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

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

DR. BABASAHEB AMBEDKAR TECHNOLOGICAL UNIVERSITY, LONERE
End ? Semester Examination (Supplementary): November 2018
Branch: B. Tech (Common to all) Semester: 11
Subject with code: Engineen'ng Mathematics ? II (MATH 201)
Date: 27/11/2018 Max Marks: 60 Duration: 03 Hrs.
INSTRUCTION: Attempt any FIVE 0f the following questions. All questions carry equal marks.
Q.1
Q.2
Q.3
Q.4
(a) Prove that c0560 ? sin69 = 1?16(c0360 + 15coszs). [6 Marks]
(b) If an(A + it?) = x + iy , prove that
. _ 2x .. _ 2y
(1) tanZA ? ?1?x2?y2 (11) tanhZB ? 1+x2+y2 . [6 Marks]
(a) Solve<1 + 3;) dx + e; (1 ?? dy = 0 . [6 Marks]
(b) Solve
x ? xdy + logxdx = 0 . [6 Marks]
Solve any TWO:
(a) Solve y" + 4y? + 13y = 1812?21. [6 Marks]
(b) Solve (D2 + 51) + 4)y = x2 + 7x + 9. [6 Marks]
(0) Solve by the method of variation of parameters
dzy _
F + y ? cosecx . [6 Marks]
(a) Find the Fourier series of f (x) = x2 in the intewal (0 , 211') and hence deduce that
n' 1 1 1 1
E=F_2_2+3_2_E+... [6Marks]
(b) Expand the function f (x) = 1:27 ? x2 in a half? range sine sen'es 111 the interval(0 , 7r).
[6 Marks]
P.T.O.
E66B3217D5B275ABOCBD2EOB029A1D41

Q5
0.6
(a) The necessary and suf?cient condition for vector F(t) to have constant magnitude is
?(t) .di?(tt) = . ' [6 M arks]
(b) A point moves in a plane so that its tangential and normal components of acceleration are
equal and the angular velocity of the tangent is constant and equal to a). Show that the path is
equiangular spiralms = Aemt + B, where A & B are constants. [6 M arks]
Solve any TWO:
(a) Find curlF' , where? = V (x3 + y3 + Z3 ? 3xyz) . [6 Marks]
(b) If F is a position vector With r = WI , show that
V. (Tn?) = (n + 3)r". [6 Marks]
(0) Show that ff f? f?E: ffs ?r?f? ds. [6 Marks]
************************
? E66B3217D5B275ABOCBD2EOB029A1D41