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If coefficients of \small (2 r+1)^{t h} term and \small (r+2)^{\operatorname{th}}  term are equal in the expansion of \small (1+x)^{43} then the value of  r  will be  
 

Option: 1

14


Option: 2

15


Option: 3

13


Option: 4

16


Answers (1)

best_answer

Coefficient of (2 r+1)^{\mathrm{th}} term in expansion of   (1+x)^{43}={ }^{43} C_{2 r}  and the coefficient of  (r+2)^{t h} term = coefficient of\{(r+1)+1\}^{\text {th }} \text { term }={ }^{43} C_{r+1}  
    According to question,  { }^{43} C_{2 r}={ }^{43} C_{r+1}={ }^{43} C_{43-(r+1)}
    then  2 r=43-(r+1) \text { or } 3 r=42 \text { or } r=14 . 

Posted by

vishal kumar

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