Home
Class 12
MATHS
Using properties of determinants, prove ...

Using properties of determinants, prove the following: `|[1,a,a^2],[a^2,1,a],[a,a^2,1]|=(1-a^3)^2`

Promotional Banner

Topper's Solved these Questions

  • CUET MOCK TEST 2022

    XII BOARDS PREVIOUS YEAR|Exercise Question|49 Videos

Similar Questions

Explore conceptually related problems

Using properties of determinants, prove the following: |[1,x,x^2],[x^2, 1,x],[x,x^2,1]|=(1-x^3)^2

Using properties of determinants, prove the following: |[x,x^2,1+px^3],[y,y^2,1+py^3],[z,z^2,1+pz^3]|=(1+pxyz)(x-y)(y-z)(z-x)

Using properties of determinants,prove the following det[[a^(2),ab,acab,b^(2)+1,bcca,cb,c^(2)+1]]=1+a^(2)+b^(2)+c^(2)

Using properties of determinants,prove the following: det[[a^(2),ab,acab,b^(2)+1,bcca,cb,c^(2)+1]]=1+a^(2)+b^(2)+c^(2)

Prove the following : |{:(1,a,a),(a,1,a),(a,a,1):}|=(2a+1)(1-a)^(2)

Using properties of determinants,prove that det[[a^(2)+2a,2a+1,12a+1,a+2,13,3,1]]=(a-1)^(3)

Using properties of determinants,prove that ([(a+1)(a+2),a+2,1(a+2)(a+3),a+3,1(a+3)(a+4),a+4,1]|=-2

By using properties of determinants.Show that: det[[1,x,x^(2)x^(2),1,xx,x^(2),1]]=(1-x^(3))^(2)

Using properties of determinants,show that |1aa^(2)-bc1^(-2)-ca1^(^^2)-ab|=0

Using properties of determinants,prove the det[[1+p,1+p+q2,3+2p,1+3p+2q3,6+3p,1+6p+3q]]=1

XII BOARDS PREVIOUS YEAR-BOARD PAPER SOLUTIONS-All Questions
  1. Find the minimum value of (a x+b y), where x y=c^2dot

    Text Solution

    |

  2. Find the coordinates of a point on the parabola y=x^2+7x+2 which is cl...

    Text Solution

    |

  3. Using properties of determinants, prove the following: |[1,a,a^2],[a^2...

    Text Solution

    |

  4. Solve the following differential equation : (sqrt(1+x^2+y^2+x^2y^2))d...

    Text Solution

    |

  5. If a=[5 6-3-4 3 2-4-7 3], then write the cofactor of the element a(...

    Text Solution

    |

  6. Write the sum of the order and degree of the differential equation ...

    Text Solution

    |

  7. Write the solution of the differential equation (dy)/(dx)=2^(-y)

    Text Solution

    |

  8. Using integration, find the area of the region bounded by the line ...

    Text Solution

    |

  9. Find the probability distribution of the number of doublets in four...

    Text Solution

    |

  10. Find the unit vector in the direction of the sum of the vectors 2 hat ...

    Text Solution

    |

  11. Find the area of a parallelogram whose adjacent sides are represent...

    Text Solution

    |

  12. Find the sum of the intercepts cut off by the plane 2x+yz=5 , on the c...

    Text Solution

    |

  13. If 2tan^(-1)(costheta)=tan^(-1)(2cos e ctheta),(theta!=0) , then find ...

    Text Solution

    |

  14. If tan^(-1)(1/(1+1. 2))+tan^(-1)(1/(1+2. 3))+...+tan^(-1)(1/(1+n(n+1))...

    Text Solution

    |

  15. Evaluate : int(sin(x-a))/(sin(x+a))dx

    Text Solution

    |

  16. Maximise z = 8x + 9y subject to the constraints given below : 2x+3...

    Text Solution

    |

  17. Evaluate : inte^(2x)dotsin(3x+1)dx

    Text Solution

    |

  18. In a parliament election, a political party hired a public relation...

    Text Solution

    |

  19. Find whether the following function is differentiable at x = 1 and ...

    Text Solution

    |

  20. If y=(x+sqrt(1+x^2))^n , then show that (1+x^2)(d^2y)/(dx^2)+x(dy)/(d...

    Text Solution

    |