Calculate the standard cell potential in (V) of the cell in which following reaction takes place :

Fe²⁺(aq) + Ag⁺(aq) $$ \to $$ Fe³⁺(aq) + Ag (s)

Given that

$$E_{A{g^ + }/Ag}^o = xV$$

$$E_{Fe^{2+ }/Fe}^o = yV$$

$$E_{Fe^{3+ }/Fe}^o = zV$$

Let $$\mathop a\limits^ \to = 3\mathop i\limits^ \wedge + 2\mathop j\limits^ \wedge + x\mathop k\limits^ \wedge $$ and $$\mathop b\limits^ \to = \mathop i\limits^ \wedge - \mathop j\limits^ \wedge + \mathop k\limits^ \wedge $$ , for some real x. Then $$\left| {\mathop a\limits^ \to \times \mathop b\limits^ \to } \right|$$ = r is possible if :

In an ellipse, with centre at the origin, if the difference of the lengths of major axis and minor axis is 10 and one of the foci is at (0,5$$\sqrt 3$$), then the length of its latus rectum is :

If $$z = {{\sqrt 3 } \over 2} + {i \over 2}\left( {i = \sqrt { - 1} } \right)$$,

then (1 + iz + z⁵ + iz⁸)⁹ is equal to :