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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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  • 27 Questions around this concept.

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QuestionMEDIUM

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.

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

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

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

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

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

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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

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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{(n+1)}{1+\left | \frac{a}{b} \right |}}

If m is an integer, then Tm  and Tm + 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)

Study other Related Concepts

Greatest Term (numerically) Current Topic

Binomial Theorem - Formula, Expansion, Problems and Applications
Some Standard Expansions
General and Middle Terms
Greatest Term (numerically)
An Important Theorem
Problems on Divisibility
Finding last digits
Important Result (Comparison)
Multinomial Theorem
Series Involving Binomial Coefficients

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