Download PTU B.Tech 2020 March Civil 3rd Sem BTAM 301 18 Mathematics Iii Question Paper

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Roll No. EEEEEEEE [ ] Total No. of Pages : 02
Total No. of Questions : 09

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INSTRUCTIONS TO CANDIDATES :

1. SECTION-A is COMPULSORY consisting of TEN questions carrying TWO marks each.
2. SECTION-B contains FIVE questions carrying FIVE marks each and students have to attempt any FOUR questions.
3. SECTION-C contains THREE questions carrying TEN marks each and students have to attempt any TWO questions.

SECTION-A

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1. Write briefly :
   1. Define gradient of a scalar point function.
   2. Define Solenoidal and irritational fields.
   3. State Gauss divergence theorem.
   4. Define Laplace transform!
   5. Write the relation between Laplace and Fourier transform.

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   6. State Convolution theorem.
   7. Write Gibbs phenomenon.
   8. Define dirac-delta function and impulse function.
   9. Write the Laplace transform of 2¢™.
   10. If u=x%i+yzj+z"xk Find the divergence of u.

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SECTION-B

1. Find the directional derivative of ¢ = 5x%y — 5%z + 2.5z% at the point P (1, 1, 1) in the direction of the line xT—l :y_—23 =z.
2. If f=(x* +y* + 2. Find n if div grad /=0.
3. Solve the equation ‘jit +2ZJ; —3y=sint, y—i 0, when ¢ = 0, by the Laplace transform method.

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4. Express f(x) =x sinx, 0
5. Find the inverse Laplace transform of se? +ne*/si+m

SECTION-C

1. Verify Stoke’s theorem for the vector field F = (x2 + yz) i — 2xy j taken around the rectangle bounded by the linesx==xa, y=0,y=05.
2. If f(x)=sinx, 0
3. a) Evaluate : gz
   

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   b) Show that V2 () = n (n + 1) ¥2, where 1* = x> + ? + 22,

NOTE : Disclosure of Identity by writing Mobile No. or Making of passing request on any page of Answer Sheet will lead to UMC against the Student.

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