$y(n)=2x(n-1) + x(2n)$ is:

1. Linear or non linear:

Ans: $y_1(n) = 2x_1(n-1) + x_1(2n) \\ y_2(n) = 2x_2(n-1) + x_2(2n) \\ \therefore y_1(n) + y_2(n) = 2x_1(n-1) + 2x_2(n-1) + x_1(2n) + x_2(2n)….. (1) \\ Replacing \ \ x(n) by x_1(n) + x_2(n); \\ y(n) = 2x_1(n-1) + 2x_2(n-1) + x_1(2n) + x_2(2n)………...… (2) \\ from (1) (2), y(n) = y_1(n) + y_2(n)$

$\therefore$ Linear System

2. Causal or non-causal

Ans: the terms 2x(n-1)&x(2n) both indicate signals in future,

Thus, System is Non-Causal.

3. Time variant or Time invariant

Ans: y(n) = 2x(n-1) + x(2n)

$\therefore$, Delaying input by k units;

y(n,k) = 2x(n-1-k) + x(2n-k) …. . . . .. (1)

& replacing n by n-1;

y(n-k) = 2x(n-k-1) + x(2(n-k))

i.e., y(n-k) = 2x(n-1-k) + x(2n-2k)… . . ... (2)

from (1) & (2), y(n,k)  y(n-k)

$\therefore$ System is TimeVariant.

4. Static or Dynamic

Ans: the terms 2x(n-1)&x(2n) both indicate signals in future/past,

Thus, System is Dynamic.