Home
Class 12
MATHS
If (1+3x-2x^(2))^(10)=a(0)+a(1)x+a(2)x^(...

If `(1+3x-2x^(2))^(10)=a_(0)+a_(1)x+a_(2)x^(2).+…+a_(20)x^(20)` then prove that
`a_(0)+a_(1)+a_(2)+……+a_(20)=2^(10)`

Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    AAKASH SERIES|Exercise ADDITIONAL SOLVED EXAMPLES|10 Videos
  • BINOMIAL THEOREM

    AAKASH SERIES|Exercise EXERCISE - 3.1 (VERY SHORT ANSWER QUESTIONS)|44 Videos
  • BINOMIAL THEOREM

    AAKASH SERIES|Exercise EXERCISE - 1.4 (Level-2) |36 Videos
  • AREAS

    AAKASH SERIES|Exercise Exercise-3.2|21 Videos
  • CIRCLE

    AAKASH SERIES|Exercise EXERCISE -1.4|38 Videos

Similar Questions

Explore conceptually related problems

If (1+3x-2x^(2))^(10)=a_(0)+a_(1)x+a_(2)x^(2).+…+a_(20)x^(20) then prove that a_(0)-a_(1)++a_(2)-a_(3)+……+a_(20)=4^(10)

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

If (1+x+x^(2))^(n)=a_(0)+a_(1)x+a_(2)x^(2)+….+a_(2n)x^(2n) , then prove that a_(0)+a_(2)+a_(4)+……+a_(2n)=(3^(n)+1)/(2)

If (1+x+x^(2))^(n)=a_(0)+a_(1)x+a_(2)x^(2)+….+a_(2n)x^(2n) , then prove that a_(1)+a_(3)+a_(5)+….+a_(2n-1)=(3^(n)-1)/(2)

If (1+x+x^(2))^(n)=a_(0)+a_(1)x+a_(2)x^(2)+….+a_(2n)x^(2n) , then prove that a_(0)+a_(3)+a_(6)+a_(9)+……=3^(n-1)

If (1+x+2x^(2)+4x^(3))^(10)=a_(0)+a_(1)x+a_(2)x^(2)+….+a_(30)x^(30) . Find the value of a_(0) +a_(1)+a_(2)+….+a_(30)

If (1+x+2x^(2)+4x^(3))^(10)=a_(0)+a_(1)x+a_(2)x^(2)+….+a_(30)x^(30) . Find the value of a_(0) +a_(2)+a_(4) +…+ a_(30)

If (1+x+2x^(2)+4x^(3))^(10)=a_(0)+a_(1)x+a_(2)x^(2)+….+a_(30)x^(30) . Find the value of a_(0)-a_(1)+a_(2)-a_(3)…+a_(30)

If (1+x+2x^(2)+4x^(3))^(10)=a_(0)+a_(1)x+a_(2)x^(2)+….+a_(30)x^(30) . Find the value of a_(1)+a_(3)+a_(5)+…+a_(29)

AAKASH SERIES-BINOMIAL THEOREM-SOLVED EXAMPLES
  1. If (3 + 7x - 9x^2)^n = a0 +a1x + a2 x^2 + ……+a(2n)x^(2n) prove the a0 ...

    Text Solution

    |

  2. If (3 + 7x - 9x^2)^n = a0 +a1x + a2 x^2 + ……+a(2n)x^(2n) prove the a0 ...

    Text Solution

    |

  3. If (1+3x-2x^(2))^(10)=a(0)+a(1)x+a(2)x^(2).+…+a(20)x^(20) then prove t...

    Text Solution

    |

  4. If (1+3x-2x^(2))^(10)=a(0)+a(1)x+a(2)x^(2).+…+a(20)x^(20) then prove t...

    Text Solution

    |

  5. If (1 + 3x - 2x^2)^10 = a0 + a1x + a2x^2 +…..+a20 x^20 thn prove that ...

    Text Solution

    |

  6. If (1 + 3x - 2x^2)^10 = a0 + a1x + a2x^2 +…..+a20 x^20 thn prove that ...

    Text Solution

    |

  7. If the 2^("nd"),3^("rd")" and "4^("th") terms in the expansion of (a+x...

    Text Solution

    |

  8. If the coefficients of x^(9),x^(10),x^(11) in expansion of (1+x)^(n) a...

    Text Solution

    |

  9. If n is a positive integer, then prove that 81^n + 20 n - 1 is divisib...

    Text Solution

    |

  10. Using binomial theorem, prove that 5^(4n)+52n-1 is divisible by 676 fo...

    Text Solution

    |

  11. 3. C0 + 7. C1 + 11. C2 +…...+ (4n+3) . Cn=

    Text Solution

    |

  12. With usual notations find the value of 3.C1 + 5.C2 + 7.C3 + ……….+n ter...

    Text Solution

    |

  13. With usual notations prove that C1+2.C2x + 3.C3x^2 + ……+2n.C(2n) ...

    Text Solution

    |

  14. Prove that (""^20C1)/(""^20C0) + 2. (""^20C2)/(""^20C1) + 3. (""^2...

    Text Solution

    |

  15. If n is a positive integer and C4 = ""^nCr then find the value of sum(...

    Text Solution

    |

  16. Prove that sum(r = 1)^(n+1) (2^(r +1) C(r - 1) )/(r (r + 1)) = (3^(n+...

    Text Solution

    |

  17. Prove that sum(r = 0)^n r^2 . Cr = n (n +1).2^(n-2)

    Text Solution

    |

  18. Prove that sum(r = 0)^n r^3 . Cr = n^2 (n +3).2^(n-3)

    Text Solution

    |

  19. If Cr denotes ""^nCr then show that C0 + (C1)/(2) + (C2)/(3) x^2 +...

    Text Solution

    |

  20. If C0, C1, C2 ,……..Cn are the coefficient in the expansion of (1 + x)^...

    Text Solution

    |