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 :

In the expansion of $${\left( {{x \over {\cos \theta }} + {1 \over {x\sin \theta }}} \right)^{16}}$$, if $${\ell _1}$$ is the least value of the term independent of x when $${\pi \over 8} \le \theta \le {\pi \over 4}$$ and $${\ell _2}$$ is the least value of the term independent of x when $${\pi \over {16}} \le \theta \le {\pi \over 8}$$, then the ratio $${\ell _2}$$ : $${\ell _1}$$ is equal to :

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:

If z be a complex number satisfying |Re(z)| + |Im(z)| = 4, then |z| cannot be :