gud question hemant ....

please check the solution of it 

Multiplying the last two expressions we have to find coefficient of t²⁴in (1+t²)¹²(1+t¹²+²⁴) 

t²⁴ term will come as a sum of three terms in the expanded expression

1st term is t²⁴ term in 1st expression multiplied by 1 in the second expression.
2nd term is t¹² term in 1st expression multiplied by t¹² term in the second expression.
3rd term is 1 in the first expression multiplied by t²⁴ term in the second expression.

Coefficients of 1 and 3 terms are 1 and 1.

Coefficient of 2 term = coefficient t¹² term in 1 st expression which is (1+t²)¹²

7th term or 6+1th term in the expansion will have t¹² term

Hence coefficient of 7th term = ¹²C₆

Therefore coefficient of t²⁴ term will be

¹²C₆ + 2 ...Answer...

 i think we are at solutions....