Let a – 2b + c = 1.

If $$f(x)=\left| {\matrix{ {x + a} & {x + 2} & {x + 1} \cr {x + b} & {x + 3} & {x + 2} \cr {x + c} & {x + 4} & {x + 3} \cr } } \right|$$, then:

The following system of linear equations
7x + 6y – 2z = 0
3x + 4y + 2z = 0
x – 2y – 6z = 0, has

The number of terms common to the two A.P.'s 3, 7, 11, ....., 407 and 2, 9, 16, ....., 709 is ______.

Let ƒ and g be differentiable functions on R such that fog is the identity function. If for some a, b $$ \in $$ R, g'(a) = 5 and g(a) = b, then ƒ'(b) is equal to :