 Hi and how are you all today? I am Priyanka. The question says, find a positive value for of m for which the coefficient of x raised to the power 2 in the expansion of 1 plus x raised to the power m is 6. Now let us quickly discuss this question. Now the coefficient of x raised to the power 2 in the expansion of 1 plus x raised to the power m is c m, 2. Right? Now according to the question, the coefficient is 6. So we have c m, 2 is equal to 6. So we have m factorial divided by 2 factorial m minus 2 factorial is 6. Further m factorial can be written as m multiplied by m minus 1 multiplied by m minus 2 factorial. 2 factorial is 2 multiplied by 1 and we have it multiplied with m minus 2 factorial. That is equal to 6. Now on cancelling out m minus 2 from the numerator and the denominator, we have m m minus 1 divided by 2 is equal to 6. Our 2 can be taken to the right hand side. We have m m minus 1 is equal to 12. Further this can be converted into quadratic equation and we have m square minus m minus 12 is equal to 12. On splitting the middle term, we have m square minus 4m plus 3m minus 12 is equal to 0. Taking out m common from the first 2 terms, we are left with m minus 4 and taking out a positive 3 from the last 2 terms, we have m minus 4 taking common out is equal to 0. We have m minus 4 common and on clubbing m plus 3 we are left with these 2 equations. That means either m is equal to minus 3 or m is equal to 4. Since in the question it just mentioned to find out the positive value of m, so our required answer will be m is equal to 4 since in the bracket we can write down m cannot be equal to minus 3. So this ends the question. Take care. Bye for now.