Home
Class 12
MATHS
If alpha,beta!=0 , and f(n)""=alpha^n+be...

If `alpha,beta!=0` , and `f(n)""=alpha^n+beta^n` and `|3 1+f(1)1+f(2)1+f(1)1+f(2)1+f(3)1+f(2)1+f(3)1+f(4)|=K(1-alpha)^2(1-beta)^2(alpha-beta)^2` , then K is equal to (1) `alphabeta` (2) `1/(alphabeta)` (3) 1 (4) `-1`

A

1

B

`-1`

C

`alphabeta`

D

`(1)/(alphabeta)`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • MATRICES & DETERMINANT

    RESONANCE|Exercise HLP|33 Videos

  • MATRICES & DETERMINANT

    RESONANCE|Exercise EXERCISE-3|31 Videos

  • INDEFINITE INTEGRATION

    RESONANCE|Exercise SELF PRACTIC PROBLEMS|25 Videos

  • NUMBER THEORY

    RESONANCE|Exercise Exercise -2 (PART - II)|4 Videos

Similar Questions

Explore conceptually related problems

Let f(n)=a^n+b^n and |(3, 1+f(1), 1f(2)),(1+f(1), 1+f(2), 1+f(3)),(1+f(2), 1+f(3), 1+f(4))|=k(1-a)^2(1-b)^2(a-b)^2 , then k= (A) 0 (B) 1 (C) -1 (D) 4

If f(x)=alpha x+beta and f(0)=f^(1)(0)=1 then f(2) =

If f(x)= alpha x+beta and f(0)=f^(')(0)=1 then f(2) =

If a+alpha=1,b+beta=2 and af(n)+alphaf(1/n)=bn+beta/n , then find the value of (f(n)+f(1/n))/(n+1/n)

| alpha alpha1 beta F|=(alpha-P)(beta-alpha)

If alpha+beta=1 , and alpha.beta=-(3)/(2) , then find alpha^(2)+beta^(2)=

If f(alpha, beta) = cos^(4)alpha/cos^(2)beta + sin^(4)alpha/sin^(2)beta then prove that f(alpha, beta) =1 ⇔ f(beta, alpha) =1 .

RESONANCE-MATRICES & DETERMINANT-PART-II:
  1. If the trivial solution is the only solution of the system of equation...

    Text Solution

    |

  2. Statement -1 : Determinant of a skew-symmetric matrix of order 3 is ze...

    Text Solution

    |

  3. Let A=((1,0,0),(2,1,0),(3,2,1)). If u(1) and u(2) are column matrices ...

    Text Solution

    |

  4. Let P and Q be 3xx3 matrices with P!=Q . If P^3=""Q^3a n d""P^2Q""=""Q...

    Text Solution

    |

  5. The number of values of k, for which the system of eauations: (k+1)x...

    Text Solution

    |

  6. If P=[(1,alpha,3),(1,3,3),(2,4,4)] is the adjoint of a 3 x 3 matrix ...

    Text Solution

    |

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

    Text Solution

    |

  8. If A is an 3xx3 non-singular matrix such that AA^'=""A^' A and B""=...

    Text Solution

    |

  9. If A=[1 2 2 2 1-2a2b] is a matrix satisfying the equation AA^T=""9I , ...

    Text Solution

    |

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

    Text Solution

    |

  11. The system of linear equations: x+lambday-z=0 lamdax-y-z=0 x+y-l...

    Text Solution

    |

  12. If A=|{:(,5a,-b),(,3,2):}| and A adj A=A A^(T), then 5a+b is equal to

    Text Solution

    |

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

    Text Solution

    |

  14. If A=|{:(,2,-3),(,-4,1):}| then adj (3A^(2)+12A) is equal to

    Text Solution

    |

  15. If the system of linear equations x+ky+3z=0 3x+ky-2z=0 2x+4y-3z=0 ...

    Text Solution

    |

  16. If |(x-4,2x,2x),(2x,x-4,2x),(2x,2x,x-4)|=(A+Bx)(x-A)^2 then the ordere...

    Text Solution

    |

  17. The system of linear equations x + y + z = 2 2x + 3y + 2z = 5 2...

    Text Solution

    |

  18. If A=[(costheta, -sin theta ),(sin theta, cos theta) ] , then the ma...

    Text Solution

    |

  19. Let d in R, and A= [{:(-2, " "4+d,("sin"theta)-2),(1, ("sin"theta)...

    Text Solution

    |

  20. Let A=|{:(,0,21,r),(,p,q,-r),(,p,-q,r):}|=A A^(T)=I(3) then |p| is

    Text Solution

    |