Home
Class 12
MATHS
Consider the determinant f(x)=|{:(0,x^...

Consider the determinant
`f(x)=|{:(0,x^(2)-a,x^(3)-b),(x^(2)+a,0,x^(2)+c),(x^(4)+b,x-c,0):}|`
Statement -1 f(x) =0 has one root x =0.
Statement -2 The value of skew -symmetric determinant of odd order is always zero.

Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    ARIHANT MATHS|Exercise Single Option Correct Type Questions|2 Videos

  • DETERMINANTS

    ARIHANT MATHS|Exercise Exercise For Session 1|7 Videos

  • DEFINITE INTEGRAL

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|38 Videos

  • DIFFERENTIAL EQUATION

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

Similar Questions

Explore conceptually related problems

Consider the determinant f(x)=|0x^2-a x^3-b x^2+a0x^2+c x^4+b x-c0|dot Statement 1: f(x)=0 has one root x=0. Statement 2: The value of skew symmetric determinant of odd order is always zero.

If f(x) = |(0, x-a, x-b),(x+a, 0, x-c),(x+b, x+c, 0)| , then the value of f(0) is :

Consider the matrix A=[{:(0,-h,-g),(h,0,-f),(g,f, 0):}] STATEMENT-1 : Det A = 0 STATEMENT-2 :The value of the determinant of a skew symmetric matrix of odd order is always zero.

" 0.The value of the determinant "|[1,x,x^(2)],[1,b,b^(2)],[1,c,c^(2)]|" is: "

f(x)={{:((3//x^2)sin2x^2,"if" x lt 0),((x^2+2x+c)/(1-3x^2), "if" x ge 0 "):} then in order that f be continuous at x=0, the value of c is

f(x)=[(cosx,-sinx,0),(sinx,cosx,0),(0,0,1)] Statement 1: f(x) is inverse of f(-x) Statement 2: f(x).f(y) = f(x+y)

Suppose a,b,c epsilon R and let f(x)=|(0,a-x,b-x),(-a-x,0,c-x),(-b-x,-c-x,0)| Then coefficient of x^(2) in f(x) is

ARIHANT MATHS-DETERMINANTS -Exercise (Questions Asked In Previous 13 Years Exam)
  1. Consider the determinant f(x)=|{:(0,x^(2)-a,x^(3)-b),(x^(2)+a,0,x^(2...

    Text Solution

    |

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

    Text Solution

    |

  3. The system of equations alphax+y+z=alpha-1, x+alphay+z=alpha-1 ...

    Text Solution

    |

  4. If a1,a2,a3,.....an.... are in G.P. then the determinant Delta=|[logan...

    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. Let a,b,c be such that b(a+c)ne 0. If |{:(,a,a+1,a-1),(,-b,b+1,b-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 which the linear equations 4x+ky+2z=0 kx...

    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 alpha,beta!=0 , and f(n)""=alpha^n+beta^n and |3 1+f(1)1+f(2)1+f(1)...

    Text Solution

    |

  14. The set of the all values of lamda for which the system of linear equa...

    Text Solution

    |

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

    Text Solution

    |

  16. The system of linear equations x+lambday-z=0 lambdax-y-z=0 x+y-l...

    Text Solution

    |

  17. The total number of distinct x in R for which |[x, x^2, 1+x^3] , [2x,...

    Text Solution

    |

  18. Let a,lambda,mu in R, Consider the system of linear equations ax+2y=la...

    Text Solution

    |

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

    Text Solution

    |