Home
Class 12
MATHS
If A(i,j) be the coefficient of a^i b^j ...

If `A_(i,j)` be the coefficient of `a^i b^j c^(2010-i-j)` in the expansion of `(a+b+c)^2010`, then

A

`A_(i,i)` is defined for `i ge 1010`

B

`A_(i,j)=A_(j,i)`

C

`A_(2i,3i)` is defined for `i ge 405`

D

`A_(0,1)=2000`

Text Solution

Verified by Experts

The correct Answer is:
B
`(b)` Clearly `a_(i,j)=(2010!)/(i!j!(2010-i-j)!)`
and `a_(j,i)=(2010!)/(j!i!(2010-i-j)!)`
Hence , `a_(i,j)=a_(j,i)`
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

Let S_(1)=underset(0 le i lt j le 100)(sumsum)C_(i)C_(j) , S_(2)=underset(0 le j lt i le 100)(sumsum)C_(i)C_(j) and S_(3)=underset(0 le i = j le 100)(sumsum)C_(i)C_(j) where C_(r ) represents cofficient of x^(r ) in the binomial expansion of (1+x)^(100) If S_(1)+S_(2)+S_(3)=a^(b) where a , b in N , then the least value of (a+b) is

Let A=([a_(i j)])_(3xx3) be a matrix such that AA^T=4Ia n da_(i j)+2c_(i j)=0,w h e r ec_(i j) is the cofactor of a_(i j)a n dI is the unit matrix of order 3. |a_(11)+4a_(12)a_(13)a_(21)a_(22)+4a_(23)a_(31)a_(32)a_(33)+4|+5lambda|a_(11)+1a_(12)a_(13)a_(21)a_(22)+1a_(23)a_(31)a_(32)a_(33)+1|=0 then the value of 10lambda is _______.

If A_(i),B_(i),C_(i) are the cofactors of a_(i),b_(i),c_(i) respectively,i=1,2,3 in Delta =|(a_(1),b_(2),c_(1)),(a_(2),b_(2),c_(2)),(a_(3),b_(3),c_(3))| show that |(A_(1),B_(1),C_(1)),(A_(2),B_(2),C_(2)),(A_(3),B_(3),C_(3))|=Delta^(0)

Let vec a= hat i+ hat j+ hat k , vec b= hat i- hat j+ hat ka n d vec c= hat i- hat j- hat k be three vectors. A vector vec v in the plane of vec aa n d vec b , whose projection on vec c is 1/(sqrt(3)) is given by a. hat i-3 hat j+3 hat k b. -3 hat i-3 hat j+3 hat k c. 3 hat i- hat j+3 hat k d. hat i+3 hat j-3 hat k

Let vec a = hat i + hat j + hat k, vec b = hat i - hat j + 2 hat k and vec c = x hat i +(x -2) hat j - hatk .If the vector vec c lies in the plane of veca and vecb , thenx equals

If side vec A B of an equilateral trangle A B C lying in the x-y plane 3 hat i , then side vec C B can be -3/2( hat i-sqrt(3) hat j) b. -3/2( hat i-sqrt(3) hat j) c. -3/2( hat i+sqrt(3) hat j) d. 3/2( hat i+sqrt(3) hat j)

Elements of a matrix A or orddr 10xx10 are defined as a_(i j)=w^(i+j) (where w is cube root of unity), then trace (A) of the matrix is 0 b. 1 c. 3 d. none of these

Let veca = hat i + hat j + hat k, vec b = 2 hat i + 3 hat j vec c = 3 hat i + 5 hat j - 2 hat k , vec d = - hat j + hat k (i) Find vec b - vec a . (ii) Find the unit vector along vec b - vec a . (iii) Prove that vec b - vec a and vec d - vec c are parallel vectors.

If A=[a_(ij)]_(mxxn) and a_(ij)=(i^(2)+j^(2)-ij)(j-i) , n odd, then which of the following is not the value of Tr(A)

CENGAGE-BINOMIAL THEOREM-Single correct Answer
  1. Find the 13^(th) term in the expansion of (9x - 1/(3sqrt(x)))^(18),x !...

    Text Solution

    |

  2. In the expansion of ((x)/(costheta)+(1)/(xsintheta))^(16), if l(1) is ...

    Text Solution

    |

  3. If A(i,j) be the coefficient of a^i b^j c^(2010-i-j) in the expansion ...

    Text Solution

    |

  4. The coefficient of x^(301 ub the expansion of (1+x)^(500)+x(1+x)^(499)...

    Text Solution

    |

  5. The coefficient of x^70 in the product (x-1)(x^2-2)(x^3-3)....(x^12-12...

    Text Solution

    |

  6. Given (1-x^(3))^(n)=sum(k=0)^(n)a(k)x^(k)(1-x)^(3n-2k) then the value ...

    Text Solution

    |

  7. Find the sum of the roots (real or complex) of the equation x^2001 + (...

    Text Solution

    |

  8. If the 4^(th) term of {sqrt(x^((1)/(1+log(10)x)))+root(12)(x)}^(6) is ...

    Text Solution

    |

  9. The number of distinct terms in the expansion of (x+y^(2))^(13)+(x^(2)...

    Text Solution

    |

  10. The value of sum(r=1)^n(sum(p=0)^(r-1) ^nCr ^rCp 2^p) is equal to

    Text Solution

    |

  11. If in the expansion of (x^(3)-(2)/(sqrt(x)))^(n) a term like x^(2) exi...

    Text Solution

    |

  12. In (3 3+1/(3 3))^n if the ratio of 7th term from the beginning to the ...

    Text Solution

    |

  13. The number of distinct terms in the expansion of is (x^(3)+(1)/(x^(3))...

    Text Solution

    |

  14. If r^[th] and (r+1)^[th] term in the expansion of (p+q)^n are equal, ...

    Text Solution

    |

  15. If (3+asqrt2)^100+(3+bsqrt2)^100=7+5sqrt2 number of pairs (a, b) for...

    Text Solution

    |

  16. The coefficient of the middle term in the expansion of (x + 2y)^(6) is

    Text Solution

    |

  17. The algebraically second largest term in the expansion of (3-2x)^(15) ...

    Text Solution

    |

  18. If 6^(th) term in the expansion of ((3)/(2)+(x)/(3))^(n) is numericall...

    Text Solution

    |

  19. Let (5 + 2sqrt6)^n= p+ f, where n in N and p in N and 0<f<1, then the ...

    Text Solution

    |

  20. The sum of last 3 digits of 3^100 is

    Text Solution

    |