If ratio of coefficient of third and fourth term in expansion of {left( {x

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7.Binomial Theorem

medium

If the ratio of the coefficient of third and fourth term in the expansion of ${\left( {x - \frac{1}{{2x}}} \right)^n}$ is $1 : 2$, then the value of $ n$ will be

$18$

$16$

$12$

$-10$

Solution

(d) ${T_3} = {\,^n}{C_2}{(x)^{n – 2}}{\left( { – \frac{1}{{2x}}} \right)^2}$ and ${T_4} = {\,^n}{C_3}{(x)^{n – 3}}{\left( { – \frac{1}{{2x}}} \right)^3}$

But according to the condition,

$\frac{{ – \,n(n – 1) \times 3 \times 2 \times 1 \times 8}}{{n(n – 1)(n – 2) \times 2 \times 1 \times 4}} = \frac{1}{2}$

$\Rightarrow n = – 10$

Standard 11

Mathematics

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hard

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Given that $4^{th}$ term in the expansion of ${\left( {2 + \frac{3}{8}x} \right)^{10}}$ has the maximum numerical value, the range of value of $x$ for which this will be true is given by

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If the coefficients of the three successive terms in the binomial expansion of $(1 + x)^n$ are in the ratio $1 : 7 : 42,$ then the first of these terms in the expansion is

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(JEE MAIN-2015)

If the ratio of the coefficient of third and fourth term in the expansion of ${\left( {x - \frac{1}{{2x}}} \right)^n}$ is $1 : 2$, then the value of $ n$ will be

Solution

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