q2 (a) if y = eax.sinbx, then prove that 2 − 1 + 0 answer · de51/dc55 engineering mathematics-i...
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![Page 1: Q2 (a) If y = eax.sinbx, then prove that 2 − 1 + 0 Answer · DE51/DC55 ENGINEERING MATHEMATICS-I JUNE 2014 © IETE 1 Q2 (a) If y = eax.sinbx,then prove that 2ay (a2 b. 2)y. 0 2](https://reader034.vdocuments.us/reader034/viewer/2022042113/5e8f087b21f3a5310a702328/html5/thumbnails/1.jpg)
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Q2 (a) If y = ,bxsin.eax then prove that 0y)ba(ay2y 2212 =++− .
Answer
Q2 (b) Find the equation of the tangent to the curve x53y2 −= parallel to the lines 5x –
4y + 13 = 0
![Page 2: Q2 (a) If y = eax.sinbx, then prove that 2 − 1 + 0 Answer · DE51/DC55 ENGINEERING MATHEMATICS-I JUNE 2014 © IETE 1 Q2 (a) If y = eax.sinbx,then prove that 2ay (a2 b. 2)y. 0 2](https://reader034.vdocuments.us/reader034/viewer/2022042113/5e8f087b21f3a5310a702328/html5/thumbnails/2.jpg)
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Answer
Q3 (a) Evaluate ∫ xdx3sin.e x2
![Page 3: Q2 (a) If y = eax.sinbx, then prove that 2 − 1 + 0 Answer · DE51/DC55 ENGINEERING MATHEMATICS-I JUNE 2014 © IETE 1 Q2 (a) If y = eax.sinbx,then prove that 2ay (a2 b. 2)y. 0 2](https://reader034.vdocuments.us/reader034/viewer/2022042113/5e8f087b21f3a5310a702328/html5/thumbnails/3.jpg)
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Answer
Q3 (b) Evaluate dx3x4x
x52
22
1 ++∫
Answer
![Page 4: Q2 (a) If y = eax.sinbx, then prove that 2 − 1 + 0 Answer · DE51/DC55 ENGINEERING MATHEMATICS-I JUNE 2014 © IETE 1 Q2 (a) If y = eax.sinbx,then prove that 2ay (a2 b. 2)y. 0 2](https://reader034.vdocuments.us/reader034/viewer/2022042113/5e8f087b21f3a5310a702328/html5/thumbnails/4.jpg)
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Q4 (a) Let A =
=
=
−8352
C,4725
B,4312
find a matrix D such that CD – AB =
0
Answer
![Page 5: Q2 (a) If y = eax.sinbx, then prove that 2 − 1 + 0 Answer · DE51/DC55 ENGINEERING MATHEMATICS-I JUNE 2014 © IETE 1 Q2 (a) If y = eax.sinbx,then prove that 2ay (a2 b. 2)y. 0 2](https://reader034.vdocuments.us/reader034/viewer/2022042113/5e8f087b21f3a5310a702328/html5/thumbnails/5.jpg)
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Q4 (b) Using Cramer’s rule, solve the following system of liner equations,
(a + b) x – (a – b) y = 4ab
(a – b) x + (a + b) y = 2 )ba( 22 −
Answer
![Page 6: Q2 (a) If y = eax.sinbx, then prove that 2 − 1 + 0 Answer · DE51/DC55 ENGINEERING MATHEMATICS-I JUNE 2014 © IETE 1 Q2 (a) If y = eax.sinbx,then prove that 2ay (a2 b. 2)y. 0 2](https://reader034.vdocuments.us/reader034/viewer/2022042113/5e8f087b21f3a5310a702328/html5/thumbnails/6.jpg)
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Q5 (a) Solve the differential equation (x + y) dy + (x – y) dx = 0 given that
y = 1 when x = 1
Answer
![Page 7: Q2 (a) If y = eax.sinbx, then prove that 2 − 1 + 0 Answer · DE51/DC55 ENGINEERING MATHEMATICS-I JUNE 2014 © IETE 1 Q2 (a) If y = eax.sinbx,then prove that 2ay (a2 b. 2)y. 0 2](https://reader034.vdocuments.us/reader034/viewer/2022042113/5e8f087b21f3a5310a702328/html5/thumbnails/7.jpg)
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Q5 (b) Solve the equation cos x(1 + cos y) dx – sin y (1 + sin x) dy = 0
![Page 8: Q2 (a) If y = eax.sinbx, then prove that 2 − 1 + 0 Answer · DE51/DC55 ENGINEERING MATHEMATICS-I JUNE 2014 © IETE 1 Q2 (a) If y = eax.sinbx,then prove that 2ay (a2 b. 2)y. 0 2](https://reader034.vdocuments.us/reader034/viewer/2022042113/5e8f087b21f3a5310a702328/html5/thumbnails/8.jpg)
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Answer
Q6 (a) Prove that the coefficient of nx is expansion of 2
x1x1
−+
is 4n
Answer
Q6 (b) Let ns denote the sum of the first n terms of an A.P. If nn2 s3s = , then prove that
6ss
n
n3 =
Answer
![Page 9: Q2 (a) If y = eax.sinbx, then prove that 2 − 1 + 0 Answer · DE51/DC55 ENGINEERING MATHEMATICS-I JUNE 2014 © IETE 1 Q2 (a) If y = eax.sinbx,then prove that 2ay (a2 b. 2)y. 0 2](https://reader034.vdocuments.us/reader034/viewer/2022042113/5e8f087b21f3a5310a702328/html5/thumbnails/9.jpg)
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Q7 (a) If A, B, C are the angles of a triangle, then prove that,
sin2A + sin2B + sin2C = 4 sinA.sinB.sinC Answer
![Page 10: Q2 (a) If y = eax.sinbx, then prove that 2 − 1 + 0 Answer · DE51/DC55 ENGINEERING MATHEMATICS-I JUNE 2014 © IETE 1 Q2 (a) If y = eax.sinbx,then prove that 2ay (a2 b. 2)y. 0 2](https://reader034.vdocuments.us/reader034/viewer/2022042113/5e8f087b21f3a5310a702328/html5/thumbnails/10.jpg)
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Q7 (b) Prove that, cos20º.cos60º.cos40º.cos80º =161
Answer
Q8 (a) Find the equation of the two straight lines through (7, 9) and making an angle of 60º
with the line 032y3x =−−
Answer
![Page 11: Q2 (a) If y = eax.sinbx, then prove that 2 − 1 + 0 Answer · DE51/DC55 ENGINEERING MATHEMATICS-I JUNE 2014 © IETE 1 Q2 (a) If y = eax.sinbx,then prove that 2ay (a2 b. 2)y. 0 2](https://reader034.vdocuments.us/reader034/viewer/2022042113/5e8f087b21f3a5310a702328/html5/thumbnails/11.jpg)
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Q8 (b) Find the area of the triangle formed by the lines y =x, y = 2x and y = 3x +4
Answer
Q9 (a) Find the equation of the circle passing through the point (1, -2) & (4, -3) and which
has its centre on the strength line 7y4x3 =+
Answer
![Page 12: Q2 (a) If y = eax.sinbx, then prove that 2 − 1 + 0 Answer · DE51/DC55 ENGINEERING MATHEMATICS-I JUNE 2014 © IETE 1 Q2 (a) If y = eax.sinbx,then prove that 2ay (a2 b. 2)y. 0 2](https://reader034.vdocuments.us/reader034/viewer/2022042113/5e8f087b21f3a5310a702328/html5/thumbnails/12.jpg)
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Q9 (b) Find the focus, vertex, axis, latus-rectum and directrix of the parabola
2x + 4x + 2y = 0 Answer
![Page 13: Q2 (a) If y = eax.sinbx, then prove that 2 − 1 + 0 Answer · DE51/DC55 ENGINEERING MATHEMATICS-I JUNE 2014 © IETE 1 Q2 (a) If y = eax.sinbx,then prove that 2ay (a2 b. 2)y. 0 2](https://reader034.vdocuments.us/reader034/viewer/2022042113/5e8f087b21f3a5310a702328/html5/thumbnails/13.jpg)
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Text Book
Applied Mathematics for Polytechnics H K Dass, 8th edition , CBS Publishes & Distributers.
A text book of comprehensive Mathematics class XI , parmanand Gupta , Laxmi Publishes (P) Ltd. New Delhi .
Engineering Mathematics ,H K Dass , S Chand & Company Ltd 13th edition , New Delhi.
![Page 14: Q2 (a) If y = eax.sinbx, then prove that 2 − 1 + 0 Answer · DE51/DC55 ENGINEERING MATHEMATICS-I JUNE 2014 © IETE 1 Q2 (a) If y = eax.sinbx,then prove that 2ay (a2 b. 2)y. 0 2](https://reader034.vdocuments.us/reader034/viewer/2022042113/5e8f087b21f3a5310a702328/html5/thumbnails/14.jpg)
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