 Hello and welcome to the session. In this session we will discuss a question which says that if 1 plus x whole x to power 12 is equal to C0 plus C1x plus C2x square plus so on up to C12 into x raise to power 12, find the value of C1 plus 2 into C2 plus 3 into C3 plus so on up to 12 into C12. Now before starting the solution of this question we should know what is the result. And that is the sum of the binomial coefficients. Now we know that 1 plus x whole raise to power n is equal to C0 plus C1x plus C2x square plus C3x cube plus so on up to Cn into x raise to power n. Now put x is equal to 1, this implies 1 plus 1 whole raise to power n is equal to C0 plus C1 plus C2 plus C3 plus so on up to Cn. Further this implies 2 raise to power n is equal to C0 plus C1 plus C2 plus C3 plus so on up to Cn. This means that the sum of the binomial coefficients is equal to 2 raise to power n. Now this result will work out as a key idea for solving out this question. And now we will start with the solution. Here we have to find the value of C1 plus 2 into C2 plus 3 into C3 plus so on up to 12 into C12. Now we know that 1 is equal to n. 2 is equal to n into n minus 1 over 1 into 2. C3 is equal to n into n minus 1 into n minus 2 over 1 into 2 into 3. And continuing likewise n is equal to 1. Now plus 2 into C2 plus 3 into C3 plus so on up to 12 into C12 will be equal to now 12. Now we know that C1 is equal to n so it will be 12 plus 2 into C2 which is n into n minus 1 over 1 into 2. So it will be 12 into 12 minus 1 over 1 into 2 plus 3 into C3. Putting the value of n as 12 here this will be 12 into 12 minus 1 the whole into 12 minus 2 the whole over 1 into 2 into 3 plus so on up to C12 which will be 12 into C12 will be equal to 1. Now this will be equal to taking 12 common it will be 12 and within brackets 1 plus cancel with 2 so it will be 12 minus 1 which is 11 plus and here it will be 12 minus 1 is 11 into 12 minus 2 which is 10 over 1 into 2 plus so on up to 1. Now this is equal to 12 within brackets 1 plus 11 plus 11 into 10 can be written as 11 minus 1 over 1 into 2 plus so on up to 1. Further this is equal to 12 within brackets 1 can be written as 11 C0 plus 11 can be written as 11 C1 plus 11 into 11 minus 1 over 1 into 2 can be written as 11 C2 plus so on up to 1 can be written as 11 C11. Now we know that sum of the dynamite coefficients is equal to 2 raise to power n so here this will be equal to and sum of these coefficients will be equal to 12 into 2 raise to power 11 the value of into C2 plus 3 into C3 plus so on up to 12 into C12 is equal to 12 into 2 raise to power 11. This is the solution of the given question and that's all for this session. Hope you all have enjoyed the session.