If y = y(x) is the solution of the differential equation, $${e^y}\left( {{{dy} \over {dx}} - 1} \right) = {e^x}$$ such that y(0) = 0, then y(1) is equal to:

The logical statement (p $$ \Rightarrow $$ q) $$\Lambda $$ ( q $$ \Rightarrow $$ ~p) is equivalent to :

Five numbers are in A.P. whose sum is 25 and product is 2520. If one of these five numbers is -$${1 \over 2}$$ , then the greatest number amongst them is:

If the sum of the coefficients of all even powers of x in the product
(1 + x + x² + ....+ x²ⁿ)(1 - x + x² - x³ + ...... + x²ⁿ) is 61, then n is equal to _______.