The volume of the greatest cylinder which can be inscribed in a cone of height 30 cm and semi-vertical angle `30^0` is (a)`4000pi/((3))` (b) `400pi/3c m^3` (c)`4000pi/(sqrt(3))cm^3` (d) none of these

Show that height of the cylinder of greatest volume which can be inscribed in a right circular cone of height h and semi vertical angle alpha is one-third that of the cone and the greatest volume of cylinder is (4)/(27) pi h^(3) tan^(2) alpha .

Show that the cone of the greatest volume which can be inscribed in a given sphere has an altitude equal to 2/3 of the diameter of the sphere.

The principal value of sin^(-1)(sin((2pi)/3)) is (a) -(2pi)/3 (b) (2pi)/3 (c) (pi)/3 (d) (5pi)/3 (e) none of these

Range of f(x)=sin^(-1)x+tan^(-1)x+sec^(-1)x is (a) (pi/4,(3pi)/4) (b) [pi/4,(3pi)/4] (c) {pi/4,(3pi)/4} (d) none of these

If y=|cosx|+|sinx|,t h e n(dy)/(dx)a tx=(2pi)/3 is (1-sqrt(3))/2 (b) 0 (c) 1/2(sqrt(3)-1) (d) none of these

The three sides of a trapezium are equal, each being 8cm. The area of the trapezium, where it is maximum, is (a) 24sqrt(3) c m^2 (b) 48sqrt(3)c m^2 (c)72 sqrt(3)c m^2 (d) none of these

The volume of a solid right circular cone is 11088 cm^(3) . If its height is 24 cm then find the radius of the cone.

In a A B C ,/_B=90^0 and b+a=4. The area of the triangle is maximum when /_C is (a) pi/4 (b) pi/6 (c) pi/3 (d) none of these