Write the equation for the relationship between specific conductivity (\( \sigma \)) and drift velocity (\( v_d \)).
Compare the Astronomical Telescope and Compound Microscope on the basis of the following:
(i) Components
(ii)Magnifying power
Explain with reason whether any one of the above devices can be used as the other device.
(i) Components
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 $