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Au Degree 6th Sem Maths (2019) Question Paper

By Venkat | February 20, 2020
Andhra University 6th Semester Maths Common Question Paper of the year 2019 is available here. Have a look at it.
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Year - 2019
[BS-S 3201/BA-S 3201]
B.Sc. (CBCS) DEGREE EXAMINATION.
Sixth Semester
Mathematics
Paper VII (A) — Elective-VII (A) — LAPLACE TRANSFORMS
(Common for B.A. and B.Sc.)
(With Effective From 2015-2016 admitted batch)
Time: Three hours        Maximum: 75 marks
PART A — (5 x 5 = 25 marks)
Answer any FIVE from the following Fight questions.
1. State and prove the existence theorem of Laplace transforms.
లాప్లాస్ రూపాంతరము యొక్క అస్థిత్వ సిదాంతమును ప్రవచించి, దానిని నిరూపించండి.
2. Find the Laplace transform of F(t) where
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Au 6th sem maths model papers, maths equations, au 6th sem maths common papers, ug papers, au old question papers, au previous question papers.



అనే ప్రమేయం F(t) యొక్క లాప్లాస్ రూపాంతరమును కనుక్కోండి.
3. Show that L{F(n) (t)}= pn L{F(t)}- r=0∑n-1 pn-1-r F(r) (0) where F(n) (t) is the nth order derivative of F(t).
F(t) యొక్క n-వ పరిమాణ అవకలని F(n) (t) అయినప్పుడుL{F(n) (t)}= pn L{F(t)}- r=0∑n-1 pn-1-r F(r) (0).
4. If L{F(t)} = f(p), then show that L{(1/t)F(t)} =  p∫∞ f(x) dx, provided Limt→0 ∫(1/t)F(t) exists.
L{F(t)}=f(p)అవుతూ, Limt→0 ∫(1/t)F(t) వ్యవస్టితం అయినప్పుడు L{(1/t)F(t)} =  p∫∞ f(x) dx అని చూపండి.
5. Evaluate L(t2 cos at).
L(t2 cos at) ని గణన చెయండి.
6. Find L-1 6/(2p-3) - (3-4p)/(3p2 -16) - (8-6p)/(16p2 +9)}.
L-1 6/(2p-3) - (3-4p)/(3p2 -16) - (8-6p)/(16p2 +9)} ను కనుక్కోండి.
7, If L-1 f(p)}=F(t), then show L-1 f(ap)}=(1/a)F(t/a).
L-1 f(p)}=F(t) అయితే L-1 f(ap)}=(1/a)F(t/a) అని చూపండి.
8. Evaluate L-1 1/p(p+1)3 }.
L-1 1/p(p+1)3 } ని గణన చెయండి.
PART B — (5 x 10 = 50 marks)
Answer the following (ONE question from each Unit).
9. (a) Show that the Laplace transform of the function F(t)= tn ,-l<n<0 exists, although it is not a function of class A.
అది తరగతి & కి చెందే ప్రమేయం కానప్పటికీ, F(t)= tn ,-l<n<0ప్రమేయం యుక్క రూపాంతరం వ్యవస్టితం అవుతుందని చూపండి.
            Or
(b) (i) Show that L(1/√𝝅t) = 1/√p.
 L(1/√𝝅t) = 1/√p అని చూపండి.
(ii) Find L(tn ); n is a positive integer.
n ఒక ధన వూర్జాంకం అయినప్పుడు L(tn ) ని కనుక్కోండి.
10. (a) Let F(t) be continuous for all t≥0 and be of exponential order a as t→∞. If F'(t) is of class A, then show that L{F’(t)} exists when p>a and L{F'(t)}= p L{F(t)}— F(0).
అన్ని t≥0 లకు F(t) అవిచ్చిన్నము మరియు t→∞ కి ఘాతిక పరిమాణం a అనుకొందాం. F(t) తరగతి A కి చెందినదైైతేే p>a అయినప్పుడు, L{F’(t)} వ్యవస్థితం L{F'(t)}= p L{F(t)}- F(0) అని చూపండి..
            Or
(b) (i) If L{F(t)}=(i/p)e1-/p , find L{e-t F(3t)}.
L{F(t)}=(i/p)e1-/p  అయితే L{e-t F(3t)} ని కనుక్కోండి.
(ii) If J0(t) = r=0∑∞ [(-1)r /(r!)2](t/2)2r , find L{J0(t)}.
J0(t) = r=0∑∞ [(-1)r /(r!)2](t/2)2r అయితే L{J0(t)} ను కనుక్కోండి.
11 (a) Prove that L{sinat/t}= tan-1 (1/p) and hence find L{sinat/t}. Verify whether L{cosat/t} exist or not.
L{sinat/t}= tan-1 (1/p) అని నిరూపించండి. తద్వారా  L{sinat/t} ని కనుక్కోండి.  L{cosat/t}వ్యవస్థితమోకాదో సరిమాడండి.
            Or
(b) Find L{erf √t} and hence evaluate L{erf 2√t}.
L{erf √t} ని కనుక్కోండి. తద్వారా L{erf 2√t} ని గణన చేయండి.
12 (a) Show that
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Au 6th sem maths model papers, maths equations, au 6th sem maths common papers, ug papers, au old question papers, au previous question papers.


అని చూపండి.
            Or

(b) Evaluate
Au 6th sem maths model papers, maths equations, au 6th sem maths common papers, ug papers, au old question papers, au previous question papers.

au 6th sem maths model paperAu 6th sem maths model papers, maths equations, au 6th sem maths common papers, ug papers, au old question papers, au previous question papers.


లను గణన చేయండి.

13. (a) State and prove the Convolution theorem for Laplace transforms.
 లాష్లాస్‌ రూపాంతరములకు అంతర సిద్దాంతాన్ని ప్రవచించి, దానిని నిరూపించండి.
            Or
(b) State the Heaviside expansion theorem. Using this theorem, find
Au 6th sem maths model papers, maths equations, au 6th sem maths common papers, ug papers, au old question papers, au previous question papers.




హెవిసైడ్‌ విస్తరణ సిద్దాంతాన్ని ప్రవచించండి. ఈ సద్దాంతాన్ని ఉపయోగించి
au 6th sem maths model paperAu 6th sem maths model papers, maths equations, au 6th sem maths common papers, ug papers, au old question papers, au previous question papers.



ని కనుక్కోండి.
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