A thin rod of mass 0.9 kg and length 1 m is suspended, at rest, from one end so that it can freely oscillate in the vertical plane. A particle of move 0.1 kg moving in a straight line with velocity 80 m/s hits the rod at its bottom most point and sticks to it (see figure). The angular speed (in rad/s) of the rod immediately after the collision will be _________.

In the circuit, given in the figure currents in different branches and value of one resistor are shown. Then potential at point B with respect to the point A is :

Two Zener diodes (A and B) having breakdown voltages of 6 V and 4 V respectively, are connected as shown in the circuit below. The output voltage V₀ variation with input voltage linearly increasing with time, is given by :
(V_input = 0 V at t = 0)
(figures are qualitative)

Two different wires having lengths L₁ and L₂, and respective temperature coefficient of linear expansion $$\alpha $$₁ and $$\alpha $$₂, are joined end-to-end. Then the effective temperature coefficient of linear expansion is :