Ravindra Jadeja smashed his maiden worldwide century as India posted their highest total against the West Indies after declaring on 649-9 in the first Test in Rajkot on Friday. Skipper Virat Kohli, on four, and Ajinkya Rahane were at the crease.
Rahul was gone for a golden duck when Caribbean pacer Shannon Gabriel trapped the Indian opener in front of the wickets.
He reached his half-century off 56 deliveries and was unbeaten on 75 off 74 deliveries at lunch as India reached 133 for one, with Pujara on 56.
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The diminutive right-hander becomes India's second youngest century-maker after Sachin Tendulkar, who in 1990 was 17 years and 112 days when he made 119 not out against in England in Manchester during his ninth Test appearance.
Shaw, who is 18 years and 329 days old, reached his hundred off just 99 deliveries in the second session on day one.
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Shaw just needed 99 balls to get the landmark as he toyed with the weakened West Indies bowling, which missed captain Jason Holder and pacer Kemar Roach.
Shaw and Pujara added 206 runs for the second wicket as the tourists were sent on a leatherhunt for large parts of the second session.
Kohli, who was on 72 overnight, hit a four off Devendra Bishoo to bring up his 100 in the first Test in Rajkot.
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More importantly, Shaw had the confidence of several hundreds under his belt when he walked out to bat for India Thursday morning. However, Shaw remained unfazed and kept playing his natural game in the company of Cheteshwar Pujara.