Download JNTUK B-Tech 2020 R19 CE 1101 Mathematics I Model Question Paper

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[B19 BS 1101]

I B. Tech I Semester (R19) Regular Examinations

MATHEMATICS -1

(Common to All Branches)

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MODEL QUESTION PAPER

Answer ONE Question from EACH UNIT

All questions carry equal marks

Max. Marks: 75 M

UNIT-I CO | KL

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1. a) Solve the system of equations 20x +y — 2z = 17, 3x + 20y —z = —18, col | 2 2x — 3y + 20z = 25 by Gauss —Siedel method.
2. b) Investigate the values of A and u so that the equations 2x+3y+5z=9; 7x+3y—2z=8; 2x+3y+?z=µ; has (i)no solution (i1) unique solution (iii) infinite number of solutions CO1 | K3

(OR)

1. a) Solve the system of equations 10x + y+z =12, 2x+10y+z =13, 2x+2y+10z =14 by Gauss- elimination method. col | k2
2. b) Define rank and find the rank of the matrix A by reducing it in to its normal form where
   

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   A is: A=

   2	3	-1	-1
   1	1	-1	-2
   3	1	3	-2
   6	3	0	-7

   COl1 | K1

UNIT-1I

1. a) Verify Cayley-Hamilton theorem and find the inverse of the matrix
   A=

   1	0	3
   2	1	-1
   1	-1	1

   CO2 | K3
2. b) Reduce the quadratic form 2x² + 2y² + 2z² — 2xy — 2yz — 2zx to canonical form by orthogonal transformation CO2 | K3

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(OR)

1. a) Find the eigenvalues and the corresponding eigen vectors of the matrix
   A=

   8	-6	2
   -6	7	-4
   2	-4	3

   CO2 | K3
2. b) If A =[ 3 1], use Cayley-Hamilton theorem to find the value of
   -1 2 CO2 | K3
   

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   2A³-3A²+ A - 4I. Also find the inverse of A.

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UNIT-III

1. a) Solve dy/dx + (tanx) y = (secx)⁵. CO3 | K2
2. b) Find the orthogonal trajectories of the family of parabolas ay² = x². CO3 | K3

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(OR)

1. a) Solve (y² + 2y)dx + (xy² + 2y² — 4x)dy = 0. CO4 | K2
2. b) A body originally at 80°C cools down to 60°C in 20 minutes, the temperature of air being 40°C. What will be the temperature of the body CO4 | K3 after 40 minutes from the original?

UNIT-IV

1. a) Solve (D³ —D)y =2x+ 1+ 4cosx. CO5 | K2

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2. b) solve : (D² -2D + y = e^x log x by the method of variation of parameters. CO5 | K2

(OR)

1. a) Solve (D² +3D +2)y =e^ex. CO5 | K2
2. b) Solve the differential equation x² d²y/dx² —x dy/dx +y=logx CO5 | K2

UNIT-V

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1. a) Find L{tcosat} and L {?₀^t e^-tcost dt}. CO6 | K2
2. b) Using convolution theorem evaluate L^-1 { 1 / ((s²+a²)(s²+b²)) }. CO6 | K3

(OR)

1. a) Find L^-1{ s / (s²-3s+2) }. CO6 | K2
2. b) solve d²y/dt² + 4dy/dt +3y =e^-t, y(0) = y'(0) = 1 by using Laplace co6 | K3 transforms

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