Home
Class 12
MATHS
If m=.^(n)C(2) show that , .^(m)C(2)=3....

If `m=.^(n)C_(2)` show that , `.^(m)C_(2)=3.^(n+1)C_(4)`

Promotional Banner

Topper's Solved these Questions

  • PERMUTATION AND COMBINATION

    CHHAYA PUBLICATION|Exercise EXERCISE 7B ( Long Answer Type Questions )|29 Videos

  • PERMUTATION AND COMBINATION

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Exams A (MCQ)|5 Videos

  • PERMUTATION AND COMBINATION

    CHHAYA PUBLICATION|Exercise EXERCISE 7B (Very Short Answer Type Questions )|20 Videos

  • PARABOLA

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

  • PLANE

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

Similar Questions

Explore conceptually related problems

If m= ^nC_2 show that ^mC_2=3^(n+1)C_4

Find the sum of the series .^(n)C_(0)+2.^(n)C_(1)x+3.^(n)C_(2)x^(2)+....+(n+1).^(n)C_(n)x^(n) and hence show that , .^(n)C_(0)+2.^(n)C_(1)x+3.^(n)C_(2)x^(2)+....+(n+1)^(n)C_(n)=(n+2)2^(n-1)

If (1+x)^(n)=^(n)C_(0)+^(n)C_(1)x+^(n)C_(2)x^(2)+…+^(n)C_(n)x^(n) , prove that, nC_(1)-2^(n)C_(2)+3^(n)C_(3)-…+(-1)^(n-1).n^(n)C_(n)=0 .

If .^(n)C_(3)=.^(n)C_(2) , then find .^(n)C_(2) .

If (1+x)^(n)=1+""^(n)C_(1)x+""^(n)C_(2)x^(2)+….+""^(n)C_(n) x^(n) show that, n*2^(n-1)=""^(n)C_(1)+2*""^(n)C_(2)+….. +n*""^(n)C_(n) .

Find the sum .^(n)C_(1) + 2 xx .^(n)C_(2) + 3 xx .^(n)C_(3) + "……" + n xx .^(n)C_(n) .

If .^(n)C_(4)=.^(n)C_(2) , then find .^(n)C_(3) .

If (1+x)^(n)=C_(0)+C_(1)+x+C_(2)x^(2)+...+C_(n)x^(n) show that, C_(0)-2^(2)*C_(1)+3^(2)*C_(2)-...+(-1)^(n)*(n+1)^(2)*C_(n)=0 (n gt 2)

If (1+x)^(n)=C_(0)+C_(1)x+C_(2)x^(2)+…+C_(n)x^(n) , show that, (2^(2).C_(0))/(1xx2)+(2^(3).C_(1))/(2xx3)+…+(2^(n+2).C_(n))/((n+1)(n+2))=(3^(n+2)-2n-5)/((n+1)(n+2))

Prove that .^(n)C_(1) + 2 xx .^(n)C_(2) + 3 xx .^(n)C_(3) + "…." + n xx .^(n)C_(n) = n2^(n-1) . Hence, prove that .^(n)C_(1).(.^(n)C_(2))^(2).(.^(n)C_(3))^(3)"......."(.^(n)C_(n))^(n) le ((2^(n))/(n+1))^(.^(n+1)C_(2)) AA n in N .

CHHAYA PUBLICATION-PERMUTATION AND COMBINATION -EXERCISE 7B ( Short Answer Type Questions )
  1. Find n and r if .^(n)C(r):^(n)C(r+1):^(n)C(r+2)=1:2:3.

    Text Solution

    |

  2. Find n and r if .^(n)P(r)=336 and^(n)C(r)=56.

    Text Solution

    |

  3. If m=.^(n)C(2) show that , .^(m)C(2)=3.^(n+1)C(4)

    Text Solution

    |

  4. Find n and r if .^(n)P(r)=.^(n)P(r+1)and^(n)C(r)=^(n)C(r-1).

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  8. Show that , (.^(n)C(r)+^(n)C(r-1))/(.^(n)C(r-1)+^(n)C(r-2))=(.^(n+1)p...

    Text Solution

    |

  9. Prove that , .^(45)C(8)+sum(r=1)^(7).^(52-r)C(7)+sum(k=1)^(5).^(57-K)C...

    Text Solution

    |

  10. Prove that , .^(15)C(8)+^(15)C(9)-.^(15)C(6)-^(15)C(7)=0

    Text Solution

    |

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

    Text Solution

    |

  12. Show that (.^(4n)C(2n))/(.^(2n)C(n))=(1.3.5......(4n-1))/({1.3.5........

    Text Solution

    |

  13. If .^(n)C(r-1)=36,.^(n)C(r)=84and.^(n)C(r+1)=126 find n and r .

    Text Solution

    |

  14. If (.^(n)C(r-1))/(a)=(.^(n)C(r))/(b)=(.^(n)C(r+1))/(c) n=(ab+2ac...

    Text Solution

    |

  15. If the number of permutations of n different things taken r at time be...

    Text Solution

    |

  16. For n in N , Prove that (n+1)[n!n+(n-1)!(2n-1)+(n-2)!(n-1)]=(n+2)!

    Text Solution

    |

  17. Evaluate : .^(20)C(5)+sum(j=2)^(5).^(25-j)C(4)

    Text Solution

    |

  18. If .^(n)C(1),^(n)C(2)and^(n)C(3) are in A.P ., find n .

    Text Solution

    |

  19. Solve : ((2x+1)!)/((x+2)!)xx((x-1)!)/((2x-1)!)=(3)/(5),( x in N N)

    Text Solution

    |

  20. Prove that if ngt7 then .^(n-1)C(3)+.^(n-1)C(4)gt^(n)C(3)

    Text Solution

    |