Home
Class 12
MATHS
Let omega!=1 be cube root of unity and S...

Let `omega!=1` be cube root of unity and `S` be the set of all non-singular matrices of the form `[1a bomega1comega^2theta1],w h e r e` each of `a ,b ,a n dc` is either `omegaoromega^2dot` Then the number of distinct matrices in the set `S` is a. 2 b. `6` c. `4` d. `8`

A

2

B

6

C

4

D

8

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBER

    MOTION|Exercise EXERCISE - 4 (LEVEL -I) PREVIOUS YEAR - JEE MAIN|12 Videos

  • CIRCLE

    MOTION|Exercise Exercise - 4 | Level - II (Previous Year | JEE Advanced|22 Videos

  • CONTINUITY

    MOTION|Exercise EXERCISE - 4 (LEVEL -II) (PREVIOUS YEAR JEE ADVANCED)|5 Videos

Similar Questions

Explore conceptually related problems

Let omega!=1 be cube root of unity and S be the set of all non-singular matrices of the form [[1,a,bomega,1,comega^(2),theta,1]], where each of a,b, and c is either omega or omega^(2). Then the number of distinct matrices in the set S is (a) 2 (b) 6 (c) 4 (d) 8

With 1,omega,omega^(2) as cube roots of unity, inverse of which of the following matrices exists?

Let A be the set of all 3xx3 skew-symmetri matrices whose entries are either -1,0, or 1 If there are exactly three os three 1s, and there (-1)'s, then the number of such matrices is

If omega(!=1) is a cube root of unity,then the sum of the series S=1+2 omega+3 omega^(2)+....+3n omega^(3n-1) is

If omega is a cube root of unity,then find the value of the following: (1-omega)(1-omega^(2))(1-omega^(4))(1-omega^(8))

If omega is a cube root of unity but not equal to 1, then minimum value of abs(a+bomega+comega^(2)) , (where a,b and c are integers but not all equal ), is

MOTION-COMPLEX NUMBER -EXERCISE - 4 (LEVEL -II) PREVIOUS YEAR - JEE ADVANCED
  1. Match the statement in Column I with those in Column II. [Note : He...

    Text Solution

    |

  2. Let a, b and c be three real numbers satisfying [a" "b" "c][[1,9,7],[...

    Text Solution

    |

  3. Let omega be the solution of x^(3)-1=0 with "Im"(omega) gt 0. If a=2 w...

    Text Solution

    |

  4. Let a,b, and c be three real numbers satistying [a,b,c][(1,9,7),(8,2,7...

    Text Solution

    |

  5. If z is any complex number satisfying abs(z-3-2i) le 2, where i=sqrt(-...

    Text Solution

    |

  6. Let omega!=1 be cube root of unity and S be the set of all non-singula...

    Text Solution

    |

  7. Let omega= e^((ipi)/3) and a, b, c, x, y, z be non-zero complex numb...

    Text Solution

    |

  8. Let z be a complex number such that the imaginary part of z is nonzero...

    Text Solution

    |

  9. Let complex numbers alpha " and " (1)/(bar alpha) lies on circles (...

    Text Solution

    |

  10. Let w = (sqrt 3 + iota/2) and P = { w^n : n = 1,2,3, ..... }, Further ...

    Text Solution

    |

  11. Let omega be a complex cube root of unity with omegane1 and P = [pij]...

    Text Solution

    |

  12. Let S=S1 nn S2 nn S3, where s1={z in C :|z|<4}, S2={z in C :ln[(z-...

    Text Solution

    |

  13. Let S=S1 nn S2 nn S3, where s1={z in C :|z|<4}, S2={z in C :ln[(z-...

    Text Solution

    |

  14. Let zk=cos((2kpi)/(10))+isin ((2kpi)/10),k=1,2,......9 {:("List I","...

    Text Solution

    |

  15. For any integer k , let alphak=cos(kpi)/7+isin(kpi)/7,w h e r e i=sqrt...

    Text Solution

    |

  16. Let a,b in R and a^(2) + b^(2) ne 0 . Suppose S = { z in C: z = (1...

    Text Solution

    |

  17. Let P=[{:((-z)^r,z^(2r)),(z^(2r),z^r):}] and Ibe the identity matrix o...

    Text Solution

    |

  18. Let a , b ,xa n dy be real numbers such that a-b=1a n dy!=0. If the co...

    Text Solution

    |

  19. Let s ,\ t ,\ r be non-zero complex numbers and L be the set of ...

    Text Solution

    |

  20. For a non-zero complex number z , let arg(z) denote the principal ar...

    Text Solution

    |