Home
Class 12
MATHS
Prove that the following. [[1+a,1,1],[1,...

Prove that the following. `[[1+a,1,1],[1,1+b,1],[1,1,1+c]]`
= abc(1+1/a+/b+1/c)

Promotional Banner

Topper's Solved these Questions

  • SAMPLE PAPER 2012

    MODERN PUBLICATION|Exercise EXERCISE|37 Videos

  • SAMPLE PAPER 2014

    MODERN PUBLICATION|Exercise EXERCISE|35 Videos

Similar Questions

Explore conceptually related problems

Prove the following: [[1,1,1],[a,b,c],[a^3,b^3,c^3]] =(b-c)(c-a)(a-b)(a+b+c)

Prove the following : [[1,bc,a(b+c)],[1,ca,b(c+a)],[1,ab,c(a+b)]] =0

Prove that the following. [[1,1,1],[b+c,c+a,c+a],[b^2+c^2,c^2+a^2,a^2+b^2]] =(b-c)(c-a)(a-b)

Prove that |{:(1+a,1,1),(1,1+b,1),(1,1,1+c):}|=abc(1+1/a+1/b+1/c)or(abc+bc+ca+ab)

Find the value of [[1,a,b+a],[1,b,c+a],[1,c,a+b]] .

Prove the following: [[a^2+1,ab,ac],[ab,b^2+1,bc],[ac,bc,c^2+1]] =1+a^2+b^2+c^2

What is the value of abs[[a,b+c,1],[b,c+a,1],[c,a+b,1]] ?

Evaluate [[1,a,b+c],[1,b,c+a],[1,c,a+b]]

Prove that: |[1, 1, 1],[a, b, c],[a^2, b^2, c^2]|=(a-b)(b-c)(c-a)

MODERN PUBLICATION-SAMPLE PAPER 2013-EXERCISE
  1. Show that the points (3,-2,4)(1,1,1) and (-1,4,-1) are collinear.

    Text Solution

    |

  2. Find the equation of a plane biscting the line segment joining (-1,4,3...

    Text Solution

    |

  3. Find the value of r, if the line  (x-1)/(1) = (y+2)/(3) = (z-1)/(-1) =...

    Text Solution

    |

  4. Find equation of the sphere if the line segment joining the Points (4,...

    Text Solution

    |

  5. Maximise Z=50x(1)+60x(2) Subject to 2x(1)+3x(2)le6,x(1),x(2)ge0.

    Text Solution

    |

  6. Find the value of |{:(17,58,97),(19,60,99),(18,59,98):}| without expan...

    Text Solution

    |

  7. Prove that the following. [[1+a,1,1],[1,1+b,1],[1,1,1+c]] = abc(1+1/...

    Text Solution

    |

  8. Find the product [{:(1,2,3),(2,3,4):}][{:(1,-2),(-2,3):}]

    Text Solution

    |

  9. Prove that "^(2n)C0 + ^(2n)C2 + .... + ^(2n)C(2n) = 2^(2n-1)

    Text Solution

    |

  10. C(3)^(2n):C(3)^(n)= 44:5, find the value of n.

    Text Solution

    |

  11. In how many ways can 2 boys and 3 girls sit in a row so that no two gi...

    Text Solution

    |

  12. If 8 person are to sit around a table what is the probability that X a...

    Text Solution

    |

  13. A class consists of 25 boys and 15 girls. If a committee of 6 is to be...

    Text Solution

    |

  14. If y = e^(ax) cos bx then find y(n)(0).

    Text Solution

    |

  15. Use the function f(x) = x^(1//x), x gt 0 to show that e^(pi) gt pi^(e)...

    Text Solution

    |

  16. Evaluate int0^1frac[ln(1+x)][1+x^2]dx

    Text Solution

    |

  17. solve , dy/dx +y/X = xy^(2).

    Text Solution

    |

  18. Obtain the volume of the parallelopiped whose sides are vectors vec a=...

    Text Solution

    |

  19. Solve the matrix inversion method x+2y+3z=8,2x+y+z=8 and x+y+2z=6

    Text Solution

    |

  20. If P(A) = 0.4, P(B//A) = 0.3 and P(B^(c)/A^(c)) = 0.2. Find P(B).

    Text Solution

    |