Total No. of Questions : 9] SEAT No. :
8
23
PB3586 [6260]-1
[Total No. of Pages : 5
ic-
F.E.
tat
0s
ENGINEERING MATHEMATICS-I
9:0
(2019 Credit Pattern) (Semester -I/II) (107001)
02 91
9:5
Time :2½Hours] [Max. Marks :70
0
40
Instructions to the candidates:
5/0 13
1) Q.1 is Compulsory.
0
2) Answer Q.2 or Q.3, Q.4 or Q.5, Q.6 or Q.7, Q.8 or Q.9.
5/2
.23 GP
3) Figures to the right indicate full marks.
4) Assume suitable data, if necessary.
E
5) Neat diagrams must be drawn wherever necessary.
81
8
C
23
6) Use of electronic pocket calculator is allowed.
ic-
Q1) Write the correct option for the following MCQs. [10]
16
tat
8.2
0s
2u
a) If u x y then
3 3 ? [2]
.24
9:0
xy
91
49
9:5
i) 3 ii) 3
30
40
iii) 2 iv) 0
01
02
5/2
u ( x, y )
GP
b) If x uv , y the ? [2]
(u, v)
5/0
v
CE
81
8
2u
23
.23
i) ii) uv
v
ic-
16
tat
v v
8.2
0s
iii) iv)
2u 2u
.24
9:0
91
49
9:5
1 1 1
30
40
c) Rank of matrixA= 0 1 0 is ....? [2]
01
02
1 1 1
5/2
GP
5/0
i) 0 ii) 1
CE
iii) 2 iv) 3
81
.23
16
8.2
.24
[6260]-1 1 P.T.O.
49
, 1 4
8
d) Using Cayley Hamilton theorem A for the matrix A= is
23
-1
2 3
ic-
given by; [2]
tat
0s
1 1
i) (A+4I) ii) (A+5I)
9:0
5 4
02 91
9:5
1 1
0
iii) (A 5I) iv) (A 4I)
40
4 5/0 13 5
0
e) If A1 =A ' then matrix A is ....? [1]
5/2
.23 GP
i) Orthogonal ii) Singular
iii) Non-Singular iv) None of above
E
81
8
C
23
u
If u x 3 4 y 3 x ,
ic-
f) =....? [1]
x
16
tat
8.2
i) 4 ii) 3 x 2 3
0s
.24
9:0
iii) 3 x 2 4 y iv) 3 x 2 1
91
49
9:5
30
40
2u
01
Q2) a) If u x y ,find
y x
[5]
02
xy
5/2
GP
x3 y 3 2 u
2
2u 2 u
2
5/0
b) If u log 2 2 , find the value of x 2 xy y [5]
x y x 2 xy y 2
CE
81
8
23
u u u
.23
0
c) If u f ( y z , z x, x y ) , Prove that
x y z ic-[5]
16
tat
8.2
0s
OR
.24
9:0
u x 1
91
49
If x au bv and y au bv , prove that x u 2
9:5
Q3) a) 2 2
[5]
y v
30
40
01
u u
02
1 y
If u sin x y , find the value of x y
2 2
b) [5]
5/2
x x y
GP
5/0
cos sin
CE
x
,y z f ( x, y ) ,then
81
c) If and show that
u u
.23
z z z z
u ( y x) ( y x )
16
[5]
u x y
8.2
.24
[6260]-1 2
49
8
23
PB3586 [6260]-1
[Total No. of Pages : 5
ic-
F.E.
tat
0s
ENGINEERING MATHEMATICS-I
9:0
(2019 Credit Pattern) (Semester -I/II) (107001)
02 91
9:5
Time :2½Hours] [Max. Marks :70
0
40
Instructions to the candidates:
5/0 13
1) Q.1 is Compulsory.
0
2) Answer Q.2 or Q.3, Q.4 or Q.5, Q.6 or Q.7, Q.8 or Q.9.
5/2
.23 GP
3) Figures to the right indicate full marks.
4) Assume suitable data, if necessary.
E
5) Neat diagrams must be drawn wherever necessary.
81
8
C
23
6) Use of electronic pocket calculator is allowed.
ic-
Q1) Write the correct option for the following MCQs. [10]
16
tat
8.2
0s
2u
a) If u x y then
3 3 ? [2]
.24
9:0
xy
91
49
9:5
i) 3 ii) 3
30
40
iii) 2 iv) 0
01
02
5/2
u ( x, y )
GP
b) If x uv , y the ? [2]
(u, v)
5/0
v
CE
81
8
2u
23
.23
i) ii) uv
v
ic-
16
tat
v v
8.2
0s
iii) iv)
2u 2u
.24
9:0
91
49
9:5
1 1 1
30
40
c) Rank of matrixA= 0 1 0 is ....? [2]
01
02
1 1 1
5/2
GP
5/0
i) 0 ii) 1
CE
iii) 2 iv) 3
81
.23
16
8.2
.24
[6260]-1 1 P.T.O.
49
, 1 4
8
d) Using Cayley Hamilton theorem A for the matrix A= is
23
-1
2 3
ic-
given by; [2]
tat
0s
1 1
i) (A+4I) ii) (A+5I)
9:0
5 4
02 91
9:5
1 1
0
iii) (A 5I) iv) (A 4I)
40
4 5/0 13 5
0
e) If A1 =A ' then matrix A is ....? [1]
5/2
.23 GP
i) Orthogonal ii) Singular
iii) Non-Singular iv) None of above
E
81
8
C
23
u
If u x 3 4 y 3 x ,
ic-
f) =....? [1]
x
16
tat
8.2
i) 4 ii) 3 x 2 3
0s
.24
9:0
iii) 3 x 2 4 y iv) 3 x 2 1
91
49
9:5
30
40
2u
01
Q2) a) If u x y ,find
y x
[5]
02
xy
5/2
GP
x3 y 3 2 u
2
2u 2 u
2
5/0
b) If u log 2 2 , find the value of x 2 xy y [5]
x y x 2 xy y 2
CE
81
8
23
u u u
.23
0
c) If u f ( y z , z x, x y ) , Prove that
x y z ic-[5]
16
tat
8.2
0s
OR
.24
9:0
u x 1
91
49
If x au bv and y au bv , prove that x u 2
9:5
Q3) a) 2 2
[5]
y v
30
40
01
u u
02
1 y
If u sin x y , find the value of x y
2 2
b) [5]
5/2
x x y
GP
5/0
cos sin
CE
x
,y z f ( x, y ) ,then
81
c) If and show that
u u
.23
z z z z
u ( y x) ( y x )
16
[5]
u x y
8.2
.24
[6260]-1 2
49
