Home
Class 12
MATHS
If x,y,z are all different from zero and...

If x,y,z are all different from zero and `|{:(1+x,1,1),(1,1+y,1),(1,1,1+z):}|=0`, then value of `x^(-1)+y^(-1)+z^(-1)` is

A

xyz

B

`x^(-1)y^(-1)z^(-1)`

C

`-x-y-z`

D

`-1`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    ACCURATE PUBLICATION|Exercise Type-II (Fill in the blanks questions)|31 Videos
  • DETERMINANTS

    ACCURATE PUBLICATION|Exercise Type-III (True or False questions)|25 Videos
  • DETERMINANTS

    ACCURATE PUBLICATION|Exercise Example (Questions caryying 6 marks)|35 Videos
  • DEFINITE INTEGRALS

    ACCURATE PUBLICATION|Exercise QUESTION CARRYING 4 MARKS|8 Videos
  • DIFFERENTAL QUATIONS

    ACCURATE PUBLICATION|Exercise QUESTIONS CARRYING 4 MARKS|41 Videos

Similar Questions

Explore conceptually related problems

If x, y, z are all distinct and |(x,x^(2),1+x^(3)),(y,y^(2),1+y^(3)),(z,z^(2),1+z^(3))|=0 then value of x y z is :

If x,y,z are different and Delta= {:|(x,x^2,1+x^3),(y,y^2,1+y^3),(z,z^2,1+z^3)|=0 , show that xyz=-1

Show that : |{:(1+x,1,1),(1,1+y,1),(1,1,1+z):}|=xyz(1+(1)/(x)+(1)/(y)+(1)/(z))

The line (x-x_1)/0=(y-y_1)/1=(z-z_1)/2 is

Prove that |(1,x,x^2),(1,y,y^2),(1,z,z^2)| = (x-y)(y-z)(z-x)

Use properties of determinants ot evaluate: {:|(x+y,y+z,z+x),(z,x,y),(1,1,1)|

Let f be an injective map with domain {x ,\ y ,\ z} and range {1, 2, 3} such that exactly one of the following statements is correct and the remaining are false. f(x)=1,\ \ f(y)!=1,\ f(z)!=2 . The value of f^(-1)(1) is (a) x (b) y (c) z (d) none of these

ACCURATE PUBLICATION-DETERMINANTS-Type-I (Multiple choice questions)
  1. If A=[{:(3,1),(1,2):}], then A(adjA) equals

    Text Solution

    |

  2. If A = ([4,3],[3,4]), then A (Adj A) equals :

    Text Solution

    |

  3. If A=[(3,2),(1,4)] , then A(adj A) equals

    Text Solution

    |

  4. The inverse of a symmetric matrix is :

    Text Solution

    |

  5. Prove that |[1,x,x^2-yz],[1,y,y^2-zx],[1,z,z^2-xy]|= 0

    Text Solution

    |

  6. If x,y in R then the determinant Delta=|{:(cosx,-sinx,1),(sinx,cosx,1)...

    Text Solution

    |

  7. If |(2x,5),(8,x)|=|(6,-2),(7,3)| , write the value of x.

    Text Solution

    |

  8. The value of determinant |{:(a-b,b+c,a),(b-a,c+a,b),(c-a,a+b,c):}| is

    Text Solution

    |

  9. The area of a triangle with vertices (-3,0),(3,0) and (0,k) is 9 sq. u...

    Text Solution

    |

  10. The determinant |{:(b^(2)-ab,b-c,bc-ac),(ab-a^(2),a-b,b^(2)-ab),(bc-ca...

    Text Solution

    |

  11. The number of distinct real roots of |{:(sinx,cosx,cosx),(cosx,sinx,co...

    Text Solution

    |

  12. If A,B and C are angles of a triangle, then the determinant: {:|(-1,...

    Text Solution

    |

  13. Let f(t)=|{:(cost,t,1),(2sint,t,2t),(sint,t,t):}|, then LT(t to o)(f(t...

    Text Solution

    |

  14. Find the maximum value of : {:|(1,1,1),(1,1+sintheta,1),(1,1,1+costh...

    Text Solution

    |

  15. Consider the determinant f(x)=|{:(0,x^(2)-a,x^(3)-b),(x^(2)+a,0,x^(2...

    Text Solution

    |

  16. If A=[{:(2,lambda,-3),(0,2,5),(1,1,3):}| , then A^(-1) exists if

    Text Solution

    |

  17. If A and B are invertibel , then which of the following is not correct

    Text Solution

    |

  18. If x,y,z are all different from zero and |{:(1+x,1,1),(1,1+y,1),(1,1,1...

    Text Solution

    |

  19. Without expanding, prove the following |(x,x+y,x+2y),(x+2y,x,x+y),(...

    Text Solution

    |

  20. There are two values of a which makes determinant, Delta=|{:(1,-2,5),(...

    Text Solution

    |