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.

Sum of the series sum_(r=1)^(n) (r^(2)+1)r! is

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

In DeltaABC, let b=6, c=10and r_(1) =r_(2)+r_(3)+r then find area of Delta ABC.

Prove that if two bubbles of radii r_(1) and r_(2)(r_(1)ltr_(2)) come in contact with each other then the radius of curvature of the common surface r=(r_(1)r_(2))/(r_(2)-r_(1))

Two satellites of masses of m_(1) and m_(2)(m_(1)gtm_(2)) are revolving round the earth in circular orbits of radius r_(1) and r_(2)(r_(1)gtr_(2)) respectively. Which of the following statements is true regarding their speeds v_(1) and v_(2) ?

A spherical capacitor consists of two concentric spherical conductors, held in position by suitable insulating supports (Fig. 2.34). Show that the capacitance of a spherical capacitor is given by C = (4 pi epsilon_(0)r_(1)r_(0))/(r_(1)-r_(2)) where r_(1) and r_(2) are the radii of outer and inner spheres, respectively.

If y=sum_(r=1)^(x) tan^(-1)((1)/(1+r+r^(2))) , then (dy)/(dx) is equal to

f(n)=sum_(r=1)^(n) [r^(2)(""^(n)C_(r)-""^(n)C_(r-1))+(2r+1)(""^(n)C_(r ))] , then

If in a triangle r_1=r_2+r_3+r , prove that the triangle is right angled.