The number of elements in the set $$\left\{ {A = \left( {\matrix{ a & b \cr 0 & d \cr } } \right):a,b,d \in \{ - 1,0,1\} \,and\,{{(I - A)}^3} = I - {A^3}} \right\}$$, where I is 2 $$\times$$ 2 identity matrix, is :

If the line y = mx bisects the area enclosed by the lines x = 0, y = 0, x = $${3 \over 2}$$ and the curve y = 1 + 4x $$-$$ x², then 12 m is equal to _____________.

Let f(x) be a cubic polynomial with f(1) = $$-$$10, f($$-$$1) = 6, and has a local minima at x = 1, and f'(x) has a local minima at x = $$-$$1. Then f(3) is equal to ____________.

Four identical hollow cylindrical columns of mild steel support a big structure of mass 50 $$\times$$ 10³ kg. The inner and outer radii of each column are 50 cm and 100 cm respectively. Assuming uniform local distribution, calculate the compression strain of each column. [Use Y = 2.0 $$\times$$ 10¹¹ Pa, g = 9.8 m/s²]