If ^nC_r denotes the number of combinations o | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The given expression is $^nC_{r+1} + ^nC_{r-1} + 2 	imes ^nC_r$. We can rewrite $2 	imes ^nC_r$ as $^nC_r + ^nC_r$. So,the expression becomes $(

Vedclass · Accepted Answer

$^{n+2}C_{r+1}$

Vedclass · Answer

(B) The given expression is $^nC_{r+1} + ^nC_{r-1} + 2 	imes ^nC_r$. We can rewrite $2 	imes ^nC_r$ as $^nC_r + ^nC_r$. So,the expression becomes $(^nC_{r+1} + ^nC_r) + (^nC_r + ^nC_{r-1})$. Using the Pascal's identity formula $^nC_r + ^nC_{r-1} = ^{n+1}C_r$,we get: $(^nC_{r+1} + ^nC_r) + (^nC_r + ^nC_{r-1}) = ^{n+1}C_{r+1} + ^{n+1}C_r$. Applying the same identity again: $^{n+1}C_{r+1} + ^{n+1}C_r = ^{n+2}C_{r+1}$. Thus,the correct option is $B$.

If $^nC_r$ denotes the number of combinations of $n$ things taken $r$ at a time,then the expression $^nC_{r+1} + ^nC_{r-1} + 2 \times ^nC_r$ equals

Similar Questions

If $OA$ is equally inclined to $OX, OY$ and $OZ$ and if $A$ is $\sqrt{3}$ units from the origin,then $A$ is:

Which of the following is $NOT$ included in the class of Bryophyta as classified by Rothmaler?

If $x^y=y^x$, then $x(x-y \log x) \frac{d y}{d x}$ is equal to :

Which of the following is not an example of a chain-growth polymer?

Which of the following reagents is used to distinguish acetone and acetophenone?

Vedclass Test Series

Exam Paper Generator

Online Exam Module