The disease known as fluorosis is caused by the reaction of fluorine with which of the following?

$A$ solution of urea (molar mass $60 \ g \ mol^{-1}$) boils at $100.18 \ ^oC$ at atmospheric pressure. If $K_f$ and $K_b$ for water are $1.86$ and $0.512 \ K \ kg \ mol^{-1}$ respectively,the above solution will freeze at ......... $^oC$.

$A$ 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 $= B_H$)

The complete set of values of $x$ for which the function $f(x) = 2 \ln(x-2) - x^2 + 4x + 1$ is increasing is:

The acceleration due to gravity on the moon is $\left(\frac{1}{6}\right)$ times the acceleration due to gravity on the earth. If the ratio of the density of the earth $\rho_{e}$ to the density of the moon $\rho_{m}$ is $\frac{5}{3}$,then the radius of the moon $R_{m}$ in terms of the radius of the earth $R_{e}$ is:

What is the maximum number of rectangular components into which a vector can be split in space?