Questions Search

This website covers previous years question papers of various universities and colleges in India. Moreover, the information on admission to various courses from various universities/institutes/colleges are also available. Research paper questions are also updated from time to time. Also the latest teaching faculty plus teachers jobs, Government jobs, Banking Jobs, and other jobs are regularly updated to help jobless candidates. Admit cards of various recruitment of Govt organisation are updated. Search your terms using the sejavascript:void(0)arch box provided.
Are you student / faculty of Vikram University Ujjain? We are collecting old question papers. If you have latest question papers 2016 / 2015 / 2014 years, then contact us through email [email protected] / [email protected] . We will give you money for your question papers you send to us.

TNPSC Group IV 2016 Model Questions AnswersTNPSC Group IV

Anna Univ B.E Civil Engineering Previous Years Question PapersBE Civil Anna Univ

Anna Univ B.E EEE Previous Years Question PapersB.E EEE Anna Univ Questions

Anna Univ B.E Mechanical Engineering Previous Years Question PapersMechanical B.E Questions

Anna Univ B.E CSE Previous Years Question PapersMechanical B.E Questions

Anna Univ B.E ECE Previous Years Question PapersMechanical B.E Questions

VTU Question PapersLatest News

Dharmsinh Desai University Previous Years Question PapersLatest News

NEW: Last 05+ Years Question Papers of CE6451 Fluid Mechanics and Machinery

NEW: ME6502 Heat and Mass Transfer AU Chennai Last 10 Set of Question Papers

NEW: CE2027 Housing Planning and Management 2014 Question Paper

Himachal Pradesh University (HPU) Previous Years Question Papers

ME2027 PPCE All Previous Years Question Papers [NEW]

GNDU Previous Years Question Papers [NEW]

Teachers TGT, PGT, PRT jobs in New Delhi Schools

GATE 2016 JANUARY

Follow by Email

Wednesday, June 22, 2016

ANU B.Tech 1st Semester Mathematics January 2013 Question Paper

University: Acharya Nagarjuna University
I/IV B.Tech Degree Examinations, January 2013
First Year
First Semester
Mathematics

Time : 3 hours
Maximum Marks : 60
Answer question No.1 Compulsory
Answer ONE question from each Unit

1. Answer the following [12 x 1 = 12M]
a) Is the set of vectors (3, 2, 7), (2, 4, 1), (1,-2, 6) linearly dependent? Justify.
b) Find the Eigen values of the 2 x 2 matrix whose first row is (5, 4) and second row is (1, 2).
c) Define the Rank of a matrix.
d) For a given Hermitian matrix H whose first row is (0, i) and second row is (-i, 0) and the 1 x 2 matrix with the column (1, i) ,find the Hermitian form.
e) State the Rolle's theorem.
f) Find the critical points of the function f(x,y) = x3+y3-3axy.
g) What is the general solution of the Euler- cauchy equation x2y11+7xy1+13y=0.
h) Find the integrating factor for the differential equation y1-y/(x+1)=e3x(x+1).
i) State the necessary and sufficient condition for the differential equation Mdx + Ndy = 0 to be exact.
j) Find the solution of the equation y11+6y1+9y=0.
k) Find the particular integral of the differential equation (D2+5D+6)y=ex.
l) Define the order of a differential equation.

UNIT - I [1 x 12 = 12M]

2. a) Using the Gauss. Jordan method, find the inverse of the 3 x 3 matrix with first row : (1, 1, 3) & second row : (1, 3 ,-3) & third row : (-2, -4, -4).
2. b) Test the consistency and solve the system of equations 2x-3y+7z=5, 3x+y-3z=13, 2x+19y-47z=32. (OR)
3. a) Find the rank of the 4 x 4 matrix with first row : (1, 2, 3, 0) & second row : (2, 4, 3, 2) & third row : (3, 2, 1, 3) & fourth row : (6, 8, 7, 5).
3. b) Find eigen values and eigen vectors of the 3 x 3 matrix with first row : (1, 1, 3) & second row : (1, 5, 1) & third row : (3, 1, 1).

UNIT - II [1 x 12 = 12M]

4. a) What is the diagonal form after reduction of the 3 x 3 matrix with first row : (-1, 2, -2) & second row : (1, 2, 1) & third row : (-1, -1, 0).
4. b) Transform the quadratic form 7x12+6x1x2+7x22=0 to principle axes.Find the conic section represented by the quadratic form. (OR)
5. a) Using Maclaurin series expand tan(x) in a series of ascending powers of x as far as the term containing x5.
5. b) Find the maximum and minimum values of x3+y3-3x-12y+20.

UNIT - III [1 x 12 = 12M]

6. a) Solve 3x(1-x2)y2y1+(2x2-1)y3=ax3.
6. b) Solve he differential equation (2x2+3y2-7)xdx-(3x2+2y2-8)ydy=0. (OR)
7. a) Solve the differential equation y1+xsin(2y)=x3cos2y.
7. b) If the air is maintained at 30ºC and the temperature of the body cools from 80ºC to 60ºC in 12 minutes, find the temperature of the body after 24 minutes.

UNIT - IV [1 x 12 = 12M]

8. a) Solve y11+2y1+4y=2x2+3e-x.
8. b) Solve by the method of variation of parameters y11-6y1+9y=2x2+3e-x(OR)
9. a) Solve the differential equation y11-3y1+2y=xe3x+sin(2x).
9. b) Find the current I(t) in an RLC circuit with R=100 ohms, L=0.1 Henry, C=10-3 F which are connected to a source of voltage E(t)=155sin(377t) assuming zero charge and current when t=0.
 

1 comment:

Pen down your valuable important comments below