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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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- a) Solve the system of equations 20x +y — 2z = 17, 3x + 20y —z = —18, col | 2 2x — 3y + 20z = 25 by Gauss —Siedel method.
- 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)
- a) Solve the system of equations 10x + y+z =12, 2x+10y+z =13, 2x+2y+10z =14 by Gauss- elimination method. col | k2
- b) Define rank and find the rank of the matrix A by reducing it in to its normal form where
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2 3 -1 -1
A= 1 1 -1 -2 -4 COl1 | K1
3 1 3 —2
6 3 0 -7
UNIT-1I
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- a) Verify Cayley-Hamilton theorem and find the inverse of the matrix
1 0 3
A= 1 2 1 -1 CO2 | K3
1 -1 1 - b) Reduce the quadratic form 2x² + 2y² + 2z² — 2xy — 2yz — 2zx to canonical form by orthogonal transformation CO2 | K3
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(OR)
- a) Find the eigenvalues and the corresponding eigen vectors of the matrix
8 -6 2
A= -6 7 —4 CO2 | K3
2 -4 3 - b) If A :[ 3 1], use Cayley-Hamilton theorem to find the value of -1 2 Cco2 | K3
2A³-3A²+ A - 4I. Also find the inverse of A.
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UNIT-III
- a) Solve dy/dx + (tanx) y = (secx)5. Cco3 | K2
- b) Find the orthogonal trajectories of the family of parabolas ay² = x³. CO3 | K3
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(OR)
- a) Solve (y³ + 2y)dx + (xy² + 2y² — 4x)dy = 0. CO4 | K2
- 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
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- a) Solve (D³ —D)y =2x+ 1+ 4cosx. CO5 | K2
- b) solve : (D² -2D + y = e? log x by the method of variation of parameters. CO5 | K2
(OR)
- a) Solve (D² +3D +2)y =e?. Cco5 | K2
- b) Solve the differential equation x² d²y/dx² —x dy/dx +y=logx CO5 | K2
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UNIT-V
- a) Find L{tcosat} and L {?0? e?cost dt}. CO6 | K2
- b) Using convolution theorem evaluate L?¹ { 1 / ((s²+1)(s²+4)) }. CO6 | K3
(OR)
- a) Find L?¹{ s / (s² - 3s + 2) }. Cco6 | K2
- b) solve d²y/dt² + 4dy/dt +3y =e?, y(0) = y'(0) = 1 by using Laplace co6 | K3 transforms
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