Home
Class 12
MATHS
The value of the determinant [[x,x+y, x+...

The value of the determinant `[[x,x+y, x+2y],[ x+2y, x,x+y],[ x+y, x+2y ,x]]` is
(a)`9x^2(x+y)`
(b) `9y^2(x+y)`
`(c)3y^2(x+y)`
(d) `7x^2(x+y)`

Text Solution

Verified by Experts

`[[x,x+y, x+2y],[ x+2y, x,x+y],[ x+y, x+2y ,x]]`
`c_1=c_1+c_2+c_3`
`=>[[3x+3y,x+y, x+2y],[ 3x+3y, x,x+y],[3x+3y, x+2y ,x]]`
`=>3x+3y``[[1,x+y, x+2y],[ 1, x,x+y],[1, x+2y ,x]]`
...
Promotional Banner

Topper's Solved these Questions

  • DERIVATIVES AS A RATE MEASURER

    RD SHARMA|Exercise Solved Examples And Exercises|149 Videos

  • DIFFERENTIABILITY

    RD SHARMA|Exercise Solved Examples And Exercises|136 Videos

Similar Questions

Explore conceptually related problems

The value of the determinant det[[x+2y,x,x+yx+2y,x,x+yx+y,x+2y,x]]9y^(2)(x+y)3y^(2)(x+y)(d),7x^(2)(x+y)

Using properties of determinants, prove the following |[x,x+y,x+2y],[x+2y,x,x+y],[x+y,x+2y,x]|=9y^2(x+y)

Simplify: (2x + 5y)(3x + 4y) - (7x + 3y)(2x + y)

Solve : (3)/(x + y ) + ( 2)/(x - y ) = 2 and (9)/(x + y ) - ( 4)/(x - y) = 1 .

( 10 )/( x+ y) + (2 ) /(x - y ) = 4 , ( 15)/( x + y ) - (9) /( x - y) = - 2 .

The value of (x-y)^3+(x+y)^3+3(x-y)^2(x+y)+3(x+y)^2(x-y) is

Solve for x and y:y^(x) = x^(y), x = 2y .

RD SHARMA-DETERMINANTS-Solved Examples And Exercises
  1. If the determinant |[a ,b,2a alpha+3b],[b ,c, 2b alpha+3c],[2a alpha+3...

    Text Solution

    |

  2. If 1.omega, omega^2 are the roots of unity, then Delta=|(1,omega^n,ome...

    Text Solution

    |

  3. If a >0 and discriminant of a x^2+2b x+c is negative, then |[a,b,ax+...

    Text Solution

    |

  4. The value of /\=|[5^2, 5^3, 5^4],[ 5^3, 5^4, 5^5],[ 5^4, 5^5, 5^6]| is...

    Text Solution

    |

  5. |(log)3 512(log)4 3(log)3 8(log)4 9|xx|(log)2 3(log)8 3(log)3 4(log)3 ...

    Text Solution

    |

  6. If a, b, c, are in A.P, then the determinant|x+2x+3x+2a x+3x+4x+2b x+4...

    Text Solution

    |

  7. If A+B+C=pi, then the value of [[sin(A+B+C) , sin(A+C) , cosC],[-sinB...

    Text Solution

    |

  8. The number of distinct real roots of |{:(cosec x, secx, secx), (secx...

    Text Solution

    |

  9. Let A=[[1,sintheta,1],[sintheta,1,sintheta],[-1,-sintheta,1]] where 0l...

    Text Solution

    |

  10. If |(2,x,5, 8,x)|=|(6,-2, 7, 3)| , then x= (a) 3 (b) +-3 (c) +-6 (d) ...

    Text Solution

    |

  11. If f(x)=|0x-a x-b x+a0x-c x+b x+c0|,t h e n f(x)=0 (b) f(b)=0 (c) f...

    Text Solution

    |

  12. If x , y , z are different from zero and [[1+x,1, 1],[ 1 ,1+y,1 ],[1 ,...

    Text Solution

    |

  13. The determinant |{:(b^2-ab, b-c, bc-ac), (a b-a^2, a-b, b^2-ab) ,(b c-...

    Text Solution

    |

  14. If x , y in R , then the determinant =|cosx-sinx1sinxcosx1cos(x+y)-si...

    Text Solution

    |

  15. The maximum value of =[[1, 1, 1],[ 1, 1+sintheta,1],[ 1,1,1+costheta]...

    Text Solution

    |

  16. The value of the determinant [[x,x+y, x+2y],[ x+2y, x,x+y],[ x+y, x+2y...

    Text Solution

    |

  17. Let f(x)=|cosx x 1 2sinx x2xsinx x x| , then (lim)(x->0)(f(x))/(x^2) i...

    Text Solution

    |

  18. If there are two values of a which makes determinant, Delta=|(1,-2,5...

    Text Solution

    |

  19. If Delta=|(a,p,x),(b,q,y),(c,r,z)|=16 then Delta(1)=|(p+x,a+x,a+p),(q+...

    Text Solution

    |

  20. The value of |1 1 1\ ^n C1\ ^(n+2)C1\ ^(n+4)C1\ ^n C2\ ^(n+2)C2\ ^(n+4...

    Text Solution

    |