If the coefficients of x⁻² and x⁻⁴ in the expansion of $${\left( {{x^{{1 \over 3}}} + {1 \over {2{x^{{1 \over 3}}}}}} \right)^{18}},\left( {x > 0} \right),$$ are m and n respectively, then $${m \over n}$$ is equal to :

Let f(x) = sin⁴x + cos⁴ x. Then f is an increasing function in the interval :

The integral $$\int {{{dx} \over {\left( {1 + \sqrt x } \right)\sqrt {x - {x^2}} }}} $$ is equal to :

(where C is a constant of integration.)

Let a₁, a₂, a₃, . . . . . . . , a_n, . . . . . be in A.P.

If a₃ + a₇ + a₁₁ + a₁₅ = 72,

then the sum of its first 17 terms is equal to :