Home
Class 12
MATHS
If C(0), C(1), C(2),.....,C(n) are binom...

If `C_(0), C_(1), C_(2),.....,C_(n)` are binomial coefficients, (where `C_(r) = .^(n)C_(r))`, then the value of `C_(0) - C_(1) + C_(2) - C_(3) + ....+(-1)^(n) C_(n)` is equal to

A

`2^(n)`

B

`2^(n)+1`

C

0

D

`2^(n-1)`

Text Solution

Verified by Experts

The correct Answer is:
c
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM AND MATHEMATICAL INDUCTION

    ML KHANNA|Exercise MISCELLANEOUS EXERCISE (Matching Entries) |3 Videos

  • AREA OF CURVES

    ML KHANNA|Exercise SELF ASSESSEMENT TEST|16 Videos

  • CO-ORDINATE GEOMETRY OF THREE DIMENSION

    ML KHANNA|Exercise SELF ASSIGNMENT TEST |11 Videos

Similar Questions

Explore conceptually related problems

If C_(0), C_(1), C_(2),..., C_(n) are binomial coefficients in the expansion of (1 + x)^(n), then the value of C_(0) - (C_(1))/(2) + (C_(2))/(3) - (C_(3))/(4) +...+ (-1)^(n) (C_(n))/(n+1) is

If C_(o)C_(1),C_(2),......,C_(n) denote the binomial coefficients in the expansion of (1+x)^(n), then the value of sum_(r=0)^(n)(r+1)C_(r) is

If C_(0),C_(1),C_(2),C_(3), . . .,C_(n) be binomial coefficients in the expansion of (1+x)^(n) , then Q. The value of the expression C_(0)-2C_(1)+3C_(2)-. . . .+(-1)^(n)(n+1)C_(n) is equal to

If C_(0),C_(1),C_(2),C_(3), . . .,C_(n) be binomial coefficients in the expansion of (1+x)^(n) , then Q. The value of the expression C_(0)+2C_(1) +3C_(2)+. . . .+(n+1)C_(n) is equal to

If C_(0), C_(1), C_(2),...,C_(n) denote the binomial coefficients in the expansion of (1 + x)^n) , then xC_(0)-(x -1) C_(1)+(x-2)C_(2)-(x -3)C_(3)+...+(-1)^(n) (x -n) C_(n)=

If C_(0),C_(1),C_(2),.........,C_(n) denote the binomial coefficients in the expansion of (1+1)^(n), then sum_(0<=r

If C_(0),C_(1), C_(2),...,C_(N) denote the binomial coefficients in the expansion of (1 + x)^(n) , then 1^(3). C_(1)-2^(3). C_(3) - 4^(3) . C_(4) + ...+ (-1)^(n-1)n^(3) C_(n)=

ML KHANNA-BINOMIAL THEOREM AND MATHEMATICAL INDUCTION -Self Assessment Test
  1. The term independent of x in the expansion of (x^(2)-(1)/(3x))^(9) is

    Text Solution

    |

  2. If (1+ x)^(n) = C(0) + C(1) x + C(2)x^(2) + ...+ C(n)x^(n) , prove tha...

    Text Solution

    |

  3. If C(0), C(1), C(2),.....,C(n) are binomial coefficients, (where C(r) ...

    Text Solution

    |

  4. If (1+x-2x^2)^6=1+a1x+a2x^(12)++a(12)x^(12), then find the value of a2...

    Text Solution

    |

  5. If (1 + x)^(n) = C(0) + C(1) x + C(2) x^(2) +… + C(n) x^(n) , prove th...

    Text Solution

    |

  6. The coefficient of x^(n) in the expansion of (1-9 x + 20 x^(2))^(-1...

    Text Solution

    |

  7. The number of integer terms in the expansion of (5^(1//2)+7^(1//6))^(...

    Text Solution

    |

  8. Find the coefficient of x^5 in the expansion of (1+x^2)^5dot(1+x)^4i s...

    Text Solution

    |

  9. Consider the expansion of ( 1+ x)^(2n+1) The coefficient of x^(99) ...

    Text Solution

    |

  10. If the coefficient of x^(7) in (ax^(2)+(1)/(bx))^(11) is equal to the ...

    Text Solution

    |

  11. The sum of the coefficeints of the polynominal (1 + x - 3x^(2))^(2163)...

    Text Solution

    |

  12. Sum of coefficients in the expansion of (x+2y+z)^(10) is

    Text Solution

    |

  13. The number of terms in the expansion of (x + y + x)^(10), is

    Text Solution

    |

  14. The number of terms in the expansion of ( x +a)^(100) + ( x -a)^(100) ...

    Text Solution

    |

  15. The coefficient of middle term in the expansion of (1+x)^(10) is

    Text Solution

    |

  16. Coefficient of 1/x in the expansion of (1 + x)^(n) (1 + 1//x)^(n) is

    Text Solution

    |

  17. The coefficient of x^(4) in ((x)/(2)-(3)/(x^(2)))^(10) is :

    Text Solution

    |

  18. The coefficient of y in the expansion of (y^(2) + c//y)^(5) is

    Text Solution

    |

  19. If pa n dq are ositive, then prove that the coefficients of x^pa n dx^...

    Text Solution

    |

  20. Given positive integers r >1,n >2 and that the coefficient of (3r d)t ...

    Text Solution

    |