Download DBATU B-Tech 1st Year 2018 Dec Engineering Mathematics I 2 Question Paper

Download DBATU (Dr. Babasaheb Ambedkar Technological University) B.Tech First Year 2018 Dec Engineering Mathematics I 2 Question Paper

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DR. BABASAHEB AMBEDKAR TECHNOLOGICAL UNIVERSITY, LONERE
End ? Semester Examination (Supplementaly): November 2018
Branch: B. Tech (Common to all) Semester: I
Subject with code: Engineering Mathematics ? I (MATH 101)
Date: 26/11/2018 Marks: 60 Duration: 03 Hrs.
INSTRUCTION: Attempt any FIVE 0f the following questions. All questions can'y equal marks.
1 ?1 2 3
Q.1 (a)Find the rank of the matu'x A : 3 ? 5) ?21 by reducing it to normal form
0 1 O 2
[6 Marks]
3 1 4
(b) Find the eigen values and eigen vectors of the matrix A = [0 2 6]. [6 M arks]
O 0 5
Q2 (a) Ify = easm _1" ,prove that(1 ? x2)yn+2 ? (2n + 1)xyn+1 ? (n2 + zzz)y71 = 0.
[6 Marks]
(b) Using Taylor?s theorem, express the polynomial
f (x) = 2x3 + 7x2 + x ? 6in powers of (x ?- 1). [6 Marks]
Q.3 Solve any TWO:
? 2 2 2 2 2 z :23: 2:2 ? _
(a) va ? log(x + y +2 ), prove that(x +31 +2 )(6x2 + By? 622) ? 2.
[6 Marks]
(b) If 2 is a homogeneous function of degree nin , y , prove that
62 52 52
x2 695?: + 295318366: + y2 By?: = u(n ? DZ. [6 Marks]
(0) Ifz = f(x,y) where x = e? + e??& y = e?? ? e? , then show that
?i?a?z? a_z_ 62 [6 Marks]
au 61; _ x?x 3?
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Q.4
Q.6
601,17, w) _
a(x' y. z) ? [4 Marks]
(a) If u = g , v = ?andw = %, show that
(b) The focal length of a mirror is found from the formula; = 11; ? % Find the percentage error inf
if u & vare both in error by 2% each. ' [4 M arks]
(c) F ind the maximum value of xmynzp, when x + y + z = C . [4 Marks]
(a) Evaluate the integral I = fol f: 6?" dy'dx.
[6 M arks]
(b) Change to polar co?ordinates to evaluatel = [00? [00? e?(x2+y2) dx dy . [6 Marks]
(c) Evaluate the integral I = fol I}; [01?25 x dz dx dy . [6 M arks]
(a) State D? Alembert?s ratio test, and hence check the convergence of the series:
n
2:11 W . 4 [6 Marks]
(b) State Cauchy?s root test,,and hence check the convergence of the series:
MW
2 (1 + j?E-yn . [6 Marks]
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E66B3217D58275ABOCBD2EOB028BF726