Download PTU B.Tech 2020 March Civil 3rd Sem M 54002 Applied Mathematics Ii Question Paper

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Roll No. Total No. of Pages : 02
Total No. of Questions : 18

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B.Tech. (ECE/IT/EEE/CSE/BT/Civil/ME/EE/EIE) (Sem.-2,3)
ENGG. MATHEMATICS-I/ENGG. MATHEMATICS-I/MATHEMATICS-II/APPLIED MATHEMATICS-II/APPLIED MATHEMATICS-III
Subject Code : AM-102/201
M.Code : 54002
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

Answer the following :

1. Are the vectors (1, 1,-1), (2, 3, -5), (2, -1, 4) linearly dependent.
2. Find the eigen values of the matrix 132 253 022
3. Is the differential equation (2 xy-cos X - 2xy + 1) dx + (sin X - x²)dy =0 exact ?

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4. Solve (2D²-2D-1) y=0.
5. Write any two applications of differential equations.
6. Find velocity of a particle which moves along the curve r =2sin3t i+2cos3t j+8tk .
7. State Green’s theorem.
8. If A=x²zi-2y²z³ j+xy²zk,then find Div(A) at the point (1, -1, 1).

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9. Write formulae of mean and variance of binomial distribution.
10. Define null hypothesis.

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SECTION-B

11. Find the rank of the matrix 234 431 124 after converting into normal form.

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12. Solve the differential equation dy/dx + (3y)/x = sinx/x³
13. Solve the differential equation (D² + 2D + 1) y = x.
14. Solve the differential equation (D² + 4) y = tan 2x using method of variation of parameters.

SECTION-C

15. Find the unit normal vector to the surface x²y + 2xz² = 8 at the point (1, 0, 2).

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16. Verify Gauss divergence theorem for F=4xzi - y² j+yzk over the cube x =0, x =1, y=0, y=1, z=0, z=1.
17. A box A contains 2 white and 4 black balls. Another box B contains 5 white and 7 black balls. A ball is transferred from the box ‘A to the box B. Then a ball is drawn from the box B. find the probability that it is white.
18. A certain stimulus administered to each of 12 patients resulted in the following increases of blood pressure : 5,2, 8,1,3,0,-2,1, 5,0, 4, 6. Can it be concluded that the stimulus will in general be accompanied by an increase in blood pressure. (Given that for v =11, t_0.05 =2.2)

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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