Total No. of Questions : 9] SEAT No. :
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23
P-3926 [Total No. of Pages : 5
ic-
[6001]-4001
tat
9s
F.E.
7:3
02 91
ENGINEERING MATHEMATICS - I
0:3
0
(2019 Pattern) (Semester - I) (107001)
31
4/0 13
0
Time : 2½ Hours] [Max. Marks : 70
7/2
.23 GP
Instructions to the candidates:
1) Question No. 1 is compulsory.
E
82
8
2) Solve Q. No. 2 or Q. No. 3, Q. No. 4 or Q. No. 5, Q. No. 6 or Q. No. 7, Q. No. 8
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23
or Q. No. 9.
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16
3) Neat diagrams must be drawn wherever necessary.
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8.2
4) Figures to the right indicate full marks.
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5) Electronic pocket calculator is allowed.
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91
6) Assume suitable data, if necessary.
49
0:3
30
31
Q1) Write the correct option for the following multiple choice questions :
01
02
7/2
¶u ¶u
GP
1 1 1
a) If u = + + then x + y is equal to [2]
4/0
x2 y 2 x2 + y 2 ¶x ¶y
CE
82
8
i) 2u ii) –2u
23
.23
iii) 0 iv) None
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tat
8.2
¶u
9s
b) If u = xy then is equal to [1]
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¶y
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91
49
0:3
i) 0 ii) yxy–1
30
31
iii) xy logx iv) xy–1
01
02
¶(u, v)
7/2
u
GP
c) If x = uv, y = then the value of is [2]
¶ ( x, y )
4/0
v
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82
-2u
i) ii) uv
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v
16
-v
8.2
v
iii) iv)
2u 2u
.24
49
P.T.O.
Other PYQs • www.studymedia.in/fe/pyqs
, d) A is orthogonal matrix then A–1 equal to [1]
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i) A ii) A T
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iii) A 2 iv) 1
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e) For what value of K the homogeneous system x + 2y – z = 0,
9s
3x + 8y – 3z = 0; 2x + 4y + (k–3)z = 0 has infinitely many solution.[2]
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i) K = 0 ii) K = 1
02 91
0:3
iii) K = 2 iv) K = 3
0
31
4/0 13 é1 4ù
f) Using Cayley Hamilton theorem A–1 for the matrix A = ê ú is
êë 2 3úû
0
7/2
.23 GP
calculated from [2]
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82
1 1
8
i) (-A - 4I) ii) (A - 4I)
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23
5 5
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1 1
iii) (A + 4I) iv) (4I - A)
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5 5
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91
49
0:3
¶ 2u ¶ 2u
30
Q2) a) If u = ln(x2 + y2), show that = . [5]
31
¶x¶y ¶y¶x
01
02
7/2
y
GP
b) If e2u = y2 – x2, cos ec v = then find the value of [5]
4/0
x
CE
82
8
æ ¶u ¶u ö æ ¶u ¶u ö
23
ççç x + y ÷÷÷.çç x + y ÷÷÷
.23
¶y ø çè ¶x
è ¶x
ic-
¶y ø
16
tat
8.2
¶u ¶u ¶u
9s
c) If u = f(x – y, y – z, z – x) then find the value of + + . [5]
.24
¶x ¶y ¶z
7:3
91
49
0:3
OR
30
31
æ ¶u ö æ ¶x ö
Q3) a) If u = ax + by, v = bx – ay find the value of ççç ÷÷÷ .ççç ÷÷÷ . [5]
01
02
è ¶x øy è ¶u øv
7/2
GP
æ xy ÷ö
4/0
¶T ¶T
b) If T =sin çç 2 ÷÷ + x 2 + y 2 , find the value of x +y . [5]
CE
çè x + y ø
82
2
¶x ¶y
.23
c) If u = f(r, s) where r = x 2 + y 2 , s = x 2 – y 2 then show that
16
¶u ¶u ¶u
8.2
y +x = 4 xy . [5]
¶x ¶y ¶r
.24
49
[6001]-4001 2
Other PYQs • www.studymedia.in/fe/pyqs
8
23
P-3926 [Total No. of Pages : 5
ic-
[6001]-4001
tat
9s
F.E.
7:3
02 91
ENGINEERING MATHEMATICS - I
0:3
0
(2019 Pattern) (Semester - I) (107001)
31
4/0 13
0
Time : 2½ Hours] [Max. Marks : 70
7/2
.23 GP
Instructions to the candidates:
1) Question No. 1 is compulsory.
E
82
8
2) Solve Q. No. 2 or Q. No. 3, Q. No. 4 or Q. No. 5, Q. No. 6 or Q. No. 7, Q. No. 8
C
23
or Q. No. 9.
ic-
16
3) Neat diagrams must be drawn wherever necessary.
tat
8.2
4) Figures to the right indicate full marks.
9s
.24
5) Electronic pocket calculator is allowed.
7:3
91
6) Assume suitable data, if necessary.
49
0:3
30
31
Q1) Write the correct option for the following multiple choice questions :
01
02
7/2
¶u ¶u
GP
1 1 1
a) If u = + + then x + y is equal to [2]
4/0
x2 y 2 x2 + y 2 ¶x ¶y
CE
82
8
i) 2u ii) –2u
23
.23
iii) 0 iv) None
ic-
16
tat
8.2
¶u
9s
b) If u = xy then is equal to [1]
.24
¶y
7:3
91
49
0:3
i) 0 ii) yxy–1
30
31
iii) xy logx iv) xy–1
01
02
¶(u, v)
7/2
u
GP
c) If x = uv, y = then the value of is [2]
¶ ( x, y )
4/0
v
CE
82
-2u
i) ii) uv
.23
v
16
-v
8.2
v
iii) iv)
2u 2u
.24
49
P.T.O.
Other PYQs • www.studymedia.in/fe/pyqs
, d) A is orthogonal matrix then A–1 equal to [1]
8
23
i) A ii) A T
ic-
iii) A 2 iv) 1
tat
e) For what value of K the homogeneous system x + 2y – z = 0,
9s
3x + 8y – 3z = 0; 2x + 4y + (k–3)z = 0 has infinitely many solution.[2]
7:3
i) K = 0 ii) K = 1
02 91
0:3
iii) K = 2 iv) K = 3
0
31
4/0 13 é1 4ù
f) Using Cayley Hamilton theorem A–1 for the matrix A = ê ú is
êë 2 3úû
0
7/2
.23 GP
calculated from [2]
E
82
1 1
8
i) (-A - 4I) ii) (A - 4I)
C
23
5 5
ic-
16
tat
1 1
iii) (A + 4I) iv) (4I - A)
8.2
9s
5 5
.24
7:3
91
49
0:3
¶ 2u ¶ 2u
30
Q2) a) If u = ln(x2 + y2), show that = . [5]
31
¶x¶y ¶y¶x
01
02
7/2
y
GP
b) If e2u = y2 – x2, cos ec v = then find the value of [5]
4/0
x
CE
82
8
æ ¶u ¶u ö æ ¶u ¶u ö
23
ççç x + y ÷÷÷.çç x + y ÷÷÷
.23
¶y ø çè ¶x
è ¶x
ic-
¶y ø
16
tat
8.2
¶u ¶u ¶u
9s
c) If u = f(x – y, y – z, z – x) then find the value of + + . [5]
.24
¶x ¶y ¶z
7:3
91
49
0:3
OR
30
31
æ ¶u ö æ ¶x ö
Q3) a) If u = ax + by, v = bx – ay find the value of ççç ÷÷÷ .ççç ÷÷÷ . [5]
01
02
è ¶x øy è ¶u øv
7/2
GP
æ xy ÷ö
4/0
¶T ¶T
b) If T =sin çç 2 ÷÷ + x 2 + y 2 , find the value of x +y . [5]
CE
çè x + y ø
82
2
¶x ¶y
.23
c) If u = f(r, s) where r = x 2 + y 2 , s = x 2 – y 2 then show that
16
¶u ¶u ¶u
8.2
y +x = 4 xy . [5]
¶x ¶y ¶r
.24
49
[6001]-4001 2
Other PYQs • www.studymedia.in/fe/pyqs
