It's 624 for 3rd wicket between Kumar Sangakkara (287) and Mahela Jayawardene (374) against South Africa.
The highest first-wicket partnership in a Test match for India is 413 runs, achieved by Vinoo Mankad and Pankaj Roy, who put on 413 runs for the first wicket in a Test match against New Zealand in January 1956.
First Wicket Partnership for India in test match is MH Mankad, P Roy 413 in the match played by India v New Zealand at Chennai 6 Jan 1956.
Second wicket test match partnership world record is in the names of Sanath Jayasuriya and Roshan Mahanama of Sri Lanka; 576 against India at Colombo in 1997.
it is 624 for any wicket partnership between KC Sangakkara and DPMD Jayawardene against south Africa in 2006
The first wicket partnership in cricket test match was held on March 11, 1910 between England and South Africa. The partners were JB Hobbs and W. Rhodes. ND McKenzie and GC Smith holds the world record for most runs, 415.
The highest 10th wicket partnership in ODI Cricket was an unbeaten 106 by Viv Richards and Michael Holding of the West Indies, vs England in 1984. Michael Holding only scored 12 of these runs, Viv Richards finished on 189 not out,
415. between Greame Smith and Neil McKenzie.
The highest tenth-wicket partnership is 151 runs, scored by Pakistani batsmen Azhar Mahmood and Mushtaq Ahmed against South Africa in October 1997. The same match saw Ali Naqvi score a century in his debut Test appearance, surpassing his first-class best at that point by a single run. It would remain his highest Test score.