Home
Class 12
MATHS
Let Deltar=|{:(r,2r-1,3r-2),(n/2,n-1,a),...

Let `Delta_r=|{:(r,2r-1,3r-2),(n/2,n-1,a),((n(n-1))/2,(n-1)^2,1/2(n-1)(3n-4)):}|`
Show that `sum_(r=1)^(n-1)Delta_r=0`

Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    ARIHANT MATHS|Exercise Expansion of Determinant|5 Videos

  • DETERMINANTS

    ARIHANT MATHS|Exercise Single Option Correct Type Questions|10 Videos

  • DEFINITE INTEGRAL

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|37 Videos

  • DIFFERENTIAL EQUATION

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|26 Videos

Similar Questions

Explore conceptually related problems

Let Delta_(a)=|{:((a-1),n,6),((a-1)^(2), 2n^(2),4n-2),((a-1)^(3),3n^(3),3n^(2)-3n):}| the value of sum_(a=1)^(n)Delta_(a) is

Let n be a positive integer and Delta_(r)=|{:(r^(2)+r,r+1,r-2),(2r^(2)+3r-1,3r,3r-3),(r^(2)+2r+3,2r-1,2r-1):}| and sum _(r=1)^(n)Delta_(r)=an^(2)+bn+c find the value of a+b+c.

If sum_(r=1)^n t_r=n/8(n+1)(n+2)(n+3), then find sum_(r=1)^n1/(t_r)dot

Sum of the series sum_(r=1)^(n) (r^(2)+1)r! is

If a_(1)=2 and a_(n)=2a_(n-1)+5 for ngt1 , the value of sum_(r=2)^(5)a_(r) is

If t_(1)=1,t_(r )-t_( r-1)=2^(r-1),r ge 2 , find sum_(r=1)^(n)t_(r ) .

Prove that ((n),(r))+2((n),(r-1))+((n),(r-2))=((n+2),(r))

Prove that (n!)/(r!(n-r)!)+(n!)/((r-1)!(n-r+1)!)= ((n+1)!)/ (r!(n-r+1)!) .

Evaluate sum_(r=1)^(n-1) cos^(2) ((rpi)/(n)) .

Find the sum of sum_(r=1)^n(r^n C_r)/(^n C_(r-1) .

ARIHANT MATHS-DETERMINANTS -Exercise (Questions Asked In Previous 13 Years Exam)
  1. Let Deltar=|{:(r,2r-1,3r-2),(n/2,n-1,a),((n(n-1))/2,(n-1)^2,1/2(n-1)(3...

    Text Solution

    |

  2. If a^2+b^2+c^2=-2, and f(x)= |{:(1+a^2x,(1+b^2)x,(1+c^2)x),((1+a^2)x,...

    Text Solution

    |

  3. The value of |alpha| for which the system of equation alphax+y+z=alpha...

    Text Solution

    |

  4. if a(1),a(2),…….a(n),……. form a G.P. and a(1) gt 0 , for all I ge 1 ...

    Text Solution

    |

  5. If D =|{:(1,1,1),(1,1+x,1),(1,1,1+y):}|"for" " "xne0,yne0 then D is

    Text Solution

    |

  6. Consider the system of equations x-2y+3z=-1 -x+y-2z=k x-3y+4z=1 ...

    Text Solution

    |

  7. Let a,b,c, be any real number. Suppose that there are real numbers x,y...

    Text Solution

    |

  8. Prove that |{:(1+a,1,1),(1,1+b,1),(1,1,1+c):}| =abc (1+(1)/(a)+(1)/(...

    Text Solution

    |

  9. If f(theta)=|{:(1,tantheta,1),(-tantheta,1,tantheta),(-1,-tantheta,1):...

    Text Solution

    |

  10. The number of values of k for which the linear equations 4x+ky+2...

    Text Solution

    |

  11. If the trivial solution is the only solution of the system of equation...

    Text Solution

    |

  12. The number of values of k, for which the system of equations (k""+""...

    Text Solution

    |

  13. If f(n)=alpha^(n)+beta^(n) and |{:(3,1+f(1),1+f(2)),(1+f(1),1+f(2),1+f...

    Text Solution

    |

  14. The set of all values of lambda for which the system of linear equ...

    Text Solution

    |

  15. Which of the following values of alpha satisfying the equation |{:((1+...

    Text Solution

    |

  16. The system of linear equations x+y+z=2,2x+y-z=3, 3x+2y+kz=4 has a uniq...

    Text Solution

    |

  17. The total number of distinct x in R for which |{:(x,,x^(2),,...

    Text Solution

    |

  18. Let a, lambda , mu in R.Consider the system of linear equations ax...

    Text Solution

    |

  19. If S is the set of distinct values of 'b' for which the following ...

    Text Solution

    |