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Calculus
(2110014)
Winter 2015 Sem-1
MCQ(s) of
Calculus
(2110014)
- Winter 2015 Sem-1
Q.
1
T
h
e
v
a
l
u
e
o
f
lim
n
→
∞
1
+
1
n
n
i
s
(A)
1
(B)
-
1
(C)
e
(D)
1
e
Answer
(C)
e
Q.
2
T
h
e
v
a
l
u
e
o
f
lim
x
→
0
x
x
i
s
(A)
1
(B)
-
1
(C)
e
(D)
1
e
Answer
(A)
1
Q.
3
M
a
c
l
a
u
r
i
n
’
s
s
e
r
i
e
s
o
f
e
-
x
i
s
(A)
∑
n
=
0
∞
x
n
n
!
(B)
∑
n
=
0
∞
-
1
n
x
n
n
!
(C)
∑
n
=
1
∞
x
n
n
!
(D)
∑
n
=
1
∞
-
1
n
x
n
n
!
Answer
(B)
∑
n
=
0
∞
-
1
n
x
n
n
!
Q.
4
I
f
f
(
x
,
y
,
z
,
w
)
=
3
cos
(
x
w
)
sin
y
5
e
y
+
(
1
+
y
2
)
/
x
y
w
+
5
x
z
w
,
t
h
e
n
∂
f
∂
z
a
t
(
1
,
2
,
3
,
4
)
i
s
(A) 20
(B) 200
(C) 0
(D) 1
Answer
(A)
20
Q.
5
M
i
n
i
m
u
m
v
a
l
u
e
o
f
f
(
x
,
y
)
=
x
2
y
2
i
s
(A) 1
(B) 2
(C) 4
(D) 0
Answer
(D)
0
Q.
6
T
h
e
s
u
m
o
f
t
h
e
s
e
r
i
e
s
∑
n
=
1
∞
1
2
n
i
s
(A) 0
(B)
3
4
(C) 1
(D) 2
Answer
(C)
1
Q.
7
V
a
l
u
e
o
f
t
h
e
lim
(
x
,
y
)
→
(
0
,
0
)
x
2
-
x
y
x
-
y
i
s
(A) 1
(B) 0
(C) -1
(D) Limit does not exist
Answer
(B)
0
Q.
8
T
h
e
v
a
l
u
e
o
f
∬
3
y
d
x
d
y
o
v
e
r
t
h
e
t
r
i
a
n
g
l
e
w
i
t
h
v
e
r
t
i
c
e
s
(
-
1
,
1
)
,
(
0
,
0
)
,
a
n
d
(
1
,
1
)
i
s
(A) 0
(B) 1
(C) 2
(D) 3
Answer
(A)
0
Q.
9
T
h
e
s
e
r
i
e
s
∑
n
=
1
∞
(
-
1
)
n
n
i
s
(A) Divergent
(B) Absolutely convergent
(C) Conditionally convergent
(D) Nothing can be said
Answer
(C)
Conditionally convergent
Q.
10
I
f
J
=
∂
(
x
,
y
)
∂
(
r
,
θ
)
a
n
d
J
*
=
∂
(
r
,
θ
)
∂
(
x
,
y
)
,
t
h
e
n
t
h
e
v
a
l
u
e
o
f
J
J
*
i
s
(A) 0
(B) 1
(C) -1
(D) Always J=J*
Answer
(B)
1
Q.
11
What does the polar equation r=a,a>0 represent?
(A) Line
(B) Rectangle
(C) Circle
(D) Parabola
Answer
(C)
Circle
Q.
12
T
h
e
c
u
r
v
e
x
3
+
y
3
=
3
a
x
y
i
s
s
y
m
m
e
t
r
i
c
a
b
o
u
t
(A) X-axis
(B) Y-axis
(C) Origin
(D) The line y=x
Answer
(D)
The line y=x
Q.
13
T
h
e
v
a
l
u
e
o
f
∫
1
∞
1
x
2
d
x
i
s
(A) 1
(B) 0
(C) -1
(D) Does not exist
Answer
(A)
1
Q.
14
I
f
f
(
x
,
y
)
=
x
y
+
sin
y
x
e
y
x
,
t
h
e
n
t
h
e
v
a
l
u
e
o
f
x
∂
f
∂
x
+
y
∂
f
∂
y
i
s
(A) 1
(B) 0
(C) -1
(D) f
Answer
(B)
0