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The plots of (1)/(X_(A))vs.(1)/(Y_(A)) (where X_(A) and Y_(A) are the mole fraction of liquid A in liquid and vapour phase respectively) is linear with slope and intercept respectively are given as: (a) (P_A^(@))/(P_B^(@)),(P_B^(@)-P_A^(@))/(P_B^(@)) (b) (P_B^(@))/(P_A^(@)),(P_A^(@)-P_B^(@))/(P_A^(@)) (c) (P_B^(@))/(P_A^(@)),(P_B^(@))/(P_B^@-P_A^(@)) (d) P_A^(@)-P_B^(@),(P_A^(@))/(P_B^(@))

Assertion : Two identical bulbs when connected across a battery, produce a total power P. When they are connected across the same battery in series total power consumed will be (P)/(4) . Reason : In parallel, P=P_(1)+P_(2) and in series P=(P_(1)P_(2))/(P_(1)+P_(2))

For any tow events A and B in a sample space, (a) P(A//B)geq(P(A)+P(B)-1)/(P(B))(P(B)!=0) is always true (b) P(Ann B )=1-P(A)-P(AnnB) does not hold (c) P(AuuB)=1-P( A )P( B ),if A and B are independent (d) P(AuuB)=1-P(A)P(B),if A and B are disjoint

Tangent at a point P_1 [other than (0,0)] on the curve y=x^3 meets the curve again at P_2. The tangent at P_2 meets the curve at P_3 & so on. Show that the abscissae of P_1, P_2, P_3, ......... P_n, form a GP. Also find the ratio area of A(P_1 P_2 P_3.) area of Delta (P_2 P_3 P_4)