If  $${\sum\limits_{i = 1}^{20} {\left( {{{{}^{20}{C_{i - 1}}} \over {{}^{20}{C_i} + {}^{20}{C_{i - 1}}}}} \right)} ^3} = {k \over {21}}$$  then k is equal to

If the line 3x + 4y – 24 = 0 intersects the x-axis at the point A and the y-axis at the point B, then the incentre of the triangle OAB, where O is the origin, is :

If the third term in the binomial expansion
of $${\left( {1 + {x^{{{\log }_2}x}}} \right)^5}$$ equals 2560, then a possible value of x is -

The sum of all values of $$\theta $$ $$ \in $$$$\left( {0,{\pi \over 2}} \right)$$ satisfying
sin² 2$$\theta $$ + cos⁴ 2$$\theta $$ = $${3 \over 4}$$ is -