Home
Class 12
MATHS
Let K be a positive real number and A=[(...

Let K be a positive real number and `A=[(2k-1,2sqrt(k),2sqrt(k)),(2sqrt(k),1,-2k),(-2sqrt(k),2k,-1)]` and `B=[(0,2k-1,sqrt(k)),(1-2k,0,2),(-sqrt(k),-2sqrt(k),0)]`. If det (adj A) + det (adj B) `=10^(6)`, then `[k]` is equal to ______ .
[Note : adj M denotes the adjoint of a square matrix M and `[k]` denotes the largest integer less than or equal to `k`.]

Text Solution

Verified by Experts

The correct Answer is:
4
Promotional Banner

Topper's Solved these Questions

  • MATRICES AND DETERMINANTS

    VMC MODULES ENGLISH|Exercise JEE MAIN ARCHIVE|92 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

Let K be a positive real number and A=[2k-1 2sqrt(k)2sqrt(k)2sqrt(k)1-2k-2sqrt(k)2k-1]a n dB=[0 2k-1sqrt(k)1-2k0 2-sqrt(k)-2sqrt(k)0] . If det (a d jA)+det(a d jB)=10^6,t h e n[k] is equal to. [Note: a d jM denotes the adjoint of a square matix M and [k] denotes the largest integer less than or equal to K ].

Let A=[(2,0,7),(0,1,0),(1,-2,1)] and B=[(-k,14k,7k),(0,1,0),(k,-4k,-2k)] . If AB=I , where I is an identity matrix of order 3, then the sum of all elements of matrix B is equal to

If sum_(k = 1)^(oo) (1)/((k + 2)sqrt(k) + ksqrt(k + 2)) = (sqrt(a) + sqrt(b))/(sqrt(c)) , where a, b, c in N and a,b,c in [1, 15] , then a + b + c is equal to

Find the sum of the series sum_(k=1)^(360)(1/(ksqrt(k+1)+(k+1)sqrt(k)))

Let S_(k) = (1+2+3+...+k)/(k) . If S_(1)^(2) + s_(2)^(2) +...+S_(10)^(2) = (5)/(12)A , then A is equal to

If for a matrix A, absA=6and adj A= {:[(1,-2,4),(4,1,1),(-1,k,0)]:} , then k is equal to

If one root x^2-x-k=0 is square of the other, then k= a. 2+-sqrt(5) b. 2+-sqrt(3) c. 3+-sqrt(2) d. 5+-sqrt(2)

Distance between line r=i+j+k+lambda(2i+j+4k) and plane rdot(i+2j-k)=3 is (1) 4/(sqrt(6)) (2) 5/(sqrt(6)) (3) 1/(sqrt(6)) (4) 0 (5) 2/(sqrt(6))

sqrt(2k^(2)+17)-x=0 If k gt 0 and x = 7 in the equation above, what is the value of k ?

If the value of the integral I=int_(0)^(1)(dx)/(x+sqrt(1-x^(2))) is equal to (pi)/(k) , then the value of k is equal to

VMC MODULES ENGLISH-MATRICES AND DETERMINANTS -JEE ADVANCED ARCHIVE
  1. Sum of real roots of the euation |{:(1,4,20),(1,-2,5),(1,2x,5x^(2)):}|...

    Text Solution

    |

  2. "Let "plambda^(4) + qlambda^(3) +rlambda^(2) + slambda +t =|{:(lambda^...

    Text Solution

    |

  3. Let K be a positive real number and A=[(2k-1,2sqrt(k),2sqrt(k)),(2sqrt...

    Text Solution

    |

  4. A system of equations lambdax +y +z =1,x+lambday+z=lambda, x + y + lam...

    Text Solution

    |

  5. Let M be a 3xx3 matrix satisfying M[0 1 0]=M[1-1 0]=[1 1-1],a n dM[1 1...

    Text Solution

    |

  6. Let z=(-1+sqrt(3)i)/(2), where i=sqrt(-1), and r, s in {1, 2, 3}. Let ...

    Text Solution

    |

  7. The total number of distinct x in R for which |{:(x,,x^(2),,...

    Text Solution

    |

  8. For a real number, alpha if the system [{:(,1,alpha,alpha^(2)),(,alp...

    Text Solution

    |

  9. Let P be a matrix of order 3xx3 such that all the entries in P a...

    Text Solution

    |

  10. Let a, b, and c be three real numbers satifying [(a, b, c)] [(1,9,7)...

    Text Solution

    |

  11. Let a, b, and c be three real numbers satifying [(a, b, c)] [(1,9,7)...

    Text Solution

    |

  12. Let omega be the solution of x^(3)-1=0 with "Im"(omega) gt 0. If a=2 w...

    Text Solution

    |

  13. Let P be an odd prime number and T(p) be the following set of 2xx2 mat...

    Text Solution

    |

  14. Let P be an odd prime number and T(p) be the following set of 2xx2 mat...

    Text Solution

    |

  15. Let P be an odd prime number and T(p) be the following set of 2xx2 mat...

    Text Solution

    |

  16. If M is a 3xx3 matrix, where det M=1a n dM M^T=1,w h e r eI is an iden...

    Text Solution

    |

  17. Given a matrix A=[a b c b c a c a b],w h e r ea ,b ,c are real positiv...

    Text Solution

    |

  18. Let a,b,c be real numbers with a^(2) +b^(2) +c^(2)=1. Then show tha...

    Text Solution

    |

  19. The value of the determinant |(sintheta, costheta, sin2theta) , (sin(t...

    Text Solution

    |

  20. Suppose f(x) is a function satisfying the following conditions: f(0)=...

    Text Solution

    |