Home
Class 12
MATHS
If A=[(alpha,2),(2,alpha)] and determin...

If `A=[(alpha,2),(2,alpha)]` and determinant `(A^3)=125,` then the value of `alpha` is (a) `+-1` (b) `+-2` (c) `+-3` (d) `+-5`

A

`+- 1`

B

`+- 2`

C

`+- 3`

D

`+- 5`

Text Solution

Verified by Experts

The correct Answer is:
C
`A=[{:(alpha,2),(2,alpha):}],det(A^(3))=125`
`|A^(3)|=125 rArr |A|=5`
`therefore alpha2-4=5 rArr alpah^(2)=9 rArr alpha = +- 3`
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRATION

    NDA PREVIOUS YEARS|Exercise MCQ|59 Videos

  • PAIR OF STRAIGHT LINES

    NDA PREVIOUS YEARS|Exercise Example|12 Videos

Similar Questions

Explore conceptually related problems

if A=[{:(alpha,2),(2, alpha):}] and |A^(3)|=125 then the value of alpha is

If A = [{:( alpha , 2),( 2,alpha ) :}] and |A^(3) | = 125 then the value of alpha is

If A=[(alpha , 2),(2,alpha)] and |A^3|=125 , then the value of alpha is :

If A=[alpha2 2alpha]a n d|A^3|=125 , then the value of alpha is a.+-1 b. +-2 c. +-3 d. +-5

If alpha^(2)=5 alpha-3 beta^(2)=5 beta-3 then the value of (alpha)/(beta)+(beta)/(alpha) is

If the ratio of the roots of the equation,x^(2)+alpha x+alpha+2=0 is equal to 2, then the value of alpha is: (3)/(2)(b)-(3)/(2)(c)-6 (d) 6

If the ratio of the roots of the equation,x^(2)+alpha x+alpha+2=0 is equal to 2, then the value of alpha is: 3/2 b.-3/2 c.-6 d.6

If 1+sin^(2)alpha=3sin alpha cos alpha , then values of cot alpha are (a) -1,1, (b) 0,1, (c) 1,2, (1) -1,1

NDA PREVIOUS YEARS-MATRICES & DETERMINANTS-MQS
  1. For the system of linear equations 2x+3y+5z=9, 7x+3y-2z=8 and 2x+3y+l...

    Text Solution

    |

  2. For the system of linear equations 2x+3y+5z=9, 7x+3y-2z=8 and 2x+3y+l...

    Text Solution

    |

  3. If A=[(alpha,2),(2,alpha)] and determinant (A^3)=125, then the value ...

    Text Solution

    |

  4. If B is a non-singular matrix and A is a square matrix, then det (B^(-...

    Text Solution

    |

  5. If a != b != c, are value of x which satisfies the equation |(0,x -a...

    Text Solution

    |

  6. If A=[cosalphasinalpha-sinalphacosalpha] , then verify that A^T\ A=I2 ...

    Text Solution

    |

  7. For the system of equaltions : x+2y+3z=1 2x+y+3z=2 5x+5y+9z=4

    Text Solution

    |

  8. A=[{:(x+y," "y),(" "x,x-y):}],B=[{:(3),(-2):}]and C=[{:(4),(-2):}]. If...

    Text Solution

    |

  9. What is the value of the determinant |{:(1," "1," "1),(1,1+xyz," "1),(...

    Text Solution

    |

  10. If |{:(x,y,0),(0,x,y),(y,0,x):}|=0, then which one of the following is...

    Text Solution

    |

  11. Consider the set A of all determinants of order 3 with entries 0 or 1 ...

    Text Solution

    |

  12. If A = [{:(cos theta,sin theta),(-sin theta,cos theta):}] then what is...

    Text Solution

    |

  13. What is the order of the product [x" "y" "z][{:(a,h,g),(h,b,f),(g,f,c)...

    Text Solution

    |

  14. if A=[{:(0,1),(1,0):}],"then"A^(4)=?

    Text Solution

    |

  15. The matrix A has x rows and (x+5) column. If the matrix B has y rows a...

    Text Solution

    |

  16. If A is a square matrix, then what is adj A^(T) - (adj A)^(T) equal to...

    Text Solution

    |

  17. The value of the determinant |{:("cos"^(2)(theta)/(2),"sin"^(2)(theta)...

    Text Solution

    |

  18. If a, b, c are non-zero real numbers, then the inverse of the matrix A...

    Text Solution

    |

  19. The system of equation kx+y+z=1, x +ky+z=k and x+y+kz=k^(2) has no sol...

    Text Solution

    |

  20. The value of the determinant |{:(1-alpha,alpha-alpha^(2),alpha^(@)),(1...

    Text Solution

    |