Home
Class 12
MATHS
A 3xx3 determinant has entries either 1 ...

A `3xx3` determinant has entries either `1` or `-1`.
Let `S_(3)=` set of all determinants which contain determinants such that product of elements of any row or any column is `-1` For example `|{:(1,,-1,,1),(1,,1,,-1),(-1,,1,,1):}|`is an element of the set `S_(3)`.
Number of elements of the set `S_(3)=`

A

10

B

12

C

16

D

18

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • DETERMINANT

    FIITJEE|Exercise EXERCIESE 1|3 Videos

  • DETERMINANT

    FIITJEE|Exercise EXERCIESE 2|2 Videos

  • DETERMINANT

    FIITJEE|Exercise SOLVED PROBLEMS (SUBJECTIVE)|7 Videos

  • DEFINITE INTEGRAL

    FIITJEE|Exercise NUMERICAL BASED|3 Videos

  • ELLIPSE

    FIITJEE|Exercise NUMERICAL BASED|4 Videos

Similar Questions

Explore conceptually related problems

If the entries in a 3xx3 determinant are either 0 or 1, then the greatest value of their determinants is

A determinant is chosen at random from the set of all determinants of order two with elements 0 or 1 only. Probability that the determinant chosen has positive value is

Find minor or element 5 in the determinant Delta=|{:(2,4,3),(1,5,2),(-1,4,1):}|

Let S={1,2,3,.....50} The number of non empty subsets A of S such that the product of elements is A is even

The cofactor of the element '4' in the determinant |(1,3,5,1),(2,3,4,2),(8,0,1,1),(0,2,1,1)| is

Multiply the following determinants and obtain four different determinants by multiplying row to row, to column , column to row and column to column |{:(3,4),(1,2):}|xx|{:(6,2),(3,1):}|

Let S={1,2,3,......,100}. The number of non-empty subsets A of S such that the product of elements in A is even is

Write minors and cofactors of the elements of the determinants: |{:(1,0,4),(3,5,-1),(0,1,2):}|

Let A be the set of all 3xx3 matrices of whose entries are either 0 or 1. The number of elements is set A, is

FIITJEE-DETERMINANT-SOLVED PROBLEMS (OBJECTIVE)
  1. If a,b,c be the pth, qth and rth terms respectively of a H.P., the |(b...

    Text Solution

    |

  2. The system of equations x+2y +3z =4, 2x+3y+4z=5,3x+4y+5z=6 has

    Text Solution

    |

  3. There are three points (a,x) ,(b,y) and (c,z) such that the straight l...

    Text Solution

    |

  4. The det Delta=|{:(d^2+r,de,df),(de,e^2+r,ef),(df,ef,f^2+r):}| is divis...

    Text Solution

    |

  5. If x,y and z are the integers in AP lying between 1 and 9 and x 51, ...

    Text Solution

    |

  6. Let f(x) =|{:(x^(3), sinx,cosx),(6,-1,0),(p,p^(2),p^(3)):}| where p is...

    Text Solution

    |

  7. The parameter on which the value of the determinant |1a a^2"cos"(p-d)x...

    Text Solution

    |

  8. A 3xx3 determinant has entries either 1 or -1. Let S(3)= set of all ...

    Text Solution

    |

  9. A 3 xx 3 determinant has its entries 1 or-1 . The number of such deter...

    Text Solution

    |

  10. A 3xx3 determinant has entries either 1 or -1. Let S(3)= set of all ...

    Text Solution

    |

  11. Consider the determinant, Delta=|(p,q,r),(x,y,z),(l,m,n)| . M(ij) d...

    Text Solution

    |

  12. Consider the determinant, Delta=|(p,q,r),(x,y,z),(l,m,n)| . M(ij) d...

    Text Solution

    |

  13. Statement -1 : Let a,b,c are the sides of a DeltaABC such that |{:(a,a...

    Text Solution

    |

  14. The value of |(.^(10)C(4).^(10)C(5).^(11)C(m)),(.^(11)C(6).^(11)C(7).^...

    Text Solution

    |

  15. Let f(x) =|(x,1,1), (sin2pix, 2x^2,1), (x^3,3x^4,1)|. If f(x) be an od...

    Text Solution

    |

  16. If a,b, and c be non-zero real numbers such that |{:(1+a,1,1),(1,1+b...

    Text Solution

    |

  17. Let A and B be two matrices (neither null nor singular ) with real ent...

    Text Solution

    |

  18. Which of the following options is the only correct combination ?

    Text Solution

    |

  19. Which of the following options is the only correct combination ?

    Text Solution

    |

  20. Which of the following options is the only correct combination ?

    Text Solution

    |