Step 1: Carefully observe the arrangement of the broken plate in Figure A. It consists of six pieces, but only five are placed. The missing piece must complete the overall structure.
Step 2: Analyze the shape and design of the missing portion. The curvature and pattern on the plate must align perfectly with the given options (\( P, Q, R, S \)).
Step 3: Compare each of the given choices with the missing space. Piece \( R \) matches the missing section precisely, both in terms of design continuity and shape. Thus, the correct answer is option C (\( R \)).
Let $ a_0, a_1, ..., a_{23} $ be real numbers such that $$ \left(1 + \frac{2}{5}x \right)^{23} = \sum_{i=0}^{23} a_i x^i $$ for every real number $ x $. Let $ a_r $ be the largest among the numbers $ a_j $ for $ 0 \leq j \leq 23 $. Then the value of $ r $ is ________.
A temperature difference can generate e.m.f. in some materials. Let $ S $ be the e.m.f. produced per unit temperature difference between the ends of a wire, $ \sigma $ the electrical conductivity and $ \kappa $ the thermal conductivity of the material of the wire. Taking $ M, L, T, I $ and $ K $ as dimensions of mass, length, time, current and temperature, respectively, the dimensional formula of the quantity $ Z = \frac{S^2 \sigma}{\kappa} $ is: