### Jntu Btech EEE First year Previous papers

Btech EEE First year All Question papers of
I B.Tech Regular Examinations, Apr/May 2007

### Mathematics Model paper Jntu

Code No: R05010102 Set No. 4
I B.Tech Regular Examinations, Apr/May 2007
MATHEMATICS-I
( Common to Civil Engineering, Electrical & Electronic Engineering,
Mechanical Engineering, Electronics & Communication Engineering,
Computer Science & Engineering, Chemical Engineering, Electronics &
Instrumentation Engineering, Bio-Medical Engineering, Information
Technology, Electronics & Control Engineering, Mechatronics, Computer
Science & Systems Engineering, Electronics & Telematics, Metallurgy &
Material Technology, Electronics & Computer Engineering, Production
Engineering, Aeronautical Engineering, Instrumentation & Control
Engineering and Automobile Engineering)
Time: 3 hours Max Marks: 80
All Questions carry equal marks
⋆ ⋆ ⋆ ⋆ ⋆
1. (a) Test the convergence of the series
p2−1
32−1 +
p3−1
42−1 +
p4−1
52−1 + ..... [5]
(b) Examine whether the following series is absolutely convergent or conditionally
convergent 1 − 1
3 ! + 1
5 ! − 1
7 ! + . . . . .. [5]
(c) Verify Rolle’s theorem for f(x) = log h x2+ab
x(a+b)i in [a,b] (x 6= 0). [6]
2. (a) Show that the functions u = x+y+z , v = x2+y2+z2-2xy-2zx-2yz and
w = x3+y3+z3-3xyz are functionally related. Find the relation between them.
(b) Find the centre of curvature at the point 􀀀a
4 , a
4 of the curve √x +√y = √a.
Find also the equation of the circle of curvature at that point. [8+8]
3. (a) In the evolute of the parabola y2= 4ax, show that the length of the curve from
its cusp x = 2a to the point where it meets the parabola y2 = 4ax is 2a(3√3
- 1)
(b) Find the length of the arc of the curve y = log ex
−1
ex+1 from x = 1 to x = 2
[8+8]
4. (a) Form the differential equation by eliminating the arbitrary constant : log y/x
= cx. [3]
(b) Solve the differential equation: ( 1+ y2) dx = ( tan −1y – x ) dy. [7]
(c) The temperature of the body drops from 1000 C to 750C in ten minutes when
the surrounding air is at 200C temperature. What will be its temperature
after half an hour. When will the temperature be 250C. [6]
5. (a) Solve the differential equation: d3y
dx3 + 4dy
dx = Sin 2x.
(b) Solve the differential equation: x2 d2y
dx2 − 2x dy
dx − 4y = x4. [8+8]
6. (a) Find L [ t2 Sin2t ] [5]
(b) Find L−1 h s+3
(s2−10s+29)i [6]
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Code No: R05010102 Set No. 4
(c) Evaluate
π/4
R0
a Sin
R0
r dr d
pa2 −r2 [5]
7. (a) Prove that ∇ × A¯×¯r
rn = (2−n)A¯
rn +
n(r¯.A¯)r¯
rn+2
(b) If ¯ F = (x2 − 27) i−6yzj +8xz2k evaluate RC
¯ F.d¯r from the point (0,0,0) to the
point (1,1,1) along the straight line from (0,0,0) to (1,0,1), (1,0,0) to (1,1,0)
and (1,1,0) to (1,1,1) [8+8]
8. Verify Stokes theorem f=x2i-yzj+k integrated around the square x=0, y=0, z=0,
x=1, y=1 and z=1.

Code No: R05010102 Set No. 3
I B.Tech Regular Examinations, Apr/May 2007
MATHEMATICS-I
( Common to Civil Engineering, Electrical & Electronic Engineering,
Mechanical Engineering, Electronics & Communication Engineering,
Computer Science & Engineering, Chemical Engineering, Electronics &
Instrumentation Engineering, Bio-Medical Engineering, Information
Technology, Electronics & Control Engineering, Mechatronics, Computer
Science & Systems Engineering, Electronics & Telematics, Metallurgy &
Material Technology, Electronics & Computer Engineering, Production
Engineering, Aeronautical Engineering, Instrumentation & Control
Engineering and Automobile Engineering)
Time: 3 hours Max Marks: 80
All Questions carry equal marks
⋆ ⋆ ⋆ ⋆ ⋆
1. (a) Test the convergence of the following series P 1
(log log n)n [5]
(b) Find the interval of convergence of the series
x + 1
2 . x3
3 + 1
2 . 3
4 . x5
5 + 1.3.5
2.4.6 . x7
7 + ..... [5]
(c) Show that log (1 + ex) = log 2 + x
2 + x2
8 − x4
192 + ..... and hence deduce that
ex
ex+1 = 1
2 + x
4 − x3
48 + ..... [6]
2. (a) Given that x+y+z=a, find the maximum value of xmynzp.
(b) Find the envelope of the circles through the origin and whose centre lies on
the ellipse x2
a2 + y2
b2 . [8+8]
3. (a) Trace the curve : r = a ( 1 + cos θ ).
(b) Find the length of the arc of the curve x = e sinθ; y = e cosθ from θ = 0 to
θ = π/2. [8+8]
4. (a) Find the differential equation of all parabolas having the axis as the axis and
(a,0) as the focus.
(b) Solve the differential equation x2dy
dx = ey − x.
(c) Find the orthogonal trajection of the family of curves x2/3 + y2/3 = a2/3.
[4+6+6]
5. (a) Solve the differential equation: d2y
dx2 + 4 dy
dx + 5y = −2Coshx given that y(0)
= 0, y′(0) = 1.
(b) Solve the differential equation: (2x − 1)3 d3y
dx3 + (2x − 1) dy
dx − 2y = x. [8+8]
6. (a) Evaluate L{et(cos2t + 1/2 sinh2t)} [5]
(b) Find L−1 1
s2+2s+5 [6]
(c) Evaluate the triple integral
1
R
0
1
R
y
1−x
R
0
x dz dx dy [5]
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Code No: R05010102 Set No. 3
7. (a) Evaluate ∇2 log r where r = px2 + y2 + z2
(b) Find constants a, b, c so that the vector A =(x+2y+az)i +(bx-3y-z)j+(4x+cy+2z)k
is irrotational. Also find ϕ such that A = ∇φ . [8+8]
8. Verify Stoke’s theorem for the vector field F=(2x-y)i-yz2j-y2zk over the upper half
surface of x2+y2+z2=1, bounded by the projection of the xy-plane. [16]

### JNTU Mathematics Previous paper

JNTU Mathematics Previous paper
Code No: R05010102 Set No. 2
I B.Tech Regular Examinations, Apr/May 2007
MATHEMATICS-I
( Common to Civil Engineering, Electrical & Electronic Engineering,
Mechanical Engineering, Electronics & Communication Engineering,
Computer Science & Engineering, Chemical Engineering, Electronics &
Instrumentation Engineering, Bio-Medical Engineering, Information
Technology, Electronics & Control Engineering, Mechatronics, Computer
Science & Systems Engineering, Electronics & Telematics, Metallurgy &
Material Technology, Electronics & Computer Engineering, Production
Engineering, Aeronautical Engineering, Instrumentation & Control
Engineering and Automobile Engineering)
Time: 3 hours Max Marks: 80
All Questions carry equal marks
⋆ ⋆ ⋆ ⋆ ⋆
1. (a) Test the convergence of the following series P n2
2n + 1
n2 [5]
(b) Find the interval of convergence of the series whose n th term is P (−1)n(n+2)
(2n +5)
[5]
(c) If a < b prove that b−a (1+b2) < tan−1b − tan−1a < b−a (1+a2) using Lagrange’s Mean value theorem. Deduce the following [6] i. 4 + 3 25 < tan−1 4 3 < 4 + 1 6 ii. 5 +4 20 < tan−1 2 < +2 4 2. (a) If u=x2-y2, v=2xy where x=r cosθ, y=rsinθ. Show that @(u,v) @(r, ) = 4r3. (b) For the cardioid r=a(1+cosθ) Prove that 2 r is constant where rho is the radius of curvature. [8+8] 3. (a) Find the volume of the solid generated by revolution of y2 = x3 (2a−x) about its asymptote. (b) Find the area of the loop of the curve r=a(1+cos θ). [8+8] 4. (a) Form the differential equation by eliminating the arbitrary constant y = a+x x2+1 . [3] (b) Solve the differential equation: (1-x 2) dy dx - xy = y3sin −1x. [7] (c) Prove that the family of confocal conics x2 a2+ + y2 b2+ = 1 are self orthogonal (λ the parameter) [6] 5. (a) Solve the differential equation: (D3 − 7D2 + 14D − 8)y = excos2x. (b) Solve the differential equation: (x2D2 − x3D + 1)y = log x sin (log x)+1 x . [8+8] 6. (a) Solve the differential equation d2x dx2 + 9x = Sin t using Laplace transforms given that x(0) = 1, x(π/2) =1 1 of 2 Code No: R05010102 Set No. 2 (b) Change the order of integration hence evaluate 1 R0 2−x Rx2 xdy dx [8+8] 7. (a) Prove that ∇x(∇xA) = -∇2A+∇(∇.A). (b) If φ = 2xy2z +x2y, evaluate RC φ dr where C consists of the straight lines from (0, 0, 0) to (1, 0, 0) then to (1, 1, 0) and then to (1, 1, 1). [8+8] 8. Verify Green’s theorem for HC (y − Sin x ) dx + Cos x dy where C is the triangle formed by the points (0,0) (π/2, 0) and (π/2, 1). [16] Download the previous paper in Pdf format click here

### Btech first year Maths Previous paper

Try to download in pdf format if the below is not clear
Code No: R05010102 Set No. 1
I B.Tech Regular Examinations, Apr/May 2007
MATHEMATICS-I

( Common to Civil Engineering, Electrical & Electronic Engineering,
Mechanical Engineering, Electronics & Communication Engineering,
Computer Science & Engineering, Chemical Engineering, Electronics &
Instrumentation Engineering, Bio-Medical Engineering, Information
Technology, Electronics & Control Engineering, Mechatronics, Computer
Science & Systems Engineering, Electronics & Telematics, Metallurgy &
Material Technology, Electronics & Computer Engineering, Production
Engineering, Aeronautical Engineering, Instrumentation & Control
Engineering and Automobile Engineering)

Time: 3 hours Max Marks: 80
All Questions carry equal marks
1.(a) Test the convergence of the series 2/1 + 2.5.8/1.5.9 + 2.5.8.11/1.5−9.13 +...O< b) Find whether the following series converges absolutely / condtionally 1/6 − 1/6 . 1/3 + 1.3.5/6.8.10 −1.3.5.7/6.8.10.12 . (c) Prove that pi/6 + p3 5 < sin−1 3 5 < π/6 + 1 8 . [6] 2. (a) Show that the functions u = x+y+z , v = x2+y2+z2-2xy-2zx-2yz and w = x3+y3+z3-3xyz are functionally related. Find the relation between them. (b) Find the centre of curvature at the point a 4 , a 4 of the curve px +py = pa. Find also the equation of the circle of curvature at that point. [8+8] 3. (a) Find the length of the curve x2(a2 – x2) = 8 a2y2. (b) Find the volume of the solid generated by revolving the lemniscates r2 = a2 Cos 2θ about the line θ = 2 . [8+8] 4. (a) Form the differential equation by eliminating the arbitrary constant : log y/x = cx. [3] (b) Solve the differential equation: ( 1+ y2) dx = ( tan −1y – x ) dy. [7] (c) The temperature of the body drops from 1000 C to 750C in ten minutes when the surrounding air is at 200C temperature. What will be its temperature after half an hour. When will the temperature be 250C. [6] 5. (a) Solve the differential equation: (D2-1)y= xsinx + x2 ex. (b) Solve the differential equation: (x2D2+xD+4)y=log x cos (2logx). [8+8] 6. (a) Prove that L [ 1 t f(t) = 1R s f(s) ds where L [f(t) ] = f (s) [5] (b) Find the inverse Laplace Transformation of 3(s2 −2)2 2 s5 [6] (c) Evaluate s s (x2 + y2)dxdy over the area bounded by the ellipse x2 a2 + y2 b2 = 1 [5] 7. (a) For any vector A, find div curl A. [6] (b) Evaluate RR s A.n ds where A=z i +x j-3y2z k and S is the surface of the cylinder x2 + y2 = 16included in the first octant between z=0 and z=5. [10] 8. Verify Stoke’s theorem for F = -y3i+x3j in the region x2+y2 < 1, z=0. [16] Click here to download the Question paper in Pdf format

### Btech first year english model paper

Code No: R05010101 Set No. 4
I B.Tech Regular Examinations, Apr/May 2007
ENGLISH
( Common to Civil Engineering, Electrical & Electronic Engineering,
Mechanical Engineering, Electronics & Communication Engineering,
Computer Science & Engineering, Chemical Engineering, Electronics &
Instrumentation Engineering, Bio-Medical Engineering, Information
Technology, Electronics & Control Engineering, Mechatronics, Computer
Science & Systems Engineering, Electronics & Telematics, Metallurgy &
Material Technology, Electronics & Computer Engineering, Production
Engineering, Aeronautical Engineering, Instrumentation & Control
Engineering, Bio-Technology and Automobile Engineering)
Time: 3 hours Max Marks: 80
All Questions carry equal marks
⋆ ⋆ ⋆ ⋆ ⋆
1. How was Copernican theory supported by Galileo? [16]
2. ‘Seek the truth and truth shall set you “In what context did Kalam recollect the
statement. [16]
3. Why does Kalam consider Sarabhai the Mahatma of Indian science? [16]
4. What does a river do? Can it play both constructive and destructive parts? Ex-
plain. [16]
5. ‘Keep on trying’ is the success mantra of Kalam. Support this view from your
study of Kalam’s experiences. [16]
6. What did the second flight of Prithvi prove to the world? Explain. [16]
7. (a) The spectacle these men presented would under other circumstances have been
so absurd as to make one laugh, but here it was tragic. Sitting in a tight little
circle with their knees drawn up and their heads together, with the goats
trying to crawl under them, they had that look of intense expectation on their
screwed-up features that one sees on the faces of spectators waiting to hear a
big gun go off. From the time we had first heard the tigress from the ridge,
neither the men nor the goats had made a sound, beyond on suppressed cough.
They were probably by now frozen with fear which they had every right to be
and even if were, I take my hat off to those four men, who had the courage to
do what I, had I been in their position, would not have dreamt of doing. For
seven days they had been hearing the most exaggerated and terrifying tales
of this dreadful beast that had dept them awake the past two nights, an now,
while darkness was coming on, and sitting unarmed in a position where they
could see nothing, they were listening to the man-eater coming nearer and
nearer; grater courage, and greater faith, it is not possible to conceive.
i. What was the spectacle that the men presented ?
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Code No: R05010101 Set No. 4
ii. What would their look of intense expectation suggest ?
iii. What was the only sound that had been heard?
iv. Would the writer have sat down with the men ?
vi. Why does the writer praise their courage and faith ?
vii. Suggest a reason why the men were sitting there with the goats ?
viii. Did the men have fire-arms with them ?
ix. Explain the meaning of the phrase frozen with fear ?
(b) Using the table given below write a detailed paragraph. Transfer the infor-
mation available in the tabular form to a descriptive paragraph . Interpret
and infer messages from the figures. Put the information in logical continuity.
Begin the paragraph with a topic sentence and follow it up with sentences
that help expand, explain, elaborate , exemplify and give an overall picture.
Production in India 1993-94 1994-95 1995-96 1969-97 1997-98
in Million tons
Rice 57.06 48.98 59.01 60.80 62.22
Wheat 35.76 32.21 50.89 75.43 80.79
Sugarcane 25.11 24.10 28.08 29.31 30.08
Tea 15.88 20.11 25.77 30.80 48.92
Coffee 12.00 10.86 18.25 23.62 40.77
8. (a) Fill in the blanks with appropriate verb forms. [4×4=16]
i. He (walk ) across the road when a bicycle hit him.
ii. If wishes (be ) horses, beggars would ride them.
iii. In this season, usually the day (dawn) at 6.00a.m.
iv. Neither of them (serve ) the mankind.
(b) Fill in the blanks with appropriate preposition / article
i. The rich must have compassion the poor people.
ii. I am very curious about knowing the result.
iii. Every student must submit article on any subject
iv. I want to purchase audio system today.
(c) Add prefixes or suffixes to the given meanings
i. archy = without government
ii. script = written afterwards
iii. construct = act of constructing
iv. book = a small book
(d) Fill in the blanks with appropriate word choosing from the bracket.
i. He is of her victory in the elocution contest (zealous / jealous
)
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Code No: R05010101 Set No. 4
ii. No man will cheat others (decent / descent )
iii. The of the food was given off to the beggars (remainder /
reminder)
iv. The enemy forces raised a of the fort , cutting off supply
routes. (siege / seize )

### Previous Btech english 1st year Paper

Code No: R05010101 Set No. 3
I B.Tech Regular Examinations, Apr/May 2007
ENGLISH
( Common to Civil Engineering, Electrical & Electronic Engineering,
Mechanical Engineering, Electronics & Communication Engineering,
Computer Science & Engineering, Chemical Engineering, Electronics &
Instrumentation Engineering, Bio-Medical Engineering, Information
Technology, Electronics & Control Engineering, Mechatronics, Computer
Science & Systems Engineering, Electronics & Telematics, Metallurgy &
Material Technology, Electronics & Computer Engineering, Production
Engineering, Aeronautical Engineering, Instrumentation & Control
Engineering, Bio-Technology and Automobile Engineering)
Time: 3 hours Max Marks: 80
All Questions carry equal marks
⋆ ⋆ ⋆ ⋆ ⋆
1. Why does Kalam say, ‘Mine was a very secure childhood, both materially and
emotionally? [16]
2. Computers provide us with new capabilities and these in turn give us new choices
for action. Explain. [16]
3. According to Dr. Kalam what are the qualities of a good team leader? [16]
4. From a scientist’s point of view the investigation of the nature and properties of
water, the elixir of life, is of the highest scientific interest. Discuss. [16]
5. Kalpana Chawla enjoyed every moment of the undergraduate course in engineering.
Substantiate. [16]
6. Sketch the character of Delia Caruthers. [16]
7. You have been asked by a firm which manufactures detergent powder to make a
study of the consumer reaction to their product and suggest measures to improve
the image and the sales of their product. Prepare a report of the study.
[16]
8. (a) Correct the following sentences. [4×4=16]
i. It is unfortunate that many youngsters get addicted to gamble.
ii. He will meet her if she will come to Hyderabad.
iii. The Director issued order for his promotion.
iv. The husband as well as the wife need advise
(b) Fill in the blanks with appropriate preposition / article
i. Govind is M.B.B.S
ii. Shatabdi is one of the fast running trains in India.
iii. They always boast their achievements.
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Code No: R05010101 Set No. 3
iv. He is very much concerned the security of his family members.
(c) Use the following idioms / phrases in your own sentences
i. to eat one’s words
ii. through thick and thin
iii. a wild goose chase
iv. crocodile tears
(d) Write the synonyms of the following words
i. negate
ii. inexperienced
iii. apt
iv. competent

### BTech ENGLISH Examinations previous question paper

Code No: R05010101 Set No. 2
I B.Tech Regular Examinations, Apr/May 2007
ENGLISH
( Common to Civil Engineering, Electrical & Electronic Engineering,
Mechanical Engineering, Electronics & Communication Engineering,
Computer Science & Engineering, Chemical Engineering, Electronics &
Instrumentation Engineering, Bio-Medical Engineering, Information
Technology, Electronics & Control Engineering, Mechatronics, Computer
Science & Systems Engineering, Electronics & Telematics, Metallurgy &
Material Technology, Electronics & Computer Engineering, Production
Engineering, Aeronautical Engineering, Instrumentation & Control
Engineering, Bio-Technology and Automobile Engineering)
Time: 3 hours Max Marks: 80
All Questions carry equal marks

1. How did Jalaluddin and Samsuddin have a hold on Kalam? [16]
2. (a) How did the word‘computer ethics’ come into being?
(b) Explain the significance of it. [7+9]
3. He racked his brain for a long while till sheer exhaustion calmed his agitated nerves
and made him accept the situation with a helpless resignation ? What was the
helpless situation and what prompted Datta to think so much? [16]
4. What is the role played by Dr. Satish Dhawan in Indian space research? [16]
5. The shy but cheerful girl with boundless energy and a strong inclination for adven-
ture, Kalpana from Karnal becomes an astronaut in NASA. How could she make
this possible? [16]
6. O. Henry supported great art or great love in the story ‘A Service of Love’. Discuss.
[16]
7. Write a detailed essay in your own words on the topic ‘Evils of drug addiction’.[16]
8. (a) Correct the following sentences. [4×4=16]
i. I don’t think he can be able to solve the problem.
ii. He was called as ‘the big brother’ by his friends.
iii. Let us discuss about the dispute
iv. The volunteers came to the meeting by foot.
(b) Fill in the blanks with appropriate preposition / article
i. I am talking about India I knew when I was young.
ii. She learnt to play violin.
iii. She was angry me.
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Code No: R05010101 Set No. 2
iv. We congratulated him his success.
(c) Use the following idioms / phrases in your own sentences
i. Bolt from the blue
ii. By hook or crook
iii. To be abreast of
iv. Be all and end all
(d) Write the synonyms of the following words
i. worsen
ii. frank
iii. consent
iv. tendency

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