_{[ x][infinity ]} logxⁿ- [x]/[x], n belongs to N=????

[x] denotes the greatest integer function

 f(a)=g(a)=k, then the nth derivatives of fⁿ (a) ,gⁿ (a)exist and are not equal for some n

if

two soap bubbles of different radii are connectedby a tube

A ) air flows  from the larger body to he smaller body

B ) airflows from smaller to the larger body

c)there is no flow of air

D)data is insufficient

a 20cm long cappillary tube is dipped in water . water raises to the height of 8cm. if the arrangement is put in freely falling elivator, the length of he water column is

a) 4cm

b) 20cm

C)8cm

D) 10cm

a candle of diameter d is floating on a liquid in a cylindrical container of D. if it burns at the rate of 2cm/hr, the top of the candle will ( ignore he volume change due to molten wax falling into the container)

1) remain at the same height

2) fall at the rate of 1cm/ hour

3) fall at the  rate of 2cm /hour

4) go up at the rate of 1cm / hr

 

 

  a spherical body of radius r and density _b falls freely from a certain height falls into a tank of water of density _w and cofficient of viscocity . if the density of the body _b  = 2_w and the speed of he body reduces to half in water. then the distance 'h'( from where it fell to the surface of the  liquid) is

2/9r² (_w - _b) g

4/81r² (w ^{- B  _{/   )}2 g}

  4/81r² ( r²  _b g² /)²

2/9( r² _w /)^{2  g}