Two simple pendulums whose lengths are $1\,m$ and $121\,cm$ are suspended side by side. Their bobs are pulled together and then released. After how many minimum oscillations of the longer pendulum will the two be in phase again?

In an industrial process,$10\, kg$ of water per hour is to be heated from $20^\circ C$ to $80^\circ C$. To do this,steam at $200^\circ C$ is passed from a boiler into a copper coil immersed in water. The steam condenses in the coil and is returned to the boiler as water at $90^\circ C$. How many $kg$ of steam is required per hour? (Specific heat of steam $= 0.5\, cal/g^\circ C$,Latent heat of vaporisation $= 540\, cal/g$,Specific heat of water $= 1\, cal/g^\circ C$)

Which of the following metals will react with water?

$\sqrt{10 - \sqrt{24} - \sqrt{40} + \sqrt{60}} = ?$

Which one of the following pairs is incorrectly matched?

The half-lives of two radioactive nuclides $A$ and $B$ are $1 \ min$ and $2 \ min$ respectively. Equal weights of $A$ and $B$ are taken separately and allowed to disintegrate for $4 \ min$. What will be the ratio of weights of $A$ and $B$ disintegrated?