The number of terms in the expansion of $${(1 + 5\sqrt {2x} )^9} + {(1 - 5\sqrt {2x} )^9}$$ is

The number of different seven-digit numbers that can be written using only the three digits 1, 2 and 3 with the condition that the digit 2 occurs twice in each number is

Given 2x $$-$$ y + 2z = 2, x $$-$$ 2y - z = $$-$$4, x + y + $$\lambda$$z = 4, then the value of $$\lambda$$ such that the given system of equation has no solution is

Let $$A = \left[ {\matrix{ 1 & { - 1} & 1 \cr 2 & 1 & { - 3} \cr 1 & 1 & 1 \cr } } \right]$$ and $$10B = \left[ {\matrix{ 4 & 2 & 2 \cr { - 5} & 0 & \alpha \cr 1 & { - 2} & 3 \cr } } \right]$$

If B is the inverse of A, then the value of $$\alpha$$ is