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Greatest Term (numerically) - Practice Questions & MCQ

Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main

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  • 35 Questions around this concept.

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If for some positive integer n, the coefficients of three consecutive terms in the binomial expansion of (1+x)^{n+5} are in the ratio 5:10:14, then the largest coefficient in this expansion is.

Find the numerically greatest term in the expansion of (2+3 x)^{9},  when  x=\frac{2}{3}.

The numerically greatest term in (x+y)^{20} \text { when } x=2.1, y=-2.5 \text { is }

The largest term in the expansion of $(3+2 x)^{50}$. where $x=\frac{1}{5}$ is

The largest term in the expansion of  (3+2 x)^{50} where  x=\frac{1}{5}  is

The greatest coefficient in the expansion of (1+x)^{2 n+1} \text { is }

If the sum of the coefficients in the expansion (x+y)^n is 1024, then the value of the greatest coefficient in the expansion is:

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Numerically, the greatest value of the term in the expansion of (3-5 x)^{15}, when x=1/5, is

Let $a_n=\frac{(1000)^n}{n!}$ for $n \in N$ Then $a_n$ is greatest, when

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The greatest coefficient in the expansion of $(1+x)^{2 n+2}$ is

Concepts Covered - 1

Greatest Term (numerically)

Numerically Greatest Value:

The number which has the highest modulus value is called the Numerically Greatest Value

Eg, out of $4,-7,-5,6,1$
-7 has the Numerically Greatest Value because its mod value $(=7)$ is the largest among all the mod values of the given numbers

Method to find the Numerically Greatest Term of the expansion $(a+b)^n$
First, find the value of $m$ which is

$
\mathrm{m}=\frac{(\mathrm{n}+1)}{1+\left|\frac{\mathrm{a}}{\mathrm{~b}}\right|}
$
If m is an integer, then $\mathrm{T}_{\mathrm{m}}$ and $\mathrm{T}_{\mathrm{m}+1}$ are numerically equal and both are greatest terms.
If $m$ is not an integer, then $T_{[m]+1}$ is the greatest term, where $[m]$ is an integral part of $m$.

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Greatest Term (numerically)

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