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Pune University - SY BSc (Sem - I) PHYSICS - I, April 2010

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Total No. of Questions : 4] [Total No. of Pages : 3 [3717] - 103 P260 S.Y. B.Sc. PHYSICS (Sem. - I) PH - 211 : Mathematical Physics (New) (Paper - I) (21211) Time : 2 Hours] Instructions to the candidates : 1) All questions are compulsory. 2) Figures to the right indicate full marks. 3) Use of calculators and logtables is allowed. 4) Neat diagrams must be drawn wherever necessary. [Max. Marks : 40 Q1) Attempt all of the following: a) State the polar form of complex number and represent it graphically.[1] b) Find degree and order of given differential equation: c) dy 2 d4y + y2 = 0. [1] 4 +6 dx dx r r r r r r rr Determine the value of P if = 3i + P j + k and = 3i 2 j 3k are perpendicular to each other. [1] d) Define conservative and non-conservative force fields. e) [1] Prove that sinh f) = i sin i . [1] r rr rr r r r Find projection of = i 2 j + k on the vector = 4i 4 j + 7k . [1] g) If h) i) j) = 4x2y 2y3z3, find 2 . r r r Find the area of parallel goam whose adjacent sides are i 2 j + 3k and r rr [1] 2i + j 4k . r r r r r 2 2 If v = xyzi + 4 xy z j xyz k , find the value of divergence of v at (1, 1, 3). [1] If z = 2 + 5 i , find (i) complex conjugate of z and (ii) product zz .[1] P.T.O. Q2) Attempt any two of the following: a) Show that x = 1 is a regular singular point of the hypergeometric equation. x ( x 1) y + [ (1 + a + b ) x c ]y y = 0 . b) If y = e i(wt kx) then show that 2 k2 = x2 w2 c) [5] 2 y y t2 . [5] If the temperature at any point in the space is given by T = xy + yz + zx, r r then determine the derivative of T in the direction of vector 3i 4 k ( at point (1, 1, 2). ) [5] Q3) Attempt any two of the following: a) b) Obtain the quardratic equation in z if its roots are (2 3 i ) . Show that the vectors r r r r r r rr r r rr , = i 3 j + 5k and C = 2 i + j 4 k = 3i 2 j + k form a right angled triangle. c) [5] [5] Using total differentiation, find the approximate value of 2 2 ( 4.99 ) + (12.02) . [5] Q4) Attempt a or b . i) If = 1+ 3i , evaluate Z3. 2 [4] ii) A) a) r r If F = 3 xyi y 2 j evaluate rr F dr , where C is the curve C 2 y = x in XY plane from (0, 0) to (2, 1). [3717] - 103 [4] 2 2 b) i) Explain how will you determine that the point x = 0 is an irregular singular point of the given linear, second order, homogeneous differential equation. [4] ii) Show that the equation: dF = (y2 y + 2xy) dx + (x2 x + 2xy) dy is an exact differential. Hence determine F . [4] B) Attempt any one of the following: r r r r r i) If = x 2 zi + xy 2 zj 3 yz 2 k , determine curl of at the point (1, 1, 1). [2] ii) Determine the value of (1 + i)8 + (1 i)8. [2] Y [3717] - 103 3 3

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Additional Info : S.Y. B.Sc. Physics (Semister - I), PH - 211 : Mathematical Physics (Paper - I) (New Course), Pune University
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