[" c."P_(3)>P_(1),W<0],[" An ideal gas "(gamma=1.5)" is expanded adiabatically.How "],[" many times has the gas to be expanded to reduce the "],[" root-mean-square velocity of molecules becomes half "],[" a."4" times "],[" c."8" times "]

Let C be a circle with centre P_(0) and AB be a diameter of C . suppose P_(1) is the midpoint of line segment P_(0) B, P_(2) the midpoint of line segment P_(1) B and so on Let C_(1),C_(2) ,C_(3) be circles with diameters P_(0)P_(1), P_(1)P_(2),P_(2)P_(3) ,... respectively Suppose the circles C_(1),C_(2),C_(2), ... are all shaded The ratio of the area of the unshaded portion of C to that of the original circle is

If the number of positive integral solutions of u+v+w=n be denoted by P_(n) then the absolute value of |{:(P_(n),P_(n+1),P_(n+2)),(P_(n+1),P_(n+2),P_(n+3)),(P_(n+2),P_(n+3),P_(n+4)):}| is

If the number of positive integral solutions of u+v+w=n be denoted by P_(n) then the absolute value of |{:(P_(n),P_(n+1),P_(n+2)),(P_(n+1),P_(n+2),P_(n+3)),(P_(n+2),P_(n+3),P_(n+4)):}| is

If the number of positive integral solutions of u+v+w=n be denoted by P_(n) then the absolute value of |{:(P_(n),P_(n+1),P_(n+2)),(P_(n+1),P_(n+2),P_(n+3)),(P_(n+2),P_(n+3),P_(n+4)):}| is

An inductance L , a cpacitance C and a resistance R may be connected to an AC souorce of angular frequency omega in three different combinations of RC, RL and LC in series. Assume that omegaL=1/(omegaC) . The power drawn by the three combinatios are P_(1), P_(2), P_(3) respectively. THen