Firstranker's choice
Code No: R10102/R10 Set No. 1
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I B.Tech I Semester Supplementary Examinations, Feb/Mar 2014
MATHEMATICS-I
(Common to Civil Engineering, Electrical & Electronics Engineering,
Mechanical Engineering, Electronics & Communication Engineering,
Computer Science & Engineering, Chemical Engineering, Electronics &
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Instrumentation Engineering, Bio-Medical Engineering, Information
Technology, Electronics & Computer Engineering, Aeronautical
Engineering, Bio-Technology, Automobile Engineering, Mining and
Petroliem Technology)
Time: 3 hours Max Marks: 75
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Answer any FIVE Questions
All Questions carry equal marks
*****
- (a) Solve (x² + y² – a²)x dx + (x² – y² – b²)y dy = 0. [7+8]
(b) If air is maintained at 20º C and the temperature of the body cools from 80° C to 60° C in 10 minutes, find the temperature of the body after 30 minutes. - (a) Solve (D² + a²)y = Sec ax [8+7]
(b) Solve (D² + 4)y = ex + Sin 2x - (a) If V = log (x² + y²) + x/(x2y), find ?V/?x, ?V/?y, ?2V/?y2 [8+7]
(b) If U = x exy where x² + y² + 2xy = 1, find ?2U/?x2 - (a) Trace the curve r = 2 + 3 sin?. [8+7]
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(b) Trace the curve y²(2a - x) = x3 - (a) Find the surface of the solid generated by revolution of the lemniscate r² = a² cos²? about the initial line. [8+7]
(b) Show that the whole length of the curve x²(a² – x²) = 8a²y² is 4pa - av2. - (a) Show that ?R xy dx dy = 8a² (p/4 - 2/3). [8+7]
(b) Evaluate ?R xy dx dy where R is the domain bounded by y-axis, the curve y=x² and the line x + y = 2 in the first quadrant. - (a) If V= exyz(i+j+k), find curl V. [8+7]
(b) Find the constants a and b so that the surface ax²-byz = (a+2)x will be orthogonal to the surface 4x²y +z³ =4 at the point (1,-1,2) - (a) Show that the area of the ellipse x²/a² + y²/b² = 1 is pab [8+7]
(b) If f = (2x² - 3z)i – 2xyj – 4xzk, evaluate- ?.f dV and
- ? ? × f dV where V is the closed region bounded by x = 0, y = 0, z = 0, 2x + 2y +z = 4.
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Firstranker's choice
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Code No: R10102/R10 Set No. 2
I B.Tech I Semester Supplementary Examinations, Feb/Mar 2014
MATHEMATICS-I
(Common to Civil Engineering, Electrical & Electronics Engineering,
Mechanical Engineering, Electronics & Communication Engineering,
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Computer Science & Engineering, Chemical Engineering, Electronics &
Instrumentation Engineering, Bio-Medical Engineering, Information
Technology, Electronics & Computer Engineering, Aeronautical
Engineering, Bio-Technology, Automobile Engineering, Mining and
Petroliem Technology)
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Time: 3 hours Max Marks: 75
Answer any FIVE Questions
All Questions carry equal marks
?
- (a) Solve ex (1 + dy/dx) = ex [8+7]
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(b) Show that the family of curves x2/(a²+?) + y2/(ß²+?) = 1, where ‘?' is a parameter is self orthogonal. - (a) Solve (D² + 9)y = 2Cos²x. [8+7]
(b) Solve d²y/dx² + 4y = 2ex Sin² x. - (a) Calculate the approximate value of v10 to four decimal places using Taylor's theorem. [8+7]
(b) Find 3 positive numbers whose sum is 600 and whose product is maximum. - (a) Trace the curve y = x2/(1+x2) [8+7]
(b) Trace the curve r = cos?. - (a) The figure bounded by a parabola and the tangents at the extremities of its latusrectum revolves about the axis of the parabola, Find the volume of the solid thus generated. [8+7]
(b) The segment of the parabola y²=4ax which is cutoff by the latus rectum revolves about the directrix. Find the volume of rotation of the annular region. - (a) Evaluate ? ?(x + y)²dx dy. over the area bounded by the ellipse x²/a² + y²/b² = 1. [8+7]
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(b) Transform the following to Cartesian form and hence evaluate ? r³ sin ? dr d?. - (a) Prove that ?r = r/r [8+7]
(b) Find the angle between the surfaces x² + y² + z² = 9 and z=x² + y²-3 at the point (2,-1,2). - (a) Evaluate ?s(yzi+zxj+xyk).dS where S is the surface of the sphere x²+y²+z²=a² in the first octant. [8+7]
(b) Evaluate ?(x² – 2xy)dx + (x²y + 3)dy around the boundary of the region defined by y²=8x and x=2.
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Firstranker's choice
Code No: R10102/R10 Set No. 3
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I B.Tech I Semester Supplementary Examinations, Feb/Mar 2014
MATHEMATICS-I
(Common to Civil Engineering, Electrical & Electronics Engineering,
Mechanical Engineering, Electronics & Communication Engineering,
Computer Science & Engineering, Chemical Engineering, Electronics &
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Instrumentation Engineering, Bio-Medical Engineering, Information
Technology, Electronics & Computer Engineering, Aeronautical
Engineering, Bio-Technology, Automobile Engineering, Mining and
Petroliem Technology)
Time: 3 hours Max Marks: 75
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Answer any FIVE Questions
All Questions carry equal marks
?
- (a) Solve y(Sinx - y) dx = Cosx dy [8+7]
(b) If the temperature of air is maintained at 20º C and the temperature of the body cools from 100° Cto80°C in 10 minutes, find the temperature of the body after 20 minutes. - (a) Solve (D² – 4D + 13)y = e2x [8+7]
(b) Solve (D² – 3 D + 2) y = Coshx - (a) If r + s + t = x, s + t = xy, t = xyz, find ?(r,s,t)/?(x,y,z) [8+7]
(b) Find the extreme points of f(x,y) = xy + 1/x + 1/y - (a) Trace the curve y = x/(1+x²) [8+7]
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(b) Trace the curve y² = (4 - x) (3 - x²) - (a) Find the length of the arc of the curve y =log (secx) from x = 0 to x = p/3. [8+7]
(b) Find the perimeter of the loop of the curve 3ay² =x(x-a)². - (a) Evaluate ? ? rdrd? over the region bounded by the cardioid r=a(1+cos?) and out side the circle r=a. [8+7]
(b) Change the order of Integration & evaluate ?02a ?0v(2 ax) dy dx - (a) Prove that (F×?)×r = -2F [8+7]
(b) Determine the constant a so that the vector V = (x+3y)i+(y-z)j+(x+az)k is solenoidal. - Apply Stokes theorem, to evaluate ? ydx + zdy + xdz where C is the curve of intersection of the sphere x²+ y²+ z²= a² and x + z = a. [15]
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Firstranker's choice
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Code No: R10102/R10 Set No. 4
I B.Tech I Semester Supplementary Examinations, Feb/Mar 2014
MATHEMATICS-I
(Common to Civil Engineering, Electrical & Electronics Engineering,
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Mechanical Engineering, Electronics & Communication Engineering,
Computer Science & Engineering, Chemical Engineering, Electronics &
Instrumentation Engineering, Bio-Medical Engineering, Information
Technology, Electronics & Computer Engineering, Aeronautical
Engineering, Bio-Technology, Automobile Engineering, Mining and
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Petroliem Technology)
Time: 3 hours Max Marks: 75
Answer any FIVE Questions
All Questions carry equal marks
?
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- (a) Solve (x + 1) dy/dx - y = e3x (x + 1)² [8+7]
(b) Find the orthogonal trajectory of the family of curves x2/3 + y2/3 = a2/3, where 'a' is a parameter - (a) Solve (D³ – 6D² + 11D – 6)y = e-2x + e-3x [8+7]
(b) Solve d²y/dx² + 8 dy/dx + 15 y = 0 - (a) If a= x/y, b= y/z, C = z/x, find d(x,y,z) [8+7]
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(b) Find the minimum value of x² + y² + z², give that xyz = a³ - (a) Trace the curve r = cos 4? [8+7]
(b) Trace the curve y²(1 - x) = x²(1+x).. - Prove that the volume of the solid generated by the revolution about the x - axis of the loop of the curve x = t², y = t3 is 32p/105 [8+7]
- (a) By changing the order of integration evaluate ?0a?v(a²-x²) dy dx. [8+7]
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(b) Evaluate ?0a ?0a-x x² + y²/a² dy dx by using change of order of integration. - (a) If V= exyz(i+j+k), find curl V. [8+7]
(b) Find the constants a and b so that the surface ax²-byz = (a+2)x will be orthogonal to the surface 4x²y +z³ =4 at the point (1,-1,2) - (a) Use divergence theorem to evaluate ?s(x³i + y³j + z³k).Nds, and S is the surface of the sphere x²+y²+z²=r². [8+7]
(b) Using Green's theorem, Find the area bounded by the hypocycloid x2/3+y2/3= a2/3, a>0. Given that the parametric equations are x =a cos³?, y =a sin³?.
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