Why did Kajol reject Yash Raj Films' offer initially?

 Kajol did turned down several Yash Raj Films offers but it was not in the early initial phase of her career. In fact her third release Yeh Dillagi (after Bekhudi & Baazigar) was a YRF production.

The very next year Kajol was seen opposite Shah Rukh Khan in an another Yash Raj Production, “Dilwale Dulhaniya Le Jayenge”.

Later, Kajol turned down a few YRF offers plainly because of script preferences, scheduling conflicts and family commitments.

Kajol turned down Dil To Pagal Hai because she didn't find the character of Nisha (later played by Karishma Kapoor) significant or compelling enough.

Also, the film included a lengthy dance competition with Madhuri Dixit and the role didn't suit Kajol’s dancing style or preferences at the time.

Kajol turned down the role of Megha in Mohabbatein (later played by Aishwarya Rai) because of her recent marriage and her decision to take a break from acting career to focus on her personal life. Also it was a minor role.

Her most notable rejection was for Veer-Zaara. Yash Chopra wanted to re-unite her with Shahrukh Khan in the iconic cross-border romance but she declined due to scheduling conflicts and creative reasons. She chose to star in Fanaa.

Fanaa was Kajol's comeback movie. It was also a YRF production, directed by Kunal Kohli.

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Why did Vinod Khanna leave Yash Raj Films?

 There are two parts of this story. Khanna had a meaty role in Chandni but there were drastic changes made in the script which upset Vinod Khanna.

The original script of Chandni had Rishi Kapoor dying before the intermission. Khanna's character was meant to step in and marry Sridevi taking over the narrative for the emotional second half.

However, the plot was heavily re-written during the shoot, resulting in keeping Rishi Kapoor alive and restricting Khanna to an extended cameo.

Also, Chopra altered Khanna’s persona in the film. Khanna was known as an action star and his entry in the film was an action sequence where he was supposed to save Sridevi from fire. This alteration of scene by Chopra ended-up Khanna's character as a purely mature, non-action romantic interest. Vinod Khanna was upset due to these reasons.

However, he worked with Chopra again in Parampara but Chopra was not the producer of the film. This collabration was a combination of mutual consent, a sort of patch-up and a last minute replacement.

Anil Kapoor walked off the project on the first day of shooting realising he had been cast as the father to the younger leads. Jackie Shroff was advised by Ghai not to do the film and Anupam Kher was busy shooting for Khel in Kenya. Khanna was the last minute replacement for Anupam Kher who was then given a different role in the film.

So, basically Khanna did not leave Yash Raj Films. His first time experience was not good and later the conditions never fell into place for him to unite with the production house.

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