List-I (Types of Hospitality Establishment) | List-II (Example) |
(A) Hotel | (I) Offers range of amenities, sports facilities and leisure activities |
(B) Lodge | (II) Hospitality to people undertaking adventure sports, etc. |
(C) Resort | (III) Offers lodging, meals |
(D) Furnished camps | (IV) Offers rented accommodation especially for sleeping but may not offer food |
Find the values of \( x, y, z \) if the matrix \( A \) satisfies the equation \( A^T A = I \), where
\[ A = \begin{bmatrix} 0 & 2y & z \\ x & y & -z \\ x & -y & z \end{bmatrix} \]
(b) Order of the differential equation: $ 5x^3 \frac{d^3y}{dx^3} - 3\left(\frac{dy}{dx}\right)^2 + \left(\frac{d^2y}{dx^2}\right)^4 + y = 0 $