Home
Class 12
MATHS
The value of sum(r=2)^(10) ""^(r)C(2).""...

The value of `sum_(r=2)^(10) ""^(r)C_(2).""^(10)C_(r)` is

A

`10460`

B

`11240`

C

`11520`

D

`12640`

Text Solution

Verified by Experts

The correct Answer is:
C
`underset(r=2)overset(10)sum.^(r)C_(2)..^(10)C_(r) = underset(r=2)overset(10)sum(r(r-1))/(2).(10!)/(r!(10-r)!)`
`= 1/2underset(r=2)overset(10)sum(10!)/((r-2)!(10-r)!)`
`= (10 xx9)/(2)underset(r=2)overset(10)sum(8!)/((r-2)!(10-r)!)`
`= 45underset(r=2)overset(10)sum.^(8)C_(r-2)`
`= 45 xx 2^(8)`
`= 11520`
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE ENGLISH|Exercise Multiple Correct Answer Type|27 Videos

  • BINOMIAL THEOREM

    CENGAGE ENGLISH|Exercise Linked Comphrension|20 Videos

  • BINOMIAL THEOREM

    CENGAGE ENGLISH|Exercise Concept Application Exercise 8.8|10 Videos

  • AREA

    CENGAGE ENGLISH|Exercise Comprehension Type|2 Videos

  • CIRCLE

    CENGAGE ENGLISH|Exercise MATRIX MATCH TYPE|7 Videos

Similar Questions

Explore conceptually related problems

The value of sum_(r=1)^(10) r. (""^(n)C_(r))/(""^(n)C_(r-1) is equal to

The value of sum_(r=0)^(3) ""^(8)C_(r)(""^(5)C_(r+1)-""^(4)C_(r)) is "_____" .

The vaule of sum_(r=0)^(n-1) (""^(C_(r))/(""^(n)C_(r) + ""^(n)C_(r +1)) is equal to

If n in N such that is not a multiple of 3 and (1+x+x^(2))^(n) = sum_(r=0)^(2n) a_(r ). X^(r ) , then find the value of sum_(r=0)^(n) (-1)^(r ).a_(r).""^(n)C_(r ) .

The value of sum_(r=0)^(10)r^(10)C_r3^r(-2)^(10-r) is 20 b. 10 c. 300 d. 30

The value of sum_(r=0)^(2n)(-1)^(r)*(""^(2n)C_(r))^(2) is equal to :

The value of sum_(r=0)^(20)(-1)^(r )(""^(50)C_(r))/(r+2) is equal to

The value of sum_(r=0)^(n) r(n -r) (""^(n)C_(r))^(2) is equal to

The value of sum_(r=0)^50 (.^(100)C_r.^(200)C_(150+r)) is equal to

The value of sum_(r=0)^(15)r^(2)((""^(15)C_(r))/(""^(15)C_(r-1))) is equal to

CENGAGE ENGLISH-BINOMIAL THEOREM-Single Correct Answer
  1. If sum(r=0)^(n){a(r)(x-alpha+2)^(r)-b(r)(alpha-x-1)^(r)}=0, then (a) b...

    Text Solution

    |

  2. If sum(r=0)^(2n)ar(x-2)^r=sum(r=0)^(2n)br(x-3)^ra n dak=1 for all kgeq...

    Text Solution

    |

  3. The value of sum(r=2)^(10) ""^(r)C(2).""^(10)C(r) is

    Text Solution

    |

  4. If .^(n+1)C(r+1):^n Cr:^(n-1)C(r-1)=11 :6:3, then n r= 20 b. 30 c. 40...

    Text Solution

    |

  5. If a, b and c are three consecutive coefficients terms in the expansio...

    Text Solution

    |

  6. Which term in the expansion of (2-3x)^(19) has algebrically the last c...

    Text Solution

    |

  7. The value of (.^(n)C(0))/(n)+(.^(n)C(1))/(n+1)+(.^(n)C(2))/(n+2)+"..."...

    Text Solution

    |

  8. The value of sum(r=1)^(n) (-1)^(r+1)(""^(n)C(r))/(r+1) is equal to

    Text Solution

    |

  9. If sum(r=0)^(n)((r+2)/(r+1)).^n Cr=(2^8-1)/6 , then n is (A) 8 (B...

    Text Solution

    |

  10. The value of underset(r=0)overset(3)sum.^(8)C(r)(.^(5)C(r+1)-.^(4)C(r)...

    Text Solution

    |

  11. Find underset(r=0) overset(10)sumr^ (10)C(r).3^(r).(-2)^(10-r)

    Text Solution

    |

  12. The value of ^15 C0 2-^(15)C12+^(15)C2 2-^(15)C 15 2 is 15 b. -15 c. 0...

    Text Solution

    |

  13. If (1+x)^n=C0+C1x+C2x^2+...+Cn x^n , then C0C2+C1C3+C2C4+...+C(n-2)Cn=...

    Text Solution

    |

  14. [+^404C4 -^303C4.^4C1+^202C4.^4C2-^101C4.^4C3]=

    Text Solution

    |

  15. The value of sum(r=0)^(40) r""^(40)C(r)""^(30)C(r) is (a) 40.^(69)C(29...

    Text Solution

    |

  16. The value of sum(r=1)^(15) (r2^(r))/((r+2)!) is equal to (a) ((17)!-2...

    Text Solution

    |

  17. (n+2)C0(2^(n+1))-(n+1)C1(2^(n))+(n)C2(2^(n-1))-.... is equal to

    Text Solution

    |

  18. The value of sum(r=0)^(20)(-1)^(r )(""^(50)C(r))/(r+2) is equal to

    Text Solution

    |

  19. If (1+x^(2))^(n) =sum(r=0)^(n) a(r)x^(r )= (1+x+x^(2)+x^(3))^(100). If...

    Text Solution

    |

  20. If (1+x^(2))^(n) = underset(r=0)overset(n)suma(r)x^(r )= (1+x+x^(2)+x^...

    Text Solution

    |