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Most Important Selected Qs for JEE AdvancedMathematicsBinomial Theorem

Let k be the coefficient of x ¹⁸ in the polynomial f(x)=(1+x)²⁰+x(1+x)¹⁹+x^2(1+x)¹⁸+ .+x¹⁸(1+x)^2 then the value of k 190 is equal to

Correct answer

7

Step-by-step solution

aligned & f(x)=(1+x)²⁰ [1+ x 1+x + ( x 1+x )^2+ + ( x 1+x )¹⁸ ] & (1+x)²¹ [1- ( x 1+x )¹⁹ ]=(1+x)²¹-(1+x)^2 x¹⁹ aligned Coefficient of x ¹⁸ in f ( x )= Coefficient of x ¹⁸ in (1+ x )²¹= ²¹ C ₁₈=1330

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