The sum of the coefficients in the expansion of $(1 + x - 3x^2)^{3148}$ is

Let $x \in \mathbb{R}$ be so small that the powers of $x$ beyond two are insignificant and negligibly small. For such $x$,if $(1-x)^3(2+x)^6$ is approximated by $a+bx+cx^2$,then $a+b+c=$

The coefficient of $x^{50}$ in the binomial expansion of $(1 + x)^{1000} + x(1 + x)^{999} + x^{2}(1 + x)^{998} + \dots + x^{1000}$ is

The lowest integer which is greater than $\left(1+\frac{1}{10^{100}}\right)^{10^{100}}$ is $.....$

Evaluate $(\sqrt{3}+\sqrt{2})^{6}-(\sqrt{3}-\sqrt{2})^{6}$ (in $\sqrt{6}$)

The number of terms in the expansion of $(a + b + c)^n$ will be