Home
Class 12
MATHS
If n is a positive integer then using th...

If n is a positive integer then using the indentiy `(1+x)^(n)=(1+x)^(3)(1+x)^(n-3)`, prove that
`""^(n)C_(r)=""^(n-2)C_(r)+3*""^(n-3)C_(r-1)*""^(n-3)C_(r-2)+""^(n-3)C_(r-3)`

Promotional Banner

Topper's Solved these Questions

  • MISCELLANEOUS EXAMPLES

    CHHAYA PUBLICATION|Exercise COORDINATE GEOMETRY (TWO DIMENSIONAL COORDINATE GEOMETRY)|124 Videos
  • MISCELLANEOUS EXAMPLES

    CHHAYA PUBLICATION|Exercise COORDINATE GEOMETRY (THREE DIMENSIONAL COORDINATE GEOMETRY)|10 Videos
  • MISCELLANEOUS EXAMPLES

    CHHAYA PUBLICATION|Exercise TRIGONOMETRY|148 Videos
  • METHOD OF SUBSTITUTION

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Examination (Assertion-Reason Type)|2 Videos
  • ORDER AND DEGREE OF DIFFERENTIAL EQUATION

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Examination (E Assertion - Reasion Type )|2 Videos

Similar Questions

Explore conceptually related problems

If .^(n)P_(r)=x.^(n)C_(r) x=

.^(n-1)C_(r)+^(n-1)C_(r-1)=

Prove that , .^(n)C_(r)+3.^(n)C_(r-1)+3.^(n)C_(r-2)+^(n)C_(r-3)=^(n+3)C_(r)

Show that .^(n)C_(r)+.^(n-1)C_(r-1)+.^(n-1)C_(r-2)=.^(n+1)C_(r) .

Show that , .^(n)C_(r)=(n-r+1)/(r).^(n)C_(r-1) .

show that ^nC_r+ ^(n-1)C_(r-1)+ ^(n-1)C_(r-2)= ^(n+1)C_r

.^(n)C_(r)+2.^(n)C_(r-1)+.^(n)C_(r-2)=.^(n+2)C_(r)(2lerlen) .

Prove that "^n C_r+^(n-1)C_r+...+^r C_r=^(n+1)C_(r+1) .

The value of (""^(n) C_(1)+2. ""^(n) C_(2)+3. ""^(n)C_(3)+…+ n""^(n)C_(n)) is-

Show that , (.^(n)C_(r)+^(n)C_(r-1))/(.^(n)C_(r-1)+^(n)C_(r-2))=(.^(n+1)p_(r))/(r.^(n+1)p_(r-1))

CHHAYA PUBLICATION-MISCELLANEOUS EXAMPLES-ALGEBRA
  1. For every natural number n, show that 7^(2n)+2^(3n-3)*3^(n-1) is alway...

    Text Solution

    |

  2. If the coefficients of the (r-1) th and (2r+3) th terms in the equatio...

    Text Solution

    |

  3. If n is a positive integer then using the indentiy (1+x)^(n)=(1+x)^(3)...

    Text Solution

    |

  4. If S(1), S(2), S(3),...S(n) are the sums of infinite geometric series,...

    Text Solution

    |

  5. If u(r)=(1)/(r!) then show that u(0)u(n)+8u(1)+u(n-1)+8^(2)u(2)u(n-2...

    Text Solution

    |

  6. a series is given by the following form : 1+(x+x^(2))+(x^(3)+x^(4)+x...

    Text Solution

    |

  7. If x= cos theta+i sin theta and 1+ sqrt(1-a^(2))=na, show that, (a)/(...

    Text Solution

    |

  8. Show that (a+ omega +omega ^(2))(a+omega ^(2)+omega ^(4))(a+omega ^(4)...

    Text Solution

    |

  9. Let z and omega tow complex number. If |z|= |omega| and areg (z) +arg...

    Text Solution

    |

  10. If z(1)+z(2) are two complex number and |(barz(1)-2bar z(2))/(2-z(1)ba...

    Text Solution

    |

  11. If x+iy moves on the line 3x+4y+5=0, prove that the minimum value of ...

    Text Solution

    |

  12. If |z^(2)|=9|z|, find the maximum and minimum values of |z|.

    Text Solution

    |

  13. Find the greatest value of |z| when |z-(6)/(z)|=2,z being a complex nu...

    Text Solution

    |

  14. Find the least value of |z+(1)/(z)| if |z| ge 3 (z being a complex ...

    Text Solution

    |

  15. If the roots of the equation ix^(2)-(b^(2)+c^(2))x+(c^(2)+d^(2))^(2)=0...

    Text Solution

    |

  16. If one root of the equation ax^(2)-2ibx-ic=0 be square of the other, t...

    Text Solution

    |

  17. Solve (7y^(2)+1)/(y^(2)-1)-4 ((y^(2)-1)/(7y^(2)+1))=-3

    Text Solution

    |

  18. Solve (x-(x)/(x+1))^(2)+2x((x)/(x+1))=3

    Text Solution

    |

  19. If alpha and beta are the roots of ax^(2)+bx+cid=0 find the equation ...

    Text Solution

    |

  20. Show that, 3^(n)-(n)/(1!)3^(n-1)+(n(n-1))/(2!)3^(n-2)-...+(-1)^(n)="...

    Text Solution

    |