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Physics
A uniform bar of length 6a and mass 8m lies on a smooth horizontal table. Two-point masses m and 2m moving in the same horizontal plane with speed 2v and v, respectively, strike the bar (as shown in the figure) and stick to the bar after collision. Denoting angular velocity (about the center of mass), total energy and center of mass velocity by , E and V_c respectively, we have after collision
Chemistry
We have taken a saturated solution of AgBr. K_sp of AgBr is 12x10^-14. If 10^-7 mole of AgNO₃ are added to 1 liter of this solution find conductivity (specified conductance) of this solution in terms of 10^-7 S/m units. Given, Molar conductance of Ag⁺, Br^-, and NO₃^- are 6x10^-3Sm²mol^-1, 8x10^-3Sm²mol^-1 and 7x10^-3Sm²mol^-1.

Mathematics
Let n and k be positive integers such that . The number of solutions (x₁, x₂, ………., x_k), all integers, satisfying x₁ + x₂ +……….+ x_k = n is …………….