Let a, $$\lambda$$, m $$\in$$ R. Consider the system of linear equations

ax + 2y = $$\lambda$$

3x $$-$$ 2y = $$\mu$$

Which of the following statements is(are) correct?

A block with mass M is connected by a massless spring with stiffness constant k to a rigid wall and moves without friction on a horizontal surface. The block oscillates with small amplitude A about an equilibrium position x₀. Consider two cases:
(i) when the block is at x₀; and
(ii) when the block is at x = x₀ + A.
In both cases, a particle with mass m( < M) is softly placed on the block after which they stick on each other. Which of the following statement(s) is(are) true about the motion after the mass m is placed on the mass M?

The ends Q and R of two thin wires, PQ and RS, are soldered (joined) together. Initially each of the wires has a length of 1 m at 10^oC. Now the end P is maintained at 10^oC, while the end S is heated and maintained at 400^oC. The system is thermally insulated from its surroundings. If the thermal conductivity of wire PQ is twice that of the wire RS and the coefficient of linear thermal expansion of PQ is 1.2 $$ \times $$ 10^-5 K^-1 , the change in length of the wire PQ is