If for x $$\in$$ $$\left( {0,{\pi \over 2}} \right)$$, log₁₀sinx + log₁₀cosx = $$-$$1 and log₁₀(sinx + cosx) = $${1 \over 2}$$(log₁₀ n $$-$$ 1), n > 0, then the value of n is equal to :

A pack of cards has one card missing. Two cards are drawn randomly and are found to be spades. The probability that the missing card is not a spade, is :

If y = y(x) is the solution of the differential equation,

$${{dy} \over {dx}} + 2y\tan x = \sin x,y\left( {{\pi \over 3}} \right) = 0$$, then the maximum value of the function y(x) over R is equal to:

Let the curve y = y(x) be the solution of the differential equation, $${{dy} \over {dx}}$$ = 2(x + 1). If the numerical value of area bounded by the curve y = y(x) and x-axis is $${{4\sqrt 8 } \over 3}$$, then the value of y(1) is equal to _________.