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7.Binomial Theorem
easy
જો ${(1 + x)^{43}}$ ની વિસ્તરણમાં ${(2r + 1)^{th}}$ અને ${(r + 2)^{th}}$ પદના સહગુણક સમાન હોય તો $r$ મેળવો.
A
$14$
B
$15$
C
$13$
D
$16$
Solution
(a) Coefficient of ${(2r + 1)^{th}}$ term in expansion of $(1 + x)^{43}$ = ${}^{43}{C_{2r}}$ and coefficient of ${(r + 2)^{th}}$ term = coefficient of ${\{ (r + 1) + 1\} ^{th}}$ term = ${}^{43}{C_{r + 1}}$
According to question ${}^{43}{C_{2r}} = {}^{43}{C_{r + 1}}$
$ = {}^{43}{C_{43 – (r + 1)}}$ then $2r = 43 – (r + 1)$or $3r = 42$ or $r = 14$.
Standard 11
Mathematics
