The last digit in $7^{300}$ is

Let $S=\{a+b \sqrt{2}: a, b \in Z \}$,$T_1=\{(-1+\sqrt{2})^n: n \in N \}$ and $T_2=\{(1+\sqrt{2})^n: n \in N \}$. Then which of the following statements is (are) $TRUE$?
$(A)$ $Z \cup T_1 \cup T_2 \subset S$
$(B)$ $T_1 \cap (0, \frac{1}{2024}) = \phi$,where $\phi$ denotes the empty set
$(C)$ $T_2 \cap (2024, \infty) \neq \phi$
$(D)$ For any given $a, b \in Z$,$\cos(\pi(a+b \sqrt{2})) + i \sin(\pi(a+b \sqrt{2})) \in Z$ if and only if $b=0$,where $i=\sqrt{-1}$

The sum of the coefficients in the expansion of $(1 + x - 3x^2)^{2163}$ will be

For $|x| < \frac{1}{5}$,the coefficient of $x^3$ in the expansion of $\frac{1}{(1-5 x)(1-4 x)}$ is

The expression $[x + (x^3 - 1)^{1/2}]^5 + [x - (x^3 - 1)^{1/2}]^5$ is a polynomial of degree

If $(1+x+x^2+x^3)^5 = \sum_{k=0}^{15} a_k x^k$,then $\sum_{k=0}^7 a_{2k}$ is equal to