Home
Class 12
MATHS
If m=""^nC2, prove that ""^nC2=3(n+1)C4....

If `m=""^nC_2`, prove that `""^nC_2=3(n+1)C_4`.

Promotional Banner

Topper's Solved these Questions

  • QUESTION PAPER 2015

    SHARAM PUBLICATION|Exercise EXERCISE|45 Videos

  • QUESTION PAPER 2017

    SHARAM PUBLICATION|Exercise EXERCISE|49 Videos

Similar Questions

Explore conceptually related problems

Solve ""^(2n)C_3:""^nC_3=44:5

Solve ""^nC_4=""^nC_11,

If 2x=y^(1/m)+y^(-1/m) , then prove that (x^2-1)y_(n+2)+(2n+1)xy_(n+1)+(n^2-m^2)y_n=0 .

If a^4 + b^4 + c^4 = 2c^2 (a^2 + b^2), prove that angle ACB = 45^@ or 135^@ .

If A=abs[[1,2,0],[1,1,0],[-1,4,0]],B=abs[[1,2,3],[1,1,-1],[4,-3,2]] and C= abs[[1,2,3],[1,1,-1],[2,2,2]] then prove that A(BC)=(AB)C

If A=[{:(2,3),(1,2):}] , then prove that A^(3)-4A^(2)+A=O .

If y^(1//m)+y^(-1//m)=2x , then prove that (x^(2)-1)y_(2)+xy_(1)=m^(2)y^(2)

Find the value of "^nC_(r-1)//"^nC_r

Prove that "^(2n)C_1 + ^(2n)C_3 + .... + ^(2n)C_(2n-1) = 2^(2n-1)

If A(x_(1), y_(1)), B(x_(2), y_(2)) , and, C(x_(3), y_(3)) are vertices of an equilateral triangle whose each side is equal to a, then prove that |(x_(1), y_(1), 2),(x_(2), y_(2), 2),(x_(3), y_(3), 2)|^(2) = 3a^(4) .

SHARAM PUBLICATION-QUESTION PAPER 2016-EXERCISE
  1. Find the feasible region of the following system 2x+yge6,x-yle3,xge0...

    Text Solution

    |

  2. Show that (a+1) is a factor of abs([(a+1),2,3],[1,a+1,3],[3,-6,a+1])

    Text Solution

    |

  3. Prove that the following. [[a,b,c],[x,y,z],[p,q,r]]=[[y,b,q],[x,a,p],[...

    Text Solution

    |

  4. If A=[[alpha,0],[1,1]] and B=[[1,0],[5,1]], show that for no values of...

    Text Solution

    |

  5. How many 4 digit numbers each greater than 6000 can be formed with be ...

    Text Solution

    |

  6. If m=""^nC2, prove that ""^nC2=3(n+1)C4.

    Text Solution

    |

  7. If the ratio of the 3rd term from the beginning to the 3rd term from t...

    Text Solution

    |

  8. Let A and B be events with P(A)=1/3,P(AuuB)=3/4,P(AnnB)=1/4, find P(Au...

    Text Solution

    |

  9. If X follows a binomial distribution with parameter n=6 and p with 4P(...

    Text Solution

    |

  10. If x = (1-cos^2 theta)/(cos theta), y = (1-cos^(2n)theta)/(cos^n theta...

    Text Solution

    |

  11. Shows that the triangle of greatest area that can be inscribed in a ci...

    Text Solution

    |

  12. Determine the area common to the parabola y^2=x and the circle x^2+y^2...

    Text Solution

    |

  13. Find the solution of the following differential equations: x dy-ydx=sq...

    Text Solution

    |

  14. Prove that vecaxx(vecbxxvecc)+ vecbxx(veccxxveca)+veccxx(vecaxxvecb) =...

    Text Solution

    |

  15. A variable plane meets the coordinate axes at P, Q, R points. If the p...

    Text Solution

    |

  16. Solve the following LPP graphically : Maximize : Z=5x1+3x2 subject to ...

    Text Solution

    |

  17. Solve the following system of equations by the matrix inversion method...

    Text Solution

    |

  18. Show that: C0Cr+C1C(r+1)+C2C(r+2)+….+C(n-r)Cn= ((2n)!)/((n-r)!(n+r)!)

    Text Solution

    |

  19. Three persons hit a target with probability 1/2,1/3 and 1/4 respective...

    Text Solution

    |

  20. Three persons hit a target with probability 1/2,1/3 and 1/4 respective...

    Text Solution

    |