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:
The remainder obtained when \(1!+2!+3!+.....+11!\) is divided by 12 is
If $C_{0}, C_{1}, C_{2}, \ldots, C_{n}$ denote the coefficients in the expansion of $(1+x)^{n}$, then the value of $C_{1}+2C_{2}+3C_{3}+\ldots+nC_{n}$ is
The coefficient of $ x^{-10}$ in $\left(x^{2} - \frac{1}{x^{3}}\right)^{10}$ is
If \( n = 1, 2, 3, \dots \), then \( \cos \alpha \cos 2\alpha \cos 4\alpha \dots \cos^{2n - 1} \alpha \) is equal to: 
The coordinates of a moving point p are (2t2 + 4, 4t + 6). Then  its locus will be a
If sin θ and cos θ are the roots of the equation  ax2 – bx + c = 0, then a, b and c satisfy the relation