General
Easy
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.

Maths-General

  1. Only S subscript 1 end subscript is true    
  2. Only S subscript 2 end subscript is true    
  3. Both S subscript 1 end subscript and S subscript 2 end subscript are true    
  4. Neither S subscript 1 end subscript nor S subscript 2 end subscript is true    

    Answer:The correct answer is: Both S subscript 1 end subscript and S subscript 2 end subscript are true

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    Related Questions to study

    General
    maths-

    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-

    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
    General
    maths-

    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?

    maths-General
    General
    maths-

    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

    maths-General
    General
    maths-

    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

    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

    maths-General
    General
    maths-

    If left curly bracket x right curly bracket denotes fractional part of x then left curly bracket fraction numerator 2 to the power of 2003 end exponent over denominator 17 end fraction right curly bracket equals

    If left curly bracket x right curly bracket denotes fractional part of x then left curly bracket fraction numerator 2 to the power of 2003 end exponent over denominator 17 end fraction right curly bracket equals

    maths-General
    General
    maths-

    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

    maths-General
    General
    maths-

    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]

    maths-General
    General
    maths-

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

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

    maths-General
    General
    maths-

    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

    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

    maths-General
    General
    maths-

    The number of rational terms in the expansion of left parenthesis 1 plus square root of 2 plus root index 3 of 3 end root right parenthesis to the power of 6 end exponent is

    The number of rational terms in the expansion of left parenthesis 1 plus square root of 2 plus root index 3 of 3 end root right parenthesis to the power of 6 end exponent is

    maths-General
    General
    maths-

    If 2 to the power of 2006 end exponent minus 2006 divided by 7, the remainder is

    If 2 to the power of 2006 end exponent minus 2006 divided by 7, the remainder is

    maths-General
    General
    maths-

    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

    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

    maths-General
    General
    maths-

    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

    Number of terms 52

    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

    maths-General
    Number of terms 52