" "-4Derive an equation for the couple acring an selectric ilpole in a aniform elccric firid."

Derive the equation for the couple acting on a electric dipole in a uniform electric field.

Derive the equation fo the locus of a point twice as far from (-2,3,4) as from (3, -1, -2).

Derive the equation of a parabola in the standard form y^(2)=4ax with diagram.

Derive the equation of state for an ideal gas.What volume will be occupied by 4 grams of CO_2 at 27^@ C and 650 mm pressure ?

Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as Assertion (A): The degree of the differential equation given by (dy)/(dx)=(x^4-y^4)/((x^2+y^2)xy) is 1. Reason (R): The degree of a differential equation is the degree of the highest order derivative when differential coefficients are free from radicals and fraction The given differential equation has first order derivative which is free from radical and fraction with power = 1, thus it has a degree of 1.

(a) Account for the following: (i) Manganese shows maximum number of oxidation states in 3d series? (ii) E^@ value for Mn^(3+)| Mn^(2+) couple is much more positive than that of Cr^(3+)| Cr^(2+) . (iii) Ti^(4+) is colourless whereas V^(4+) is coloured in an aqueous solution. (b) Write the chemical equations for the preparation of KMnO_4 from MnO_2 . Why does purple colour of acidified permanganate solution decolourise when it oxidise Fe^(2+) to Fe^(3+) .