JEE Main 2020 — Binomial Theorem Question with Solution
From: JEE Main 2020 (Online) 4th September Morning Slot
Question
Let
Then is equal to ______.
Then is equal to ______.
Enter your answer
Show full solutionCorrect answer: 8
Correct answer
8
Step-by-step explanation
Note : Multinomial Theorem :
The general term of the expansion is
where n1 + n2 + ..... + nn = n
Here, in general term is
Coefficient of is
where
For, Coefficient of x7 :
2n1 + n2 = 7
Possible values of n1, n2 and n3 are
Coefficient of x7
Coefficient of x13 = a13
Here 2n1 + n2 = 13
possible values of n1, n2 and n3 are
Coefficient of x13
The general term of the expansion is
where n1 + n2 + ..... + nn = n
Here, in general term is
Coefficient of is
where
For, Coefficient of x7 :
2n1 + n2 = 7
Possible values of n1, n2 and n3 are
| 3 | 1 | 6 |
| 2 | 3 | 5 |
| 1 | 5 | 4 |
| 0 | 7 | 3 |
Coefficient of x7
Coefficient of x13 = a13
Here 2n1 + n2 = 13
possible values of n1, n2 and n3 are
| 6 | 1 | 3 |
| 5 | 3 | 2 |
| 4 | 5 | 1 |
| 3 | 7 | 0 |
Coefficient of x13
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