Step 1: Observe the word "ARCH" in Figure B. Four circular cutouts have been made within the letters. These cutouts contain unique sections of the letters.
Step 2: Compare the cutouts from Figure B with the given options (\( P, Q, R, S \)). The correct group should exactly match the missing sections in terms of alignment, shape, and letter strokes.
Step 3: After careful observation, the group labeled \( R \) contains the four exact cutouts extracted from "ARCH". The patterns within the circles align with the letter fragments in Figure B. 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: