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Asked to bat first after the coin landed in the Cobras` favour, Kieron Pollard (58 off 37 balls) and debutant Sarul Kanwar (45 off 21) powered Mumbai to a daunting 176 for five before rain intervened at the break.
What seemed like a steady drizzle soon transformed into heavy downpour, making the turf at the M Chinnaswamy Stadium unplayable.
As there was no let-up in rain, the umpires were left with no option but to call off the group A tie at 11.05 pm, 35 minutes before the cut-off time.
The first abandoned match in the history of Champions League T20 ensured both teams settle for a point each.
Mumbai still lead the table with five points but their hopes of progressing to last-four stage now rests on their next match, a must-win one for the Harbhajan Singh-led side.
Cobras have three points after three games while Chennai Super Kings and New South Wales have two each.
Earlier, Pollard smashed a blistering half-century while Kanwar played a cameo at the top to help Mumbai to a position of strength.
Pollard, who struck three sixes and six fours, was well supported by James Fraklin (18), who was involved in a 69-run fourth-wicket partnership with the West Indian.