Binomial Theorem · JEE Main previous year questions

2018 3 questions

1. Q242018 · 16 Apr 2018 · Shift 1

   The coefficient of $x^2$ in the expansion of the product $(2-x^2).((1+2x+3x^2{)}^6+(1-4x^2{)}^6)$ is :

   1. A.107
   2. B.106
   3. C.108
   4. D.155
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   Answer: B

2. Q232018 · 15 Apr 2018 · Shift 1

   If n is the degree of the polynomial, $${\left[\frac{2}{\sqrt{5x^3+1}-\sqrt{5x^3-1}}\right]}^8+{\left[\frac{2}{\sqrt{5x^3+1}+\sqrt{5x^3-1}}\right]}^8$$ and m is the coefficient of $x^n$ in it, then the ordered pair (n, m) is equal to :

   1. A.$(24,(10{)}^8)$
   2. B.$(8,5(10{)}^4)$
   3. C.$(12,(20{)}^4)$
   4. D.$(12,8(10{)}^4)$
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   Answer: C

3. Q192018 · 8 Apr 2018 · Shift 1

   The sum of the co-efficients of all odd degree terms in the expansion of ${\left(x+\sqrt{x^3-1}\right)}^5+{\left(x-\sqrt{x^3-1}\right)}^5,(x>1)$ is

   1. A.$2$
   2. B.$-1$
   3. C.$0$
   4. D.$1$
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   Answer: A