Will you exchange the rook for a bishop and two pawns?Why or Why Not?

Will you exchange the rook for a bishop and two pawns?Why or Why Not?

not a good idea because 1. the rook more valuable than the bishop and pawns. 2. the rook is good on long files and ranks. so i dont think its a good idea.

In terms of material points a rook is not more valuable than a bishop and two pawns (yes a rook is more valuable than a lone bishop).  As a matter of fact some assign 3 1/2 points to a bishop rather than 3 points, possibly even making a bishop and two pawns slightly more valuable than a rook.  

Material points should only be a slightly partial factor when making that decision though.  The major factor would be the resulting position, especially considering that the position will become unbalanced after such an exchange.  And if one exchanges a bishop and two pawns for a rook and their position does not pan out as hoped then they have that perhaps slight material edge to fall back on.  

Likely yes. Bishops are still useful in the middlegame.

It depends on the actual position. If the two extra pawns are poorly placed, then probably I will let the opportunity slip.

More important that setting some arbitrary value to a piece is concrete analysis. Piece values are best thought of an average value, not an absolute value. Saying that a bishop is always worth 3 is like saying your IQ is 100 because the average IQ is 100.

It's very often the case that piece values are irrelevant. In the famous Evergreen Game, Adolf Anderssen was down a full queen and a full rook, but checkmated his opponent with two bishops and a rook. Was his opponent's queen more valuable than the bishop that delivered checkmate? Not in that game it wasn't. The positions on the board determine the real value of pieces, not some arbitrary number.

It's probably fine but... it's more about how active the pieces remaining on the board are.

Is this some sort of homework problem? 

Ehh, everything in chess is positional.  A monster bishop AND two pawns, for a poorly placed rook, in a heartbeat.  A tall pawn and two normal pawns for a well placed rook, no way. 

This is the board

It looks like a draw, but as a practical matter, I'd take black, easily.  One thing to understand in that position is that, assuming competent play by both sides, only black has a chance of winning.  Even if White were somehow to win both pawns (and I can't imagine how White could win more than one), then the rook vs bishop en dgame would still be a draw, assuming the black king is able to hoof it to h8, rather than a8.

Whose move is it?  If White, then Rb8 picks off the b-pawn, and the two sides might as well shake hands and call it a draw immediately.  If black, then there's time for Bd7 and b6-b5, and maybe you can push for a win, though I doubit it.

Yes always depends on the position, also magnus did this yesterday 

it depends on the strength of the pawns. Connected passed pawns on the 7th rank are worth way more than a rook for example

Depends on placement of the pieces, position on the board, how advanced pawns are, etc. Sometime you will have to do it to make your position better, sometimes you will lose because of it so there is no right answer without looking at the position. :)