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

`alphabetagamma`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|15 Videos

  • DETERMINANTS

    ARIHANT MATHS|Exercise Exercise (Passage Based Questions)|21 Videos

  • DETERMINANTS

    ARIHANT MATHS|Exercise Exercise For Session 4|10 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

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 .

ARIHANT MATHS-DETERMINANTS -Exercise (Single Option Correct Type Questions)
  1. If alpha,beta!=0 , and f(n)""=alpha^n+beta^n and |3 1+f(1)1+f(2)1+f(1)...

    Text Solution

    |

  2. Let Delta(x)=|(x+a,x+b,x+a-c),(x+b,x+c,x-1),(x+c,x+d,x-b+d)| and int0^...

    Text Solution

    |

  3. If Delta (x)=|{:(x,1+x^(2),x^(3)),(log(1+x^(2)),e^(x),sinx),(cosx,tanx...

    Text Solution

    |

  4. If a, b, c are sides of a triangle and |(a^2,b^2,c^2),((a+1)^2,(b+1...

    Text Solution

    |

  5. If |{:(alpha,x,x,x),(x,beta,x,x),(x,x,gamma,x),(x,x,x,delta):}| =f(x)-...

    Text Solution

    |

  6. If |{:(a,b-c,c+b),(a+c,b,c-a),(a-b,a+b,c):}|=0 the line ax +by +c=0 p...

    Text Solution

    |

  7. If f(x) =a+bx+cx^(2) and alpha,beta "and" gamma are the roots of the...

    Text Solution

    |

  8. When the determinant |{:(cos2x,sin^(2)x,cos4x),(sin^(2)x,cos2x,cos^(2)...

    Text Solution

    |

  9. If [] denotes the greatest integer less than or equal to the real numb...

    Text Solution

    |

  10. The determinant |{:(y^(2),-xy,x^(2)),(a,b,c),(a',b',c'):}| is equal to

    Text Solution

    |

  11. If A,B and C are angle of a triangle of a triangle ,the value of |{:(...

    Text Solution

    |

  12. If |{:(x^(n),x^(n+2),x^(2n)),(1,x^(a),a),(x^(n+5),x^(a+6),x^(2n+5)):}|...

    Text Solution

    |

  13. If x,y and z are the integers in AP lying between 1 and 9 and x 51, ...

    Text Solution

    |

  14. If a(1),b(1),c(1),a(2),b(2),c(2) "and" a(3),b(3),c(3) are three digit ...

    Text Solution

    |

  15. If a,b,and c are sides of Delta ABC such that |{:(c,bcosB+alphabeta,ac...

    Text Solution

    |

  16. If x(1),x(2) "and" y(1),y(2) are the roots of the equations 3x^(2) ...

    Text Solution

    |

  17. The value of |(.^(10)C(4).^(10)C(5).^(11)C(m)),(.^(11)C(6).^(11)C(7).^...

    Text Solution

    |

  18. The value of the determinant |{:(1,sin(alpha-beta)theta,cos (alpha-be...

    Text Solution

    |

  19. If f(x), h(x) are polynomials of degree 4 and |(f(x), g(x),h(x)),(a, b...

    Text Solution

    |

  20. If f(x) =|{:(cos (x+alpha),cos(x+beta),cos(x+gamma)),(sin (x+alpha),si...

    Text Solution

    |