Home
Class 11
MATHS
If (1 + x - 2 x^(2))^(6) = 1 + C(1) x + ...

If `(1 + x - 2 x^(2))^(6) = 1 + C_(1) x + C_(2) x^(2) + C_(3) x^(3) + …+ C_(12) x^(12)`,
then the value of `C_(2) + C_(4) + C_(6) + …+ C_(12)` is

A

30

B

65

C

31

D

63

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM AND ITS APPLCIATIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|103 Videos

  • CARTESIAN CO-ORDINATE SYSTEM

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|27 Videos

Similar Questions

Explore conceptually related problems

If (1 + x)^(n) = C_(0) + C_(1)x + C_(2)x^(2) + C_(3) x^(3) + C_(4) x^(4) + ..., find the values of (i) C_(0) - C_(2) + C_(4) - C_(0) + … (ii) C_(1) - C_(3) + C_(5) - C_(7) + … (iii) C_(0) + C_(3) + C_(6) + …

If (1 + x)^(n) = C_(0) + C_(1) x + C_(2) x^(2) + C_(3) x^(3) + …+ C_(n) x^(n) , find the sum of the series (C_(0))/(2) -(C_(1))/(6) + (C_(2))/(10) + (C_(3))/(14) -...+ (-1)^(n) (C_(n))/(4n+2) .

(1 + x)^(n) = C_(0) + C_(1) x + C_(2) x^(2) + C_(3) x^(3) + … + C_(n) x^(n) , prove that C_(0) - 2C_(1) + 3C_(2) - 4C_(3) + … + (-1)^(n) (n+1) C_(n) = 0

If (1 + x)^(n) = C_(0) + C_(1) x + C_(2) x^(2) + C_(3) x^(3) + … + C_(n) x^(n) , prove that C_(0) - (C_(1))/(2) + (C_(2))/(3) -…+ (-1)^(n) (C_(n))/(n+1) = (1)/(n+1) .

If (1 + x)^(n) = C_(0) + C_(1) x + C_(2) x^(2) + C_(3) x^(3) + …+ C_(n) x^(n) , show that C_(1) - (C_(2))/(2) + (C_(3))/(3) - …(-1)^(n-1) (C_(n))/(n) = 1 + (1)/(2) + (1)/(3) + …+ (1)/(n) .

If (1 + x)^(n) = C_(0) + C_(1)x + C_(2) x^(2) + C_(3) x^(3) + …+ C_(n) x^(n) prove that (C_(0))/(1) + (C_(2))/(3) + (C_(4))/(5) + ...= (2^(n))/(n+1) .

If (1 + x)^(n) = C_(0) + C_(1) x + C_(2) x^(2) + …+ C_(n) x^(n)," prove that " 1^(2)*C_(1) + 2^(2) *C_(2) + 3^(2) *C_(3) + …+ n^(2) *C_(n) = n(n+1)* 2^(n-2) .

If (1 + x)^(n) = C_(0) + C_(1) x + C_(2) x^(2) +… + C_(n) x^(n) , prove that C_(0) + 2C_(1) + 3C_(2) + …+ (n+1)C_(n) = (n+2)2^(n-1) .

If (1 + x)^(n) = C_(0) + C_(1)x + C_(2) x^(2) + …+ C_(n) x^(n) , then for n odd, C_(1)^(2) + C_(3)^(2) + C_(5)^(2) +....+ C_(n)^(2) is equal to

If (1 + x)^(n) = C_(0) + C_(1) x + C_(2) x^(2) + …+ C_(n) x^(n) , prove that (1*2) C_(2) + (2*3) C_(3) + …+ {(n-1)*n} C_(n) = n(n-1) 2^(n-2) .

OBJECTIVE RD SHARMA ENGLISH-BINOMIAL THEOREM AND ITS APPLCIATIONS -Chapter Test
  1. Find the following sum : (1)/(n!) + (1)/(2!(n-2)!) + (1)/(4!(n-4)!)+...

    Text Solution

    |

  2. The coefficient of x^(n) y^(n) in the expansion of [(1 + x)(1+y) (x...

    Text Solution

    |

  3. If (1 + x - 2 x^(2))^(6) = 1 + C(1) x + C(2) x^(2) + C(3) x^(3) + …+ C...

    Text Solution

    |

  4. Find the ratio of the coefficient of x^(15) to the term independent of...

    Text Solution

    |

  5. Find the number of terms in the expansion of (x+y+z)^(n).

    Text Solution

    |

  6. In the expansion of (1+x)^30 the sum of the coefficients of odd powers...

    Text Solution

    |

  7. In the expansion of (x^(2) + 1 + (1)/(x^(2)))^(n), n in N,

    Text Solution

    |

  8. The term independent ofx in the expansion of (1+x)^10*(1+1/x)^10 is

    Text Solution

    |

  9. In the expansion of (x^(3) - (1)/(x^(2)))^(15) , the constant term,i...

    Text Solution

    |

  10. The middle term in the expansion of (1 - (1)/(x))^(n) (1 - x)^(n) is

    Text Solution

    |

  11. The total number of terms which are dependent on the value of x in the...

    Text Solution

    |

  12. The coefficient of x^6 in {(1+x)^6+(1+x)^7+........+(1+x)^(15)} is

    Text Solution

    |

  13. The number of real negative terms in the binomial expansion of (1+i x)...

    Text Solution

    |

  14. Find the number of terms in the expansion of (x+sqrt(x^2-1))^6+(x-sqr...

    Text Solution

    |

  15. If the last tem in the binomial expansion of (2^(1/3)-1/(sqrt(2)))^n i...

    Text Solution

    |

  16. The coefficient of x^(6) a^(-2) in the expansion of ((x^(2))/(a)-(a)/...

    Text Solution

    |

  17. If in the expansion of (1 + ax)^(n),n in N, the coefficient of x an...

    Text Solution

    |

  18. In the expansion of (x^3-1/(x^2))^n ,n in N , if the sum of the coeff...

    Text Solution

    |

  19. The coefficient of x^20 in the expansion of (1+x^2)^40.(x^2+2+1/x^2)^-...

    Text Solution

    |

  20. about to only mathematics

    Text Solution

    |