In a Brazilian test, the front view of a homogeneous rock sample is shown in the figure. The failure initiates at the point, where the rock sample is subjected to stress. The failure initiates at the point marked as:
In a bord and pillar panel, a square pillar of size 35 m \( \times \) 35 m (centre to centre) is extracted to form four equal square-shaped stooks as shown. The width of each gallery and crosscut is 5 m. The height of the working seam is 3 m. The reduction in safety factor after pillar splitting by using Bieniawski’s pillar strength formula, in %, is _______ (rounded off to 2 decimal places).
Bieniawski's pillar strength formula is given by \( S_p = S_1 \left( 0.64 + 0.36 \frac{w}{h} \right) \), where \( S_1 \) is the strength of a 0.9 m\(^3\) coal block, \( w \) is the pillar width, and \( h \) is the mining height.
Three villages P, Q, and R are located in such a way that the distance PQ = 13 km, QR = 14 km, and RP = 15 km, as shown in the figure. A straight road joins Q and R. It is proposed to connect P to this road QR by constructing another road. What is the minimum possible length (in km) of this connecting road?
Note: The figure shown is representative.
For the clock shown in the figure, if
O = O Q S Z P R T, and
X = X Z P W Y O Q,
then which one among the given options is most appropriate for P?
“His life was divided between the books, his friends, and long walks. A solitary man, he worked at all hours without much method, and probably courted his fatal illness in this way. To his own name there is not much to show; but such was his liberality that he was continually helping others, and fruits of his erudition are widely scattered, and have gone to increase many a comparative stranger’s reputation.” (From E.V. Lucas’s “A Funeral”)
Based only on the information provided in the above passage, which one of the following statements is true?