For a given series LCR circuit it is found that maximum current is drawn when value of variable capacitance is $$2.5 \mathrm{~nF}$$. If resistance of $$200 \Omega$$ and $$100 \mathrm{~mH}$$ inductor is being used in the given circuit. The frequency of ac source is _________ $$\times 10^3 \mathrm{~Hz}$$ (given $$\mathrm{a}^2=10$$)

Three balls of masses $$2 \mathrm{~kg}, 4 \mathrm{~kg}$$ and $$6 \mathrm{~kg}$$ respectively are arranged at centre of the edges of an equilateral triangle of side $$2 \mathrm{~m}$$. The moment of inertia of the system about an axis through the centroid and perpendicular to the plane of triangle, will be ________ $$\mathrm{kg} \mathrm{~m}^2$$.

In the given figure an ammeter A consists of a $$240 \Omega$$ coil connected in parallel to a $$10 \Omega$$ shunt. The reading of the ammeter is ________ $$\mathrm{mA}$$.

A coil having 100 turns, area of $$5 \times 10^{-3} \mathrm{~m}^2$$, carrying current of $$1 \mathrm{~mA}$$ is placed in uniform magnetic field of $$0.20 \mathrm{~T}$$ such a way that plane of coil is perpendicular to the magnetic field. The work done in turning the coil through $$90^{\circ}$$ is _________ $$\mu \mathrm{J}$$.