.0 eV. The longest wavelength of light that can cause photoelectron emission is approximately:

Two particles \( P_1 \) and \( P_2 \), having equal charges accelerated by the same potential difference enter a region of uniform magnetic field and describe circular paths of radii \( R_1 \) and \( R_2 \), respectively. The ratio of the mass of \( P_1 \) to that of \( P_2 \) will be

If \(A=\left[\begin{array}{cc}-2 & 3 \\ 1 & 2\end{array}\right]\) and \(B=\left[\begin{array}{cc}-1 & 0 \\ 2 & 3\end{array}\right]\), then \((3 A+2 B)^{\prime}\) is:

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 one of the following events does not occur during gene regulation in eukaryotes?

The reduction of cyclohexanone with \(NaBH _4\) produces

Total internal reflection can take place only, if