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JEE Main 20207 JanuaryEvening Shift
Exam
JEE Main
Year
2020
Date
7 January
Shift
Evening Shift
Subject
Mathematics
Chapter
Binomial Theorem

JEE Main 2020 · 7 January · Evening Shift · Mathematics · Binomial Theorem

The coefficient of x ^ 7 in the expression (1 + x) ^ 10 + x (1 + x)...

The coefficient of x7{x}^{7} in the expression (1+x)10+x(1+x)9+x2(1+x)8+....+x10{\left(1 + x\right)}^{10} + x{\left(1 + x\right)}^{9} + {x}^{2}{\left(1 + x\right)}^{8} + . . . . + {x}^{10}, is

Options

  1. A210210
  2. B330330
  3. C120120
  4. D420420

Correct answer

B. 330330

Step-by-step solution

As the given series is in G.P., so its sum is

(1+x)10[1−(x1+x)11](1−x1+x)\dfrac{{\left(1 + x\right)}^{10}\left[1 - {\left(\dfrac{x}{1 + x}\right)}^{11}\right]}{\left(1 - \dfrac{x}{1 + x}\right)}

(1+x)10[(1+x)11−x11](1+x)11×1(1+x)=(1+x)11−x11\dfrac{{\left(1 + x\right)}^{10}\left[{\left(1 + x\right)}^{11} - {x}^{11}\right]}{{\left(1 + x\right)}^{11} \times \dfrac{1}{\left(1 + x\right)}} = {\left(1 + x\right)}^{11} - {x}^{11}

Coefficient of x7{x}^{7}, is 11C7=11C4=330{11}_{{C}_{7}} = {11}_{{C}_{4}} = 330

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