12263/64 Pune - H. Nizamuddin AC Duronto - यह है पुणेकर वालों की राजधानी जिसका speed है सबसे Great, नहीं पहुंची है अब तक अपने लक्ष्य स्थान पर Late. - Sahil Khandare

There is no direct train from coimbatore Nearest railway station is Rishikesh or Haridwar. You can take Madurai Dehradun Express 12687 or Kochuveli-Dehradun Weekly SF Express 12287 to Haridwar Junction. From there by bus to Badrinath. The ideal time is from May to October, except monsoons (July to mid-September) .During the monsoon season, there is undue threat of having landslides, which can further disrupt the journey for a couple of days to week. So it is advisable to avoid during monsoon season.

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You can take raptisagar till LKO and from there any train to haridwar and from haridwar there will be ample of busses to badrinath Direct but to kedar no direct road, Till gaurikund by bus and from Gaurikund 14 km trekking!!!
Or else second option as said by krishnan sir

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