If the coefficient of x7 and x8 in 2-x-3n are equal- then n is equal to

The correct option is D 55T_r+1in (2+x/3 )^n= ^nC_r2^n r(x/3 )^r=^nC_r2^n r/3^rx^r ∴ Coefficient of x^r=^nC_r2^n r/3^r ∴ ^nC_r2^n 7/3^7=^nC_82^n 8/3^8 ⇒2/n 7=1 ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Sum of Product of Binomial Coefficients

If the coeffi...

Question

If the coefficient of $x^{7} a n d x^{8} i n {(2 + \frac{x}{3})}^{n}$ are equal, then n is equal to

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B 55
$T_{r + 1} i n {(2 + \frac{x}{3})}^{n} =^{n} C_{r} 2^{n - r} {(\frac{x}{3})}^{r} =^{n} C_{r} \frac{2^{n - r}}{3^{r}} x^{r} ∴ C o e f f i c i e n t o f x^{r} =^{n} C_{r} \frac{2^{n - r}}{3^{r}} ∴^{n} C_{r} \frac{2^{n - 7}}{3^{7}} =^{n} C_{8} \frac{2^{n - 8}}{3^{8}} \Rightarrow \frac{2}{n - 7} = \frac{1}{8 \times 3} \Rightarrow n - 7 = 48 \Rightarrow n = 55$

Suggest Corrections

Similar questions

Q. If coefficients of

x^{7}

and

x^{8}

are equal in

{(2 + \frac{x}{3})}^{n}

then

n =

Q. If the coefficients of

x^{7}

and

x^{8}

{(2 + \frac{x}{3})}^{n}

are equal then n

=

Q. The coefficient of

x^{7}

and

x^{8}

in the expansion of

{(2 + \frac{x}{3})}^{n}

are equal, then

n

is equal to-

Q. In the expansion of

(2 + \frac{x}{3})^{n}

, coefficients of

x^{7}

and

x^{8}

are equal. Then

n =

Q. If the co-efficient of

x^{7}

and

x^{8}

{(2 + \frac{x}{3})}^{n}

are equal, then n is-

Join BYJU'S Learning Program

If the coefficient of x7 and x8 in (2+x3)n are equal, then n is equal to

The correct option is B 55Tr+1in(2+x3)n=nCr2n−r(x3)r=nCr2n−r3rxr∴ Coefficient of xr=nCr2n−r3r∴nCr2n−737=nC82n−838⇒2n−7=18×3⇒n−7=48⇒n=55

If the coefficient of $x^{7} a n d x^{8} i n {(2 + \frac{x}{3})}^{n}$ are equal, then n is equal to