The term independent of x in the expansion of (x−3x2)18 is
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a
18C6
b
18C636
c
18C12
d
36
answer is B.
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Detailed Solution
Given expansion (x−3x2)18 We know that rth term in the expansion of (x+a)n isTr+1=nCr xn−r ar then Tr+1= 18Crx18−r(−3x2)r Tr+1= 18Cr x18−r (−3)r (x−2)r = 18Cr (−3)r x18−3r...................(1) And this will be Without x only if x18−3r compare with x0 term independent of x in the expansion⇒x18−3r=x0 ⇒18−3r=0 ∵r=6 in Eqn (1)We get 18C6 (−3)6 x18−18 ∵ 18C6 36