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

a = 3 b

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a = b^{3}

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b = a^{3}

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none of these

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Solution

The correct option is A $a = b^{3}$
${(1 - 3 x + 10 x^{2})}^{n} = \sum \frac{(n)!}{(r_{1})! (r_{2})! (r_{3})!} {{(1)}^{r_{1}} . ({- 3 x)}^{r_{2}} . ({10 x)}^{r_{3}}}$
We can get the sum of the coefficient by taking $x = 1$
Hence, $a = {(1 - 3 + 10)}^{n} = 8^{n} = 2^{3 n}$
Similarly ${(1 + x^{2})}^{n} = \sum_{r = 0}^{n}^{n} C_{r} (x^{2})^{r}$
Taking $x = 1;$ $b = 2^{n}$
Hence, $a = b^{3}$
Hence, the answer is $a = b^{3} .$

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

The correct option is A a=b3(1−3x+10x2)n=∑(n)!(r1)!(r2)!(r3)!{(1)r1.(−3x)r2.(10x)r3}We can get the sum of the coefficient by taking x=1Hence, a=(1−3+10)n=8n=23nSimilarly (1+x2)n=∑nr=0nCr(x2)rTaking x=1; b=2nHence, a=b3Hence, the answer is a=b3.

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