question_answer

If the coefficients of rth,\[(r+1)th\] and\[(r+2)th\]terms in the binomial expansion of\[{{(1+y)}^{m}}\]are in AP, then m and r satisfy the equation     AIEEE  Solved  Paper-2005

A) \[{{m}^{2}}-m(4r-1)+4{{r}^{2}}+2=0\]

B) \[{{m}^{2}}-m(4r+1)+4{{r}^{2}}-2=0\]

C) \[{{m}^{2}}-m(4r+1)+4{{r}^{2}}+2=0\]

D) \[{{m}^{2}}-m(4r-1)+4{{r}^{2}}-2=0\]

Correct Answer: B

Solution :

(i) The coefficient ofth term of is. (ii) If a, b, c are in AP, then According to the given conditions,