Mathematics-I B.Tech Question Paper : vardhaman.org

College : Vardhaman College Of Engineering
Degree : B.Tech
Semester : I
Subject : Mathematics-I
Document type : Question Paper
Website : vardhaman.org

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Mathematics-I Question Paper :

VARDHAMAN COLLEGE OF ENGINEERING
B. Tech I Semester Supplementary Examinations July – 2014
(Regulations : VCE-R11A)
(Common to All Branches)
Date : 03 July, 2014
Time: 3 hours
Max Marks: 75

Related : Vardhaman College Of Engineering Environmental Science B.Tech Question Paper : www.pdfquestion.in/6290.html

Answer ONE question from each Unit
All Questions Carry Equal Marks
All parts of the question must be answered in one place only

Unit – I :
1. a) Solve cos2 x dy y tan x 7M
b) Find the orthogonal trajectories of the family of coaxial circles x2 + y2+ 2x y+ c= 0 Where y  is a parameter? 8M
a) Solve y 1 1 cos y dx – x log x x sin y- dy 0  8M
b) The temperature of a cup of coffee is 920C, when freshly poured, the room temperature being 240C. In one minute it has cooled to 880C. How much time must elapse before the temperature of the cup becomes 650C? 7M

Unit – II :
3.a) Solve – D2 – 3D – 2- y – ex sin x 7M
b) Solve – 2 6 9- – 3 – D D y e x – – – x by the method of variation of parameters. 8M
4. Determine q and i in an LCR circuit with L=0.5H, R=6O, C=0.02, e – 24  and initial
condition q = i= 0 15M

Unit – III :
5. a) If m and n are positive integers, verify Rolle’s theorem for the function
b) If x – u – 1- v- , y – uv , prove that JJ1 – 1 7M
6. a) Verify Cauchy’s Mean value theorem for the function f x = x – a x -b in [a,b]  8M
b) Obtain the Radius of curvature of the curve asteroid at the point (0,1) 8M

Unit – IV :
7. a) Obtain Laplace transforms of the following esint/t 7M
b) If f (t) is a periodic function with period T, show that JJ1 =1 7M
8. Solve by the method of transforms, the equation y ”’- 2y ”- y ‘- 2y – 0 given  y = (0) y (0) and y (0 6) 8M

Unit – V :
9. a) If F – grad(x3 y – y3z – z3x – x2 y2z2 ), 7M
b) Prove that F – (z- e- xsiny)i – (1- e- xcosy) j – (x- 8 z)k 8M
10. Verify Green’s theorem in the plane – – – – – – – – 3 2 2 4 6 dy where C is the region bounded by y x and y x2 15M

VARDHAMAN COLLEGE OF ENGINEERING
B. Tech I Semester Supplementary Examinations June – 2014
(Regulations : VCE-R11A)
MATHEMATICS-I
(Common to All Branches)
Date : 03 July, 2014
Time: 3 hours
Max Marks: 75
Answer ONE question from each Unit
All Questions Carry Equal Marks
All parts of the question must be answered in one place only

Unit – I :
1. a) Find the orthogonal trajectories of the family of coaxial circles x2 + y2 + 2xy + c = 0 wherey is a parameter. 8M
b) Form the differential equation by eliminating arbitrary constant a from log yx ax 7 M 2.
a) Solve x(2×2 = 3y2 + 7)dx =y(3×2 = 2y2 ?8)dy = 0 8M
b) If a substance cools from 3700c to 3300c in 10 mins, when the temperature of the surrounding air is 2900c, find the temperature of the substance after 40 mins. 7M

Unit – III :
2. a) Evaluate 1 2 0 y y xy dx dy by changing the order of integration. 7M
b) Verify Cauchy’s Mean value theorem for the function f (x) = ex ; g + x (ex in a,b 8M )
3. Solve by using Laplace transforms y + 2y + y ‘? 2y = 0 7M
a. Verify Green’s theorem for where C is bounded by y + x + y = x2 15M

Four Year B. Tech I Semester Supplementary Examinations June – 2014 :
Regulations: VCE-R11
Engineering Drawing :
(Common to Mechanical Engineering, Aeronautical Engineering & Civil Engineering)
Date: 15 June, 2014 AN
Time: 3 hours
Max Marks: 75
Answer ONE question from each Unit
All Questions Carry Equal Marks
All parts of the question must be answered in one place only

Unit – I :
1. a) Divide a line of 85mm into 9 equal parts using dividing line by any angle method. 8M
b) Construct a scale of 1:8 to show decimeter and centimeter and to read up to 1m. Show a length of 7.6 dm on it. 7M
2. a) The major and minor axes of an ellipse are 120mm and 80mm. Draw an ellipse by oblong method 8M
b) Draw the involute of a regular hexagon of side 20 mm. 7M

Unit – II :
3. The front view of a straight line AB is 60 mm long and is inclined at 60? to the reference line xy. The end point A is 15 mm above HP and 20 mm in front of VP. Draw the projections ofthe line AB if it is inclined at 45? to VP and is situated in the first quadrant. Determine its true length and inclination with HP. 15M
4. A line AB has its end A 20mm above HP and 25mm in front of VP and the other end is 45mm above HP and 55mm in front of VP. The distance between the end projectors is 60mm. Draw its projections and also find its true length and true inclinations of the line with HP and VP. 15M

Unit – III :
5. Draw the top, front and left views of a pentagonal prism of sides of base 25 mm and height 60 mm resting on an edge of base on HP such that the axis is inclined at 300 to HP and parallel to VP. 15M
6. A pentagonal prism is resting on one of the corners of its base on HP. The longer edge containing that corner is inclined at 45? to HP. The axis of the prism appears to be inclined at an angle of 30? to VP. Draw the projections of the solid. 15M

Unit – IV :
7. A pentagonal prism, side of base 25mm and axis 60mm long, rests with one of the edges of its base on HP. Its axis is inclined at 30oto HP and parallel to VP. It is cut by a horizontalsection plane passing through the highest corner of the base. Draw the sectional top view. 15M
8. A cone base 50mm diameter and axis 65mm long, rests with its base on HP. It is cut by a section plane perpendicular to VP, inclined at 45o to HP and passing through a point on the axis 35mm above the base. Draw the sectional top view and the true shape of section. 15M

Unit – V :
9. Draw the development of the truncated portion of a square pyramid of 30 mm side of the base and height 50 mm rests with its base on HP with one of the edges of the base parallel to VP. The truncated surface is inclined at 450 to the axis and bisecting it. 15M
10. A cone of base diameter 40mm and axis 60mm long is resting on its base on HP. It is cut by a section plane perpendicular to Vp and parallel to an extreme generator and passing through a point on the axis at a distance of 20mm from the apex. Draw the development of the retained solid. 15M