If the sum of the coefficients in the expansion of $(1 - 3 x + 10 x^{2})^{n}$ is a and if the sum of the coefficients in the expansion $(1 + x^{2})^{n}$ is b, then,

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!

None of these

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

Open in App

Solution

The correct option is B
We have a = sum of the coefficient in the expansion of
$(1 - 3 x + 10 x^{2})^{n} = (1 - 3 + 10)^{n} = (8)^{n}$
$\Rightarrow (1 - 3 x + 10^{2})^{n} = (2)^{3 n}, [putting x=1]$
Now, b = sum of the coefficients in the expansion of $(1 + x^{2})^{n} = (1 + 1)^{n} = 2^{n} .$
Clearly, $a = b^{3}$

Suggest Corrections

Similar questions

Q. If the sum of the coefficients in the expansion

(1 - 3 x + 10 x^{2})^{n}

a

and sum of coefficients in the expansion of

(1 + x^{2})^{n}

is b,then

Q. If the sum of the coefficients in the expansion of

(1 - 3 x + 10 x^{2})^{n}

a

and if the sum of the coefficients in the expansion of

(1 + x^{2})^{n}

b

, then

Q. The sum of the coefficients in the expansion of

(1 - 2 x + 5 x^{2})^{n}

is a and the sum of the coefficients in the expansion of

(1 + x)^{2 n}

b

. Then

If a and b denote the sum of the coefficients of $x^{n}$ in the expansions of $(1 - 3 x + 10 x^{2})^{n}$ and $(1 + x^{2})^{n}$ respectively, then write the relation between a and b.

Q. If the sum of coefficients in the expansion of

{(1 - x sin θ + x^{2})}^{n}

P

, then

Join BYJU'S Learning Program

If the sum of the coefficients in the expansion of (1–3x+10x2)n is a and if the sum of the coefficients in the expansion (1+x2)n is b, then,

The correct option is B We have a = sum of the coefficient in the expansion of (1−3x+10x2)n=(1−3+10)n=(8)n ⇒(1−3x+102)n=(2)3n,[putting x=1] Now, b = sum of the coefficients in the expansion of (1+x2)n=(1+1)n=2n. Clearly,a=b3

If the sum of the coefficients in the expansion of $(1 - 3 x + 10 x^{2})^{n}$ is a and if the sum of the coefficients in the expansion $(1 + x^{2})^{n}$ is b, then,