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Sir,

what are the meaning of the following sentences.

1. He was sitting right next to Akash.

here the word 'right' confused me.

2. I can't make up my mind.

3. "What was that ?" asked neel with start.

here the word 'start' confused me.

4. She liked to cook cakes, more than that to eat cake, and most of all to see it eaten by happy children.

Here what does she like more cooking or eating.

5. Don Alphonso sit right here ,by this fountain ,eat babinca.

The word "right" and "by" confused me
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1. 'Right' means 'immediately, directly, exactly,very'.

2. 'I cannot make a decision.'

3. A 'start' is a quick movement of alarm.

4. She most liked seeing cake eaten, she next liked eating it herself, and she least liked cooking it.

5. 'Right' means as in (1) above, and 'by' means 'next to'.
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Hanuman,

I'd like to add a little about the use of the adverb "right". I hope it will be useful to others as well.

The adverb "right" is typically used as a modifier of other adverbs, prepositional phrases, and adverbial clauses of time and place.

Examples:

TIME: exactly, immediately, without any delay or hesitation
right now, right before (the war), right after (he saw me), right up to (the last minute), right when (you least expect it), right at (8 o'clock)

For almost all uses involving time, "just" may substitute for "right", but "straight" may not substitute for "right".

PLACE AT: exactly, directly, without any intervening distance
right here, right there, right where (I want it), right at (the corner), right next to (the table), right beside (the bed), right above/over (his head), right below (the knee), right on (target), right under (the chair), right in front of (City Hall), right behind (the bus), right across (the lake)

For almost all uses involving place at, "just" may substitute for "right". "straight" may substitute for "right" only when the 'front/back' horizontal axis or the vertical axis is implied (straight in front of, straight behind, straight above/over, straight under/below, straight across).

PLACE TO / FROM: directly, without any deviation in path
(to get) right to (the point), (to come) right back, (to go) right on/onto (the plane), (to go) right ahead, (to go) right there, (to go/come) right home, (to run) right into (a wall), (to go/come) right up (the stairs), (to go/come) right down (the stairs), (to run) right across (the field), (for the wind to blow) right through (the house), right from (the oven), right off (the grill)

For almost all uses involving place to or from, "just" may not substitute for "right" (in the locative reading), but "straight" may substitute for "right".

Extra factoids:

"right away", "right off", "right off the bat" - idioms meaning "immediately".
"Right on!" - idiom showing agreement and encouragement - This expression seems to be falling out of use lately.
"right", "just", and "straight" do not readily combine with adverbs of manner except for the expressions "just so" and "just like/as ..." At least I can't think of any. Maybe other participants can add to the list.

Jim