JEE Mathematics 2023 Question with Solution

Step-by-step solution

Common mistakes

• Choosing only one term containing $2x^3$ is incorrect because the coefficient of $x^7$ can arise from multiple combinations of factors in the multinomial expansion. Instead, account for all non-negative integer selections whose total power of $x$ is $7$.

• Treating $(1 - x + 2x^3)^{10}$ as a simple binomial is wrong because there are three terms inside the bracket. Use multinomial reasoning or systematic case selection instead of the binomial general term alone.

• Ignoring the negative sign from the term $-x$ leads to sign errors in the final coefficient. Track the parity of the number of times $-x$ is chosen so that the sign of each contributing term is correct.