We know:
\[ W_{\text{ext}} = \Delta U + \Delta KE \quad (\text{P.E.} = -\vec{M} \cdot \vec{B}) \]
\[ = -MB \cos 90^\circ + MB \cos 0^\circ \]
\[ W_{\text{ext}} = MB \]
\[ = NIAB \]
\[ = 200 \times 100 \times 10^{-6} \times 2.5 \times 10^{-4} \times 1 = 5 \, \mu\text{J} \]
Let \( y = f(x) \) be the solution of the differential equation
\[ \frac{dy}{dx} + 3y \tan^2 x + 3y = \sec^2 x \]
such that \( f(0) = \frac{e^3}{3} + 1 \), then \( f\left( \frac{\pi}{4} \right) \) is equal to:
Find the IUPAC name of the compound.
If \( \lim_{x \to 0} \left( \frac{\tan x}{x} \right)^{\frac{1}{x^2}} = p \), then \( 96 \ln p \) is: 32