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Q.

If  30C12+2 30C22+3 30C32++30 30C302=α 60 ! (30 ! )2 then α is equal to

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a

60

b

10

c

15

d

30

answer is D.

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Detailed Solution

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 30C12+2 30C22+3 30C32+.+30 30C302=α60(30_)2
Wkt aC02+(a+d)C12+(a+2d)C22+..+(a+nd)Cn2=(2a+nd)22nCn
Now 0 30C02+1 30C12+230C22+..+30 30C3020 30C02=α60_(30_)2
2(0)+30(1)260C300=α 60C30  Here a=0,d=11560C30=α60C30α=15

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