The number of non-real roots of the equation $x^{10}-3 x^8+5 x^6-5 x^4+3 x^2-1=0$ is

Let $N$ be the set of positive integers. The number of distinct triplets $(x, y, z)$ satisfying $x, y, z \in N, x

A question paper has 3 parts and each part contains 4 questions. The number of different ways in which a candidate can answer 8 questions choosing at least two from each part is

If $k$ is the coefficient of $x^5$ in the expansion of $\left(2 x^2-\frac{1}{3 x^3}\right)^5$, then $\frac{3 k}{2}=$