The coefficient of x^6 in the expansion of (1+x+x^2)^6 is

Answers (1)

Solution:    We have ,   (1+x+x^2)^6

                Rightarrow   [1+x(1+x)]^6=1+^6c_1 x(1+x)+^6c_2x^2(1+x)^2+.....+^6c_6x^6(1+x)^6

                The coefficient of  x^6 is 

               Rightarrow          (^6c_3)(^6c_3)+(^6c_4)(^6c_2)+(^6c_5)(^6c_1)+1

               Rightarrow                   =20+90+30+1=141.

              ecause                    ^nc_r=fracn!(n-r)!r!  

Most Viewed Questions

Preparation Products

Knockout CUET (Physics, Chemistry and Mathematics)

Complete Study Material based on Class 12th Syllabus, 10000+ Question Bank, Unlimited Chapter-Wise and Subject-Wise Mock Tests, Study Improvement Plan.

₹ 7999/- ₹ 4999/-
Buy Now
Knockout CUET (Physics, Chemistry and Biology)

Complete Study Material based on Class 12th Syllabus, 10000+ Question Bank, Unlimited Chapter-Wise and Subject-Wise Mock Tests, Study Improvement Plan.

₹ 7999/- ₹ 4999/-
Buy Now
Knockout JEE Main (Six Month Subscription)

- AI Coach Study Modules, - Unlimited Mock Tests, - Study Improvement Plan.

₹ 9999/- ₹ 8499/-
Buy Now
Knockout JEE Main (Nine Month Subscription)

- AI Coach Study Modules, - Unlimited Mock Tests, - Study Improvement Plan.

₹ 13999/- ₹ 12499/-
Buy Now
Knockout NEET (Six Month Subscription)

- AI Coach Study Modules, - Unlimited Mock Tests, - Study Improvement Plan.

₹ 9999/- ₹ 8499/-
Buy Now
Boost your Preparation for JEE Main with our Foundation Course
 
Exams
Articles
Questions