Thursday, April 27, 2017

Dibrugarh University (BA - 2nd Semester) Question Papers - Mathematics General (May'2012)

2012
(May)
MATHEMATICS
(General)
Course: 201
(Matrices, Ordinary Differential Equations, Numerical Analysis)
Full Marks: 80
Pass Marks: 32
Time: 3 hours
The figures in the margin indicate full marks for the questions

1. (a) Define rank of a matrix. 1
(b) Ifbe an-rowed square matrix; then write the characteristic equation for the Matrix. 1
2. (a) Find the rank of the following matrix by reducing it to normal form: 3
(b) Prove that the rank of the transpose of a matrix is same as that of the original matrix. 3
3. (a) Show that the following equations are consistent and solve:
(b) State Cayley-Hamilton theorem and verify it with the following matrix: 2+5=7
Or
Determine the characteristic roots and corresponding characteristic vectors of the following matrix:

GROUP – B
(Ordinary Differential Equations)

4. (a) What is the condition that the equationbe an exact differential equation? 1
(b) Write down the Bernoulli’s equation. 1
(c) Find the complementary function of the differential equation 1
5. Solve any two: 6x2=12
6. Solve any one: 5
7. Apply the method of variation of parameters to solve the following equation: 5
8. Solve: 2+3=5
  1. , where

GROUP – C
(Numerical Analysis)

9. (a) Define interpolation. 1
(b) With usual notation, prove that 1
(c) State True or False: The iterative methods are based on the principle of successive approximation. 1
10. Apply Gauss-Jordan method to solve: 7
Or
Discuss the bisection method for solution of an algebraic equation.
11. (a) Determineby using Newton-Raphson method, using four iterations. 7
(b) Deduce Newton’s forward interpolation formula. 7
12. (a) Derive Simpson’s one-third rule for numerical integration. 4
Or
Findby trapezoidal rule.
(b) Find by using Lagrange’s interpolation formula from the following table: 2
:
0
1
2
5
:
1
3
12
147

Labels

Absorption Costing (1) Accountancy (4) accounting for partnership firms (3) Accounting for Share Capital (3) accounts of non trading concern (3) advanced financial accounting (18) AHSEC (149) ahsec 11 (47) ahsec 12 (60) ahsec notes (136) AHSEC Question Papers (35) Assam Slet (10) bcfm (11) bills of exchange (6) branch accounting (3) Budgetary Control (3) Budgetary Control Notes (2) business communication (28) Business Environment Notes (17) business regulatory framewrok (49) Business Statistics Notes (28) cash flow statement (5) cbse 12 (39) cbse notes (53) commerce (13) company law (23) corporate accounting (33) corporate laws (14) cost accounting (63) cost and management accounting (34) cpt (36) cpt 200 (7) cpt notes (30) dibrugarh university (1179) dibrugarh university notes (611) dibrugarh university question paper (474) dibrugarh university solved papers (267) dibrugarh university syllabus (47) direct tax law (49) eco - 01 (4) ECO - 02 (2) ECO - 03 (2) ECO - 05 (6) ECO - 06 (1) ECO - 07 (1) eco - 08 (4) eco - 09 (1) ECO - 10 (2) ECO - 11 (3) ECO - 12 (7) ECO - 13 (2) ECO - 14 (4) entrepreneurship (14) fianancial accounting (3) financial accounting (48) Financial Accounting Notes (23) financial management (18) Financial statements analysis (14) funds flow statement (3) guwahati university (289) guwahati university syllabus (52) Hire Purchase (5) Human Resource Management (12) icwai (38) icwai notes (39) ignou solved assignments (83) ignou solved question papers (121) income from house property (5) income from salary (4) Income Under the head Salaries (11) information technology (10) Installment Purchase (4) issue of shares (4) kkhsou (13) M.com (62) Management Accounting Notes (31) MCQ (11) paper I (1) paper II (9) paper III (1) principle of business mangement (16) Principles of Marketing Notes (16) royalty accounts (3) sale of goods act (8) semester I (165) Semester II (156) semester III (92) semester IV (149) semester V (136) semester VI (91) slet (13) Slet Ne (10) Small Business Management (7) solved assignments (22) UGC - NET: Commerce (08) (14) UGC - NET: Commerce (08) Paper II (3) UGC - NET: Commerce (08) Paper III (14) ugcnet solved question papers (23) Variance Analysis Notes (1)