QJEEM20Mac79a: JEE Main 2020 Mathematics - Class 11 JEEM20Mac79a Solution: The coefficient of x 7 in the expression (1 + x) 10 + x(1 + x)…

Question

Verified Solution • 2025–26 Session moderate

The coefficient of x⁷ in the expression
(1 + x)¹⁰ + x(1 + x)⁹ + x²(1 + x)⁸ + ......+ x¹⁰ is:

Accepted Answer

(1 + x)¹⁰ + x(1 + x)⁹ + x²(1 + x)⁸ + ......+ x¹⁰

This is a G.P where

First term, a = (1 + x)¹⁰

common ratio, r =

\frac{x}{1 + x}

Number of terms = 11

Sum of G.P

=

\frac{{(1 + x)}^{10} (1 - {(\frac{x}{1 + x})}^{11})}{1 - \frac{x}{1 + x}}

= (1 + x)¹¹ – x¹¹

So Coefficient of x⁷ is ¹¹C₇ = 330

Step-by-Step Verified Solution