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JEE Main202325 Jan 2023Morning ShiftMathematicsBinomial TheoremActual

The constant term in the expansion of 2 x + 1 x 7 + 3 x 2 5 is _____ .

Correct answer

0

Step-by-step solution

Any term in the expansion of 2 x + 1 x 7 + 3 x 2 5 is given by 5 ! a ! · b ! · c ! 2 x a x - 7 b 3 x 2 c where a + b + c = 5       . . . i = 2 a 3 c 5 ! a ! · b ! · c ! x a x - 7 b x 2 c = 2 a 3 c 5 ! a ! · b ! · c ! x a - 7 b + 2 c Now for term to be independent of x , we know a - 7 b + 2 c = 0       . . . ii Solving i   &   ii , we get b = c + 5 8 Also, a ,   b ,   c ∈ 1 , 2 , 3 , 4 , 5 So, a = 1 ,   b = 1 ,   c =

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