Home
Class 12
MATHS
Let f(n)= (k=1)Σ^n k^2(n Ck)^ 2 then the...

Let `f(n)= (k=1)Σ^n k^2(n C_k)^ 2` then the value of f(5) equals

A

`1000`

B

`1250`

C

`1750`

D

`2500`

Text Solution

Verified by Experts

The correct Answer is:
C
`(c )` `k^(n)C_(k)=n^(n-1)C_(k-1)`
`:.sum_(k=1)^(n)k^(2)("^(n)C_(k))^(2)`
`=n^(2)sum_(k=1)^(n)("^(n-1)C_(k-1))^(2)`
`=n^(2)("^(2n-2)C_(n-1))`
`:. F(5)=25("^(8)C_(4))=1750`
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE|Exercise Multiple Correct Answer|4 Videos

  • BINOMIAL THEOREM

    CENGAGE|Exercise Comprehension|11 Videos

  • BINOMIAL THEOREM

    CENGAGE|Exercise JEE Previous Year|16 Videos

  • AREA UNDER CURVES

    CENGAGE|Exercise Question Bank|20 Videos

  • BINOMIAL THEORM

    CENGAGE|Exercise Question Bank|31 Videos

Similar Questions

Explore conceptually related problems

Let f(n)=(k=1)?^(n)k^(2)(nC_(k))^(2) then the value of f(5) equals

If n is a positive integer and C_(k)=""^(n)C_(k) , then the value of sum_(k=1)^(n)k^(3)((C_(k))/(C_(k-1)))^(2) is :

Let f:R rarr R be a function which satisfies f(x+y)=f(x)+f(y) AA x, y in R . If f(1)=2 and g(n)=sum_(k-1)^((n-1))f(k),n in N then the value of n , for which g(n)=20 , is :

If sum_(k=0)^(n)(k^(2)+k+1)(k!)=(2018)(2018!) then the value of n is equal to

If a=(e^(2 pi i))/(7) and f(x)=A_(0)+sum_(k=1)^(20)A_(k)x^(k) then the value of sum_(r=0)^(6)f(a^(r)x)=n(A_(0)+A_(n)x^(n)+A_(2n)x^(2n)), then the value of n is

If n is a positive integer and C_(k)=.^(n)C_(k) then find the value of sum_(k=1)^(n)k^(3)*((C_(k))/(C_(k-1)))^(2)

Let (1 + x)^(n) = sum_(r=0)^(n) C_(r) x^(r) and , (C_(1))/(C_(0)) + 2 (C_(2))/(C_(1)) + (C_(3))/(C_(2)) +…+ n (C_(n))/(C_(n-1)) = (1)/(k) n(n+1) , then the value of k, is

If U_(n) = |[1,K,K],[2n,K^(2)+K+1,K],[2n+1,K^(2)+K+1,K]| and sum_(n=1)^(K)U_(n)=-90 then absolute value of K is equal to

CENGAGE-BINOMIAL THEOREM-Single correct Answer
  1. The sum S(n)=sum(k=0)^(n)(-1)^(k)*^(3n)C(k), where n=1,2,…. is

    Text Solution

    |

  2. If for n in I , n > 10 ;1+(1+x)+(1+x)^2++(1+x)^n=sum(k=0)^n ak*x^k ...

    Text Solution

    |

  3. Given "^(8)C(1)x(1-x)^(7)+2*^(8)C(2)x^(2)(1-x)^(6)+3*^(8)C(3)x^(3)(1-x...

    Text Solution

    |

  4. The value of 99^(50)-(99)/(1)*98^(50)+(99.98)/(1.2)97^(50)-……-(99.98)/...

    Text Solution

    |

  5. Let f(n)= (k=1)Σ^n k^2(n Ck)^ 2 then the value of f(5) equals

    Text Solution

    |

  6. The value of sum(r=1)^(n)(-1)^(r-1)((r )/(r+1))*^(n)C(r ) is

    Text Solution

    |

  7. The value of ((100),(0))((200),(150))+((100),(1))((200),(151))+......+...

    Text Solution

    |

  8. Let t(100)=sum(r=0)^(100)(1)/(("^(100)C(r ))^(5)) and S(100)=sum(r=0)^...

    Text Solution

    |

  9. Let S(1)=underset(0 le i lt j le 100)(sumsum)C(i)C(j), S(2)=underset(0...

    Text Solution

    |

  10. "^(74)C(37)-2 is divisibl by

    Text Solution

    |

  11. If "^(n)C(0)-^(n)C(1)+^(n)C(2)-^(n)C(3)+...+(-1)^(r )*^(n)C(r )=28 , t...

    Text Solution

    |

  12. If the value of "^(n)C(0)+2*^(n)C(1)+3*^(n)C(2)+...+(n+1)*^(n)C(n)=576...

    Text Solution

    |

  13. The value of ((50),(6))-((5),(1))((40),(6))+((5)/(2))((30),(6))-((5),(...

    Text Solution

    |

  14. The value of the expansion (sumsum)(0 le i lt j le n) (-1)^(i+j-1)"^(n...

    Text Solution

    |

  15. sum(m=1)^(n)(sum(k=1)^(m)(sum(p=k)^(m)"^(n)C(m)*^(m)C(p)*^(p)C(k)))=

    Text Solution

    |

  16. If ((1-3x)^(1//2)+(1-x)^(5//3))/(sqrt(4-x)) is approximately equal to ...

    Text Solution

    |

  17. The sum of the series 1 + (1)/(3^(2)) + (1 *4)/(1*2) (1)/(3^(4))+( ...

    Text Solution

    |

  18. Coefficient of x^(2^(m+1)) in the expansion of 1/((1+x)(1+x^2)(1+x^4)(...

    Text Solution

    |

  19. If (2x^2+3x+4)^(10)=sum(r=0)^(20) ar x^r, then (a7)/(a(13)=

    Text Solution

    |

  20. "^(30)C(0)*^(20)C(10)+^(31)C(1)*^(19)C(10)+^(32)C(2)*18C(10)+....^(40)...

    Text Solution

    |