The graphical solution set for the system of inequations $$x-2 y \leq 2,5 x+2 y \geq 10,4 x+5 y \leq 20, x \geq 0, y \geq 0$$ is given by

Let $$\mathrm{f}(0)=-3$$ and $$\mathrm{f}^{\prime}(x) \leq 5$$ for all real values of $$x$$. The $$\mathrm{f}(2)$$ can have possible maximum value as

Light of wavelength ',$$\lambda$$' is incident on a slit of width '$$\mathrm{d}$$'. The resulting diffraction pattern is observed on a screen at a distance '$$D$$'. The linear width of the principal maximum is then equal to the width of the slit if $$D$$ equals

Two S.H.Ms. are represented by equations $$\mathrm{y}_1=0.1 \sin \left(100 \pi \mathrm{t}+\frac{\pi}{3}\right)$$ and $$\mathrm{y}_2=0.1 \cos (100 \pi \mathrm{t})$$ The phase difference between the speeds of the two particles is