MAH CET MCA Binomial Theorem Previous Year Questions (PYQs)
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The coefficient of $x^{n}$ in the expansion of $(1+x)^{2n}$ and $(1+x)^{2n-1}$ are in the ratio
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Solution
$\text{Coeff}{x^n},(1+x)^{2n}=\binom{2n}{n}$ and $\text{Coeff}{x^n},(1+x)^{2n-1}=\binom{2n-1}{n}$.
$\displaystyle \binom{2n}{n}=\frac{(2n)}{n,n}=\frac{2n}{n}\cdot\frac{(2n-1)}{n,(n-1)}=2\binom{2n-1}{n}$.
So ratio $=2:1$.
The number of irrational terms in the expansion of $(5^{\frac{1}{6}}+2^{\frac{1}{8}})$ is
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Solution
The coefficient of $x^n$ in the expansion of $(1−9x+20x^2)^{−1}$ is
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Solution
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