A balloon filled with helium (32^oC and 1.7 atm.) bursts. Immediately afterwards the expansion of helium can be considered as

Pressure inside two soap bubbles are 1.01 and 1.02 atmosphere, respectively. The ratio of their volumes is :

A 750 Hz, 20 V (rms) source is connected to a resistance of 100 $$\Omega $$, an inductance of 0.1803 H and a capacitance of 10 $$\mu $$F all in series. The time in which the resistance (heat capacity 2 J/^oC) will get heated by 10^oC. (assume no loss of heat to the surroudnings) is close to :

A charged particle carrying charge 1 $$\mu $$C is moving
with velocity $$\left( {2\widehat i + 3\widehat j + 4\widehat k} \right)$$ ms^–1. If an external
magnetic field of $$\left( {5\widehat i + 3\widehat j - 6\widehat k} \right)$$× 10^–3 T exists in the region where the particle is moving then the
force on the particle is $$\overrightarrow F $$ × 10^–9 N. The vector $$\overrightarrow F $$ is :