“I sing everything,” Asha Bhosle told an adoring audience at Carnegie Hall on Thursday night, and she was not exaggerating. who turns 75 in September, is probably the most recorded singer in history. As the voice of Bollywood musicals called a playback singer, because actresses sing and dance while her vocals are heard and a queen of South Asian pop, she has recorded more than 12,000 songs in a career that dates to 1943. (One of her few rivals is her older sister, Lata Mangeshkar, another hugely prolific playback singer. At Carnegie Hall Ms. Bhosle sang one of her sister’s hits, “Lag Ja Gale.”)

Ms. Bhosle has sung Indian classical and semiclassical styles and all the culture-hopping pop hybrids that Bollywood composers have devised. Bollywood music is wonderfully multifarious; there’s no telling what might show up in a song, from traditional tabla rhythms to funk guitars to synthesizers. Ms. Bhosle’s Carnegie Hall set encompassed the pristine, unaccompanied Hindustani classical-style singing as well as styles from across India and twists on disco, rock, polka, waltzes and Latin music.

They all found room for her voice: high, clear, sweet and girlish even now. It can hover in the weightless, long-breathed, intricately rippling phrases of classical style or push, lightly but firmly, over a danceable beat, whether it’s Eastern or Western or a mix. Through her career Ms. Bhosle has collaborated not just with film composers but also with Indian classical musicians, like Ali Akbar Khan, and with Westerners from Boy George to Michael Stipe of R.E.M. to the Kronos Quartet.