For `2lt=r`

nCr + 2.nC (r-1) + nC (r-2) = (n + 2) Cr (2 <= r <= n)

Consider the family of circles x^2 + y^2= r^2 2 lt r lt 5 . If in the first quadrant, the common tangent to a circle of this family and the ellipse frac{x^(2)}{25} +frac{y^(2)}{4} =1 meets the axes at A and B then find the equation of the locus of middle point of AB.

A particle of mass m approaches a region of force starting from r=+infty The potential energy function in terms of distance r from the origin is given by, U(r) = K/(2a^(3))(3a^(2)-r^(2)) for 0 lt r lt a =K//r for r gt a (a) Derive the force F(r) and determine whether it is repulsive or attractive. (b) With what velocity should the particle start at r=infty to cross over to other side of the origin. (c) If the velocity of the particle at r= infty is sqrt((2K)/(am)) towards the origin describe the motion.

In Delta ABC , if r_(1) lt r_(2) lt r_(3) , then find the order of lengths of the sides

An artificial earth satellite is taken from a higher orbit to a lower orbit i.e. r_(2) lt r_(1) . In this process, the gravitational potential energy

A soap bubble of radius r_(1) is placed on another soap bubble of radius r_(2)(r_(1) lt r_(2)) . The radius R of the soapy film separating the two bubbles is :