Home
Class 11
MATHS
If the coefficients of 2nd, 3rd and 4th ...

If the coefficients of 2nd, 3rd and 4th terms in the expansion of `(1+x)^(2n)` are in A.p., then prove that `2n^2-9n+7=0`.

Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    PATHFINDER|Exercise QUESTION BANK|225 Videos
  • CARTESIAN COORDINATES AND STRAIGHT LINE

    PATHFINDER|Exercise QUESTION BANK|249 Videos

Similar Questions

Explore conceptually related problems

If the coefficients of 2nd, 3rd and 4th terms in the expansion of (1+x)^(2n) are in AP, Show that 2n^(2)-9n+7=0 .

If the coefficients of 2nd,3rd and 4th terms in the (1+x)^(2n) are in A.Pshow that 2n^2-9n+7=0

The coefficients of 5th ,6th and 7th terms in the expansion of (1+x)^(n) are A.P . ,find n .

If the coefficients of 2nd, 3rd and 4th terms of (1+x)^(2n) are in A.P., then n equals

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

If the coefficients of 5th, 6th , and 7th terms in the expansion of (1+x)^n are in A.P., then n= a. 7 only b. 14 only c. 7 or 14 d. none of these

If the coefficients of the pth , (p+1)and (p+2) terms in the expansions of (1+x)^(n) are in A.P , show that , n^(2)-n(4p+1)+4p^(2)-2=0

The sum of the coefficients of the terms of the expansion of (3x-2y)^n is

In the coefficients of rth, (r+1)t h ,a n d(r+2)t h terms in the binomial expansion of (1+y)^m are in A.P., then prove that m^2-m(4r+1)+4r^2-2=0.

If the coefficients of (p +1) th and (p+3)th terms in the expansion of (1+x)^(2n) be equal show that , p =n-1 .

PATHFINDER-BINOMIAL THEOREM AND PRINCIPLE OF MATHEMATICAL INDUCTION-QUESTION BANK
  1. Find the coefficient of x in the expansion (1-x^2+2x^4)(1-1/x)^6.

    Text Solution

    |

  2. If (1+x+x^2)^n=a0+a1x+a2x^2+.......+a(2n)x^(2n), then prove that a0+a2...

    Text Solution

    |

  3. If the coefficients of 2nd, 3rd and 4th terms in the expansion of (1+x...

    Text Solution

    |

  4. If the coefficients of four consecutive terms in the expansion of (1+x...

    Text Solution

    |

  5. The 3rd,4th and fifth terms in the expansion of (x+a)^n are 252, 1512,...

    Text Solution

    |

  6. The coefficient of three consecutive terms in the expansion of (1+x)^n...

    Text Solution

    |

  7. Find the number of integral terms in the expansion of (5^(1/2)+7^(1/8)...

    Text Solution

    |

  8. Show that the integral part of the value of (9+4sqrt5)^n is odd for po...

    Text Solution

    |

  9. If the 3rd, 4th. 5th and sixth term in the expansion of (x+alpha)^n ar...

    Text Solution

    |

  10. If coefficient of x^2 and x^11 are 27 and -192 respectively of (1+ax+2...

    Text Solution

    |

  11. Find the coefficient of x^5 in the expansion of (1+x)^21+(1+x)^22+...+...

    Text Solution

    |

  12. Determine the x-independent term in the expansion of (1+4x)^p(1+1/(4x)...

    Text Solution

    |

  13. For ninN , 2^(3n)-1 is divisible by

    Text Solution

    |

  14. For ninN , n^3+2n is divisible by

    Text Solution

    |

  15. ForninN , 3^(2n-1)+2^(n+1) is always divisible by

    Text Solution

    |

  16. For ninN 2^(3n)-7n-1 is always divisible by

    Text Solution

    |

  17. The greatest positive integer divides (n+1)(n+2)..........(n+r) is

    Text Solution

    |

  18. Applying the principle of mathematical induction (P.M.I.) prove that 1...

    Text Solution

    |

  19. Using mathematical induction show 7+77+777+......+n terms =7/81(10^(n+...

    Text Solution

    |

  20. Applying P.M.I. prove that x^n-y^n is always divisible by x+y where n...

    Text Solution

    |