$$\mathop {\lim }\limits_{x \to \infty } \left( {{n \over {{n^2} + {1^2}}} + {n \over {{n^2} + {2^2}}} + {n \over {{n^2} + {3^2}}} + ..... + {1 \over {5n}}} \right)$$ is equal to :

If   A = $$\left[ {\matrix{ 1 & {\sin \theta } & 1 \cr { - \sin \theta } & 1 & {\sin \theta } \cr { - 1} & { - \sin \theta } & 1 \cr } } \right]$$;

then for all $$\theta $$ $$ \in $$ $$\left( {{{3\pi } \over 4},{{5\pi } \over 4}} \right)$$, det (A) lies in the interval :

Let z₁ and z₂ be two complex numbers satisfying | z₁ | = 9 and | z₂ – 3 – 4i | = 4. Then the minimum value of | z₁ – z₂ | is :

If   ⁿC₄, ⁿC₅ and ⁿC₆ are in A.P., then n can be :