Raju, Sohan, and Tina are partners in a firm sharing profits and losses in the ratio of 2 : 2 : 1. Tina is guaranteed a minimum amount of ₹40,000 as a share of profit every year. Any deficiency arising on that account shall be borne by Raju. If profit of the firm for the year ended 31st March, 2023 is ₹1,60,000, Raju will bear a deficiency of:
Step 1: Calculate Tina's profit share. \[ \text{Tina's share of profit} = \frac{1}{5} \times 1,60,000 = ₹32,000. \] Step 2: Determine the deficiency. \[ \text{Deficiency} = ₹40,000 - ₹32,000 = ₹8,000. \] Since Raju is responsible for the deficiency, he will bear ₹8,000.
Draw a rough sketch for the curve $y = 2 + |x + 1|$. Using integration, find the area of the region bounded by the curve $y = 2 + |x + 1|$, $x = -4$, $x = 3$, and $y = 0$.
A school is organizing a debate competition with participants as speakers and judges. $ S = \{S_1, S_2, S_3, S_4\} $ where $ S = \{S_1, S_2, S_3, S_4\} $ represents the set of speakers. The judges are represented by the set: $ J = \{J_1, J_2, J_3\} $ where $ J = \{J_1, J_2, J_3\} $ represents the set of judges. Each speaker can be assigned only one judge. Let $ R $ be a relation from set $ S $ to $ J $ defined as: $ R = \{(x, y) : \text{speaker } x \text{ is judged by judge } y, x \in S, y \in J\} $.