Home
Class 11
MATHS
In the expansion of (1+a)^(m+n), prove t...

In the expansion of `(1+a)^(m+n)`, prove that coefficients of `a^m` and `a^n` are equal.

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    JBD PUBLICATION|Exercise EXAMPLE|36 Videos

Similar Questions

Explore conceptually related problems

If in the expansion of (1 +x)^(m) (1 - x)^(n) , the coefficients of x and x^(2) are 3 and - 6 respectively, the value of m and n are

In the expansion of (1+x)^n , the coefficient of x^(p-1) and of x^(q-1) are equal. Show that p+q=n+2, p ne q .

Statement-I : In the expansion of (1+ x)^n ifcoefficient of 31^(st) and 32^(nd) terms are equal then n = 61 Statement -II : Middle term in the expansion of (1+x)^n has greatest coefficient.

Prove that the coefficient of x^n in the expansion of (1+x)^(2n) is twice the coefficient of x^n in the expansion of (1+x)^(2n-1)

Show that the coefficient of x^n in the expansion of (1+x)^(2n) is twice the coefficient of x^n in the expansion of (1+ x)^(2n-1) .

If the greatest term in the expansion of (1+x)^(2n) has the greatest coefficient if and only if xepsilon(10/11, 11/10) and the fourth term in the expansion of (kx+ 1/x)^m is n/4 then find the value of mk.

If x^p occurs in the expansion of (x^2+1/x)^(2n) , prove that its coefficient is : ((2n)!)/([1/3(4n-p)!][1/3(2n+p)!]) .

In the binomial expansion (a+b)^n , the coefficients of fourth and thirteenth terms are equal to each other. Find n.

Show that , if the greatest term in the expansion of (1 + x)^(2n) has also the greatest coefficient then x lies between (n)/(n +1) " and" (n+1)/(n)

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

JBD PUBLICATION-BINOMIAL THEOREM-EXAMPLE
  1. Find an approximation of (0.99)^5 using the first three terms of its e...

    Text Solution

    |

  2. (a + b)^4 -(a -b)^4 ਪਤਾ ਕਰੋ ਅਤੇ ਇਸਦੀ ਵਰਤੋਂ ਕਰਕੇ (sqrt3+sqrt2)^4-(sqrt...

    Text Solution

    |

  3. Write the general term in the expansion of: (2x+1/x)^5.

    Text Solution

    |

  4. Write the general term in the expansion of (x^(2)-yx)^(12), x ne 0

    Text Solution

    |

  5. Find 3rd term in the expansion of (3x-y^3/6)^4.

    Text Solution

    |

  6. Find 5th term in the expansion of (2x^2-1/3x)^11.

    Text Solution

    |

  7. Find the rth term from the end in the expansion of (x+a)^n.

    Text Solution

    |

  8. Find the 4th term from the end in the expansion of ((4x)/5-5/(2x))^9

    Text Solution

    |

  9. Find a positive value of m for which the coefficient of x^2 in the exp...

    Text Solution

    |

  10. In the expansion of (1+x)^n, the coefficient of x^(p-1) and of x^(q-1)...

    Text Solution

    |

  11. In the expansion of (1+a)^(m+n), prove that coefficients of a^m and a^...

    Text Solution

    |

  12. Find the coefficient of a^-6 b^4 in the expansion of (1/a-(2b)/3)^10.

    Text Solution

    |

  13. The coefficients of three consecutive terms in the expansion of (1+a)^...

    Text Solution

    |

  14. Expand each of the following expressions: (2x-3)^6.

    Text Solution

    |

  15. Expand the following expressions, using Binomial Theorem: (1+2x+x^2)^3...

    Text Solution

    |

  16. Simplify (x+2y)^10+(x-2y)^10.

    Text Solution

    |

  17. ਮੁੱਲ ਪਤਾ ਕਰੋ:-(a^2+ sqrt(a^2-1))^4 + (a^2- sqrt(a^2-1))^4

    Text Solution

    |

  18. Find the expnsion of (3x^2-2ax+3a^2)^3 using Binomial Theorem.

    Text Solution

    |

  19. Find the term independent of x in the expansion of: (2x+3/x^2)^9.

    Text Solution

    |

  20. Find the middle terms in the expansion of (3-x^(3)/6)^(7)

    Text Solution

    |