If `cot [cot^(-1)((7)/(25))]=(1)/(mu),` where `mu in R.` Then find `[mu],` where `[*]` denotes GIF

If mu=u^y then find mu_(uy)

Statement-1 : A glass convex lens (refractive index, mu_(1)=1.5 ), when immersed in a liquid of refractive index mu_(2)=2 , functions as a diverging lens. Statement-2 : The focal length of a lens is given by (1)/(f)=(mu-1)((1)/(R_(1))-(1)/(R_(2))) , where mu is the relative refractive index of the material of the lens with respect to the surrounding medium.

int_(0)^(oo)[cot^(-1)x]dx (where [.] denotes the

If the greatest and least values of the function f(x)=arctan x-(1)/(2)ln x on [(1)/(sqrt(3)),sqrt(3)] are lambda and mu respectively. Then (A) [lambda +mu]=1 where [.]= greatest Integer function (B) (lambda +mu)=2 where (.)= least Integer function (C) (lambda+mu)=0 where (.)= least Integer function (D) [lambda +mu]=-1 where [.]= greatest Integer function

Let int _(0)^(1) (4x ^(3) (1+(x ^(4)) ^(2010)))/((1+x^(4))^(2012))dx = (lamda)/(mu) where lamda and mu are relatively prime positive integers. Find unit digit of mu.

The solution set of inequality (tan^(-1)x)(cot^(-1)x)-(tan^(-1)x)(1+(x)/(2))-2cot^(-1)x+2(1+(pi)/(2))gtlim_(yrarr-oo)[sec^(-1)y-(pi)/(2)] is (where [ . ]denotes the G.I.F.)

A cyclist rides along the circumference of a circular horizontal plane of radius R , with the friction coefficient mu=mu_(0)(1-(r )/(R )) , where mu_(0) is constant and r is distance from centre of plane O . Find the radius of the circle along which the cyclist can ride with the maximum velocity, what is this valocity?