Download DBATU B-Tech 1st Year 2019 Winter Engineering Mathamatics I Question Paper

Download DBATU (Dr. Babasaheb Ambedkar Technological University) B.Tech First Year 2019 Winter Engineering Mathamatics I Question Paper

DR. BABASAHEB AMBEDKAR TECHNOLOGICAL UNIVERSITY, LONERE
End Semester Winter Examination ? Dec 2019
Course: B. Tech (All Courses) Sem: I
Subject N ame: Engineering Mathematics-I Subject Code: BTMA101
Max Marks: 60M Datez-11/12/2019 Duration:- 3 Hrs.
Instructions to the Students:
1. All questions are compulsory.
2. Use of non-programmable calculator is allowed.
3. F igures to right indicate full marks.
4. Illustrate your answer with neat sketches, diagram etc. whatever necessary.
5. If some part of parameter is noticed to be missing you may appropriately assume it and should mention it
clearly.
Marks
Q. 1 Solve the following questions.
1 2 3 ?1
A) Reduce t0 the Normal form and ?nd the rank of the given matrix. A 2 '1 '1 '3 '1 4
1 0 1 1
0 1 1 ?1
B) Test the consistency and solve:
2x1+x2 ?x3 +3x4 =11, xl?Zx2 +x3 +x4 =8 , 4x1+7x2 +2x3 ?x4 = 0 , 3x1+5x2 +4x3 +4x4 =17 4
C) Find the eigen value & eigen vector for least positive eigen value of the matrix :
_ 4
A = ?
Q.2 Solve any three of the following.
1: y : _ - _ _ 622 ?1
A) If xy Z ?C showthatatpomtx?y?Z , =?[x ex] 4
8x8);
B) Ifuz (?iverify ?=6_u?+6u d" 4
d: am: 63
2 2 2
C If?: ? Lthenprovethatx26u+ x au+ 26u=? ??1 4
) 2 y y
?5 + y 6x 8x8)? u ?
D) Ifu=f x? y y?J?Ziprovethat?a?u+?a?u+?a?u: 4
6x 6y 4L
Q. 3 Solve any three of the following.
A) Expand f x y 2 ex? in Maclaurin?s theorem up to fourth term. 4
B) Ifx=u ?V y=uv provethatJJVZ 4
C) A rectangular box open at the top is to have volume of 256 cubic feet, determine the 4
dimensions of the box required least material for the construction of the box.
D) Examine the function x3 + y3 ? axy for maxima & minima where a > 4
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Q.4 Solve any three of the following.
2a
A) Evaluate I x (Zax ? x2 )dx
0
B) Trace the Curve y2 a?x = x2 a +x
C) Trace the Curve x = a 005% , y = a sin3t
D) Trace the Curve 1? =61 COS 39
Q. 5 Solve the following questions.
A a /
) Change the order of integration I = I I f (x, y)dxdy
0 x
a \IUI?XZ
B) Change to polar and evaluate I I A
o [?(l?z a2 ?x2 ?y2
C) F ind the volume bounded by the cylinders x2+y2 = ax & Z2 = ax
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