$A$ man is admitted to a hospital. He is suffering from an abnormally low body temperature,loss of appetite,and extreme thirst. His brain scan would probably show a tumour in

The work done in moving an object from the origin to a point whose position vector is $r = 3 \hat{i} + 2 \hat{j} - 5 \hat{k}$ by a force $F = 2 \hat{i} - \hat{j} - \hat{k}$ is:

Two rods of same material have same length and area. The heat $\Delta Q$ flows through them for $12 \, \text{minutes}$ when they are joined in series. If now both the rods are joined in parallel,then the same amount of heat $\Delta Q$ will flow in ........ $\text{minutes}$.

If $\vec{a} = \hat{i} - \hat{j} - \hat{k}$ and $\vec{b} = \lambda\hat{i} - 3\hat{j} + \hat{k}$ and the orthogonal projection of $\vec{b}$ on $\vec{a}$ is $\frac{4}{3}(\hat{i} - \hat{j} - \hat{k})$,then $\lambda$ is equal to:

$A$ bar magnet of magnetic moment $M$ and moment of inertia $I$ is freely suspended such that the magnetic axial line is in the direction of the magnetic meridian. If the magnet is displaced by a very small angle $\theta$,the angular acceleration is (Magnetic induction of earth's horizontal field $= B_H$)

For $a, b, h > 0$,if the slope of one of the lines represented by $a^2 x^2 + 2hxy + b^2 y^2 = 0$ is twice that of the other,then the value of $\frac{h}{ab}$ is