\( 5^8 \)
\( 3^8 \)
The determinant of A is:
$|A| = \begin{vmatrix} K & 4 \\ 4 & K \end{vmatrix} = K \cdot K - 4 \cdot 4 = K^2 - 16.$
Using the property of determinants:
$|A|^3 = (|A|)^3 = 729.$
Take the cube root:
$|A| = \sqrt[3]{729} = 9.$
Thus:
$K^2 - 16 = 9 \implies K^2 = 25.$
Therefore:
$K = \pm 5.$
The value of $K^8$ is:
$K^8 = (K^2)^4 = 25^4.$
Calculate:
$25^4 = (25^2)^2 = 625^2 = 390625.$
Final Answer:
$5^8$
List-I (Name of account to be debited or credited, when shares are forfeited) | List-II (Amount to be debited or credited) |
---|---|
(A) Share Capital Account | (I) Debited with amount not received |
(B) Share Forfeited Account | (II) Credited with amount not received |
(C) Calls-in-arrears Account | (III) Credited with amount received towards share capital |
(D) Securities Premium Account | (IV) Debited with amount called up |