iare.ac.in B.Tech Mathematical Techniques Semester II Question Paper : Institute Of Aeronautical Engineering

Name of the Organisation : Institute Of Aeronautical Engineering
Exam : B.Tech Semester Examinations
Subject : Mathematical Techniques
Semester : 2
Document Type : Previous Question Paper
Website : https://www.iare.ac.in

B.Tech Semester II Mathematical Techniques Question Papers

Institute Of Aeronautical Engineering (IARE) B.Tech Engineering Mechanics Previous Question Paper Semester II for the year 2021.

Related / Similar Question Paper : iare.ac.in B.Tech Probability And Statistics Semester II Question Paper

B.Tech Semester II Mathematical Techniques Questions

MODULE – I
1. (a) State convolution theorem in Laplace transforms. Write the Laplace transform of the first derivative and the second derivative. [7M]
(b) Find the Laplace transform of cos 2t − cos 3tt [7M]

MODULE – II
2. (a) State Fourier integral theorem. Write the Fourier sine integral and cosine integral of f(x). Also state Fourier transform of f(x). [7M]

(b) Find the Fourier sine and cosine transform of f(x) = e−ax. [7M]

MODULE – III
3. (a) Evaluate the double integral
π∫ 0 a sin θ∫ 0 rdrdθ [7M]
(b) Find by triple integration, the volume of the solid bounded by the co-ordinate planes x=0,y=0,z=0 and the plane x+ y+ z =1. [7M]

4. (a) Determine ∫ 2 0 ∫ √2x−x2 0 (x2 + y2)dydx by changing into polar co-ordinates. [7M]
(b) Find the volume of tetrahedron bounded by the co-ordinate planes and the plan x
a + y
b + z
c = 1 [7M]

MODULE – IV
5. (a) Verify Green’s theorem for ∫ C
(2xy − x2)dx + (x2 + y2)dy where “C” is bounded by y=x2 and y2=x. [7M]
(b) Find the work done by the force ⃗ F = (3×2 − 6yz)⃗ i + (2y + 3xz)⃗ j + (1 − 4xyz2)⃗ k in moving particle from the point (0,0,0) to the point(1,1,1) along the curve C: x=t, y=t2, z=t3. [7M]

6. (a) Verify Stokes theorem for the function ⃗ F = x2⃗ i + xy⃗j integrated round the square in the plane z=0 whose sides are along the line x=0, y=0, x=a, y=a. [7M]
(b) Find the directional derivative of the function xyz2+xz at the point P(1,1,1) in the direction of the normal to the surface 3xy2+y=z at (0,1,1). [7M]

MODULE – V
7. (a) Eliminate the arbitrary function from the surface z = xy+ f(x2+y2) and hence, obtain the corresponding partial differential equation. [7M]
(b) Solve the partial differential equation x(y2+z)p – y(x2+z)q = (x2-y2)z. [7M]

8. (a) Find the differential equation of all spheres whose centres lie on z-axis with a given radius r. [7M]
(b) Solve (p2+q2)y = qz [7M]

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