Download PTU B.Tech 2020 March Civil 1st and 2nd Sem AM 101 Applied Mathematics I Question Paper

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Roll No. [T T [ ] Total No. of Pages : 02

Total No. of Questions : 09

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B.Tech (CSE/CE/IT/ECE/Civil/ME/EIE/EEE/EE) (Sem.-1)

ENGG. MATHEMATICS/ENGG. MATHEMATICS-I/APPLIED MATHEMATICS-I

Subject Code : AM-101

M.Code : 54001

Time : 3 Hrs. Max. Marks : 60

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INSTRUCTIONS TO CANDIDATES :

1. SECTION-A is COMPULSORY consisting of TEN questions carrying TWO marks each.
2. SECTION -B & C have FOUR questions each.
3. Attempt any FIVE questions from SECTION B & C carrying EIGHT marks each.
4. Select atleast TWO questions from SECTION - B & C.

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SECTION-A

I. Write short notes on :

1. a) Give the formula for curvature of parametric-curves.
2. b) Give the formula for centre of gravity.
3. ¢) If u=¢e^x, then find ?u/?x.

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4. d) If u = yx², x=at, y = 2at; then find du/dt.
5. e) Write Taylor’s series for a function of two variables.
6. f) Give the standard equation of paraboloid.
7. g) Give the expression of Beta function.
8. h) Write the formula for integral test for convergence of infinite series.

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9. i) Find the modulus of (~1+iv3)(1+i).
10. j) Find the value of u, if u + iv = cos (a +iß) .

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SECTION-B

1. Write complete steps for the tracing of any Cartesian curve.

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2. Find the area bounded by the curve a⁴y² =x⁵ (a² —x²).
3. If u=sin^-1 (2xy/(x+y)), then using Euler’s theorem prove that x(?u/?x)+ y(?u/?y)=tanu .
4. Find the equations of tangent and normal to the curve y = 2x³ —4x + 5 at (3, 11).

SECTION-C

1. Find the equation of sphere through the points (2, 0, 1), (1, -5, -1), (0, -2, 3) and (4, -1, 2).

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2. Evaluate the integral ? 2x²-y / 1-2-y 2x²y²dxdy.
3. Test the convergence of the series S 1/(n log n) .
4. Simplify (1+ sin? + i cos ?) / (1 + sin? — i cos ?) using De-Moivre’s theorem.

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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