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 `K`be a positive real number and`A=[2k-1 2sqrt(k)2sqrt(k)2sqrt(k)1

1.	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`].
Answer» Correct Answer - D `abs(A) = (2k-1)(-1+4k^(2))+ 2sqrt(k) (2sqrt(k)+4ksqrt(k))` `+ 2 sqrt(k)(4ksqrt(k)+2sqrt(k)) (2k-1) (4k^(2)-1)` `+ 4k + 8k^(2) + 8k^(2) + 4k` `=(2k-1)(4k^(2)-1)+8k+16k^(2)` `= 8k^(3) - 4k^(2)-2k + 1 + 8k + 16k^(2)` `=8k^(3) + 12k^(2) + 6k +1` `abs(B) = 0 ` is skew-symmetric matrix of odd order. `rArr (8k^(3) + 12k^(2) + 6k+1)^(2) = (10^(3))^(2)` `rArr (2k+1)^(3) = 10^(3)` `rArr 2k +1 =10` `rArr k = 4.5` `rArr [k] = 4`

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