Home
Class 12
MATHS
If a1b1c1,a2b2c2 and a3b3c3 are three d...

If `a_1b_1c_1,a_2b_2c_2` and `a_3b_3c_3` are three digit even natural numbers and `Delta =|[c_1,a_1,b_1],[c_2,a_2,b_2],[c_3,a_3,b_3]|`,t h e n `Delta ` i s divisible by 2 but not necessarily by 4 divisible by 4 but not necessarily by 8 divisible by 8 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 A_1B_1C_1 , A_2B_2C_2 and A_3B_3C_3 are three digit numbers, each of which is divisible by k, then Delta = |(A_1,B_1,C_1),(A_2,B_2,C_2),(A_3,B_3,C_3)| is divisible by ____

If Delta=|(a_1,b_1,c_1),(a_2,b_2,c_2),(a_3,b_3,c_3)| and Delta_1=|(a_1+pb_1,b_1+qc_1,c_1+ra_1),(a_2+pb_2,b_2+qc_2,c _2+ra_2),(a_3+pb_3,b_3+qc_3,c_3+ra_3)| then Delta_1=

Prove that the value of each the following determinants is zero: |[a_1,l a_1+mb_1,b_1],[a_2,l a_2+mb_2,b_2],[a_3,l a_3+m b_3,b_3]|

If D= |{:(a_1,b_1,c_1),(a_2,b_2,c_2),(a_3,b_3,c_3):}| and A_1,B_1,C_1 etc. are the respective cofactors of the elements a_1,b_1,c_1 etc. then D will be-

If x_i=a_i b_i c_i,i=1,2,3 are three-digit positive integer such that each x_1 is a multiple of 19, then for some integers n , prove that |[a_1,a_2,a_3],[b_1,b_2,b_3],[c_1,c_2,c_3]| is divisible by 19.

Delta = |(a, a^2, 0),(1, 2a+b,(a+b)),(0, 1, 2a+3b)| is divisible by a. a+b b. a+2b c. 2a+3b d. a^2

If |x_1y_1 1x_2y_2 1x_3y_3 1|=|a_1b_1 1a_2b_2 1a_3b_3 1| then the two triangles with vertices (x_1, y_1),(x_2,y_2),(x_3,y_3) and (a_1,b_1),(a_2,b_2),(a_3,b_3) are equal to area (b) similar congruent (d) none of these

A function is defined as f:{a_1,a_2,a_3,a_4,a_5,a_6}rarr{b_1,b_2,b_3} then number of functions in which f(a_i)neb_i is divisible by

If w is a complex cube root of unity, then value of =|[a_1+b_1w, a_1w^2+b_1,c_1+b_1 w],[ a_2+b_2w, a_2w^2+b_2,c_2+b_2 w],[ a_3+b_3w ,a_3w^2+b_3,c_3+b_3 w] | is a. 0 b. -1 c. 2 d. none of these

CENGAGE PUBLICATION-DETERMINANTS-All Questions
  1. The value of the determinant of n^(t h) order, being given by |[x, 1, ...

    Text Solution

    |

  2. Prove that a!=0,|[x+a, x,x],[x,x+a,x],[x,x,x+a^2]|=0 represents a stra...

    Text Solution

    |

  3. If a1b1c1,a2b2c2 and a3b3c3 are three digit even natural numbers and ...

    Text Solution

    |

  4. If =|[a b c, b^2c,c^2b],[ a b c,c^2a, c a^2],[a b c, a^2b,b^2a]|=0,(a ...

    Text Solution

    |

  5. The value of |[yz, z x,x y],[ p,2p,3r],[1, 1, 1]|,w h e r ex ,y ,z ar...

    Text Solution

    |

  6. Show that the determinant |a^2+b^2+c^2 bc+ca+ab bc+ca+ab bc+ca+ab a^2+...

    Text Solution

    |

  7. If x!=0,y!=0,z!=0 and |[1+x,1,1],[1+y,1+2y,1],[1+z,1+z,1+3z]|=0, then ...

    Text Solution

    |

  8. If x!=y!=za n d|[x,x^2, 1+x^3],[y ,y^2 ,1+y^3],[z, z^2, 1+z^3]|=0, th...

    Text Solution

    |

  9. Prove that |2 alpha+beta+gamma+delta alphabeta+gammadelta alpha+beta...

    Text Solution

    |

  10. Solve for x , |[x,-6,-1], [ 2,-3x,x-3], [-3, 2x, x+2]|=0.

    Text Solution

    |

  11. The value of the determinant |{:(1,,1,,1),(.^(m)C(1),,.^(m+1)C(1),...

    Text Solution

    |

  12. Solve the equation |[a-x, c, b], [ c, b-x, a], [b, a, c-x]|=0 where a...

    Text Solution

    |

  13. If a^2+b^2+c^2=-2a n df(x)= |[1+a^2x,(1+b^2)x,(1+c^2)x],[(1+a^2)x,1+b...

    Text Solution

    |

  14. Consider the set A of all determinants of order 3 with entries 0 or 1 ...

    Text Solution

    |

  15. Solve: |[x^2-1, x^2+2x+1, 2x^2+3x+1], [2x^2+x-1, 2x^2+5x-3, 2x^2+4x-3...

    Text Solution

    |

  16. If |[x,3, 6],[ 3, 6,x],[6,x,3]|=|[2,x,7],[x,7, 2],[ 7, 2,x]|=|[4, 5,x]...

    Text Solution

    |

  17. If A1B1C1 , A2B2C2 and A3B3C3 are three digit numbers, each of which ...

    Text Solution

    |

  18. If f^(prime)(x)=|[mx, mx-p, m x+p], [n, n+p, n-p], [mx+2n, m x+2n+p, m...

    Text Solution

    |

  19. If sum(n=1)^nalphan=a n^2+b n ,w h e r ea ,b are constants and alpha...

    Text Solution

    |

  20. The determinant |[x p+y, x, y], [y p+z, y, z],[0,x p+y, y p+z]|=0...

    Text Solution

    |