The greatest coefficient in the expansion of x-y-z-t15 isA- 15 -3 - 1-5 -B- 5 -3 -4 -3C- 15 -3 -4 -3D- 15 -3 -4 -2

The correct option is C 15!/3!(4!)^3 greatest coefficient = n!/(q!)^m r((q+1)!)^r where q is quotient and r is remainder when n is divided by m. Here n = 15 a ...

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Standard XII

Mathematics

Multinomial Expansion

The greatest ...

Question

The greatest coefficient in the expansion of $(x + y + z + t)^{15}$ is

$\frac{15!}{3! (4!)^{2}}$

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$\frac{15!}{3! 4!}$

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$\frac{5!}{3! (4!)^{3}}$

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$\frac{15!}{3! (4!)^{3}}$

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Solution

The correct option is D
$\frac{15!}{3! (4!)^{3}}$

greatest coefficient $= \frac{n!}{(q!)^{m - r} ((q + 1)!)^{r}}$

where q is quotient and r is remainder when n is divided by m. Here n = 15 and m =4

q=3 And r = 3

So coefficient $= \frac{15!}{3! (4!)^{3}}$

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The greatest coefficient in the expansion of (x+y+z+t)15 is

The correct option is D 15!3!(4!)3 greatest coefficient =n!(q!)m−r((q+1)!)r where q is quotient and r is remainder when n is divided by m. Here n = 15 and m =4 q=3 And r = 3 So coefficient =15!3!(4!)3

The greatest coefficient in the expansion of $(x + y + z + t)^{15}$ is

The correct option is D
$\frac{15!}{3! (4!)^{3}}$

greatest coefficient $= \frac{n!}{(q!)^{m - r} ((q + 1)!)^{r}}$

where q is quotient and r is remainder when n is divided by m. Here n = 15 and m =4

q=3 And r = 3

So coefficient $= \frac{15!}{3! (4!)^{3}}$