Home
Class 12
MATHS
The total number of different terms in t...

The total number of different terms in the product `(.^(101)C_(0) - .^(101)C_(1)x+.^(101)C_(2)x^(2)-"….."-.^(101)C_(101)x^(101))(1+x+x^(2)+"…."+x^(100))^(101)` is `"____"`.

Text Solution

Verified by Experts

The correct Answer is:
102
`(.^(101)C_(0).^(101)C_(1)x+.^(101)C_(2)x^(2)-"...."-.^(101)C_(101)x^(101))(1+x+x^(2)+"...." +x^(100))^(101)`
`= (1-x)^(101).((1-x^(101))/(1-x))^(101)`
`= (1-x^(101))^(101)`
`:.` Number of different terms `= 102`
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE|Exercise JEE Previous Year|16 Videos

  • BINOMIAL THEOREM

    CENGAGE|Exercise Single correct Answer|62 Videos

  • BINOMIAL THEOREM

    CENGAGE|Exercise Matrix|4 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 coefficient of x^(50) in (x+^(101)C_(0))(x+^(101)C_(1)).....(x+^(101)C_(50)) is

i+i^(2)+i^(3)+"………"+i^(101)=

Find the degree of the expression (1+x)(1+x^6)(1+x^(11))(1+x^(101))dot

Prove that (.^(n)C_(1)sin2x+.^(n)C_(2)sin4x+.^(n)C_(3)sin6x+"…..")/(1+.^(n)C_(1)cos2x+.^(n)C_(2)cos4x+.^(n)C_(3)cos 6x+"……")

If f(x) =.^(40)C_(1).x(1-x)^(39) + 2..^(40)C_(2)x^(2)(1-x)^(38)+3..^(40)C_(3)x^(3)(1-x)^(37)+"….."+40..^(40)C_(40)x^(40) , then the value of f(3) is

If f(x)=prod_(n=1)^(100)(x-n)^(n(101-n)) ; then (f(101))/(f'(101))=

Find the coefficient of x^(50) in the expansion of (1+x)^(101)xx(1-x+x^2)^(100)dot

Find the degree of the expression (1+x)(1+x^6)(1+x^(11))........(1+x^(101))dot

CENGAGE-BINOMIAL THEOREM-Exercise (Numerical)
  1. The largest value of x for which the fourth tem in the expansion (5^2/...

    Text Solution

    |

  2. Let a and b be the coefficients of x^3 in (1+x+2x^2+3x^3)^4a n d(1+x+2...

    Text Solution

    |

  3. If R is remainder when 6^(83)+8^(83) is divided by 49, then the value ...

    Text Solution

    |

  4. The remainder, if 1+2+2^2++2^(1999) is divided by 5 is.

    Text Solution

    |

  5. Given (1-2x+5x^2-10 x^3)(1+x)^n=1+a1x+a2x^2+ and thata1 2=2a2 then the...

    Text Solution

    |

  6. The largest real value of x such that sum(k=0)^4((3^(4-k))/((4-k)!))((...

    Text Solution

    |

  7. Coefficient of x^(2009) in (1+x+x^(2)+x^(3)+x^(4))^(1001) (1-x)^(1002)...

    Text Solution

    |

  8. The total number of different terms in the product (.^(101)C(0) - .^(1...

    Text Solution

    |

  9. The constant term in the expansion of (x -2/x^(2))^(9) is

    Text Solution

    |

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

    Text Solution

    |

  11. The value of (.^(21)C(1) - .^(10)C(1)) + (.^(21)C(2) - .^(10)C(2)) + (...

    Text Solution

    |

  12. Let a=3^(1/(223))+1 and for all geq3,let f(n)=^n C0dota^(n-1)-^n C1do...

    Text Solution

    |

  13. Let 1+sum(r=1)^(10)(3^rdot(10)Cr+rdot(10)Cr)=2^(10)(alpha. 4^5+beta)w ...

    Text Solution

    |

  14. The value of (lim)(nvecoo)sum(r=1)^(r-1)(sum(t=0)^(r-1)1/(5^n)dot^n Cr...

    Text Solution

    |

  15. If sum(r=0)^(10)((r+2)/(r+1))^^n Cr=(2^8-1)/6 , then n is 8 b. 4 c. 6 ...

    Text Solution

    |

  16. If S(n) = (.^(n)C(0))^(2) + (.^(n)C(1))^(2) + (.^(n)C(n))^(n), then ma...

    Text Solution

    |

  17. The value of .^(40)C(0) xx .^(100)C(40) - .^(40)C(1) xx .^(99)C(40) + ...

    Text Solution

    |

  18. The value of sum(0leiltjle5) sum(""^(5)C(j))(""^(j)C(i)) is equal to "...

    Text Solution

    |

  19. If (1-x-x^(2))^(20) = sum(r=0)^(40)a(r).x^(r ), then value of a(1) + 3...

    Text Solution

    |

  20. The value of sum(r=1)^(11)tan^(2)((r pi)/(24)) is

    Text Solution

    |