Questions

L.C.M. of 252, 308 and 198 = 2772.

So, A, B and C will again meet at the starting point in 2772 sec. i.e., 46 min. 12 sec.

Let the required number be 'X'

Condition 1 :  

$$\begin{gathered} XX = 2X \\ => 2X2 = X \\ => X = 12 \end{gathered}$$

Condition 2 :

$$\begin{gathered} X × X = X2 \\ => X = 12 \end{gathered}$$

Therefore, 12 is the number which becomes double when it is divided by itself and becomes half when it is multiplied by itself.

The Von Hippel Award, the Materials Research Society's highest honor, recognizes those qualities most prized by materials scientists and engineers—brilliance and originality of intellect, combined with vision that transcends the boundaries of conventional scientific disciplines. The Von Hippel Award is named after Arthur von Hippel (1898-2003), who was a pioneer in the study of dielectrics, semiconductors, ferromagnetics and ferroelectrics.

Eminent Scientist and Bharat Ratna Prof C.N.R. Rao was awarded 2017 Von Hippel Award. He is first Indian and first Asian to win this honour. The award will be presented to Prof Rao for his interdisciplinary contributions to development of novel functional materials, including nanomaterials, graphene, superconductivity, 2D materials and colossal magnetoresistance at Boston in November 2017.