Sudha and Sudhir were partners in a firm sharing profits and losses in the ratio of 4 : 1. On 1st April, 2023, their fixed capitals were ₹12,00,000 and ₹4,00,000 respectively. On 1st July, 2023, Sudha invested ₹2,00,000 as additional capital. On 1st August, 2023, Sudhir withdrew ₹50,000 from his capital.
The partnership deed provided for the following:
(i) Interest on capital @ 6% p.a.
(ii) Interest on drawings @ 8% p.a.
During the year, Sudha withdrew ₹60,000 and Sudhir withdrew ₹40,000 for personal use. After providing interest on capital and charging interest on drawings, the net profit of the firm for the year ended 31st March, 2024 was ₹3,50,000.
Prepare Current Accounts of Sudha and Sudhir.
Two batteries of emf's \(3V \& 6V\) and internal resistances 0.2 Ω \(\&\) 0.4 Ω are connected in parallel. This combination is connected to a 4 Ω resistor. Find:
(i) the equivalent emf of the combination
(ii) the equivalent internal resistance of the combination
(iii) the current drawn from the combination
Four students of class XII are given a problem to solve independently. Their respective chances of solving the problem are: \[ \frac{1}{2},\quad \frac{1}{3},\quad \frac{2}{3},\quad \frac{1}{5} \] Find the probability that at most one of them will solve the problem.