Maths-
General
Easy

Question

If the sum of the coefficients in the expansion of left parenthesis q plus r right parenthesis to the power of 20 end exponent left parenthesis 1 plus left parenthesis p minus 2 right parenthesis x right parenthesis to the power of 20 end exponent is equal to square of the sum of the coefficients in the expansion of left square bracket 2 r q x minus left parenthesis r plus q right parenthesis times y right square bracket to the power of 10 end exponent text  , where  end text p comma r comma q are positive constants, then

  1. square root of r q end root less or equal than p    
  2. fraction numerator r plus q over denominator 2 end fraction greater or equal than p    
  3. r,p and q are in G.P.    
  4. 1/r, 1/p an 1/q are in H.P.    

The correct answer is: fraction numerator r plus q over denominator 2 end fraction greater or equal than p


    Sum of co–efficient of left parenthesis q plus r right parenthesis to the power of 20 end exponent left parenthesis 1 plus left parenthesis p minus 2 right parenthesis x right parenthesis to the power of 20 end exponent text  is  end text equals left parenthesis q plus r right parenthesis to the power of 20 end exponent left parenthesis p minus 1 right parenthesis to the power of 20 end exponent left square bracket text  put  end text x equals 1 right square bracket
    text is  end text equals left parenthesis q plus r right parenthesis to the power of 20 end exponent left parenthesis p minus 1 right parenthesis to the power of 20 end exponent left square bracket text  put  end text x equals 1 right square bracket
    Square of the sum of co–efficient of left parenthesis 2 r q invisible function application x minus left parenthesis r plus q right parenthesis times y right parenthesis to the power of 10 end exponent equals left parenthesis 2 r q minus left parenthesis r plus q right parenthesis right parenthesis to the power of 20 end exponent left square bracket text  put  end text x equals y equals 1 right square bracket
    text So  end text left parenthesis q plus r right parenthesis to the power of 20 end exponent left parenthesis p minus 1 right parenthesis to the power of 20 end exponent equals left parenthesis 2 r q minus left parenthesis q plus r right parenthesis right parenthesis to the power of 20 end exponent
    table row cell rightwards double arrow p minus 1 equals fraction numerator 2 r q over denominator r plus q end fraction minus 1 rightwards double arrow p equals fraction numerator 2 r q over denominator r plus q end fraction end cell row cell rightwards double arrow p equals text end text text H end text text. end text text M end text text. end text text end text text o end text text f end text text end text r text end text text a end text text n end text text d end text text end text q end cell end table
    £ A.M. of r and q = (r + q)/2.

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