The Central Sugarcane Breeding Research Institute is situated at:

The position vector of a point lying on the line joining the points whose position vectors are $\hat{i}+\hat{j}-\hat{k}$ and $\hat{i}-\hat{j}+\hat{k}$ is:

$A$ piece of iron is heated in a flame. It first becomes dull red, then becomes reddish yellow, and finally turns to white hot. The correct explanation for the above observation is possible by using:

The vectors $3\,i + j - 5\,k$ and $a\,i + b\,j - 15\,k$ are collinear,if

When a big drop of water is formed from $n$ small drops of water,the energy loss is $3E$,where $E$ is the energy of the bigger drop. If $R$ is the radius of the bigger drop and $r$ is the radius of the smaller drop,then the number of smaller drops $(n)$ is:

$100 \ g$ of water is heated from $30^{\circ}C$ to $50^{\circ}C$. Neglecting the slight expansion of water,the change in its internal energy is ....... $kJ$? (Specific heat of water = $4184 \ J/kg\cdot K$)