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# Previous Year Exam Questions of Advanced Engineering Mathematics of IKGPTU - AEM by Ravichandran Rao

• Advanced Engineering Mathematics - AEM
• 2014
• PYQ
• I K G Punjab Technical University - IKGPTU
• Automobile Engineering
• B.Tech
• 3 Views
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#### Previous Year Exam Questions of Advanced Engineering Mathematics of IKGPTU - AEM by Ravichandran Rao / 3

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Roll No. Total no of pages :3 Total No. of Qustions :09 B.Tech (Sem.1st) Engineering Mathematics-I Subject Code :BTAM-101 Paper ID : [ A1101 ] Time: 3 Hrs. Max. Marks :60 Note:- (1) Q  uestion-I is compulsory to attempt, Consisting of ten short answer type question carrying two marks each. (2) Attempt five questions (carrying eight marks each) by electing at least two questions each form Section-A and Section B Q1. (a) Graph the set of points whose polar co-ordinates satisfy the conditions. r ≤ 0,θ=π/4 (b) Obtain the local extreme values of the function ƒ(x,y)=x2+2xy (c) (d) ππ Evaluate ∫∫ 0x sin y dydx. y ∞ ∂ƒ ∂ƒ If ƒ (x,y)= ∑ (xy)n, given |xy|<1, then find ∂x , ∂y . n=0 → → → (e) F→and G are irrotational vector point functions, then show that F xG is a solenoidal function. (f) State Stoke’s Theorem. (g) If F→ =grad (x3+y3+z3-3xyz),then find curl F→ . ( ( (h) Find the work done by the force field F→ =xy +(y-x)j over the straight line from i (1,1) to (2,3). (i) Rectify the curve x=acos3 t,y=asin3t. (j) Find the possible percentage error in computing the resistance r from the formula (2x10=20) 1 = 1 + 1 , if r and r in error by 2%. r r 1 r2 1 2 M-54091 1 P.T.O

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Section-A Q2. (a) Trace the curve x3+y3=3axy by giving all salient features in detail. (b) Find the volume of the solid generated by the revolution of the curve r = a(1+cosθ) about initial line. Q3. (a) If ρ be the radius of curvature at any point P of the curve y2=4ax and S is its focus, then show that ρ varies as (SP) 2 3 (5,3) (5,3) (b) Find the area between the curve y2(2a-x)=x3 and its asymptote. Q4. (a) Find the points on the surface z2= xy +1 nearest to the origin. (b) Expand ƒ(x,y)=tan-1 xy in ascending powers of (x-1) and (y-1) up to second degree terms. ∂2u (4,4) ∂2u +y ∂u Q5. (a) If u=tan-1xx-y , then prove that x2 ∂x2 +2xy ∂x∂y +y2 ∂y2 =2 sin u cos3u 3 3 2 (4,4) (b) If u=log (x3+y3+z3-3xyz), then prove that ( ∂x∂ + ∂y∂ + ∂z∂ )2 u= -9(x+y+z) -2 Section-B Q6. (a) Using triple integral find the volume of the tetrahedron bounded by the co-ordinate planes and the plane x + y + z = 1 a b c (b) Evaluate : 12-x xy dxdy by changing the order of integration. ∫∫ 0x (4,4) 2 → → → ∫∫S F•N Fds, where S is the portion of the sur→ ( ( ( (b) If F =yzi -xzj +xyk , then evaluate 2 ∆ → ( Q7. (a) Prove that Curl (Curl F ) =grad (divF ) - (3,5) face of the sphere x +y +z =1,in the first octant. 2 2 2 Q8. (a) Apply Stoke’s theorem to evaluate the line integral ∫c[ydx+zdy+xdz], Where C is the curve of intersection of the sphere x2+y2+z2=a2 and the plane x+z=a. (b) Using Green’s theorem evaluate the line integral ∫c[(y-sinx)dx+cosxdy] Where C is the plane triangle bounded by the lines y=0, x= π /2, y=(2 / π) x M-54091 2 P.T.O

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( ( ( Q9. (a) Verify Divergence theorem for F→=(x2-yz)i +(y2-xz)j +(z2-xy)k Taken over the rectangular parallelepiped 0 ≤ x ≤ a,0 ≤ y ≤ b,0 ≤ z ≤ c. (b) Evaluate ∫∫e x2+y2 dxdy, where R is semicircular region bounded by the x-axis and R the curve y=√1-x2 , by changing to polar co-ordinates. ***** M-54091 3 (5,3)