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DR. BABASAHEB AMBEDKAR TECHNOLOGICAL UNIVERSITY, LONERE
End – Semester Examination (Supplementary): May 2019
Branch: B. Tech (Common to all)
Semester: I
Subject with code: Engineering Mathematics – I (MATH 101)
Date: 28.05.2019
Marks: 60
Duration: 03 Hrs.
INSTRUCTION: Attempt any FIVE of the following questions. All questions carry equal marks.
Q.1
(
a) Solve the equations:
+ ꢁꢂ + ꢃꢄ + ꢅ = ꢆ ; ꢁꢀ + ꢃꢂ + ꢇꢄ + ꢁꢅ = ꢆ ; ꢈꢀ + ꢉꢂ + ꢁꢄ = ꢆ
ꢑ ꢃ
ꢀ
[6 ꢊꢋꢌꢍꢎ]
[6 ꢊꢋꢌꢍꢎ]
ꢈ
(
b) Find the eigen values and eigen vectors of the matrix ꢏ = ꢐꢆ
ꢁ
ꢉꢓ.
ꢆ
ꢆ ꢒ
Q.2
(
a) Find the ꢔꢕꢖ order derivative of ꢂ = ꢗꢘꢙꢃꢀ .
[6 ꢊꢋꢌꢍꢎ]
[6 ꢊꢋꢌꢍꢎ]
b) Using Taylor’s theorem, express the polynomial ꢚ(ꢀ) = ꢁꢀꢈ + ꢛꢀꢁ + ꢀ − ꢉ
in the powers of (ꢀ − ꢑ).
(
Q.3 Solve any TWO:
ꢜ
ꢜ
ꢄ
ꢜꢄ
ꢜꢂ
ꢀꢁꢢꢂ
ꢁ
if ꢄ = ꢝꢞꢟꢠꢑ
ꢡ ꢀꢢꢂ ꢣ .
(
(
a) Evaluate
,
[6 ꢊꢋꢌꢍꢎ]
ꢀ
b) If ꢄ is a homogeneous function of degree ꢔ in ꢀ ꢋꢤꢥ ꢂ , prove that
ꢜ
ꢁꢄ
ꢁ + ꢁꢀꢂ
ꢜꢁꢄ
ꢜꢁꢄ
ꢀꢁ ꢜ
+ ꢂꢁ ꢁ = ꢔ(ꢔ − ꢑ)ꢄ.
[6 ꢊꢋꢌꢍꢎ]
[6 ꢊꢋꢌꢍꢎ]
ꢀ
ꢜꢀꢜꢂ
ꢜꢂ
ꢜꢦ ꢜꢦ ꢜꢦ
c) If ꢦ = ꢚ(ꢂ − ꢄ , ꢄ − ꢀ , ꢀ − ꢂ) , show that ꢜꢀ + ꢜꢂ + ꢜꢄ = ꢆ.
(
1
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