The number of one-one functions f : {a, b, c, d} $$\to$$ {0, 1, 2, ......, 10} such

that 2f(a) $$-$$ f(b) + 3f(c) + f(d) = 0 is ___________.

In an examination, there are 5 multiple choice questions with 3 choices, out of which exactly one is correct. There are 3 marks for each correct answer, $$-$$2 marks for each wrong answer and 0 mark if the question is not attempted. Then, the number of ways a student appearing in the examination gets 5 marks is ____________.

Let $$A\left( {{3 \over {\sqrt a }},\sqrt a } \right),\,a > 0$$, be a fixed point in the xy-plane. The image of A in y-axis be B and the image of B in x-axis be C. If $$D(3\cos \theta ,a\sin \theta )$$ is a point in the fourth quadrant such that the maximum area of $$\Delta$$ACD is 12 square units, then a is equal to ____________.

Let a line having direction ratios, 1, $$-$$4, 2 intersect the lines $${{x - 7} \over 3} = {{y - 1} \over { - 1}} = {{z + 2} \over 1}$$ and $${x \over 2} = {{y - 7} \over 3} = {z \over 1}$$ at the points A and B. Then (AB)² is equal to ___________.