In a bombing attack, there is 50% chance that a bomb will hit the target. Atleast two independent hits are required to destroy the target completely. Then the minimum number of bombs, that must be dropped to ensure that there is at least 99% chance of completely destroying the target, is __________.

The coefficient of x⁴ in the expansion of
(1 + x + x² + x³)⁶ in powers of x, is ______.

Let the vectors $$\overrightarrow a $$, $$\overrightarrow b $$, $$\overrightarrow c $$ be such that
$$\left| {\overrightarrow a } \right| = 2$$, $$\left| {\overrightarrow b } \right| = 4$$ and $$\left| {\overrightarrow c } \right| = 4$$. If the projection of
$$\overrightarrow b $$ on $$\overrightarrow a $$ is equal to the projection of $$\overrightarrow c $$ on $$\overrightarrow a $$
and $$\overrightarrow b $$ is perpendicular to $$\overrightarrow c $$, then the value of
$$\left| {\overrightarrow a + \vec b - \overrightarrow c } \right|$$ is ___________.

A spaceship in space sweeps stationary interplanetary dust. As a result, its mass
increases at a rate $${{dM\left( t \right)} \over {dt}}$$ = bv²(t), where v(t) is its instantaneous velocity. The instantaneous acceleration of the satellite is :