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

Using properties of determinants, prove that following `|(a+b+2c,a,b),(c,b+c+2a,b),(c,a,c+a+2b)|=2(a+b+c)^3`

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

15.Using properties of determinants,prove the following b+c+aa+b

Using properties of determinants, prove the following |(3a,-a+b,-a+c),(a-b,3b,c-a),(a-c,b-c,3c)|=3(a+b+c)(ab+bc+ca)

Prove that : |{:(a+b+2c,a,b),(c,b+c+2a,b),(c,a,c+a+2b):}|=2(a+b+c)^(3)

Using properties of determinants,prove that: (a+b)^(2),ca,cbca,(c+b)^(2),abcb,ab,(c+a)^(2)]]=2abc(a+b+c)^(3)

Using properties of determinants, show the following: |[(b+c)^2,ab, ca],[ab,(a+c)^2,bc ],[ac ,bc,(a+b)^2]|=2abc(a+b+c)^3

Using properties of determinants, show that |(b+a,a,a),(b,c+a,b),(c,c,a+b)|=4abc

Using properties of determinants Prove that |{:(a+b+c,,-c,,-b),(-c,,a+b+c,,-a),( -b,,-a,,a+b+c):}| = 2 (a+b) (b+c) (c+a)

Using properties of determinants,prove the following : det[[a,a^(2),bcb,b^(2),cac,c^(2),ab]]=(a-b)(b-c)(c-a)(bc+ca+ab)

Using properties of determinants,prove the b+c,a,ab,c+a,bc,c,a+b]|=4abc

15.Using properties of determinants,prove the following det[[a-b,b-c,c-ab+c,c+a,a+b]]=a^(3)+b^(3)+c^(3)-3abc,]|=

XII BOARDS PREVIOUS YEAR-BOARD PAPER SOLUTIONS-All Questions
  1. Show that: int0^("pi"/2)"\ "sqrt(tan"x") +"\ "sqrt(cot"x")=sqrt(2)"pi...

    Text Solution

    |

  2. Prove that the curves "x"="y"^2 and "x y"="k" intersect at right an...

    Text Solution

    |

  3. Using properties of determinants, prove that following |(a+b+2c,a,b),(...

    Text Solution

    |

  4. If |[x+2, 3],[x+5, 4]|=3 , find the value of x

    Text Solution

    |

  5. Let "T" be the set of all triangles in a plane with "R" as relation...

    Text Solution

    |

  6. Show that the points (1,0), (6,0), (0,0) are collinear.

    Text Solution

    |

  7. If "f"("x")=sqrt((sec"x"-1)/(sec+1))" " find "f '"("x")dot Also f...

    Text Solution

    |

  8. If xsqrt(1+y)+ysqrt(1+x)=0, find ("dy")/("dx") . To prove (dy)/(dx)=...

    Text Solution

    |

  9. Find the maximum are of the isosceles triangle inscribed in the ell...

    Text Solution

    |

  10. show that the semi vertical angle of a right circular cone of given ...

    Text Solution

    |

  11. If the equation of a line "A B" is ("x"-3)/1=("y"+2)/(-2)=("z"-5)/4...

    Text Solution

    |

  12. If "f"("x") is an invertible function, find the inverse of "f"("x")...

    Text Solution

    |

  13. If [[(x+3y),y],[7-x,4]]=[(4,-1),(0,1)], find the values of x and y.

    Text Solution

    |

  14. Solve for x: tan^-1((1-x)/(1+x))=1/2 tan^-1 x, x > 0

    Text Solution

    |

  15. Evaluate: int("x"+cos6"x")/(3"x"^2+sin6"x")" dx"

    Text Solution

    |

  16. Form the differential equation representing the parabolas having ve...

    Text Solution

    |

  17. Solve the following differential equation: (3"x y"+"y"^2)"dx"+("x"^...

    Text Solution

    |

  18. If int("e"^("a x")+"b x")"dx"=4"e"^(4"x")+(3"x"^2)/2"\ ","\ " find the...

    Text Solution

    |

  19. A and B throw a pair of die turn by turn. The first to throw 9 is a...

    Text Solution

    |

  20. Find the equation of the line passing through the point "P"(4,6,2) ...

    Text Solution

    |