Home
Class 12
MATHS
If x^n occurs in the expansion (x+1//x^2...

If `x^n` occurs in the expansion `(x+1//x^2)^n` , then the coefficient of `x^m` is `((2n)!)/((m)!(2n-m)!)` b. `((2n)!3!3!)/((2n-m)!)` c. `((2n)!)/(((2n-m)/3)!((4n+m)/3)!)` d. none of these

A

`((4n)!)/(((4n-m)/(3) )!.((8n+m)/( 3))!)`

B

`((4n)!)/(n!(4n-m)!)`

C

`((4n)! 3! 3!)/( (4n-3)!)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • BINOMIAL THEOREM

    MTG-WBJEE|Exercise WB JEE Previous Years Questions ( CATEGORY 1 : Single Option Correct Type (1 Mark))|13 Videos

  • BINOMIAL THEOREM

    MTG-WBJEE|Exercise WB JEE WORKOUT ( CATEGORY 2 : Single Option Correct Type (2 Marks))|15 Videos

  • APPLICATION OF INTEGRALS

    MTG-WBJEE|Exercise WE JEE PREVIOUS YEARS QUESTIONS (CATEGORY 3 : ONE OR MORE THAN ONE OPTION CORRECT TYPE)|3 Videos

  • CIRCLES

    MTG-WBJEE|Exercise WB JEE PREVIOUS YEARS QUESTIONS (CATEGORY 3 : One or More One Option Correct Type)|2 Videos

Similar Questions

Explore conceptually related problems

If x^(m) occurs in the expansion (x+1/x^(2))^(n) , then the coefficient of x^(m) is ((2n)!)/((m)!(2n-m)!) b.((2n)!3!3!)/((2n-m)!) c.((2n-m)/(3))!((4n+m)/(3))! none of these

If x^(p) occurs in the expansion of (x^(2)+1/x)^(2n) prove that its coefficient is ((2n)!)/([(1)/(3)(4n-p)]![(1)/(3)(2n+p)]!)

Knowledge Check

  • If in the expansion of (1+x)^(m)(1-x)^(n) , the coefficient of x and x^(2) are 3 and - 6 respectively, then m is

    A
    6
    B
    9
    C
    12
    D
    24

  • If in the expansion of (1+x)^(m)(1-x)^(n) , the coefficients of x and x^(2) are 3 and - 6 respectively, then m is

    A
    6
    B
    9
    C
    12
    D
    24

    • Similar Questions

    Explore conceptually related problems

    The coefficient of 1/x in the expansion of (1+x)^(n)(1+1/x)^(n) is (n!)/((n-1)!(n+1)!) b.((2n)!)/((n-1)!(n+1)!) c.((2n-1)!(2n+1)!)/((2n-1)!(2n+1)!) d.none of these

    If in the expansion of (1+x)^(m)(1-x)^(n), the coefficients of x and x^(2) are 3 and -6 respectively,then m is:

    Differential coefficient of (x^((l+m)/(m-n)))^(1/(n-l))*(x^((m+n)/(n-l)))^(1/(l-m))*(x^((n+l)/(l-m)))^(1/(m-n)) wrt x is

    If 'n' is a positive integer then prove that the coefficient fo x^(m) in the expansion of (x^(2)+(1)/(x))^(2n) is :

    If 'n' is a positive integer then prove that the coefficient fo x^(m) in the expansion of (x^(2)+(1)/(x))^(2n) is :

    The middle term in the expansion of ((2x)/(3)-(3)/(2x^(2)))^(2n) is ^(2n)C_(n) b.(-1)^(n)2nC_(n)x^(-n) c.^(2n)C_(n)x^(-n)d .none of these

    Home
    Profile