Adele's hit album "25" is up for best British album, while she has also been shortlisted for British female solo artist, British single for "Hello", British artist video for "Hello".
Her nominations come after "25" sold 2.5 million copies in the UK in its first six weeks.
Years & Years secured nods in categories-- British single and British artist video for "King", British breakthrough act and British group.
Bay's nominations include British male solo artist, British breakthrough act, British single for "Hold Back The River", British album of the year for "Chaos and the Calm".
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Rock band Eagles of Death Metal, whose gig in Paris was attacked by terrorists last year, is up for best international group, which also includes Alabama Shakes, Major Lazer, Tame Impala and Irish rock band U2.
Singer Jess Glynne also settles with three nominations in categories including British female solo artist and British breakthrough act.
Other contenders for British album of the year are Coldplay for "A Head Full of Dreams", Florence + the Machine - "How Big, How Blue, How Beautiful" and "Jamie xx - In Colour".
International male solo artist category has names like Drake, Father John Misty, Justin Bieber, Kendrick Lamar and The Weeknd. Ariana Grande, Bjork, Courtney Barnett, Lana Del Rey and Meghan Trainor comprise the International female solo artist category.
Adele is due to perform at next month's ceremony at the O2 Arena in London on February 24.