AIEEE 2002 Math Solved Paper

We know, (a+b)n=‌nC0⋅an+‌nC1⋅an−1⋅b+...+‌nCn⋅bn
Remember to find sum of coefficient of binomial expansion we ave to put 1 in place of all the variable.
So put a=b=1
∴2n=‌nC0+‌nC1+‌nC2...+‌nCn
According to question, 2n=4096=212
⇒n=12
So (a+b)n=(a+b)12
Here n=12 is even so formula for greatest term is
T‌

π

2

+1=‌nC‌

n

2

⋅a‌

n

2

⋅b‌

n

2

For n=12, greatest term T6+1=‌12C6⋅a6⋅b6
∴ Coefficient of the greatest term =‌12C6=‌

12!

6!6!

=924