Home
Class 12
MATHS
If [] denotes the greatest integer less ...

If `[]` denotes the greatest integer less than or equal to the real number under consideration, and `-1lt=x<0,0lt=y<1,1lt=z<2,` then the value of the determinant `|[[x]+1, [y],[z]], [[x], [y]+1, [z]], [[x], [y], [z]+1]|` is a. `[x]` b. `[y]` c. `[z]` d. none of these

Promotional Banner

Topper's Solved these Questions

  • DETERMINANT

    CENGAGE PUBLICATION|Exercise Multiple Correct Answer|5 Videos
  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Multiple correct answers type|11 Videos

Similar Questions

Explore conceptually related problems

If [.] denotes the greatest ingeter less then or equal to the real number under consideration and -1lexlt0,leylt1,1lezlt2 then find the value of the determinant |{:([x]+1," "[y]," "[z]),(" "[x],[y]+1," "[z]),(" "[x]," "[y],[z]+1):}|

Let [x] denote the greatest integer less than or equal to x for any real number x. Then underset(n tooo)lim([nsqrt(2)])/(n) is equal to-

if [x] denotes the greatest integer less than or equal to x then integral int_0^2x^2[x] dx equals

If [x] denotes the greatest integer less than or equal to x, the extreme values of the function f(x)=[1+sinx]+[1+sin2x]+[1+sin3x]+…+[1+sin nx], n in 1^+, x in(0,pi) are

Let [ x ] denote the greatest integer less than or equal to x, then the value of the integral int_-1^1 (absx - 2[x]) dx is equal to

Let f(x)=[tanx[cotx]], x in [(pi)/(12),(pi)/(2)), (where [.] denotes the greatest integer less than or equal to x). The number of points, where f(x) is discontinuous is

Let [x] denote the greatest integer less than or equal to x, then the value of the integral int_(-1)^(1)(|x|-2[x])dx is equal to-

Let [x] denote the greatest integer less than or equal to x for any real number x. Then lim_(n to oo) ([n sqrt(2)])/(n) is equal to

[x] denotes the greatest integer, less than or equal to x, then the value of the integral int_(0)^(2)x^(2)[x]dx equals

If [x] denotes the greatest integer less than or equal to x, then evaluate lim_(ntooo) (1)/(n^(2))([1.x]+[2.x]+[3.x]+...+[n.x]).

CENGAGE PUBLICATION-DETERMINANTS-All Questions
  1. If |[a,b-c,c+b],[a+c,b,c-a],[a-b,a+b,c]|=0 , then the line a x+b y+c=0...

    Text Solution

    |

  2. If 2a x-2y+3z=0,x+a y+2z=0,a n d, 2x+a z=0 have a nontrivial solutio...

    Text Solution

    |

  3. If [] denotes the greatest integer less than or equal to the real numb...

    Text Solution

    |

  4. If f(x)=a+b x+c x^2 and alpha,beta,gamma are the roots of the equation...

    Text Solution

    |

  5. If x ,y \ a n d \ z are not all zero and connected by the equations ...

    Text Solution

    |

  6. Find lambda for which the system of equations x+y-2z=0,2x-3y+z=0,x-...

    Text Solution

    |

  7. If p ,q ,r are in A.P. then value of determinant |[a^2+2^(n+1)+2p, b^2...

    Text Solution

    |

  8. For what values of k , the following system of equations possesses a...

    Text Solution

    |

  9. Let a ,b , c in R such that no two of them are equal and satisfy |(2a...

    Text Solution

    |

  10. Solve for x by Cramers rule x+y+z=6, x-y+z=2 3x+2y-4z=-5

    Text Solution

    |

  11. The value of the determinant |(k a, k^2+a^2, 1),(k b, k^2+b^2, 1),(k c...

    Text Solution

    |

  12. Find the value of a \ a n d \ b if the system of equation a^2x-b y=a...

    Text Solution

    |

  13. If (x1-x2)^2+(y1-y2)^2=a^2, (x2-x3)^2+(y2-y3)^2=b^2, (x3-x1)^2+(y3-y1...

    Text Solution

    |

  14. f(x)=|[cosx,x,1],[2sinx,x^2,2x],[tanx,x,1]| . Then value of lim(x->0)(...

    Text Solution

    |

  15. If a system of three linear equations x+4a y+a=0,x+3b y+b=0, and x+2c...

    Text Solution

    |

  16. Let alpha be a repeated root of a quadratic equation f(x)=0 and A(x...

    Text Solution

    |

  17. If |[a^2+lambda^2,ab+clambda,ca-blambda],[ab-clambda,b^2+lambda^2,bc+a...

    Text Solution

    |

  18. Value of |{:(1+x(1),,1+x(1)x,,1+x(1)x^(2)),(1+x(2),,1+x(2)x,,1+x(2)x^(...

    Text Solution

    |

  19. If f(x)=|(a1+x, b1+x, c1+x), (a2+x, b2+x, c2+x),(a3+x, b3+x, c3+x)|, s...

    Text Solution

    |

  20. The value of determinant |[b c-a^2,a c-b^2,a b-c^2],[a c-b^2,a b-c^2,b...

    Text Solution

    |