Doy 55 puntos por esta par de preguntas?

En la primera pregunta hay un error.

Propondré corregirla de la siguiente forma<img src="https://tex.z-dn.net/?f=%5Ctext%7BHallar%20el%20resto%20de%20dividir%20%7D%5Cunderbrace%7B3535...35%7D_%7B64~cifras%7D%5Ctext%7B%20entre%2011%7D%5C%5C%20%5C%5C%5Ctextbf%7BSoluci%5C%27on%7D%5C%5C%5C%5C%5Cunderbrace%7B3535...35%7D_%7B64~cifras%7D%3D35%5Ctimes%5Cunderbrace%7B1010...101%7D_%7B64~cifras%7D%5C%5C%5C%5C%5Cunderbrace%7B3535...35%7D_%7B64~cifras%7D%3D35%5Ctimes%281%2B10%5E2%2B10%5E4%2B10%5E6%2B...%2B10%5E%7B62%7D%29%5C%5C%5C%5C...%5C%5C10%5Cequiv%20-1%20%5Cmod%2011%5C%5C35%5Cequiv%202%5Cmod%2011...%5C%5C%5C%5C%5Cunderbrace%7B3535...35%7D_%7B64~cifras%7D%5Cequiv%202%5Ctimes%281%2B%28-1%29%5E2%2B...%2B%28-1%29%5E%7B62%7D%29%20%5Cmod%2011%5C%5C%5C%5C" /><img src="https://tex.z-dn.net/?f=%5Cunderbrace%7B3535...35%7D_%7B64~cifras%7D%5Cequiv%202%2863%29%5Cmod%2011%5C%5C%5C%5C%5Cunderbrace%7B3535...35%7D_%7B64~cifras%7D%5Cequiv%202%28-3%29%5Cmod%2011%5C%5C%5C%5C%5Cunderbrace%7B3535...35%7D_%7B64~cifras%7D%5Cequiv%20-6%5Cmod%2011%5C%5C%5C%5C%5Cunderbrace%7B3535...35%7D_%7B64~cifras%7D%5Cequiv%205%5Cmod%2011%5C%5C" />Así el residuo de dividir es 5.

= = = = = = = = = = = = = = = = = = = = = = = <img src="https://tex.z-dn.net/?f=4530%20%2B%20a%20%3D%208k%5C%5C8k%27%2B2%20%2B%20a%20%3D%208k%5C%5Ca%3D%208k%27%27-2%5C%5Ca%3D6%5C%5C%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%5C%5C%5Coverline%7B7x6x%7D%3D9r%5C%5C7%2Bx%2B6%2Bx%3D9r%5C%5C2x%2B13%3D9r%5C%5C2x%3D9r%27-4%5C%5Cx%3D9r%27%27-2%5C%5C%5C%5C%5Cboxed%7Bx%3D7%7D" />.