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Match each differential equation in Group I to its family of solution curves from Group II.
Group I
P. dy/dx = y/x
Q. dy/dx = -y/x
R. dy/dx = x/y
S. dy/dx = -x/y
Group II
1. Circles
2. Straight lines
3. Hyperbolas
- P-2, Q-3, R-3, S-1
- P-1, Q-3, R-2, S-1
- P-2, Q-1, R-3, S-3
- P-3, Q-2, R-1, S-2
Correct answer: P-2, Q-3, R-3, S-1
Solution
The correct option matches each differential equation to its corresponding family of solution curves based on their forms. For example, P represents a linear relationship leading to straight lines, while Q describes a negative relationship resulting in hyperbolas, and R and S also correspond to hyperbolas and circles respectively.
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(Note: K denotes a constant in the options)
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