Let $r$ be the remainder when $2021^{2020}$ is divided by $2020^2$. Then $r$ lies between

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

Assertion $(A)$: If $a_1, a_2, \ldots, a_n$ are the $n$ distinct roots of the equation $x^n-2=0$, then $1+\left(1-a_1\right)\left(1-a_2\right) \ldots\left(1-a_n\right)=0$.
Reason $(R)$: If $\alpha_1, \alpha_2, \ldots, \alpha_n$ are the roots of $f(x) \equiv p_0 x^n+p_1 x^{n-1}+\ldots+p_n=0$, then the roots of $f(g(x))=0$ are $g^{-1}(\alpha_i)$ for $i=1, 2, \ldots, n$.
The correct option among the following is:

The degree of the polynomial $(x+\sqrt{x^4-1})^9+(x-\sqrt{x^4-1})^9$ is

Find the coefficient of $x^{49}$ in the expansion of $(2x + 1)(2x + 3)(2x + 5) \dots (2x + 99)$.

Which is larger: $(1.01)^{1000000}$ or $10,000$?