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**Code No: R05010102 Set No. 1**

I B.Tech Regular Examinations, Apr/May 2007

MATHEMATICS-I

I B.Tech Regular Examinations, Apr/May 2007

MATHEMATICS-I

( Common to Civil Engineering, Electrical & Electronic Engineering,

Mechanical Engineering, Electronics & Communication Engineering,

Computer Science & Engineering, Chemical Engineering, Electronics &

Instrumentation Engineering, Bio-Medical Engineering, Information

Technology, Electronics & Control Engineering, Mechatronics, Computer

Science & Systems Engineering, Electronics & Telematics, Metallurgy &

Material Technology, Electronics & Computer Engineering, Production

Engineering, Aeronautical Engineering, Instrumentation & Control

Engineering and Automobile Engineering)

Time: 3 hours Max Marks: 80

Answer any FIVE Questions

**All Questions carry equal marks**

1.(a) Test the convergence of the series 2/1 + 2.5.8/1.5.9 + 2.5.8.11/1.5−9.13 +...O< b) Find whether the following series converges absolutely / condtionally 1/6 − 1/6 . 1/3 + 1.3.5/6.8.10 −1.3.5.7/6.8.10.12 . (c) Prove that pi/6 + p3 5 < sin−1 3 5 < π/6 + 1 8 . [6] 2. (a) Show that the functions u = x+y+z , v = x2+y2+z2-2xy-2zx-2yz and w = x3+y3+z3-3xyz are functionally related. Find the relation between them. (b) Find the centre of curvature at the point a 4 , a 4 of the curve px +py = pa. Find also the equation of the circle of curvature at that point. [8+8] 3. (a) Find the length of the curve x2(a2 – x2) = 8 a2y2. (b) Find the volume of the solid generated by revolving the lemniscates r2 = a2 Cos 2θ about the line θ = 2 . [8+8] 4. (a) Form the differential equation by eliminating the arbitrary constant : log y/x = cx. [3] (b) Solve the differential equation: ( 1+ y2) dx = ( tan −1y – x ) dy. [7] (c) The temperature of the body drops from 1000 C to 750C in ten minutes when the surrounding air is at 200C temperature. What will be its temperature after half an hour. When will the temperature be 250C. [6] 5. (a) Solve the differential equation: (D2-1)y= xsinx + x2 ex. (b) Solve the differential equation: (x2D2+xD+4)y=log x cos (2logx). [8+8] 6. (a) Prove that L [ 1 t f(t) = 1R s f(s) ds where L [f(t) ] = f (s) [5] (b) Find the inverse Laplace Transformation of 3(s2 −2)2 2 s5 [6] (c) Evaluate s s (x2 + y2)dxdy over the area bounded by the ellipse x2 a2 + y2 b2 = 1 [5] 7. (a) For any vector A, find div curl A. [6] (b) Evaluate RR s A.n ds where A=z i +x j-3y2z k and S is the surface of the cylinder x2 + y2 = 16included in the first octant between z=0 and z=5. [10] 8. Verify Stoke’s theorem for F = -y3i+x3j in the region x2+y2 < 1, z=0. [16] Click here to download the Question paper in Pdf format