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Question

Assertion (A): Number of the dissimilar terms
in the sum of expansion left parenthesis x plus a right parenthesis to the power of 102 end exponent plus left parenthesis x minus a right parenthesis to the power of 102 end exponent is 206
Reason (R): Number of terms in the expansion of left parenthesis x plus b right parenthesis to the power of n end exponent is n+1

  1. Both A and R are true and R is correct explanation of A    
  2. Both A and R are true but R is not correct explanation of A    
  3. A is true but R is false    
  4. A is false but R is true    

The correct answer is: A is false but R is true


    Number of terms 52

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    I f A equals left parenthesis 300 right parenthesis to the power of 600 end exponent comma B=600!, C equals left parenthesis 200 right parenthesis to the power of 600 end exponent then

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    The arrangement of the following with respect to coefficient of x to the power of r end exponent in ascending order where vertical line x vertical line less than 1 A) x to the power of 5 end exponent in left parenthesis 1 minus x right parenthesis to the power of negative 3 end exponent where vertical line x vertical line less than 1 B) x to the power of 7 end exponent i n left parenthesis 1 plus 2 x plus 3 x to the power of 2 end exponent plus horizontal ellipsis infinity right parenthesiswhere vertical line x vertical line less than 1 C) x to the power of 10 end exponent in left parenthesis 1 plus x right parenthesis to the power of negative 1 end exponent where vertical line x vertical line less than 1 D) x to the power of 3 end exponent in left parenthesis 1 plus x right parenthesis to the power of 4 end exponent

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    A: If the term independent of x in the expansion of left parenthesis square root of x minus fraction numerator n over denominator x to the power of 2 end exponent end fraction right parenthesis to the power of 10 end exponent is 405, then n=
    B: If the third term in the expansion of left parenthesis fraction numerator 1 over denominator n end fraction plus n to the power of l o g subscript n end subscript 10 end exponent right parenthesis to the power of 5 end exponent is 1000, then n=(here n<10)
    C: If in the binomial expansion of left parenthesis 1 plus x right parenthesis to the power of n end exponent comma the coefficients of 5thcomma 6th and 7th terms are in A.P then n= [Arranging the values of n in ascending order]

    A: If the term independent of x in the expansion of left parenthesis square root of x minus fraction numerator n over denominator x to the power of 2 end exponent end fraction right parenthesis to the power of 10 end exponent is 405, then n=
    B: If the third term in the expansion of left parenthesis fraction numerator 1 over denominator n end fraction plus n to the power of l o g subscript n end subscript 10 end exponent right parenthesis to the power of 5 end exponent is 1000, then n=(here n<10)
    C: If in the binomial expansion of left parenthesis 1 plus x right parenthesis to the power of n end exponent comma the coefficients of 5thcomma 6th and 7th terms are in A.P then n= [Arranging the values of n in ascending order]

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    The arrangement of the following binomial expansions in the ascending order of their independent terms A left parenthesis square root of x minus fraction numerator 3 over denominator x to the power of 2 end exponent end fraction right parenthesis to the power of 10 end exponent B left parenthesis x plus fraction numerator 1 over denominator x end fraction right parenthesis to the power of 6 end exponent C left parenthesis 1 plus x right parenthesis to the power of 32 end exponent D left parenthesis fraction numerator 3 over denominator 2 end fraction x to the power of 2 end exponent minus fraction numerator 1 over denominator 3 x end fraction right parenthesis to the power of 9 end exponent

    The arrangement of the following binomial expansions in the ascending order of their independent terms A left parenthesis square root of x minus fraction numerator 3 over denominator x to the power of 2 end exponent end fraction right parenthesis to the power of 10 end exponent B left parenthesis x plus fraction numerator 1 over denominator x end fraction right parenthesis to the power of 6 end exponent C left parenthesis 1 plus x right parenthesis to the power of 32 end exponent D left parenthesis fraction numerator 3 over denominator 2 end fraction x to the power of 2 end exponent minus fraction numerator 1 over denominator 3 x end fraction right parenthesis to the power of 9 end exponent

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    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

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    404 C subscript 4 end subscript minus C subscript 4 end subscript. C subscript 1 end subscript plus 2024 minus 1014 equals

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