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Question

A:blank to the power of 2 n end exponent c subscript n end subscript equals C subscript 0 end subscript superscript 2 end superscript plus C subscript 1 end subscript superscript 2 end superscript plus C subscript 2 end subscript superscript 2 end superscript plus C subscript 3 end subscript superscript 2 end superscript plus horizontal ellipsis horizontal ellipsis horizontal ellipsis.. plus C subscript n end subscript superscript 2 end superscript B:blank to the power of 2 n end exponent c subscript n end subscript equals term independent of x in left parenthesis 1 plus x right parenthesis to the power of n end exponent left parenthesis 1 plus fraction numerator 1 over denominator x end fraction right parenthesis to the power of n end exponent C:blank to the power of 2 n end exponent c subscript n end subscript equals fraction numerator 1.3.5.7 horizontal ellipsis horizontal ellipsis horizontal ellipsis horizontal ellipsis. left parenthesis 2 n minus 1 right parenthesis over denominator n factorial end fraction then

  1. A, B are false, C is true    
  2. Ais false, B and C are true    
  3. A and B are true; C is false    
  4. A, B, C are true    

The correct answer is: A and B are true; C is false


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    Related Questions to study

    General
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    I The sum of the binomial coefficients of the expansion open parentheses table row 1 row cell x plus negative end cell row x end table close parentheses is 2 to the power of n end exponent
    II The term independent of x in the expansion of open parentheses table row 1 row cell x plus negative end cell row x end table close parentheses is 0 when is even.
    Which of the above statements is correct?

    I The sum of the binomial coefficients of the expansion open parentheses table row 1 row cell x plus negative end cell row x end table close parentheses is 2 to the power of n end exponent
    II The term independent of x in the expansion of open parentheses table row 1 row cell x plus negative end cell row x end table close parentheses is 0 when is even.
    Which of the above statements is correct?

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    S subscript 1 end subscript: The fourth term in the expansion of left parenthesis 2 x plus fraction numerator 1 over denominator x to the power of 2 end exponent end fraction right parenthesis to the power of 9 end exponent is equal to the second term in the expansion of left parenthesis 1 plus x to the power of 2 end exponent right parenthesis to the power of 84 end exponent then the positive value of x is fraction numerator 1 over denominator 2 square root of 3 end fraction
    S subscript 2 end subscript:In the expansion of left parenthesis x to the power of 2 end exponent plus fraction numerator a over denominator x to the power of 3 end exponent end fraction right parenthesis to the power of 10 end exponent, the coefficients of x to the power of 5 end exponent and x to the power of 15 end exponent are equal, then the positive value of a is 8

    S subscript 1 end subscript right parenthesis Find 4th and second term
    S subscript 2 end subscript right parenthesis Find coefff x to the power of 5 end exponent and x to the power of 15 end exponent

    S subscript 1 end subscript: The fourth term in the expansion of left parenthesis 2 x plus fraction numerator 1 over denominator x to the power of 2 end exponent end fraction right parenthesis to the power of 9 end exponent is equal to the second term in the expansion of left parenthesis 1 plus x to the power of 2 end exponent right parenthesis to the power of 84 end exponent then the positive value of x is fraction numerator 1 over denominator 2 square root of 3 end fraction
    S subscript 2 end subscript:In the expansion of left parenthesis x to the power of 2 end exponent plus fraction numerator a over denominator x to the power of 3 end exponent end fraction right parenthesis to the power of 10 end exponent, the coefficients of x to the power of 5 end exponent and x to the power of 15 end exponent are equal, then the positive value of a is 8

    maths-General
    S subscript 1 end subscript right parenthesis Find 4th and second term
    S subscript 2 end subscript right parenthesis Find coefff x to the power of 5 end exponent and x to the power of 15 end exponent
    General
    maths-

    S1: If the coefficients of x to the power of 6 end exponent and x to the power of 7 end exponent in the expansion of left parenthesis fraction numerator x over denominator 4 end fraction plus 3 right parenthesis to the power of n end exponent are equal, then the number ofdivisors ofn is 12.
    S2: If the expansion of left parenthesis x to the power of 2 end exponent plus fraction numerator 2 over denominator x end fraction right parenthesis to the power of n end exponent for positive integer n has 13 th term independent of x Then the sum of divisors of n is 39.

    S1: If the coefficients of x to the power of 6 end exponent and x to the power of 7 end exponent in the expansion of left parenthesis fraction numerator x over denominator 4 end fraction plus 3 right parenthesis to the power of n end exponent are equal, then the number ofdivisors ofn is 12.
    S2: If the expansion of left parenthesis x to the power of 2 end exponent plus fraction numerator 2 over denominator x end fraction right parenthesis to the power of n end exponent for positive integer n has 13 th term independent of x Then the sum of divisors of n is 39.

    maths-General
    General
    maths-

    I Three consecutive binomial coefficients cannot be in GP.
    II Three consecutive binomial coefficients cannot be in A.P.
    Which of the above statement is correct?

    Standard Results

    I Three consecutive binomial coefficients cannot be in GP.
    II Three consecutive binomial coefficients cannot be in A.P.
    Which of the above statement is correct?

    maths-General
    Standard Results
    General
    maths-

    I The no of distinct terms in the expansion of left parenthesis x subscript 1 end subscript plus x subscript 2 end subscript plus horizontal ellipsis. plus x subscript n end subscript right parenthesis to the power of 3 end exponent is n plus 2 c subscript 3 end subscript
    II The no of irrational terms in the expansion left parenthesis 2 to the power of 1 divided by 5 end exponent plus 3 to the power of 1 divided by 10 end exponent right parenthesis to the power of 55 end exponent is 55

    I) Formula
    II) False

    I The no of distinct terms in the expansion of left parenthesis x subscript 1 end subscript plus x subscript 2 end subscript plus horizontal ellipsis. plus x subscript n end subscript right parenthesis to the power of 3 end exponent is n plus 2 c subscript 3 end subscript
    II The no of irrational terms in the expansion left parenthesis 2 to the power of 1 divided by 5 end exponent plus 3 to the power of 1 divided by 10 end exponent right parenthesis to the power of 55 end exponent is 55

    maths-General
    I) Formula
    II) False
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    If left parenthesis 3 plus x to the power of 2008 end exponent plus x to the power of 2009 end exponent right parenthesis to the power of 2010 end exponent equals a subscript 0 end subscript plus a subscript 1 end subscript x plus a subscript 2 end subscript x to the power of 2 end exponent plus plus a subscript n end subscript x to the power of n end exponent then a subscript 0 end subscript minus fraction numerator a subscript 1 end subscript over denominator 2 end fraction minus fraction numerator a subscript 2 end subscript over denominator 2 end fraction plus a subscript 3 end subscript minus fraction numerator a subscript 4 end subscript over denominator 2 end fraction minus fraction numerator a subscript 5 end subscript over denominator 2 end fraction plus a subscript 6 end subscript

    If left parenthesis 3 plus x to the power of 2008 end exponent plus x to the power of 2009 end exponent right parenthesis to the power of 2010 end exponent equals a subscript 0 end subscript plus a subscript 1 end subscript x plus a subscript 2 end subscript x to the power of 2 end exponent plus plus a subscript n end subscript x to the power of n end exponent then a subscript 0 end subscript minus fraction numerator a subscript 1 end subscript over denominator 2 end fraction minus fraction numerator a subscript 2 end subscript over denominator 2 end fraction plus a subscript 3 end subscript minus fraction numerator a subscript 4 end subscript over denominator 2 end fraction minus fraction numerator a subscript 5 end subscript over denominator 2 end fraction plus a subscript 6 end subscript

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