Home
Class 12
MATHS
Let A=[(2,b,1),(b,b^(2)+1,b),(1,b,2)] wh...

Let `A=[(2,b,1),(b,b^(2)+1,b),(1,b,2)]` where `b gt 0`. Then the minimum value of `("det.(A)")/(b)` is

A

`-sqrt3`

B

`-2sqrt3`

C

`2sqrt3`

D

`sqrt3`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • MATRICES AND DETERMINANTS

    VMC MODULES ENGLISH|Exercise JEE ADVANCED ARCHIVE|78 Videos
  • MATRICES AND DETERMINANTS

    VMC MODULES ENGLISH|Exercise Numerical ValueType for JEE Main|15 Videos
  • JEE MAIN REVISON TEST-23

    VMC MODULES ENGLISH|Exercise MATHEMATICS (SECTION 2)|5 Videos
  • MOCK TEST 1

    VMC MODULES ENGLISH|Exercise PART III : MATHEMATICS (SECTION-2)|10 Videos

Similar Questions

Explore conceptually related problems

If a > 1, b > 1, then the minimum value of log_b a + log_a b is

Let ab=1,Delta=|{:(1+a^2-b^2, 2ab,-2b),(2ab,1-a^2+b^2, 2a),(2b,-2a,1-a^2-b^2):}| then the minimum value of Delta is :

If A=[{:(2,3),(-1,-2):}] and B=sum_(r=1)^(10)A^r , then the value of det (B)is equal to

The minimum possible distnace between the points A(a, a-1) and B(b, b^(2)+b+1)AA a, b in R is D units, then the value of D^(2) is

Let f(x)=(1+b^2)x^2+2b x+1 and let m(b) be the minimum value of f(x)dot As b varies, the range of m(b) is (a) [0,} b. (0,1/2) c. 1/2,1 d. (0,1]

lim_(x to 0) (1+ax)^(b/x) =e^(2) , " where" a, b in N such that a+ b = 3 , then the value of (a,b) is

Let f(x)=(1+b^2)x^2+2b x+1 and let m(b) the minimum value of f(x) as b varies, the range of m(b) is (A) [0,1] (B) (0,1/2] (C) [1/2,1] (D) (0,1]

Let a ,b >0, let 5a-b ,2a+b ,a+2b be in A.P. and (b+1)^2, a b+1,(a-1)^2 are in G.P., then the value of (a^(-1)+b^(-1)) is _______.

Let a ,b >0, let 5a-b ,2a+b ,a+2b be in A.P. and (b+1)^2, a b+1,(a-1)^2 are in G.P., then the value of (a^(-1)+b^(-1)) is _______.

If a and b are positive integers satisfying (a+3)^(2)+(b+1)^(2)=85 , what is the minimum value of (2a+b)?

VMC MODULES ENGLISH-MATRICES AND DETERMINANTS -JEE MAIN ARCHIVE
  1. |(a-b-c,2a,2a),(2b,b-c-a,2b),(2c,2c,c-a-b)|

    Text Solution

    |

  2. Let a(1),a(2),a(3), …, a(10) be in G.P. with a(i) gt 0 for i=1, 2, …, ...

    Text Solution

    |

  3. Let A=[(2,b,1),(b,b^(2)+1,b),(1,b,2)] where b gt 0. Then the minimum v...

    Text Solution

    |

  4. Let d in R, and A[{:(,-2,4+d,(sin theta-2)),(,1,(sin theta)+2,d),(,5,(...

    Text Solution

    |

  5. If B = [{:(5, 2alpha, 1),(0, 2, 1),(alpha, 3, -1):}] is the inver...

    Text Solution

    |

  6. Matrix=[[e^t,e^-t(sint-2cost),e^-t(-2sint-cost)],[e^t,-e^-t(2sint+cost...

    Text Solution

    |

  7. Let A and B be two invertible matrices of order 3xx3. If det. (ABA^(T)...

    Text Solution

    |

  8. If A = [(costheta,-sintheta),(sintheta,costheta)], then the matrix A^(...

    Text Solution

    |

  9. If [x] denotes the greatest integer le x, then the system of liner equ...

    Text Solution

    |

  10. Let lambda be a real number for which the system of linear equations ...

    Text Solution

    |

  11. If the system of linear equation x+y+z=5, x+2y+2z = 6, x+3y + lambda z...

    Text Solution

    |

  12. If the system of equations, 2x + 3y-z = 0, x + ky -2z = 0 " and " 2x-y...

    Text Solution

    |

  13. If the system of linear equations x-2y + kz = 1, 2x + y+ z = 2, 3x-y...

    Text Solution

    |

  14. The greatest value of for which the system of linear equations x-c...

    Text Solution

    |

  15. The set of all values of lambda for which the system of linear equatio...

    Text Solution

    |

  16. An ordered pair (alpha, beta) for which the system of linear equations...

    Text Solution

    |

  17. If the system of linear equations 2x+2y+3z=a 3x-y+5z=b x-3y+2z=...

    Text Solution

    |

  18. The number of possible value of theta lies in (0,pi), such that system...

    Text Solution

    |

  19. If the system of linear equations x-4y+7z=g, 3y-5z=h, -2x+5y-9z=k is c...

    Text Solution

    |

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

    Text Solution

    |