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
`a. 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 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

sum_(i = 1)^n sum_(j = 1)^i sum_(k = 1)^j 1 is equal to

Let a and b be two real numbers such that a > 1, b >1. If A=((a,0),(0,b)), then (lim)_(n->oo) A^-n is (a) unit matrix (b) null matrix (c) 2I (d) non 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. (|A|+K)^(n-2) b. (|A|+K)^n c. (|A|+K)^(n-1) d. none of these

S.D. of numbers observation a_1, a_2, a_3,…..a_n is sigma then the S.D. of the observations lambdaa_1, lambdaa_2, lambdaa_3, lambdaa_3,....... lambdaa_n is

The centre of the circle given by vec r.( 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. (1,3,4) c. (-1,3,4) 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 d_i is the deviation of a class mark y_i from 'a' the ' assumed mean ' and F _1 is the frequency, then m_g= x+(1)/(sumf_1)(sumf_i d_i) then x 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)

If A=[[3,-3, 4], [2,-3, 4], [0,-1, 1]] , then a. a d j(a d j A)=A b. |a d j(a d j A)|=1 c. a d j A=I d. none of these

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

CENGAGE PUBLICATION-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 |[3,a+b+c,a^3+b^3+c^3],[a+b+c,a^2+b^2+c^2,a^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 de...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  9. If f(x),g(x) and h(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 i...

    Text Solution

    |

  11. Show that: |[a, b-c,c+b], [a+c, b, c-a],[a-b,b+a, c]|=(a+b+c)(a^2+b^2...

    Text Solution

    |

  12. In triangle A B C , if |[1, 1, 1],[cot(A/2),cot(B/2),cot(C/2)],[tan(B/...

    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 xi=ai bi ci,i=1,2,3 are three-digit positive integer such that ea...

    Text Solution

    |

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

    Text Solution

    |

  17. If a , b ,c are all different and |[a,a^3,a^4-1],[b,b^3,b^4-1],[c,c^...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  20. Prove that |x^2x^2-(y-z)^2y z y^2y^2-(z-x)^2z x z^2z^2-(x-y)^2x y|=(...

    Text Solution

    |