Download PTU B.Tech 2020 March IE 1st Sem Applied Mathematics Question Paper

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Roll No. EEEEEEEEEEE Total No. of Pages : 02

Total No. of Questions : 07

B.Tech. (Ind. Engg. & Mgt. (Spl. in TQM)) PT (Sem.-1)

APPLIED MATHEMATICS

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Subject Code : IEM-104

M.Code : 61004

Time : 3 Hrs. Max. Marks : 40

INSTRUCTIONS TO CANDIDATES :

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1. Attempt Any EIGHT questions from SECTION-A carrying TWO marks each.
2. Attempt any FOUR questions out of SIX questions from SECTION-B carrying SIX marks each.

SECTION-A

Attempt the following :

1. a) Solve the quadratic equation x²—\2ix+12=0.

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2. b) Prove that 2 sin² ? + cosec² ? = 2.
3. c) Two lines passing through point (2, 3) intersect each other at an angle of 60°. If the slope of one line is 2, find the equation of other line.
4. d) Find the equation of ellipse whose directrix is x —y + 3 = 0, focus (-1, 1) and eccentricity is 1/2.
5. e) Define scalar matrix.
6. f) If a = 2i + 2j - k, b = 6i - 3j + 2k find a x b and a vector perpendicular to both a and b. Also determine sine of angle between a and b.

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7. g) Differentiate (1+tanx)/(1-tanx) w.r.t. X.
8. h) Find gradient of a curve.
9. i) Evaluate ?₀¹ (2x² +3x+1) by second fundamental theorem.
10. j) Find the maximum and minimum value of the function f(x) = sin 2x + 5

SECTION-B

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1. Prove that tan ? + 2 tan 2? + 4 tan 4? + 8 cot 8? = cot ?.
2. Using matrices solve the system of equations for x, y and z
   x+2y-3z=6
   3x+2y-2z=3
   2x—y+z=2

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3. In binomial expansion of (1 + x)ⁿ, coefficients of fifth, sixth and seventh terms are in A.P. Find all possible values of n.
4. Differentiate (x^cosx + (sinx)^tanx) w.r.t. x.
5. Evaluate ?₀^p/2 cos²x log sin x dx .
6. Solve y' —2y =cos3x.

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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