Home
Class 12
MATHS
If sum(r=0)^(n) (pr+2).""^(n)C(r)=(25)(6...

If `sum_(r=0)^(n) (pr+2).""^(n)C_(r)=(25)(64)` where `n, p in N`, then

A

`p = 3`

B

`p = 4`

C

`n = 7`

D

`n = 6`

Text Solution

Verified by Experts

The correct Answer is:
A, C
`S = underset(r=0)overset(n)sum(pr+2)..^(n)C_(r)`
`:. =underset(r=0)overset(n)sum(p(n-r)+2). .^(n)C_(r) ," " (:'.^(n)C_(r)=.^(n)C_(n-r))`
Adding these, we get
`2S = (pn+4) underset(r=0)overset(n)sum.^(n)C_(r)`
`rArr S = (pn+4) xx 2^(n-1)`
So, `n = 7` and `7p + 4 = 25` or `p = 3`.
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE|Exercise Exercise (Comprehension)|20 Videos

  • BINOMIAL THEOREM

    CENGAGE|Exercise Matrix|4 Videos

  • BINOMIAL THEOREM

    CENGAGE|Exercise Exercise (Single)|90 Videos

  • AREA UNDER CURVES

    CENGAGE|Exercise Question Bank|10 Videos

  • CIRCLE

    CENGAGE|Exercise MATRIX MATCH TYPE|6 Videos

Similar Questions

Explore conceptually related problems

The value of sum_(r=1)^(n+1)(sum_(k=1)^n "^k C_(r-1)) ( where r ,k ,n in N) is equal to a. 2^(n+1)-2 b. 2^(n+1)-1 c. 2^(n+1) d. none of these

If sum_(r=0)^(n){("^(n)C_(r-1))/('^(n)C_(r )+^(n)C_(r-1))}^(3)=(25)/(24) , then n is equal to

Prove that sum_(r=0)^(2n)r(.^(2n)C_r)^2=n^(4n)C_(2n) .

If a_(n) = sum_(r=0)^(n) (1)/(""^(n)C_(r)) , then the value of (sumsum)_(0leiltjlen) (i/(""^(n)C_(i))+j/(""^(n)C_(j)))

If sum_(r=0)^(10)((r+2)/(r+1)).^n C_r=(2^8-1)/6 , then n is (A) 8 (B) 4 (C) 6 (D) 5

If s_(n) = sum_(r = 0)^(n) 1/(""^(n)C_(r)) and t_(n) = sum _(r = 0)^(n) r/(""^(n)C_(r)) ,then t_(n)/s_(n) is equal to

Prove that sum_(r=1)^k(-3)^(r-1)^(3n)C_(2r-1)=0,w h e r ek=3n//2 and n is an even integer.

If ""^(n)P_r = ""^(n)P_(r-1) and ""^(n)C_(r) = ""^(n)C_(r-1) , find the values of n and r.

The value of sum_(k=0)^(7)[(((7),(k)))/(((14),(k)))sum_(r=k)^(14)((r ),(k))((14),(r ))] , where ((n),(r )) denotes "^(n)C_(r ) is

If ""^(n)P_(r)=3024 & ""^(n)C_(r)=126 then the value of r =

CENGAGE-BINOMIAL THEOREM-Exercise (Multiple)
  1. Let (1+x^2)^2(1+x)^n=sum(k=0)^(n+4)ak x^kdotIfa1,a2a n d a3 are in ari...

    Text Solution

    |

  2. For natural numbers m ,n ,if(1-y)^m(1+y)^n=1+a1y+a2y^2+ ,a n da1=a2=10...

    Text Solution

    |

  3. The middle term in the expansion of (x//2+2)^8 is 1120, then x in R i...

    Text Solution

    |

  4. In the expansion of (3-sqrt(17/4+3sqrt2))^15 the 11th term is a

    Text Solution

    |

  5. For the expansion (x sin p + x^(-1)cos p)^(10), (p in R),

    Text Solution

    |

  6. For which of the following values of x ,5t h term is the numerically g...

    Text Solution

    |

  7. Which of the following is/are true ?

    Text Solution

    |

  8. If sum(r=0)^nr/(^n Cr)=sum(r=0)^n(n^2-3n+3)/(2.^n Cr) , then a.n=1 b. ...

    Text Solution

    |

  9. The value of ^n C1+^(n+1)C2+^(n+2)C3++^(n+m-1)Cm is equal to ^m+n C(n-...

    Text Solution

    |

  10. If the number of terms in the expansion of (1-2/x+4/(x^(2))) x ne 0, i...

    Text Solution

    |

  11. In the expansion of (7^(1//3)+11^(1//9))^(6561) ,

    Text Solution

    |

  12. If (1 - x)^(n) = C(0) + C(1)x + C(2)x^(2) + ......... + C(n)x^(n), the...

    Text Solution

    |

  13. In the expansion of (a+b)^(n), if two consecutive terms are equal, the...

    Text Solution

    |

  14. If for z as real or complex, (1+z^2+z^4)^8=C0+C1z2+C2z4++C(16)z^(32)t ...

    Text Solution

    |

  15. If f(m) = sum(i=0)(m) ({:(30),(30-i):})({:(20),(m-i):}) where ({:(p),...

    Text Solution

    |

  16. If (1+x)^n=C0+C1x+C2x2++Cn x^n , n in N ,t h e nC0-C1+C2-+(-1)^(n-1)C...

    Text Solution

    |

  17. If sum(r=0)^(n) (pr+2).""^(n)C(r)=(25)(64) where n, p in N, then

    Text Solution

    |

  18. If (x+1/x+1)^(6)=a(0)+(a(1)x+(b(i))/(x))+(a(2)x^(2)+(b(2))/(x^(2)))+"....

    Text Solution

    |

  19. The value of .^(n)C(0) xx .^(2n)C(r) - .^(n)C(1)xx.^(2n-2)C(r)+.^(n)C(...

    Text Solution

    |

  20. The sum 2 xx .^(40)C(2) + 6 xx .^(40)C(3) + 12 xx .^(40)C(4) + 20 xx ....

    Text Solution

    |