AIPMT 2011 Mains Mock Test

A galvanometer of resistance $G$ is shunted by a resistance $S$ ohm. To keep the main current in the circuit unchanged, the resistance to be put in series with the galvanometer is:

A particle covers half of its total distance with speed $v_1$ and the rest half distance with speed $v_2$. Its average speed during the complete journey is:

A thermocouple of negligible resistance produces an $e.m.f.$ of $40\mu {\text{V/}}^{\circ }\text{C}$ in the linear range. A galvanometer of resistance $10\Omega$ with sensitivity $1\mu \text{A/div}$ is used. The smallest temperature difference detectable is:

A mass $m$ moving with velocity $v$ (along $x$ -axis) collides and sticks to a mass $3m$ moving with velocity $2v$ (along $y$ -axis). The final velocity of the combination is:

A converging beam of rays incident on a diverging lens intersects at $15\text{cm}$ on the opposite side. If the lens is removed, they meet $5\text{cm}$ closer. The focal length is: