Binomial Theorem · JEE Main previous year questions

2012 3 questions

1. Q52012 · 26 May 2012 · Shift 1

   The middle term in the expansion of ${\left(1-\frac{1}{x}\right)}^n(1-x{)}^n$ in powers of $x$ is

   1. A.$-{}^{2n}{C}_{n-1}$
   2. B.$-{}^{2n}{C}_n$
   3. C.${}^{2n}{C}_{n-1}$
   4. D.${}^{2n}{C}_n$
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   Answer: D

2. Q42012 · 12 May 2012 · Shift 1

   The number of terms in the expansion of $(y^{1/5}+x^{1/10}{)}^{55}$, in which powers of $x$ and $y$ are free from radical signs are

   1. A.six
   2. B.twelve
   3. C.seven
   4. D.five
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   Answer: A

3. Q232012 · 7 May 2012 · Shift 1

   If $f(y)=1-(y-1)+(y-1{)}^2-(y-1{)}^3+\cdots -(y-1{)}^{17}$ then the coefficient of $y^2$ in it is

   1. A.${}^{17}{\mathrm{C}}_2$
   2. B.${}^{17}{\mathrm{C}}_3$
   3. C.${}^{18}{\mathrm{C}}_2$
   4. D.${}^{18}{\mathrm{C}}_3$
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   Answer: D