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Sri Lanka were served well by Chamari Athapaththu and Harshitha Samarawickrama.
Seamer Renuka Singh Thakur and spinner Radha Yadav took three wickets each as India restricted Bangladesh to 80/8 before opener Shafali Verma and Smriti Mandhana chased it down in just 11 overs.
Shafali scored a 48-ball 81 as India posted 178/3 before beating Nepal by 82 runs.
With two wins in as many games, India occupy the top spot in Group A with four points and a Net Run Rate of +3.298.
Indian openers Shafali Verma (40) and Smriti Mandhana (45) helped India chased down 109 in style.
Defending champions India open their campaign against Pakistan on July 19.
India beat arch-rivals Pakistan by 54 runs at Sharjah on April 13, 1984, to emerge champions.
The Indians eves lost to the Kiwis 10-17 in their opening Group D encounter. Later, they went down to three-time champions Australia 7-21.
Pranav Prince, Aneesha Cleetus and Sreekala R are part of the national teams that will be in action in Singapore from March 27.
Vaisakh K Manoj has earned his maiden senior India call-up.
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