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Total No. of Questions : 05]
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RJ-111
B.Sc.-B.Ed. (Secondary) Examination, 2024
(First Semester)
PHYSICS
Mathematical Physics-I
DC-I
Time : 3 Hours]
[Maximum Marks : 60
Note : Attempt all questions. Each question is provided with internal choice and carries equal marks.
1.
(a)
What is meant by gradient of a scalar field ? Derive its expression in terms of the operator $\vec{\nabla}$.
(b)
Define divergence of a vector field. Obtain its value in Cartesian coordinates and prove that $\text{div } \vec{A} = \vec{\nabla} \cdot \vec{A}$. Where $\vec{\nabla}$ is a vector operator.
Or
(a)
Explain the meaning of scalar field and vector field. Give examples of each field. How are they graphically represented ?
(b)
Explain the meaning of curl of a vector field. Write its significance. Show that curl of a conservative force field is zero.
2.
(a)
What do you mean by first order ODE equations ? Explain with examples.
(b)
Explain seperable ODE's with example.
Or
(a)
What do you mean by exact ODEs ? Write its applications in physics.
(b)
Explain linear ODE's with examples.
3.
(a)
Explain second-order linear ODEs with constant coefficients.
(b)
Write application of second order ODE's for spring mass system.
Or
Explain Homogeneous and non-homogeneous equations in detail.
Write application of second order ODE's for pendulum.
4.
Write short notes on the following :
(a)
Bessel Functions
(b)
Legendre Functions.
Or
Write short notes on the following :
(a)
Applications of Fourier series in physics
(b)
Rodriques representation.
5.
Write short notes on any two of the following :
(i)
Basic theorem of Laplace transform
(ii)
Fourier transform-inverse theorem
(iii)
Integral Transforms
(iv)
Application of Fourier and Laplace transform in physics.