Center of Mass Momentum a question bank (Physics)

On a friction-less surface, a block of mass M moving at speed $v$ collides elastically with another block (of mass M) initially at rest. After collision, the first block moves at an angle $\theta$ to its initial direction and has speed $\dfrac{v}{3}$. The speed of the second block after collision is

A particle 'A' of mass ' 2m' and having initial velocity $'u_A'$ collides with particle B of mass ' m / 2' at rest. The collision is head on and elastic. If $\lambda_A$ and $\lambda_B$ are the de-Broglie wavelength of the particles 'A' and 'B' after collision, such that $\lambda_A = x\,\lambda_B$. The value of $x$ is