For incoherent waves:
\[ I_1 = I_A + I_B = I_0 + 9I_0 = 10I_0 \]For coherent waves:
\[ I_2 = I_A + I_B + 2\sqrt{I_A I_B} \cos 60^\circ \] \[ I_2 = I_0 + 9I_0 + 2\sqrt{I_0 \times 9I_0} \cdot \frac{1}{2} = 13I_0 \]Given:
\[ \frac{I_1}{I_2} = \frac{10}{13} \]Thus:
\[ x = 13 \]A sub-atomic particle of mass \( 10^{-30} \) kg is moving with a velocity of \( 2.21 \times 10^6 \) m/s. Under the matter wave consideration, the particle will behave closely like (h = \( 6.63 \times 10^{-34} \) J.s)
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