PTU B.Tech Industry Engineering 1st Semester May 2019 61004 APPLIED MATHEMATICS Question Papers

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Total No. of Pages : 02

Total No. of Questions : 07

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

APPLIED MATHEMATICS

Subject Code : IEM-104

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M.Code: 61004

Time: 3 Hrs.

Max. Marks : 40

INSTRUCTIONS TO CANDIDATES :

1. Attempt Any EIGHT questions from SECTION-A carrying TWO marks each.

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2. Attempt any FOUR questions out of SIX questions from SECTION-B carrying SIX marks each.

SECTION-A

1. Answer briefly :
   1. If 10^x = 3 find the value of x.
   2. Find sin75°, if sin 45° = 1/v2 , and sin30° = 1/2.
   3. Find the coordinates of the point which divides the join of points (1, 2) and (3, 5) in ratio 1:2 internally.

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   4. Find the value of the determinant | 4 2 −1 2 −2 −3 −1 −6 −2 |
   5. Find the angle between the vectors v = i - j + k and w = - i + 2k.
   6. Find dy/dx if y = (x² + 1)e^2x.
   7. Evaluate the integral ? e^xxdx.
   8. Solve the differential equation dy/dx = x³e^y.

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   9. Expand (x²+2a)ⁿ using Binomial Theorem.
   10. Write down the Polar equivalent of 1–i.

SECTION-B

1. Prove that : sin? sin(60° – ?) sin(60° + ?) = (1/4) sin 3?.

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2. Find the length of major and minor axis, coordinate of the vertices and the foci, eccentricity and length of latus rectum of the ellipse : y² + 36x² = 36.
3. The cost of 4 kg onion, 3 kg wheat and 2 kg rice is Rs. 60. The cost of 2 kg onion, 4 kg wheat and 6 kg rice is Rs. 90. The cost 6 kg onion, 2 kg wheat and 3 kg rice is Rs. 70. Find the cost of each item by matrix or determinant method.
4. A circular disc of radius 4 cm is being heated. Due to thermal expansion, its area increases at a rate of 12cm²/s. Find the rate at which radius is increasing.
5. Find the value of integral ? (x²+3x+2)/(2x) dx.
6. Find the area of the region bounded the curve y = x² and the lines x = 1, x = 4 and x - axis.

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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.