Use principle of homogenity of dimensions to find which one of the following relations is correct : (i) `T^2 =4pi^2r^2`
(ii) `T^2 =(4pi^2r^3)/(G)`
(iii) `T^2 = (4pi^2 r^3)/(GM)`

Using the principle .of homogeneity of dimensions find which of the following is correct T^2=4pi^2r^3

Find the which of the following are correct using dimensional analysis. (i) t^(2)=4pi^(2)a^(3) (ii) t^(2)=(4pi^(2)a^(3))/G (iii) t^(2)=(4pi^(2)a^(3))/(GM) where t is the time period, a is the radius of the orbit of a planet and M is the mass of sun.

Which among the following relations is correct? (a) t_(3//4) = 2t_(1//2) (b) t_(3//4) = 3t_(1//2) (c) t_(3//4) = 1/2t_(1//2) (d) t_(3//4) = 1/3t_(1//2)

Differentiate the following w.r.t.x (i) pi^2 (ii) e^2 (iii) -14

Differentiate the following w.r.t.x. (i) 2002 (ii) e^((-1)) (iii) pi^(2)

Evaluate the following integral : int_0^(pi/4) sin^3(2t) cos(2t) dt