The coefficient of $$x^7$$ in $${(1 - x + 2{x^3})^{10}}$$ is ___________.

Some couples participated in a mixed doubles badminton tournament. If the number of matches played, so that no couple played in a match, is 840, then the total number of persons, who participated in the tournament, is ___________.

Let a, b, c be three distinct positive real numbers such that $${(2a)^{{{\log }_e}a}} = {(bc)^{{{\log }_e}b}}$$ and $${b^{{{\log }_e}2}} = {a^{{{\log }_e}c}}$$.

Then, 6a + 5bc is equal to ___________.

Given below are two statements:

Statement I : If the number of turns in the coil of a moving coil galvanometer is doubled then the current sensitivity becomes double.

Statement II : Increasing current sensitivity of a moving coil galvanometer by only increasing the number of turns in the coil will also increase its voltage sensitivity in the same ratio

In the light of the above statements, choose the correct answer from the options given below :