List of top Mathematics Questions on Binomial theorem asked in WBJEE

If \( (1 + x - 2x^2)^6 = 1 + a_1x + a_2x^2 + \ldots + a_{12}x^{12} \), then the value of \( a_2 + a_4 + a_6 + \ldots + a_{12} \) is:
If \((1 + x + x^2 + x^3)^5 = \sum_{k=0}^{15} a_k x^k\), then \(\sum_{k=0}^{7} (-1)^k \cdot a_{2k}\) is equal to:
The coefficient of \(a^{10}b^7c^3\) in the expansion of \((bc + ca + ab)^{10}\) is:
If \( n \) is a positive integer, the value of:
\[ (2n + 1) \binom{n}{0} + (2n - 1) \binom{n}{1} + (2n - 3) \binom{n}{2} + \dots + 1 \cdot \binom{n}{n} \] is: