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 `"____"`.

A

A. 100

B

B. 101

C

C. 102

D

D. 103

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 PUBLICATION|Exercise Archives|16 Videos

  • BINOMIAL THEOREM

    CENGAGE PUBLICATION|Exercise Multiple Correct Answer|4 Videos

  • BINOMIAL THEOREM

    CENGAGE PUBLICATION|Exercise Matrix|4 Videos

  • AREA

    CENGAGE PUBLICATION|Exercise Comprehension Type|2 Videos

  • CIRCLE

    CENGAGE PUBLICATION|Exercise For problems 3 and 4|2 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

The sum of the series (.^(101)C_(1))/(.^(101)C_(0)) + (2..^(101)C_(2))/(.^(101)C_(1)) + (3..^(101)C_(3))/(.^(101)C_(2)) + "….." + (101..^(101)C_(101))/(.^(101)C_(100)) is "____" .

Addition: (1100.101)_(2) + (1001.11)_(2) + (11.01)_(2)

Subtraction: (11.011)_(2) - (10.101)_(2)

The number of terms in the expansion of (1+x)^(101) (1+x^2-x)^(100) in powers of x is

Subtraction: (1100.101)_(2)-(1001.11)_(2)

Solution set of ((x-1)^(101)(x-2)^(102)(x-3)^(103))/((x-1)^(201)(x+2)^(202)(x+3)^(203))>0 is

find the value of :- (101)^2

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

Which is larger : (99^(50)+100^(50)) or (101)^(50) .

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

    Text Solution

    |

  2. Let aa n db 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+2^3+....+2^1999 in divided by 5 is

    Text Solution

    |

  5. Given (1-2x+5x^2-10x^3)(1+x)^n=1+a1x+a2x^2+.... and that a1^2=2a2, the...

    Text Solution

    |

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

    Text Solution

    |

  7. The coefficient of x^(103) in (1+x+x^(2) +x^(3)+x^(4))^(199)(x-1)^(201...

    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 (log(x^(logx))-log(x^(2))100)^...

    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 sum of the series (.^(101)C(1))/(.^(101)C(0)) + (2..^(101)C(2))/...

    Text Solution

    |

  12. Let a=3^(1/(223))+1 and for all n geq3,l e tf(n)=^n C0dota^(n-1)-^n C1...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  15. If underset(r=0)overset(n)sum((r+2)/(r+1)).^(n)C(r)=(2^(8)-1)/(6). the...

    Text Solution

    |

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

    Text Solution

    |

  17. The value of .^(40)C0+.^40C1 + .^40C2 + + .^40C20

    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)^(49)(2r^(2) - 48r +1)/((50-r).""^(50)C(r)) is "...

    Text Solution

    |