If C r 20 is the co-efficient of x r in the expansion of ( 1 + x ) 20 , then the value of ∑ r = 0 20 r…

If Cr20 is the co-efficient of xr in the expansion of (1+x)20, then the value of ∑r=020r2Cr20 is equal to:
  1. 420×218
  2. 380×218
  3. 380×219
  4. 420×219

Solution

∑r=020r2Cr20=∑rr·Cr20=∑r=120r·20.Cr-119

⇒20∑r=120(r-1+1)·19Cr-1=20∑r=120(r-1)·19Cr-1+∑r=120Cr-119

⇒2019∑r=220Cr-218+∑r=120Cr-119

⇒(380)218+20·219⇒220·(95+10)=(105)220=420×218

Asked in: JEE Main 2021 (26 Aug Shift 1)

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