Home
Class 12
MATHS
The value of 99^(50)-(99)/(1)*98^(50)+(9...

The value of `99^(50)-(99)/(1)*98^(50)+(99.98)/(1.2)97^(50)-……-(99.98)/(1.2)*2^(50)+(99)/(1)*1^(50)` is

A

`0`

B

`-1`

C

`-2`

D

`-3`

Text Solution

Verified by Experts

The correct Answer is:
A
`(a)` `99^(50)-99.98^(50)+(99.98)/(1.2)(97)^(50)-....+99`
`=^(99)C_(0)99^(50)-^(99)C_(1)(99-1)^(50)+^(99)C_(2)(99-2)^(50)-....+^(99)C_(98)(99-98)^(50)+^(99)C_(99)(99-99)^(50)`
`=99^(50)('^(99)C_(0)-^(99)C_(1)+^(99)C_(2)-^(99)C_(3)+...)+^(50)C_(1)*99^(49)('^(99)C_(1)-2*^(99)C_(2)+3*^(99)C_(3)-....)+....`
`=0+0+0+....+0=0`
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|10 Videos

  • CIRCLE

    CENGAGE|Exercise MATRIX MATCH TYPE|6 Videos

Similar Questions

Explore conceptually related problems

The value of int_(0)^(1) x ( 1-x ) ^(99) dx is

An equation a_(0) + a_(2)x^(2) + "……" + a_(99)x^(99) + x^(100) = 0 has roots .^(99)C_(0), .^(99)C_(1), C_(99)C_(2), "…..", .^(99)C_(99) The value of (.^(99)C_(0))^(2) + (.^(99)C_(1))^(2) + "….." + (.^(99)C_(99))^(2) is equal to

The sum of coefficients of integral powers of x in the binomial expansion of (1-2sqrt(x))^(50) is: (1) 1/2(3^(50)+1) (2) 1/2(3^(50)) (3) 1/2(3^(50)-1) (4) 1/2(2^(50)+1)

The value of .^(40)C_(0) xx .^(100)C_(40) - .^(40)C_(1) xx .^(99)C_(40) + .^(40)C_(2) xx .^(98)C_(40) "……." + .^(40)C_(40) xx .^(60)C_(40) is equal to "____" .

Find the value of 4tan^(-1)1/5-tan^(-1)1/(70)+tan^(-1)1/(99)

Solve cos^(50)x-sin^(50)x=1

The value of lim_(xtooo) ((100)/(1-x^(100))-(50)/(1-x^(50))) is ___________.

The value of sec(sin^-1(sin((-50pi)/9))+cos^-1(cos(31pi)/9))

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)=sum(k=1)^(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 divisible 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. Let (2x^(2)+3x+4)^(10)=sum(r=0)^(20)a(r )x^(r ), then the value of (a(...

    Text Solution

    |

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

    Text Solution

    |