Home
Class 12
MATHS
Let {D1, D2, D3 ,Dn} be the set of third...

Let `{D_1, D_2, D_3 ,D_n}` be the set of third order determinant that can be made with the distinct non-zero real numbers `a_1, a_2, a_qdot` Then `sum_(i=1)^n D_i=1` b. `sum_(i=1)^n D_i=0` c. `D_i-D_j ,AAi ,j` d. none of these

Promotional Banner

Topper's Solved these Questions

  • DETERMINANT

    CENGAGE|Exercise Multiple Correct Answer|5 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE|Exercise Exercise|337 Videos

Similar Questions

Explore conceptually related problems

Find the sum Sigma_(j=1)^(n) Sigma_(i=1)^(n) I xx 3^j

If Z is an idempotent matrix, then (I+Z)^n I+2^n Z b. I+(2^n-1)Z c. I-(2^n-1)Z d. none of these

Let A be an nth-order square matrix and B be its adjoint, then |A B+K I_n| is (where K is a scalar quantity) (|A|+K)^(n-2) b. (|A|+)K^n c. (|A|+K)^(n-1) d. none of these

If the inverse of the matrix [[1,2],[3,-5]]^(n) is 1/11[[a,b],[c,d]] , then the ascending order of a, b, c, d is

If D_k=1nn2k n^2+n+1n^2+n2k-1n^2n^2+n+1a n dsum_(k=1)^n D_k=56. then n equals 4 b. 6 c. 8 d. none of these

If A^3=O ,t h e nI+A+A^2 equals a. I-A b. (I+A^1)^(-1) c. (I-A)^(-1) d. none of these

If A is a square matrix of order n such that |a d j(a d jA)|=|A|^9, then the value of n can be 4 b. 2 c. either 4or2 d. none of these

If a-1,a_2, ,a_n are positive real numbers whose product is a fixed number c , then the minimum value of a1 + d2 +..... + an-1 + 2an is

A_1,A_2,..., A_n are the vertices of a regular plane polygon with n sides and O as its centre. Show that sum_(i=1)^n vec (OA)_i xx vec(OA)_(i+1)=(1-n)(vec (OA)_2 xx vec(OA)_1)

The centre of the circle given by vec rdot( hat i+2 hat j+2 hat k)=15a n d| vec r-( hat j+2 hat k)|=4 is a. (0,1,2) b. (1,3,5) c. (-1,3,4) d. none of these

CENGAGE-DETERMINANTS-All Questions
  1. If a+b+c=0, one root of [[a-x, c, b],[c, b-x, a],[ b, a, c-x]]=0 is ...

    Text Solution

    |

  2. Factorize the following |3a+b+c a^3+b^3+c^3a+b+c a^2+b^2+c^2a^4+b^4+ ...

    Text Solution

    |

  3. Let {D1, D2, D3 ,Dn} be the set of third order determinant that can be...

    Text Solution

    |

  4. If g(x)-(f(x))/((x-a)(x-b)(x-c)),w h e r ef(x) is a polynomial of d...

    Text Solution

    |

  5. If the equation 2x+3y+1=0,3x+y-2=0,a n da x+2y-b=0 are consistent, ...

    Text Solution

    |

  6. If w is a complex cube root of unity, then value of =|a1+b1w a1w^2+b1c...

    Text Solution

    |

  7. Let f(x)=|cos(x+x^2)sin(x+x^2)- cos(x+x^2)...

    Text Solution

    |

  8. Which of the following has/have value equal to zero? |8 2 7 12 3 5 16 ...

    Text Solution

    |

  9. If f(x),g(x)a n dh(x) are three polynomials of degree 2, then prove th...

    Text Solution

    |

  10. If a ,b ,c are in G.P. with common ratio r1a n dalpha,beta,gamma are...

    Text Solution

    |

  11. Show that: |a b-cc+b a+c b c-a a-bb+a c|=(a+b+c)(a^2+b^2+c^2)dot

    Text Solution

    |

  12. In triangle A B C , if |1 1 1cotA/2cotB/2cotC/2tanB/2+tanC/2tanB/2+tan...

    Text Solution

    |

  13. If a ,b ,c ,d ,e, and fare in G.P. then the value of |((a^2),(d^2),x)...

    Text Solution

    |

  14. Prove that: |[(b+c)^2,a^2,a^2],[b^2,(c+a)^2,b^2],[c^2,c^2,(a+b)^2]|=2a...

    Text Solution

    |

  15. " if " x(i) =a(i) b(i) C(i) i= 1,2,3 are three- digit positive integer...

    Text Solution

    |

  16. The system of linear equations x+lambday-z=0 lambdax-y-z=0 x+y-lambd...

    Text Solution

    |

  17. If p q r!=0 and the system of equation (p+a)x+b y+c z=0 a x+(q+b)...

    Text Solution

    |

  18. If c<1 and the system of equations x+y-1=0,2x-y-c=0,a n db x+3b y-c=0 ...

    Text Solution

    |

  19. Prove that |(x^2,x^2-(y-z)^2,yz),(y^2,y^2-(z-x)^2,zx),(z^2,z^2-(x-y)^2...

    Text Solution

    |

  20. If a,b and c are real numbers, and Delta ={:[( b+c,C+a,a+b),( c+a,a...

    Text Solution

    |