Orange light of wavelength  $6000\times {10}^{–10} \mathrm{m}$ illuminates a single slit of width $0.6\times {10}^{–4} \mathrm{m}$. The maximum possible number of diffraction minima produced on both sides of the central maximum is __________

Two coherent sources of sound, $S_1$ and $S_2,$ produce sound waves of the same wavelength $\lambda =1 \mathrm{m}$ are in phase. $S_1$ and $S_2$ are placed $1.5 \mathrm{m}$ apart (see fig). A listener, located at $\mathrm{L}$, directly in front of $S_2$, finds that the intensity is at a minimum when he is $2 \mathrm{m}$ away from $S_2$. The listener moves away from $S_1$, keeping the distance from $S_2$ fixed. The adjacent maximum of intensity is observed when the listener is at a distance $d$ from $S_1$. Then $d$ is :

In the figure below, $P$ and $Q$ are two equally intense coherent sources emitting radiation of wavelength $20\mathrm{m}.$ The separation between $\mathrm{P}$ and $\mathrm{Q}$ is $5\mathrm{m}$ and the phase of $\mathrm{P}$ is ahead of that of $\mathrm{Q}$ by $90°.\mathrm{A},\mathrm{B}$ and C are three distinct point of observation, each equidistant from the midpoint of PQ. The intensities of radiation at $\mathrm{A},\mathrm{B},\mathrm{C}$ will be in the ratio :