# Previous Year Exam Questions for Applied Mathematics-1 - M-1 of 2016 - JNTUK by Yashwanth S

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Set No - 1 Subject Code: R161102/R16 I B. Tech I Semester Regular Examinations December - 2016 MATHEMATICS-I (Common to all branches) Time: 3 hours Max. Marks: 70 Question Paper Consists of Part-A and Part-B Answering the question in Part-A is Compulsory, Four Questions should be answered from Part-B ***** PART-A 1. (a) Find the orthogonal trajectory of r = 2a 1 + cos θ (b) Find the P.I of ( D + 2)2 y = x 2 et if 0 < t < 1 (c) Find L(f(t)) where f (t ) = 0 if t > 1 2s 2 − 1 −1 (d) Evaluate L 2 2 ( s + 1)( s + 4 ) du (e) Find If u = sin ( x 2 + y 2 ) , where a 2 x 2 + b 2 y 2 = c 2 dx (f) Solve the PDE pq (px + qy -z)3 = 1 ∂ 2u ∂ 2u ∂ 2u +4 2 =0 (g) Classify the Nature of PDE 2 + 2 ∂x ∂x∂y ∂y [7 x 2 = 14] PART-B dy x 2 + y 2 + 1 = dx 2 xy (b) A resistance of 100 ohms, an inductance of 0.5 Henry is connected in series with a battery of 20 volts. Find the current in the circuit, if initially there is no current in the circuit [7+7] 3 2 −x 3. (a) Solve the D.E ( D + 1) y = cos(2 x − 1) + x e 2. (a) Solve the D.E (b) Consider an electrical circuit containing an inductance L, Resistance R and capacitance C. let q be the electrical charge on the condenser plate and ‘i’ be the current in the circuit at any time. Given that L = 0.25 henries, R = 250 ohms, q = 2x10-6 farads and there is no applied E.M.F in the circuit. At time zero the current is zero and the charge is 0.002 coulomb. Then find the charge (q) and current (i) at any time. [7+7] Page 1 of 2 |''|''|||''|'''|||'|

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