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Mathematics-I: Code No: MA1501 Model Question Paper I B. Tech I Semester External Examinations

This document is a model question paper for Mathematics 1 for the first semester of an engineering degree. It contains 6 questions in Part A worth 2 marks each and 4 questions in Part B worth 12 marks each. Part A questions cover topics like integrating factors, solving differential equations, Jacobian determinants and finding areas. Part B questions involve solving differential equations, finding dimensions to minimize material use, sketching curves, evaluating triple integrals and applying Stokes' theorem. Students must answer all Part A questions and 4 out of the 6 Part B questions.

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Krish Pavan
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3K views2 pages

Mathematics-I: Code No: MA1501 Model Question Paper I B. Tech I Semester External Examinations

This document is a model question paper for Mathematics 1 for the first semester of an engineering degree. It contains 6 questions in Part A worth 2 marks each and 4 questions in Part B worth 12 marks each. Part A questions cover topics like integrating factors, solving differential equations, Jacobian determinants and finding areas. Part B questions involve solving differential equations, finding dimensions to minimize material use, sketching curves, evaluating triple integrals and applying Stokes' theorem. Students must answer all Part A questions and 4 out of the 6 Part B questions.

Uploaded by

Krish Pavan
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as DOCX, PDF, TXT or read online on Scribd
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Code No: MA1501 R14

Model Question Paper


I B. Tech I Semester External Examinations
MATHEMATICS-I
(Common to All branches)
Time: 3 Hours Max. Marks: 60

Note: All Questions from Part A are to be answered at one place.


Answer any Four Questions from Part B

PART - A
6 X 2 = 12 M

1. Which integrating factor makes the non - exact differential equation (xy3 + y) dx + 2(x2
y2 + x + y4) dy = 0 to exact differential equation?

2. Solve (D2 – 2D + 4)2 y = 0

3. If x = eu cos v, y = eu sin v, find J =  ( x, y )


 (u , v )

4. Find the area between the parabolas y2 = 4ax and x2 = 4ay.

5. Find the directional derivative of f(x,y,z) = xy2 + yz3 at the point (2,-1,1) in the direction
of vector I + 2 J + 2K?

6. Find the work done by the force F  (2 y  3)i  xz j  ( yz  x)k when it moves a practical

from the point (0,0,0) to (2,1,1) along the curve x = 2t2 , y = t, z = t3.
PART- B
4 X 12 = 48 M
1. a) dy
Solve x  y  x3 y6 6M
dx
b) If 30% of radioactive substance disappeared in 10 days, how long will it take for 90%
of it to disappear? 6M

2. a) Solve (D2 -4D + 3) y = sin 3x cos2x 6M


b) Solve (D4 -1) y = ex cos x 6M

 ( x, y , z )
3. a) If u = xyz, v = x2 + y2 + z2 , w = x + y + z find 6M
(u, v, w)
b) A rectangular box open at the top is to have volume of 32 cubic ft. Find the
dimensions of the box requiring least material for its construction. 6M

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4. a) Trace the curve x3 + y3 = 3axy 6M

z dx dy dz , taken over the volume bounded by the surfaces x2 + y2 = a2, x2 + y2 =


2
b)

z and z = 0. 6M

5. a) Find the values of a and b such that the surfaces ax2 – byz = (a+2) x and 4x2 y + z3 = 4
cut orthogonally at (1,-1,2). 6M
 
b) Show that  2 r n  n(n  1)r n2 6M

6. Verify Stok’s theorem for F  ( x 2  y 2 )i  2 xy j taken around the rectangle bounded by

the lines x =  a, y  0, y  b. 12M

***

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