Home
Class 12
MATHS
Coefficient of x^(m) in the expansion of...

Coefficient of `x^(m)` in the expansion of
`S = (1 + x)^(2m) + x(1 +·x)^(2m-1) + x^(2)(1 + x)^(2m- 2) + .... +x^(2m)` is

A

`""^(2m)C_(m)+""^(2m+1)C_(m-1)`

B

`""^(2m+1)C_(m)`

C

`0`

D

`2m^(2)+2m+1`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • MATHEMATICAL INDUCTION AND BINOMIAL THEOREM

    MCGROW HILL PUBLICATION|Exercise SOLVED EXAMPLES ( Numerical Answer Type Questions)|20 Videos

  • MATHEMATICAL INDUCTION AND BINOMIAL THEOREM

    MCGROW HILL PUBLICATION|Exercise EXERCISE (Concept-based Single Correct Answer Type Questions)|10 Videos

  • MATHEMATICAL INDUCTION AND BINOMIAL THEOREM

    MCGROW HILL PUBLICATION|Exercise SOLVED EXAMPLES ( LEVEL 1 Single Correct Answer Type Questions)|80 Videos

  • LIMITS AND CONTINUITY

    MCGROW HILL PUBLICATION|Exercise Previous Years B-Architecture Entrance Examination Paper|12 Videos

  • MATHEMATICAL REASONING

    MCGROW HILL PUBLICATION|Exercise QUESTIONS FROM PREVIOUS YEARS. B. ARCHITECTURE ENTRANCE EXAMINATION PAPERS|11 Videos

Similar Questions

Explore conceptually related problems

Find the coefficient of : x^(m) in the expansion of (x+(1)/(x))^(n).

Coefficient of x^(2^(m+1)) in the expansion of (1)/((1+x)(1+x^(2))(1+x^(4))(1+x^(8))....(1+x^(2^(m))))(|x|<1) is

If the coefficient of x^8 in the expansion of (1+ (x^2)/( 2!) + (x^4)/( 4!) + (x^6)/( 6!) + (x^8)/( 8!))^(2) is (1)/(M) , then a divisor of M is

In the expansion of (1+x)^(2m)(x/(1-x))^(-2m) the term independent of x is

Coefficient of 'x' in the expansion of (x^m+1/x^2)^(22) is 1540 and m is a natural number. Find m=?

If the coefficient of x^(2) + coefficient of x in the expanssion of (1+x)^(m)(1-x)^(n),(mnen) is equal to – m, then the value of n – m is equal to:

STATEMENT - 1 : The term independent of x in the expansion of (x+1/x+2)^(m) is ((2m) !)/((m !)^(2)) STATEMENT - 2 : The coefficient of x^(b) in the expansion of (1+x)^(n) is .^(n)C_(b) .

The natural number m , for which the coefficient of x in the binomial expansion of (x ^(m) + (1)/(x^(2)))^(22) is 1540 , is _______.

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:

MCGROW HILL PUBLICATION-MATHEMATICAL INDUCTION AND BINOMIAL THEOREM-SOLVED EXAMPLES ( LEVEL 2 Single Correct Answer Type Questions)
  1. E=(3^(log(3)sqrt(9^(|x-2|)))+7^((1/5)log(7)(4).3^(|x-2|)-9 ))^(7)

    Text Solution

    |

  2. Let a(n) denote the term independent of x in the expansion of [x+(sin(...

    Text Solution

    |

  3. Find the largest term in the expansion of (3+2x)^(50),w h e r ex=1//5.

    Text Solution

    |

  4. If n is odd, then sum of the series C(0)^(2)-C(1)^(2)+C(2)^(2)-C(2)^(3...

    Text Solution

    |

  5. If (1 + x)^(n) = C(0) + C(1) x + C(2) x^(2) + …+ C(n) x^(n) , prove t...

    Text Solution

    |

  6. If (1 + x)^(n) = C(0) + C(1) x + C(2) x^(2) + ... + C(n) x^(n), then v...

    Text Solution

    |

  7. If C(r) stands for ""^(n)C(r), then the sum of the series (2((n)/(2))!...

    Text Solution

    |

  8. The sum of coefficients of integral powers of x in the binomial exp...

    Text Solution

    |

  9. Given that the 4th term in the expansion of [2+(3//8x)]^(10) has the m...

    Text Solution

    |

  10. Assuming x to be so small that x^(3) and higher powers of x can be neg...

    Text Solution

    |

  11. If (1+x+x^(2))^(8)=a(0)+a(1)x+a(2)x^(2)+…a(16)x^(16) for all values of...

    Text Solution

    |

  12. Coefficient of x^(11) in the expansion of (1+x^2)(1+x^3)^7(1+x^4)^(12)...

    Text Solution

    |

  13. The coefficients of three consecutive terms of (1+x)^(n+5) are in the ...

    Text Solution

    |

  14. Sum of the series sum(k=0)^(n)""^(n)C(k)(-1)^(k)1/(a(k)) where a(k...

    Text Solution

    |

  15. Suppose m and n are positive integers and let S=sum(k=0)^n (-1)^k 1/(...

    Text Solution

    |

  16. Coefficient of x^(m) in the expansion of S = (1 + x)^(2m) + x(1 +·x)...

    Text Solution

    |

  17. Sum of the first 20 terms of the series 1/((2)(4))+((1)(3))/((2)(4)(...

    Text Solution

    |

  18. The term independent of x in the expansion of (1-1/(2x)+3x^(7))(x^(2...

    Text Solution

    |

  19. Let P(x) be a polynomial with real coefficients such that int(0)^(1)x^...

    Text Solution

    |

  20. Suppose [x] denote the greatest integer lex and ninN, then lim(nto o...

    Text Solution

    |