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jee advanced
| 2017
Solutions for all the questions from jee advanced
of year 2017
EXAM
board examination
iit jee
jee advanced
jee main
neet
YEAR
All
2017
SUBJECT
math
maths
class 12
Maths
Calculus
Continuity And Differentiability
Let
f
:
R
0
,
1
be a continuous function. Then, which of the following function (s) has (have) the value zero at some point in the interval (0,1)?
e
x
−
∫
0
x
f
(
t
)
sin
t
d
t
(b)
f
(
x
)
+
∫
0
2
π
f
(
t
)
sin
t
d
t
(c)
x
−
∫
0
2
π
−
x
f
(
t
)
cos
t
d
t
(d)
x
9
−
f
(
x
)
class 11
Maths
Algebra
Complex Numbers
Let
a
,
b
,
x
a
n
d
y
be real numbers such that
a
−
b
=
1
a
n
d
y
=
0
.
If the complex number
z
=
x
+
i
y
satisfies
I
m
(
z
+
1
a
z
+
b
)
=
y
, then which of the following is (are) possible value9s) of x? (a)
−
1
−
1
−
y
2
(b)
1
+
1
+
y
2
(c)
−
1
+
1
−
y
2
(d)
−
1
−
1
+
y
2
class 11
Maths
Algebra
Permutations And Combinations
Word of length 10 are formed using the letters A,B,C,D,E,F,G,H,I,J. Let
x
be the number of such words where no letter is repeated; and let
y
be the number of such words where exactly one letter is repeated twice and no other letter is repeated. The,
9
x
y
=
class 12
Maths
Algebra
Matrices
Which of the following is (are) NOT the square of a
3
×
3
matrix with real entries? (a)
⎣
⎢
⎡
1
0
0
0
1
0
0
0
−
1
⎦
⎥
⎤
(b)
⎣
⎢
⎡
−
1
0
0
0
−
1
0
0
0
−
1
⎦
⎥
⎤
(c)
⎣
⎢
⎡
1
0
0
0
1
0
0
0
1
⎦
⎥
⎤
(d)
⎣
⎢
⎡
1
0
0
0
−
1
0
0
0
−
1
⎦
⎥
⎤
class 11
Maths
Co-ordinate Geometry
Circles
For how many values, of p, the circle
x
2
+
y
2
+
2
x
+
4
y
−
p
=
0
and the coordinate axes have exactly three common points?
class 11
Maths
Calculus
Limits And Derivatives
Let
f
:
R
R
be a differentiable function such that
f
(
0
)
,
f
(
2
π
)
=
3
a
n
d
f
p
r
i
m
e
(
0
)
=
1
.
If
g
(
x
)
=
∫
x
2
π
[
f
p
r
i
m
e
(
t
)
cos
e
c
t
−
cot
t
cos
e
c
t
f
(
t
)
]
d
t
f
or
x
(
0
,
2
π
]
,
then
(
lim
)
x
0
g
(
x
)
=
class 11
Maths
Co-ordinate Geometry
Hyperbola
If
2
x
−
y
+
1
=
0
is a tangent to the hyperbola
a
2
x
2
−
1
6
y
2
=
1
then which of the following CANNOT be sides of a right angled triangle? (a)
a
,
4
,
2
(b)
a
,
4
,
1
(c)
2
a
,
4
,
1
(d)
2
a
,
8
,
1
class 12
Maths
Calculus
Continuity And Differentiability
Let
[
x
]
be the greatest integer less than or equal to
x
˙
Then, at which of the following point (s) function
f
(
x
)
=
x
cos
(
π
(
x
+
[
x
]
)
)
is discontinuous? (a)
x
=
1
(b)
x
=
−
1
(c)
x
=
0
(d)
x
=
2
class 12
Maths
Algebra
Probability
Let
X
a
n
d
Y
be two events that
P
(
X
)
=
3
1
,
P
(
X
|
Y
)
=
2
1
a
n
d
P
(
Y
|
X
)
=
5
2
then:
P
(
Y
)
=
1
5
4
(b)
P
(
X
∪
Y
)
=
5
2
P
(
X
p
r
i
m
e
|
Y
)
=
2
1
(d)
P
(
X
∩
Y
)
=
5
1
class 11
Maths
Co-ordinate Geometry
Parabola
If a chord, which is not a tangent of the parabola
y
2
=
1
6
x
has the equation
2
x
+
y
=
p
,
and midpoint
(
h
,
k
)
,
then which of the following is(are) possible values (s) of
p
,
h
a
n
d
k
?
p
=
−
1
,
h
=
1
,
k
=
−
3
p
=
2
,
h
=
3
,
k
=
−
4
p
=
−
2
,
h
=
2
,
k
=
−
4
p
=
5
,
h
=
4
,
k
=
−
3
1
2
3
4
5
6
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jee advanced
| 2017
Solutions for all the questions from jee advanced
of year 2017
Filter Results
EXAM
board examination
iit jee
jee advanced
jee main
neet
YEAR
All
2017
SUBJECT
math
maths
class 12
Maths
Calculus
Continuity And Differentiability
Let
f
:
R
0
,
1
be a continuous function. Then, which of the following function (s) has (have) the value zero at some point in the interval (0,1)?
e
x
−
∫
0
x
f
(
t
)
sin
t
d
t
(b)
f
(
x
)
+
∫
0
2
π
f
(
t
)
sin
t
d
t
(c)
x
−
∫
0
2
π
−
x
f
(
t
)
cos
t
d
t
(d)
x
9
−
f
(
x
)
class 11
Maths
Algebra
Complex Numbers
Let
a
,
b
,
x
a
n
d
y
be real numbers such that
a
−
b
=
1
a
n
d
y
=
0
.
If the complex number
z
=
x
+
i
y
satisfies
I
m
(
z
+
1
a
z
+
b
)
=
y
, then which of the following is (are) possible value9s) of x? (a)
−
1
−
1
−
y
2
(b)
1
+
1
+
y
2
(c)
−
1
+
1
−
y
2
(d)
−
1
−
1
+
y
2
class 11
Maths
Algebra
Permutations And Combinations
Word of length 10 are formed using the letters A,B,C,D,E,F,G,H,I,J. Let
x
be the number of such words where no letter is repeated; and let
y
be the number of such words where exactly one letter is repeated twice and no other letter is repeated. The,
9
x
y
=
class 12
Maths
Algebra
Matrices
Which of the following is (are) NOT the square of a
3
×
3
matrix with real entries? (a)
⎣
⎢
⎡
1
0
0
0
1
0
0
0
−
1
⎦
⎥
⎤
(b)
⎣
⎢
⎡
−
1
0
0
0
−
1
0
0
0
−
1
⎦
⎥
⎤
(c)
⎣
⎢
⎡
1
0
0
0
1
0
0
0
1
⎦
⎥
⎤
(d)
⎣
⎢
⎡
1
0
0
0
−
1
0
0
0
−
1
⎦
⎥
⎤
class 11
Maths
Co-ordinate Geometry
Circles
For how many values, of p, the circle
x
2
+
y
2
+
2
x
+
4
y
−
p
=
0
and the coordinate axes have exactly three common points?
class 11
Maths
Calculus
Limits And Derivatives
Let
f
:
R
R
be a differentiable function such that
f
(
0
)
,
f
(
2
π
)
=
3
a
n
d
f
p
r
i
m
e
(
0
)
=
1
.
If
g
(
x
)
=
∫
x
2
π
[
f
p
r
i
m
e
(
t
)
cos
e
c
t
−
cot
t
cos
e
c
t
f
(
t
)
]
d
t
f
or
x
(
0
,
2
π
]
,
then
(
lim
)
x
0
g
(
x
)
=
class 11
Maths
Co-ordinate Geometry
Hyperbola
If
2
x
−
y
+
1
=
0
is a tangent to the hyperbola
a
2
x
2
−
1
6
y
2
=
1
then which of the following CANNOT be sides of a right angled triangle? (a)
a
,
4
,
2
(b)
a
,
4
,
1
(c)
2
a
,
4
,
1
(d)
2
a
,
8
,
1
class 12
Maths
Calculus
Continuity And Differentiability
Let
[
x
]
be the greatest integer less than or equal to
x
˙
Then, at which of the following point (s) function
f
(
x
)
=
x
cos
(
π
(
x
+
[
x
]
)
)
is discontinuous? (a)
x
=
1
(b)
x
=
−
1
(c)
x
=
0
(d)
x
=
2
class 12
Maths
Algebra
Probability
Let
X
a
n
d
Y
be two events that
P
(
X
)
=
3
1
,
P
(
X
|
Y
)
=
2
1
a
n
d
P
(
Y
|
X
)
=
5
2
then:
P
(
Y
)
=
1
5
4
(b)
P
(
X
∪
Y
)
=
5
2
P
(
X
p
r
i
m
e
|
Y
)
=
2
1
(d)
P
(
X
∩
Y
)
=
5
1
class 11
Maths
Co-ordinate Geometry
Parabola
If a chord, which is not a tangent of the parabola
y
2
=
1
6
x
has the equation
2
x
+
y
=
p
,
and midpoint
(
h
,
k
)
,
then which of the following is(are) possible values (s) of
p
,
h
a
n
d
k
?
p
=
−
1
,
h
=
1
,
k
=
−
3
p
=
2
,
h
=
3
,
k
=
−
4
p
=
−
2
,
h
=
2
,
k
=
−
4
p
=
5
,
h
=
4
,
k
=
−
3
1
2
3
4
5
6
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page
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