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8. Sequences and Series
hard
જો $^n{C_4},{\,^n}{C_5},$ અને ${\,^n}{C_6},$ એ સમાંતર શ્રેણીમાં હોય તો $n$ મેળવો.
A
$9$
B
$14$
C
$11$
D
$12$
(JEE MAIN-2019)
Solution
$2.{\,^n}{C_5}{ = ^n}{C_4}{ + ^n}{C_6}$
$2.\frac{{\left| n \right.}}{{\left| {5\left| {n – 5} \right.} \right.}} = \frac{{\left| n \right.}}{{\left| {4\left| {n – 4} \right.} \right.}} + \frac{{\left| n \right.}}{{\left| {6\left| {n – 6} \right.} \right.}}$
$\frac{2}{5}.\frac{1}{{n – 5}} = \frac{1}{{\left( {n – 4} \right)\left( {n – 5} \right)}} + \frac{1}{{30}}$
$n=14$ satisfying equation.
Standard 11
Mathematics
