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Here's a challenge , a plausibility check and a TL idea floating around in my mind. With a POD of 1625 , is there any possibility for the English / ( Or more plausibily , the British) to achieve the following two pre requisites:

1:Exerting the Same Level of Control over the Indian Subcontinent as in OTL 1850 +

2: Ruling China either directly , or at the very least via a puppet Emperor of China or any arrangement in between.

By China , I mean China proper, excluding Xinjiang , Manchuria , or Outer Mongolia , Qinghai or Gansu , though the British may control parts of these provinces , or even the vast majority of it , either through local intermeditaries Ala via the Princely States analogue , or directly on the level of say , Bengal after the BEIC dissolved.

Can the British achieve such a feat by 1900 at latest , and hold on to both regions for at least 50 years?
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