Let $$0 < \theta < {\pi \over 2}$$. If the eccentricity of the

hyperbola $${{{x^2}} \over {{{\cos }^2}\theta }} - {{{y^2}} \over {{{\sin }^2}\theta }}$$ = 1 is greater

than 2, then the length of its latus rectum lies in the interval :

If y = y(x) is the solution of the differential equation,

x$$dy \over dx$$ + 2y = x², satisfying y(1) = 1, then y($$1\over2$$) is equal to :

If $$A = \left[ {\matrix{ {\cos \theta } & { - \sin \theta } \cr {\sin \theta } & {\cos \theta } \cr } } \right]$$, then the matrix A^–50 when $$\theta $$ = $$\pi \over 12$$, is equal to :

For $$x \in R - \left\{ {0,1} \right\}$$, Let f₁(x) = $$1\over x$$, f₂ (x) = 1 – x

and f₃ (x) = $$1 \over {1 - x}$$ be three given

functions. If a function, J(x) satisfies

(f₂ o J o f₁) (x) = f₃ (x) then J(x) is equal to :