Printed Pages --6+2-8 A000212(014) Roll No. : B. Tech. (Second Semester) Examination April-May 2023 (AICTE Scheme) (Common to all Branches) (PI Group) 1. (a) Evaluate : MATHEMATICS-II Time Allowed : Three hou Maximsm Marks : 100 Minimum Pass Marks : 35 AIPRR Unit-< A000212(014) Note: Aempt all questions. Part (a) of each question is compulsory. Attempt any two parts from (b),. (c) and (d). LIBRARY RAIPJR.. (C.G.) TECHA 4 PTO
|2 1+x+y (b) Evaluate by changing the order of integration (c) Verify Gren's theorem for the following integral is y-planc. L[s-8ydt +(4y-6ry)d] where C is the boundary of the region bounded by the parabolas y = r and y =. (d) Find the area of the ellipse examples. Unit-II 2. (a) Define exact differential equation. Explain with A900212(014) 8 8 8 4 (b), Solve the differential equation: 2ry dy -(r' +y'+i) dr =0 (c) Solve: p= tan|x-: (d) Solve: |3| (1-*)+y = y and J,(x). dx 3. (a) Define Bessel's function of first kind. Find J, () d'y Unit-II (b) Sove the differential equation : A00212(014) 8
A000212(014) A00M312(0I4) (d) If f* = A+iB. prove that where Cis the circle (c) Reduce tan" (cose +isin 0) to the form a+ib. Z-3 dz Z=u+iy if u+V= 8 (c) Evaluate: (b) Define analytic function. Find the analytic function in the transfomation. 4. (a) What is 4 (2-1)(2-3)(+2) z-6z,-1 Unit-IV of (b) Define Laurent's serles. Find the Laurent's expansion 8 the circle|z=1. 4 (d) Find the series solution of 5. (a) Evaluate (2-2)dz where C is the upper half of d? dd'y, Unit-V 2 A (c) Solve: tan A and '+ 8 8 8 B |41 region 3<|z+2<5. conformal mapping? Explain Bilincar 2y = e
|6| (d) Define Residue theorem. Apply the Calculus of 8 residue to prove that 2 0
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