NTA JEE Main 4th September 2020 Shift 2

A test consists of 6 multiple choice questions, each having 4 alternative answers of which only one is correct. The number of ways, in which a candidate answers all six questions such that exactly four of the answers are correct, is __________

Let PQ be a diameter of the circle $$x^2 + y^2 = 9$$. If $$\alpha$$ and $$\beta$$ are the lengths of the perpendiculars from P and Q on the straight line, $$x + y = 2$$ respectively, then the maximum value of $$\alpha\beta$$ is __________

If the variance of the following frequency distribution:

is 50, then x is equal to __________

Let $$\{x\}$$ and $$[x]$$ denote the fractional part of $$x$$ and the greatest integer $$\leq x$$ respectively of a real number $$x$$. If $$\int_0^n \{x\}dx$$, $$\int_0^n [x]dx$$ and $$10(n^2 - n)$$, $$(n \in N, n > 1)$$ are three consecutive terms of a G.P. then $$n$$ is equal to __________

If $$\vec{a} = 2\hat{i} + \hat{j} + 2\hat{k}$$, then the value of $$\left|\hat{i} \times (\vec{a} \times \hat{i})\right|^2 + \left|\hat{j} \times (\vec{a} \times \hat{j})\right|^2 + \left|\hat{k} \times (\vec{a} \times \hat{k})\right|^2$$, is equal to: