Download PTU B.Sc (Non-Medical) 2020 March 1st Sem 75744 Mathematical Physics Question Paper

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Roll No. Total No. of Pages : 02

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INSTRUCTIONS TO CANDIDATES :

1. SECTION-A is COMPULSORY consisting of TEN questions carrying ONE marks each.
2. SECTION-B contains FIVE questions carrying FIVE marks each and students have to attempt any FOUR questions.
3. SECTION-C contains THREE questions carrying TEN marks each and students have to attempt any TWO questions.

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SECTION-A

1. Write briefly :
   1. Find the Wronskian of {xz, —2x², 3x³}
   2. Solve y’dx + (xy +x²) dy=0.
   3. Find the integrating factor of the equation (e^y —2mxy²) dx + 2mx²ydy = 0
   4. Find the angle between the planes x +y+z=1 and x +2y +3z=0.

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   5. Prove that vector product is not associative, in general, ie, a x (b x c) ? (a x b) x c
   6. Prove that ? f df = ? df x w
   7. If the vector function f(t) have constant magnitude then prove f
   8. Define dirac delta function.
   9. Evaluate ?f, if f(r, ?) = r² — b² cos ? where b is a constant.

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   10. Show that f(r, ?, f) = r sin ? cos f satisfies Laplace’s equation.

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SECTION-B

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1. Solve (x+y-z)p+(x+y-z)q=2(z-y).
2. Find the volume of the parallelepiped if the edge vectors are [4, 9, —1], [2, 6, 0], [5, -4, 2].
3. For the function f = y/(x²+y²), find the value of directional derivative making an angle 30° with the positive x-axis at point (0, 1).
4. Apply Green’s theorem in the plane to evaluate ?C [(2x² -y²)dx+(x²+y²)dy] where C is boundary of the surface enclosed by the x-axis and the semi-circle y=v(1-x²).
5. Evaluate I(c)=(2/pc²) ? e^-x2/c2 sin x dx explicity and let c ? 0 to show that lim I(c)=sinx.

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SECTION-C

1. Define scalar triple product and their interpretation in terms of volume.
2. State and prove Stoke’s theorem.
3. Use a CAS to evaluate div u and curl u if u (r, ?, z) = r² cos ? e_r — r² sin² ? e_? + z e_z.

NOTE : Disclosure of Identity by writing Mobile No. or Making of passing request on any page of Answer Sheet will lead to UMC against the Student.

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