Jamia Millia Islamia Binomial Theorem Previous Year Questions (PYQs) – Page 2 of 2
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Showing 13 questions
The coefficient of the middle term in the expansion of $(2 + 3x)^4$ is
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4
Solution
Total terms = $4 + 1 = 5$
Middle term = $\dfrac{5 + 1}{2} = 3^\text{rd}$ term
$\text{T}_3 = \binom{4}{2} (2)^{2} (3x)^{2} = 6 \times 4 \times 9x^2 = 216x^2$
Coefficient = 216
The general term in the expansion of $(x + y)^n$ is:
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Solution
According to the Binomial Theorem, the general term is:
$T_{r+1} = {^nC_r}, x^{,n-r} y^r$
If A and B are coefficients of $x^n$ in $(1+x)^{2n}$ and $(1+x)^{2n-1}$ respectively, then $\dfrac{A}{B}$ equals
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Solution
$A = \binom{2n}{n},\ B = \binom{2n-1}{n} \Rightarrow \dfrac{A}{B} = 2.$
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