In the binomial expansion of $${\left( {a - b} \right)^n},\,n \ge 5,$$ the sum of the $${5^{th}}$$ and $${6^{th}}$$ terms is zero. Then $$a/b$$ equals

Let the positive numbers $$a,b,c,d$$ be in A.P. Then $$abc,$$ $$abd,$$ $$acd,$$ $$bcd,$$ are

The number of integer values of $$m$$, for which the $$x$$-coordinate of the point of intersection of the lines $$3x + 4y = 9$$ and $$y = mx + 1$$ is also an integer, is

Let $${z_1}$$ and $${z_2}$$ be $${n^{th}}$$ roots of unity which subtend a right angle at the origin. Then $$n$$ must be of the form