Home
Class 12
MATHS
If 1lt=rlt=n , then \ n^(n-1)Cr 1 =(n-r+...

If `1lt=rlt=n ,` then `\ n^(n-1)C_r_ _1 =(n-r+1)\ ^n C_(r-1)dot`

Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGONOMETRIC FUNCTIONS

    RESONANCE DPP ENGLISH|Exercise All Questions|15 Videos

  • MATRICES

    RESONANCE DPP ENGLISH|Exercise All Questions|7 Videos

Similar Questions

Explore conceptually related problems

Let n\ a n d\ r be non negative integers such that 1lt=rlt=ndot Then, \ ^n C_r=n/rdot\ \ ^(n-1)C_(r-1)\ dot

Prove by combinatorial argument that .^(n+1)C_r=^n C_r+^n C_(r-1)dot

Prove that: (i) r.^(n)C_(r) =(n-r+1).^(n)C_(r-1) (ii) n.^(n-1)C_(r-1) = (n-r+1) .^(n)C_(r-1) (iii) .^(n)C_(r)+ 2.^(n)C_(r-1) +^(n)C_(r-2) =^(n+2)C_(r) (iv) .^(4n)C_(2n): .^(2n)C_(n) = (1.3.5...(4n-1))/({1.3.5..(2n-1)}^(2))

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

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

""^(n) C_(r+1)+2""^(n)C_(r) +""^(n)C_(r-1)=

Let n\ a n d\ r be no negative integers suych that rlt=n .Then, \ ^n C_r+\ ^n C_(r-1)=\ ^(n+1)C_r

Prove that combinatorial argument that ^n+1C_r=^n C_r+^n C_(r-1)dot

Find the sum of sum_(r=1)^n(r^n C_r)/(^n C_(r-1) .

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

RESONANCE DPP ENGLISH-JEE MAINS-All Questions
  1. If a hyperbola passes through the foci of the ellipse (x^2)/(25)+(y^2)...

    Text Solution

    |

  2. Area bounded by the curve y=maxdot{(sin x ,cos x)} and x -axis, betwee...

    Text Solution

    |

  3. If 1lt=rlt=n , then \ n^(n-1)Cr 1 =(n-r+1)\ ^n C(r-1)dot

    Text Solution

    |

  4. The length of the transverse axis of the hyperbola 9x^(2)-16y^(2)-18x ...

    Text Solution

    |

  5. Value of the parameter ' a ' such that the area bounded by y=a^2x^2+a...

    Text Solution

    |

  6. The line y=m x bisects the area enclosed by the curve y=1+4x-x^2 and t...

    Text Solution

    |

  7. The chord of contact of the pair of tangents drawn from each point on ...

    Text Solution

    |

  8. The extremities of a diagonal of a rectangle are (0,0) and (4,3). The ...

    Text Solution

    |

  9. If the equation (5x-1)^2+(5y-2)^2=(lambda^2-2lambda+1)(3x+4y-1)^2 repr...

    Text Solution

    |

  10. If x(1),x(2)& x(3) are three distinct numbers which satisfy the ralati...

    Text Solution

    |

  11. The area (in sq. units) of the quadrilateral formed by the tangents ...

    Text Solution

    |

  12. The value of int (sin x cos x)/(sqrt(1-sin^(4)x)) dx is equal to :

    Text Solution

    |

  13. Let C be the centre, BCB the minor axis and S the focus (ae, 0) for ...

    Text Solution

    |

  14. If a^3+b^3+6a b c=8c^3 & omega is a cube root of unity then: (a)a , b ...

    Text Solution

    |

  15. If x^(2)+ax+10=0and x^(2)+bx-10=0 have common root, then a^(2)-b^(2) i...

    Text Solution

    |

  16. A person standing on the bank of a river observes that the angle of ...

    Text Solution

    |

  17. The upper 3/4 th portion of a vertical pole subtends an angle theta su...

    Text Solution

    |

  18. From the top of a cliff 25 m high the angle of elevation of a tower...

    Text Solution

    |

  19. The angles of elevation of the top of a tower from two points at a dis...

    Text Solution

    |

  20. Differentiate tan^(-1)((1+2x)/(1-2x))wdotrdottsqrt(1+4x^2) and tan^(...

    Text Solution

    |