Home
Class 11
MATHS
If (1+x-2x^2)^6=1+a1x+a2x^2+……+a(12)x^12...

If `(1+x-2x^2)^6=1+a_1x+a_2x^2+……+a_(12)x^12` then

A

`a_2+a_4+a_6+…….+a_12=31`

B

`a_1+a_3+a_5+……+a_11=-32`

C

`a_1+a_2+a_3+…….+a_12=-1`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A, B, C
Promotional Banner

Topper's Solved these Questions

  • BASIC MATHEMATICS

    PATHFINDER|Exercise QUESTION BANK |266 Videos
  • BINOMIAL THEOREM AND PRINCIPLE OF MATHEMATICAL INDUCTION

    PATHFINDER|Exercise QUESTION BANK|68 Videos

Similar Questions

Explore conceptually related problems

Let n be a positive integer such that (1+x+x^2)^n=a_0+a_1x+a_2x^2+…….+a_(2n)x^(2n) then sum_(r=0)^(2n) a_r is

If (1+x-2x^(2))^(6) = 1 + a_(1)x+a_(2)x^(2) + "……" + a_(12)x^(12) , then find the value of a_(2) + a_(4) +a_(6)+ "……" + a_(12) .

If (1+x+x^2)^n=a_0+a_1x+a_2x^2++a_(2n)x^(2n), find the value of a_0+a_3+a_6++ ,n in Ndot

If (1+x+x^2)^n=a_0+a_1x+a_2x^2+.......+a_(2n)x^(2n) , then prove that a_0+a_2+a_4+....+a_(2n)=1/2(3^n+1) .

If log(1-x+x^2)=a_1x+a_2x^2+a_3x^3+……… then a_3+a_6+a_9+……… is equal to

If (1+x+x^2)^n=a_0+a_1x+a_2x^2+....+a_(2n)X^(2n) ,show that a_0+a_3+a_6+.....=a_1+a_4+a_7+...=a_2+a_5+a_8+...=3^(n-1)

If (1+px+x^(2))^(n)=1+a_(1)x+a_(2)x^(2)+…+a_(2n)x^(2n) . Which of the following is true for 1 lt r lt 2n

If (1+px+x^(2))^(n)=1+a_(1)x+a_(2)x^(2)+…+a_(2n)x^(2n) . The value of a_(1)+3a_(2)+5a_(3)+7a_(4)+….(4n-1)a_(2n) when p=-3 and n in even is

If (1+x+x^2++x^p)^n=a_0+a_1x+a_2x^2++a_(n p)x^(n p), then find the value of a_1+2a_2+3a_3+ddot+n pa_(n p)dot

If (1+x)^n=a_0+a_1x+a_2x^2+…..+a_nx^n then show that (a_0-a_2+a_4-……)^2+(a_1-a_3+a_5-……)^2=a_0+a_1+a_2+……a_n

PATHFINDER-BINOMIAL THEOREM-QUESTION BANK
  1. The coefficient of x^(65) in the expansion of (1+x)^(131)(x^2-x+1)^(30...

    Text Solution

    |

  2. Remainder when 5^(40) is divided by 11.

    Text Solution

    |

  3. If (1+x-2x^2)^6=1+a1x+a2x^2+……+a(12)x^12 then

    Text Solution

    |

  4. Number of values of r satisfying the equation ,^69C(3r-1) -^(69)C(r^2)...

    Text Solution

    |

  5. In the expansion of (x+(a/x^2))^n, (ane0) if term independent of x doe...

    Text Solution

    |

  6. If f(n)=sum(r=1)^n[r(n ^(n-1)C(r-1)-r^C(r-1))+(2r+1)^nCr]

    Text Solution

    |

  7. The value of ,^nC0 + ^(n+1)C1 +^(n+2)C2+……+^(n+k)Ck is equal to

    Text Solution

    |

  8. If the expansion of (x+(alpha/x))^n and (x+(beta/x^2))^n in powers of ...

    Text Solution

    |

  9. The coefficient of the middle term in the expansion of (1+x)^(2n) is

    Text Solution

    |

  10. If the term independent of x in the expansion of (sqrtx+(k/x^2))^10 is...

    Text Solution

    |

  11. If n is a positive integer then in the trinomial expansion of (x^2+2x+...

    Text Solution

    |

  12. Which of the following will not be true?

    Text Solution

    |

  13. Consider following two infinite series in real r and 0 C=1+rcostheta...

    Text Solution

    |

  14. Consider following two infinite series in real r and 0 C=1+rcostheta...

    Text Solution

    |

  15. First three terms in the expansion of (x+a)^n are respectively 128, 22...

    Text Solution

    |

  16. The sum of even terms in the expansion of (x+a)^n is

    Text Solution

    |

  17. Match List - I with List-II

    Text Solution

    |

  18. Match List-I with List-II

    Text Solution

    |

  19. If the second term of the expansion [a^(1/13)+(a/sqrt(a^(-1))] is 14a^...

    Text Solution

    |

  20. (1+x)(1+x+x^2)(1+x+x^2+x^3)…….(1+x+x^2+…….+x^(100)) when written in th...

    Text Solution

    |