The engine of a train moving with speed $$10 \mathrm{~ms}^{-1}$$ towards a platform sounds a whistle at frequency $$400 \mathrm{~Hz}$$. The frequency heard by a passenger inside the train is: (neglect air speed. Speed of sound in air $$=330 \mathrm{~ms}^{-1}$$ )

Two forces having magnitude $$A$$ and $$\frac{A}{2}$$ are perpendicular to each other. The magnitude of their resultant is:

At any instant the velocity of a particle of mass $$500 \mathrm{~g}$$ is $$\left(2 t \hat{i}+3 t^{2} \hat{j}\right) \mathrm{ms}^{-1}$$. If the force acting on the particle at $$t=1 \mathrm{~s}$$ is $$(\hat{i}+x \hat{j}) \mathrm{N}$$. Then the value of $$x$$ will be:

A cylindrical wire of mass $$(0.4 \pm 0.01) \mathrm{g}$$ has length $$(8 \pm 0.04) \mathrm{cm}$$ and radius $$(6 \pm 0.03) \mathrm{mm}$$. The maximum error in its density will be: