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Differential Equations - General Aptitude - General Aptitude (GA) Previous Year Questions
Practice Differential Equations - General Aptitude - General Aptitude (GA) previous year questions organised from real papers, with year-wise coverage and clear topic navigation.
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Differential Equations question pattern
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| Paper | Year / session | Questions in this view | Open |
|---|---|---|---|
| Physics (PH) 2015 | 2015 | 1 | View paper |
All Differential Equations previous year questions
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2015 · General Aptitude (GA) · General Aptitude · Differential Equations
Physics (PH) 2015
A function \( y(z) \) satisfies the ordinary differential equation \( y'' + \frac{1}{z} y' - \frac{m^2}{z^2} y = 0 \), where \( m = 0,1,2,3,\ldots \). Consider the four statements P, Q, R, S as given below.
P: \( z^m \) and \( z^{-m} \) are linearly independent solutions for all values of \( m \)
Q: \( z^m \) and \( z^{-m} \) are linearly independent solutions for all values of \( m>0 \)
R: \( \ln z \) and 1 are linearly independent solutions for \( m = 0 \)
S: \( z^m \) and \( \ln z \) are linearly independent solutions for all values of \( m \)
The correct option for the combination of valid statements is
P: \( z^m \) and \( z^{-m} \) are linearly independent solutions for all values of \( m \)
Q: \( z^m \) and \( z^{-m} \) are linearly independent solutions for all values of \( m>0 \)
R: \( \ln z \) and 1 are linearly independent solutions for \( m = 0 \)
S: \( z^m \) and \( \ln z \) are linearly independent solutions for all values of \( m \)
The correct option for the combination of valid statements is