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- Applied Mathematics-1 - M-1
- 2018
- PYQ
**Biju Patnaik University of Technology Rourkela Odisha - BPUT**- Civil Engineering
- B.Tech
**1517 Views**- 18 Offline Downloads
- Uploaded 10 months ago

Registration No : Total Number of Pages : 02 B.Tech. BS1101 1st Semester Back Examination 2018-19 MATHEMATICS - I BRANCH : AEIE, AERO, AUTO, BIOMED, BIOTECH, CHEM, CIVIL, CSE, ECE, EEE, EIE, ELECTRICAL, ENV, ETC, FASHION, FAT, IEE, IT, ITE, MANUFAC, MANUTECH, MARINE, MECH, METTA, METTAMIN, MINERAL, MINING, MME, PE, PLASTIC, TEXTILE Time : 3 Hours Max Marks : 70 Q.CODE : E808 Answer Question No.1 which is compulsory and any FIVE from the rest. The figures in the right hand margin indicate marks. Q1 a) b) c) d) e) f) g) h) i) j) Q2 Q3 Q4 Q5 a) Answer the following questions : Define polar formula of curvature. Define an asymptote of the curve and when an asymptote does not exist? What do you mean by integrating factor? How it helps to solve differential equations? Define Euler’s formula for homogeneous function of degree n. Define particular integral of differential equations of higher order with constant coefficient. What is the basis of Eigen vector when does it exist? What is the rank of a matrix? Write its basic importance? Find the Legendre polynomial P1(x) and P2(x). How can you say a real square matrix is orthogonal? Explain the condition for which a system of linear equation will possess more than one solution. 1 2 3 Find the rank of the matrix A= 3 4 5 . 4 6 8 (2 x 10) (5) b) 1 0 −1 Find the Eigen values and Eigen vectors of the matrix A= 1 2 1 2 2 3 (5) a) Solve the equation (1 − (5) b) Reduce the equation hence solve it. a) Solve the differential equation: b) Solve the differential equation: " − 4 ′ + 4 = a) Solve the following differential equation (2 + 3) " − (2 + 3) ′ − 12 = 6 , where b) ) − = + 4 = 0, by power series method. (2 2 ) to a linear equation and − = 1+ Obtain the rectilinear asymptotes of the curve + + (5) . , where (5) ′ = . (5) (5) ′ = . −1 = ( + 1) (5)

Q6 a) b) Q7 a) b) Q8 a) b) c) d) Prove that the center of curvature at points of a cycloid lie on an equal cycloid. Solve: ( + 6 + 8) = + + sin 2 (5) Solve: 1 + + cos + ( + log − sin ) = 0 Solve the following system of linear equation by Gauss elimination method : 2 + 3 − = 0, 5 − 3 + = 7, 8 + 9 − 3 = 2. (5) (5) Write short answer on any TWO : Rank of Matrix Legendre equation and Legendre polynomial Linear independent and linear dependent. Linear differential equations and its solutions. (5) (5 x 2)

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