If `(r)/(r _(1))= (r_(2))/(r _(3)),` then show that `c=90^(@).`

If ((n),(r)) = ((n),(r+2)), then r = …… ,

In a triangle, if r_(1) gt r_(2) gt r_(3), then show a gtb gt c.

((44),(r-2)) = ((44),(r+2)), then r = ……

Show that (b-c)/(r _(1))+ (c-a)/(r _(2))+(a-b)/(r _(3)) =0.

If r_(1),r_(2) and r_(3) are the position vectors of three collinear points and scalars l and m exists such that r_(3)=lr_(1)+mr_(2) , then show that l+m=1.

If x=a + (a)/(r ) + (a)/(r^(2)) + …..oo, y= b - (b)/(r ) + (b)/(r^(2))-……..oo and z= c + (c )/(r^(2)) + (c )/(r^(4))+ ….oo then prove that (xy)/(z)= (ab)/(c )

The distance between two particles of masses m_(1)andm_(2) is r. If the distance of these particles from the centre of mass of the system are r_(1)andr_(2) respectively, then show that r_(1)=r((m_(2))/(m_(1)+m_(2)))andr_(2)=r((m_(1))/(m_(1)+m_(2)))

If both (x-2) and (x - (1)/(2)) are fractors of p x ^(2)- 5x +r, then show that p=r.

Write ‘True’ or ‘False’ and justify your answer: The volume of the frustum of a cone (1)/(3)pi h(r_(1)^(2)+r_(2)^(2)-r_(1)r_(2)) where h is the vertical height of the frustum and r_(1),r_(2) are the radii of the ends.