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A boy has a collection of blue and green...

A boy has a collection of blue and green marbles. The number of blue marbles belong to the set `{2,3,4,…..,13}`. If two marbles are chosen simultaneously and at random from his collection, then the probability that they have different coloursis `(1)/(2)`. Possible number of the blue marbles is

A

`3`

B

`6`

C

`10`

D

`12`

Text Solution

Verified by Experts

The correct Answer is:
A, B, C
`(a,b,c)` Let the no. of blue marbles is `a` and no. of green marbles is `b` .
`:.(ab)/("^(a+b)C_(2))=(1)/(2)`
`implies(a+b)(a+b-1)=4ab`
`impliesb^(2)-(2a+1)b+a^(2)-a=0`
but `b in R implies D=(2a+1)^(2)-4(a^(2)-a)=8a+1`
`:. 8a+1` must be a perfect square.
Hence possible values of `a` are `3,6,10`
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