If n and r are positive integers such that`0ltrltn` then show that the roots of the quadratic equation`nC_r x^2+2. ^nC_(r+1)x+^nC_(r+2)=0` are real.

If n and r are positive integers such that 0ltrltn then roots of the equation ^nC_r x^2+2.^nC_(r+1)x+^nC_(r+2)=0 are necessarily (A) imaginary (B) real and equal (C) real and unequal (D) real but may be equal or unequal

If n and r are integers such that 1

Prove that "^nC_r + 2. ^nC_(r-1) + ^nC_(r-2) = ^(n+2)C_r

If n is a positive integer,sum_(r=0)^(n)(^(^^)nC_(r))^(2)=

If n is a positive integer, for (1+x)^(n) ,then sum_(r=0)^(n).^nC_(r)=

Prove that two +ive integers n,r cannot be found such that ^nC_r ,^nC_(r+1),^nC_(r+2) and ^nC_(r+3) are in A.P.

Write the expression ^nC_(r+1)+^(n)C_(r-1)+2xx^(n)C_(r) in the simplest form.