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Most Important Selected Qs for JEE AdvancedMathematicsBinomial Theorem

Let a and b be the coefficient of x^3 in (1+x+2 x^2+3 x^3 )^4 and (1+x+2 x^2+3 x^3+4 x^4 )^4 respectively. Find the value of (a-b) .

Correct answer

00

Step-by-step solution

We have b= coefficient of x^3 in ( (1+x+2 x^2+3 x^3 )+4 x^4 )^4 aligned & = coefficient of x^3 in [ ^4 C₀ (1+x+2 x^2+3 x^3 )^4 (4 x^4 )^0+ ^4 C₁ (1+x+2 x^2+3 x^3 )^3 (4 x^4 )^1+ . . . . ] & = coefficient of x^3 in (1+x+2 x^2+3 x^3 )^4=a aligned Hence a - b =0 Ans.

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