Indian coppers are notoriously tricky to track down. Often, the key distinguishing features have been either omitted from the design or are "off the flan" - These coins were struck from dies that were much larger than the blanks they were struck upon.
In this case, you're fortunate - a primary mintmark is present. On the side you've labelled "obverse" (which is, in fact, the obverse) just to the left of centre, there's a large symbol that looks kind of like a lowercase "Times New Roman" i, only with a bent base. This is the Overseer's mark of the Jodhpur mint from about 1936 to about 1940; you'll find coins like this listed in Krause under Indian States - Jodhpur, KM# 131-133 (Edward VIII) and 141-143 (George VI).
In this case, I can't see any trace of a date, and I think it's "George" rather than "Edward", so that makes it KM# 143.
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Does anyone have any idea how I might be able to identify the smaller coin?
I recall that the old Craig catalogue had a handy list of Indian States mintmarks - it sure saved a lot of the flipping you have to do with Krause nowadays. If anyone knows a website where someone's attemped to list these mintmarks, I'd be delighted to know.
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