Home
Class 11
MATHS
If p and q are positive, then prove that...

If `p and q` are positive, then prove that the coefficients of `x^p and x^q` in the expansion of `(1+x)^(p+q)` will be equal.

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    CENGAGE PUBLICATION|Exercise All Questions|877 Videos

Similar Questions

Explore conceptually related problems

The coefficients of x^p and x^q in the expansion of (1+x)^(p+q) are

If A and B are the coefficients of x ^(p) and x ^(q) respectively in the expansion of (1+x) ^(p+q), then-

If the coefficients of x^39 and x^40 are equal in the expansion of (p+qx)^49 . then the possible values of p and q are

Find the term independent of x in the expansion of (1+x)^(p)(1+(1)/(x))^(q),p,q being positive integers.

If the sum of the coefficients in the expansion of (q+r)^(20)(1+(p-2)x)^(20) is equal to square of the sum of the coefficients in the expansion of [2rqx-(r+q)*y]^(10) , where p , r , q are positive constants, then

If p and q are two given statements the prove that , ~(p^^q)-=(~p)vv(~q)

If (x+i y)^5=p+i q , then prove that (y+i x)^5=q+i pdot

If p and q are two given statements the prove that , ~(prArrq)-=(p)^^(~q)

If p. q are odd integers. Then the roots of the equation 2px^(2)+(2p+q)x+q=0 are

If p,q are odd integers, then the roots of the equation 2px^(2)+(2p+q)x+q=0 are

CENGAGE PUBLICATION-BINOMIAL THEOREM-All Questions
  1. In ( 2^(1/3)+1/3^(1/ 3))^n if the ratio of 7th term from the beginnin...

    Text Solution

    |

  2. If the coefficient of 4th term in the expansion of (a+b)^n is 56, then...

    Text Solution

    |

  3. If p and q are positive, then prove that the coefficients of x^p and x...

    Text Solution

    |

  4. Find the number of irrational terms in the expansion of (5^(1//6)+2^(1...

    Text Solution

    |

  5. If x^p occurs in the expansion of (x^2+1/x)^(2n) , prove that its coef...

    Text Solution

    |

  6. The co-efficient of a^(3)b^(4)c^(5) in the expansion of (bc+ca+ab)^(6)...

    Text Solution

    |

  7. The coefficient of x^7 in the expansion of (1-x-x^2+x^3)^6 is

    Text Solution

    |

  8. If the number of terms in the expansion of (x+y+z)^n are 36, then find...

    Text Solution

    |

  9. The coefficient of a^3b^4c in the expansion of (1+a-b+c)^9 is equal to

    Text Solution

    |

  10. The coefficient of x^4 in the expansion of (1+x+x^2+x^3)^11 is

    Text Solution

    |

  11. Find the number of terms which are free from radical signs in the e...

    Text Solution

    |

  12. Find the coefficient of x^5 in the expression of (1+x^2)^5(1+x)^4.

    Text Solution

    |

  13. Find the coefficient of x^(13) in the expansion of (1-x)^5xx(1+x+x^2+x...

    Text Solution

    |

  14. Find the sum .^(10)C1+^(10)C3+^(10)C5+^(10)C7+^(10)C9

    Text Solution

    |

  15. Find the sum of 1/(1!(n-1)!)+1/(3!(n-3)!)+1/(5!(n-5)!)+ ...,

    Text Solution

    |

  16. If n is an even positive integer, then find the value of x if the gr...

    Text Solution

    |

  17. If |x|<1, then find the coefficient of x^n in the expansion of (1+2x+3...

    Text Solution

    |

  18. If (r+1)t h term is the first negative term in the expansion of (1+x)^...

    Text Solution

    |

  19. If |x|<1, then find the coefficient of x^n in the expansion of (1+x+x^...

    Text Solution

    |

  20. If |x|>1, then expand (1+x)^(-2)dot

    Text Solution

    |