The magnitude of the change in oxidising power of the $$MnO_4^ - /M{n^{2 + }}$$ couple is x $$\times$$ 10^$$-$$4 V, if the H⁺ concentration is decreased from 1M to 10^$$-$$4 M at 25$$^\circ$$C. (Assume concentration of $$MnO_4^ - $$ and $$M{n^{2 + }}$$ to be same on change in H⁺ concentration). The value of x is ___________. $$\left[ {Given\,:{{2.303RT} \over F} = 0.059} \right]$$

The total number of amines among the following which can be synthesized by Gabriel synthesis is __________.

If a curve y = f(x) passes through the point (1, 2) and satisfies $$x {{dy} \over {dx}} + y = b{x^4}$$, then for what value of b, $$\int\limits_1^2 {f(x)dx = {{62} \over 5}} $$?

For which of the following curves, the line $$x + \sqrt 3 y = 2\sqrt 3 $$ is the tangent at the point $$\left( {{{3\sqrt 3 } \over 2},{1 \over 2}} \right)$$?