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AP EAMCET201923 Apr 2019Morning ShiftMathematicsBinomial TheoremActual

The coefficient of (x^4 ) in the expansion of ( 1 (1-x)(1-2 x)(1-3 x) ) is

Options

  1. A602
  2. B301
  3. C( 601 2 )
  4. D302

Correct answer

B. 301

Step-by-step solution

( aligned & Since, 1 (1-x)(1-2 x)(1-3 x) & =(1-x)⁻¹(1-2 x)⁻¹(1-3 x)⁻¹ & = (1+x+x^2+x^3+x^4 ) (1+2 x+4 x^2+8 x^3+16 x^4 ) & (1+3 x+9 x^2+27 x^3+81 x^4 ) aligned ) [Expand till (x^4 )-term because coefficient of (x^4 ) is required and ((1-a x)^ -n ) ( .=1+a x+a^2 x^2+a^3 x^3+ . . . . . . ] ) So, coefficient of (x^4 ) is ( aligned & 81+54+36+24+16+27+18+12+8+9+ & 6+4+3+2+1=301 aligned ) Hence, option (b) is correct.

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