Simplify `root(r)((9^(r+1/4).sqrt(3.3^(-r)))/(3.sqrt(3^(-r))))`

sqrt((9^((r + (I)/4)) sqrt(3.3^(-r)))/(3.sqrt(3^(-r)))) = k , then the value of k is

Three equal circles each of radius r touch one another.The radius of the circle touching all the three given circles internally is (2+sqrt(3))r(b)((2+sqrt(3)))/(sqrt(3))r((2-sqrt(3)))/(sqrt(3))r(d)(2-sqrt(3))r

If lim_(n rarr oo)(sum_(r=1)^(n)sqrt(r)sum_(r=1)^(n)(1)/(sqrt(r)))/(sum_(r=1)^(n)r)=(k)/(3) then the value of k is

The largest area of the trapezium inscribed in a semi-circle or radius R, if the lower base is on the diameter is (3sqrt(3))/(4)R^(2)( b) (sqrt(3))/(2)R^(2)(3sqrt(3))/(8)R^(2) (d) R^(2)

The volume of the largest possible cube that can be inscribed in a hollow spherical ball of radius rcm is (2)/(sqrt(3))r^(2)( b) (4)/(3)r^(2)(c)(8)/(3sqrt(3))r^(3)(d)(1)/(3sqrt(3))r^(3)

sum_(r=1)^(n)sin^(-1)((sqrt(r)-sqrt(r-1))/(sqrt(r(r+1)))) is equal to tan^(-1)(sqrt(n))-(pi)/(4)tan^(-1)(sqrt(n+1))-(pi)/(4)tan^(-1)(sqrt(n))(d)tan^(-1)(sqrt(n)+1)