Given : `V=4/3 pi r^3`, find `(dV)/(dr)` and hence `[(dV)/(dr)]_(r=2)` .

If .^(15)C_(3r)=.^(15)C_(r+3), find .^(r)C_(2) .

If the formula f : R rarr R be given by f(x) = x^2 2 and g : R rarr R be given by g(x) = (x)/(x-1). X ne 1 . Find fog and gof. Hence find (fog) (2) and (gof (-3)

Show that the electric field intensity at a point in an electric field is equal to the negative of the potential gradient of the field at that point. E = -(dV)/(dr)

If theta in [0,3 pi] and r in R . Then , find the pair of ( r , theta ) satisfying 2 sin theta = r^(4)- 2r^(2)+3 .

If f : R rarr R and g : R rarr R be two mapping such that f(x) = sin x and g(x) = x^(2) , then find the values of (fog) (sqrt(pi))/(2) "and (gof)"((pi)/(3)) .

If r is the radius, S the surface area and V the volume of a spherical bubble, prove that (i) (dV)/(dt)=4pir^(2)(dr)/(dt)

The d.r of the line (4-x)/2=(3-y)/5=(z+1)/6 are

The radial distribution function [P(r)] is used to determine the most probble radius, which is used to find the electron in a givenorbital. (dp(r))/(dr) for 1s - orbital of hydrogen like atom having atomic number Z, is (dp)/(dr)=(4Z^(3))/(a_(o)"^(3))(2r(2Zr^(2))/(a_(o)))e^(-2zr//a_(o)): Then which of the following sttements is/are correct ?

Let A = R- {3} and B = R- {1}. If f: ArarrB is a function defined by f(x)= (x-2)/(x-3) show that f is one -one and onto, hence find f^(-1) .

If the sides be a,b,c, than find (r_(1)- r)(r _(2)+r_(3)).