Home
Class 11
MATHS
If the 11 letters A, B, ..., K denote an...

If the 11 letters A, B, ..., K denote an arbitrary permutation of he integers `(1,2,ddot,11),` then `(A-1)(B-2)(C-3)...(K-11)` will be a. necessarily zero b. always odd c. always even d. none of these

Promotional Banner

Topper's Solved these Questions

  • LOGARITHM

    CENGAGE PUBLICATION|Exercise All Questions|177 Videos
  • PROBABILITY

    CENGAGE PUBLICATION|Exercise All Questions|1 Videos

Similar Questions

Explore conceptually related problems

If nth-order square matrix A is a orthogonal, then |adj(adjA)| is (a)always -1 if n is even (b) always 1 if n is odd (c) always 1 (d) none of these

Find the area of the vertices A,B,C and D of the quadrilateral whose vertices have coordinates (1,1) ,(3,4),(5,-2) and (4,-7).

Four non –zero vectors will always be a. linearly dependent b. linearly independent c. either a or b d. none of these

If the matrix [(a,b),(c,d)] is commutative with the matrix [(1,1),(0,1)] then

If x is real, then x//(x^2-5x+9) lies between a. -1a n d-1//11 b. 1a n d-1//11 c. 1a n d1//11 d. none of these

The greatest integer by which 1+sum_(r=1)^(30)rxxr ! is divisible is a. composite number b. odd number c. divisible by 3 d. none of these

Let A be an nth-order square matrix and B be its adjoint, then |A B+K I_n| is (where K is a scalar quantity) a. (|A|+K)^(n-2) b. (|A|+K)^n c. (|A|+K)^(n-1) d. none of these

If a , b , c are consecutive positive integers and log(1+a c)=2K , then the value of K is

Find the value of cos B for the triangle formed by joining the points A(6,11,2),B(1,-1,2)and C(1,2,6).

Find the area of the quadrilateral A B C D having vertices A(1,1),B(7,-3),C(12 ,2), and D(7, 21) .

CENGAGE PUBLICATION-PERMUTATIONS AND COMBINATIONS-All Questions
  1. In how many ways 3 boys and 15 girls can sits together in a row such ...

    Text Solution

    |

  2. If the lines y = 3x + 7 and 2y + px = 3 perpendicular to each other, f...

    Text Solution

    |

  3. If the 11 letters A, B, ..., K denote an arbitrary permutation of he ...

    Text Solution

    |

  4. In how many ways can four people, each throwing a dice once, make a su...

    Text Solution

    |

  5. If the straight lines kx – 5y + 4 = 0 and 4x – 2y + 5 = 0 are perpendi...

    Text Solution

    |

  6. In how many ways can 5 girls and 3 boys be seated in a row so that no ...

    Text Solution

    |

  7. If 9^(th) term of an A.P. is zero, prove that its 29^(th) term is doub...

    Text Solution

    |

  8. In how many ways can four people, each throwing a dice once, make a su...

    Text Solution

    |

  9. Find n ,if(n+1)! =12xx(n-1)!dot

    Text Solution

    |

  10. Three numbers are in AP. If theirsum is 27 and their product is 648. F...

    Text Solution

    |

  11. Find the total number of integers 'n' such that 2 le n le 2000 and ...

    Text Solution

    |

  12. The number of polynomials of the form x^3 + ax^2 + bx + c which are di...

    Text Solution

    |

  13. Find the number of diagonals in a polygon with n sides.

    Text Solution

    |

  14. Find the total number of n -digit number (n >1) having property that n...

    Text Solution

    |

  15. Prove that (n !)^2 < n^n n! < (2n)!, for all positive integers n.

    Text Solution

    |

  16. Find the sum of the series sum(r=1)^n r/((r+1) !)dot

    Text Solution

    |

  17. Find the exponent of 80 in 200!.

    Text Solution

    |

  18. Prove that .^nPr = ^(n-1)Pr + r^(n-1)P(r-1)

    Text Solution

    |

  19. How many ways are there to seat n married couples (ngeq3) around a tab...

    Text Solution

    |

  20. A round-table conference is to be held among 20 delegates belonging fr...

    Text Solution

    |