Download DBATU B-Tech 1st Year 2017 May Engineering Mathematics I 1 Question Paper

Download DBATU (Dr. Babasaheb Ambedkar Technological University) B.Tech First Year 2017 May Engineering Mathematics I 1 Question Paper

DR. BABASAHEB AMBEDKAR TECHNOLOGICAL UNIVERSITY, LONERE
SEMESTER EXAMINATION: WM. ;;,?3 7 7C 5 7,1?
, Mechanical/Electrical/ExTC/Chcmical/Petrochemical/Computcr/lT/Civil
Subject : Engineering Mathematics-I (New) ES r} 1 O \ Semester : I
Time : 03 Hrs Max. Marks : 60
2 MAY 2017
INSTRUCTION: ATTEMPT ANY FIVE QUESTIONS.
1 2 3 2
Q]. (a) Find the rank ofthc matrix A = [2? 3 5 1] by reducing it to normal form. [4 Marks]
.1 3 5 4
(b) Fcr what values of k is the following system of equations consistent, and hence solve for [4 Marks]
them:
x+y+z= 1;x+2y+4z=k;x+4y+102=k2.
3 1 4-
(c) Find the eigen values and eigen vectors of the matrix A = 0 2 6 . [4 Marks]
0 0 5
Q2. (a) Find the nth derivative of tar."1 (13;) in terms of r and 6. [4 Marks]
(b) If y = (x2 ? 1)", prove that (x ? 1)yn+2 + 2xyn+1 ? n(n + 1)yn = 0. [4 Marks]
(c) Expand f(x+h) = tan?1(x + h) in powers of h and hence ?nd the value of [4 Marks]
tan?1(1.003) upto ?ve places of'decimal.
2 2 z 2 Z 2 ,.
Q3. (a) If x?+ y + 2 =1, provethat (?1?) + a?) + a?) =2[x:?:+y:?;+z:?:. [4 Mam]
a2+u b2+u cZ+u 0x 5 62
(b) If 2 is a homogeneous function of degree n in x, y , then prove that [4 Marks]
622 622 622
2?,+2x 2?=nn?1z.
at 6x1 y 6x6y+y 6y2 ( )
(c) If F = F(x,y,z) where x = u -- v + w, y = uv + vw + wu, z = xyz , then show that [4 Marks]
6F 6F 6F 6F 6F , 6F
?+ .__- 4?: ? 2 ?+3 ?.
uau L61:+W0w xax+ yay 262
-?-+ P.T.O.

Q4. (:1) Expand f (x, y) = cos x si? y . as; f_ar as the terms ofthird degree. [4 Marks]
(b) lf?lhe sides and angles ol?a plane lria?gle'v'ary fn such a way that its circum-radius remains [4 Marks]
da db dc
cos A (:05 [3 cos C
constant, prove that = 0, .where da, db, dc are smaller increments
in he sides a,b,c respectively.
(c) Find the maximum and minimum distances from the origin to the curve [4 Marks]
15x2 + 4xy + 6y2 = 140.
05? (a) Change to polar co-nrdinates and evaluate l = fow foo) e?(x2+3?2) dx dy. [4 Marks]
2
(b) Evaluate l = fol f?dxdy by changing the order ofintegration. [4 Marks]
V ?1
, 4 2v? alf? ,
(c) Evaluate I 2 f0 f0 ID x uydxdz. [4 Marks]
Q6. (21) Find the interval ofconvergencc ofthe series Enlix". [4 Marks]
(b) Test the convergence ot?the series 2 (2:27! x". [4 Marks]
(0) Test the convergence 0fthe series 231:1 JT?V . [4 Marks]
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