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jee advanced
| 2018
Solutions for all the questions from jee advanced
of year 2018
EXAM
board examination
iit jee
jee advanced
jee main
neet
YEAR
All
2018
SUBJECT
math
maths
class 11
Maths
Algebra
Permutations And Combinations
The number of 5 digit numbers which are divisible by 4, with digits from the set
{
1
,
2
,
3
,
4
,
5
}
and the repetition of digits is allowed, is ________.
class 11
Maths
Algebra
Logarithm And Its Application
The value of
(
(
(
lo
g
)
2
9
)
2
)
(
l
o
g
)
2
(
(
l
o
g
)
2
9
)
1
×
(
7
)
(
l
o
g
)
4
7
1
is ________.
class 11
Math
All topics
Trigonometric Equation
Let
a
,
b
,
c
be three non-zero real numbers such that the equation
3
a
cos
x
+
2
b
sin
x
=
c
,
x
∈
[
−
2
π
,
2
π
]
, has two distinct real roots
α
and
β
with
α
+
β
=
3
π
. Then, the value of
a
b
is _______.
class 12
Maths
Calculus
Continuity And Differentiability
Let
f
:
R
→
R
and
g
:
R
→
R
be two non-constant differentiable functions. If
f
p
r
i
m
e
(
x
)
=
(
e
(
f
(
x
)
−
g
(
x
)
)
)
g
p
r
i
m
e
(
x
)
for all
x
∈
R
, and
f
(
1
)
=
g
(
2
)
=
1
, then which of the following statement(s) is (are) TRUE?
f
(
2
)
<
1
−
(
lo
g
)
e
2
(b)
f
(
2
)
>
1
−
(
lo
g
)
e
2
(c)
g
(
1
)
>
1
−
(
lo
g
)
e
2
(d)
g
(
1
)
<
1
−
(
lo
g
)
e
2
class 12
Maths
Algebra
Vector Algebra
Let
a
and
b
be two unit vectors such that
a
.
b
=
0
For some
x
,
y
∈
R
, let
c
=
x
a
+
y
b
+
(
a
×
b
If
(
∣
c
∣
=
2
and the vector
c
is inclined at same angle
α
to both
a
and
b
then the value of
8
cos
2
α
is
class 12
Maths
Calculus
Continuity And Differentiability
For every twice differentiable function
f
:
R
→
[
−
2
,
2
]
with
(
f
(
0
)
)
2
+
(
f
p
r
i
m
e
(
0
)
)
2
=
8
5
, which of the following statement(s) is (are) TRUE?There exist
r
,
s
∈
R
where
r
<
s
, such that
f
is one-one on the open interval
(
r
,
s
)
(b) There exists
x
0
∈
(
−
4
,
0
)
such that
∣
∣
∣
f
p
r
i
m
e
(
x
0
)
∣
∣
∣
≤
1
(c)
(
lim
)
x
→
∞
f
(
x
)
=
1
(d) There exists
α
∈
(
−
4
,
4
)
such that
f
(
α
)
+
f
(
α
)
=
0
and
f
p
r
i
m
e
(
α
)
=
0
class 11
Maths
Algebra
Complex Numbers
For a non-zero complex number
z
, let
a
r
g
(
z
)
denote theprincipal argument with
π
<
a
r
g
(
z
)
≤
π
Then, whichof the following statement(s) is (are) FALSE?
a
r
g
(
−
1
,
−
i
)
=
4
π
,
where
i
=
−
1
(b) The function
f
:
R
→
(
−
π
,
π
]
,
defined by
f
(
t
)
=
a
r
g
(
−
1
+
i
t
)
for all
t
∈
R
, iscontinuous at all points of
R
, where
i
=
−
1
(c) For any two non-zero complex numbers
z
1
and
z
2
,
a
r
g
(
z
2
z
1
)
−
a
r
g
(
z
1
)
+
a
r
g
(
z
2
)
is an integer multiple of
2
π
(d) For any three given distinct complex numbers
z
1
,
z
2
and
z
3
, the locus of the point
z
satisfying the condition
a
r
g
(
(
z
−
z
3
)
(
z
2
−
z
1
)
(
z
−
z
1
)
(
z
2
−
z
3
)
)
=
π
, lies on a straight line
class 11
Maths
Calculus
Limits And Derivatives
For each positive integer
n
, let
y
n
=
n
1
(
(
n
+
1
)
(
n
+
2
)
n
+
n
˙
)
n
1
For
x
∈
R
let
[
x
]
be the greatest integer less than or equal to
x
. If
(
lim
)
n
→
∞
y
n
=
L
, then the value of
[
L
]
is ______.
class 12
Maths
Calculus
Application Of Integrals
Let
f
:
[
0
,
∞
)
→
R
be a continuous function such that
f
(
x
)
=
1
−
2
x
+
∫
0
x
e
x
−
t
f
(
t
)
d
t
for all
x
∈
[
0
,
∞
)
. Then, which of the following statement(s) is (are) TRUE?The curve
y
=
f
(
x
)
passes through the point
(
1
,
2
)
(b) The curve
y
=
f
(
x
)
passes through the point
(
2
,
−
1
)
(c) The area of the region
{
(
x
,
y
)
∈
[
0
,
1
]
×
R
:
f
(
x
)
≤
y
≤
1
−
x
2
}
is
4
π
−
2
(d) The area of the region
{
(
x
,
y
)
∈
[
0
,
1
]
×
R
:
f
(
x
)
≤
y
≤
1
−
x
2
}
is
4
π
−
1
class 11
Maths
Algebra
Permutations And Combinations
Let
X
be the set consisting of the first 2018 terms of the arithmetic progression
1
,
6
,
1
1
,
,
¨
and
Y
be the set consisting of the first 2018 terms of the arithmetic progression
9
,
1
6
,
2
3
,
¨
. Then, the number of elements in the set
X
∪
Y
is _____.
1
2
3
4
5
6
7
8
9
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jee advanced
| 2018
Solutions for all the questions from jee advanced
of year 2018
Filter Results
EXAM
board examination
iit jee
jee advanced
jee main
neet
YEAR
All
2018
SUBJECT
math
maths
class 11
Maths
Algebra
Permutations And Combinations
The number of 5 digit numbers which are divisible by 4, with digits from the set
{
1
,
2
,
3
,
4
,
5
}
and the repetition of digits is allowed, is ________.
class 11
Maths
Algebra
Logarithm And Its Application
The value of
(
(
(
lo
g
)
2
9
)
2
)
(
l
o
g
)
2
(
(
l
o
g
)
2
9
)
1
×
(
7
)
(
l
o
g
)
4
7
1
is ________.
class 11
Math
All topics
Trigonometric Equation
Let
a
,
b
,
c
be three non-zero real numbers such that the equation
3
a
cos
x
+
2
b
sin
x
=
c
,
x
∈
[
−
2
π
,
2
π
]
, has two distinct real roots
α
and
β
with
α
+
β
=
3
π
. Then, the value of
a
b
is _______.
class 12
Maths
Calculus
Continuity And Differentiability
Let
f
:
R
→
R
and
g
:
R
→
R
be two non-constant differentiable functions. If
f
p
r
i
m
e
(
x
)
=
(
e
(
f
(
x
)
−
g
(
x
)
)
)
g
p
r
i
m
e
(
x
)
for all
x
∈
R
, and
f
(
1
)
=
g
(
2
)
=
1
, then which of the following statement(s) is (are) TRUE?
f
(
2
)
<
1
−
(
lo
g
)
e
2
(b)
f
(
2
)
>
1
−
(
lo
g
)
e
2
(c)
g
(
1
)
>
1
−
(
lo
g
)
e
2
(d)
g
(
1
)
<
1
−
(
lo
g
)
e
2
class 12
Maths
Algebra
Vector Algebra
Let
a
and
b
be two unit vectors such that
a
.
b
=
0
For some
x
,
y
∈
R
, let
c
=
x
a
+
y
b
+
(
a
×
b
If
(
∣
c
∣
=
2
and the vector
c
is inclined at same angle
α
to both
a
and
b
then the value of
8
cos
2
α
is
class 12
Maths
Calculus
Continuity And Differentiability
For every twice differentiable function
f
:
R
→
[
−
2
,
2
]
with
(
f
(
0
)
)
2
+
(
f
p
r
i
m
e
(
0
)
)
2
=
8
5
, which of the following statement(s) is (are) TRUE?There exist
r
,
s
∈
R
where
r
<
s
, such that
f
is one-one on the open interval
(
r
,
s
)
(b) There exists
x
0
∈
(
−
4
,
0
)
such that
∣
∣
∣
f
p
r
i
m
e
(
x
0
)
∣
∣
∣
≤
1
(c)
(
lim
)
x
→
∞
f
(
x
)
=
1
(d) There exists
α
∈
(
−
4
,
4
)
such that
f
(
α
)
+
f
(
α
)
=
0
and
f
p
r
i
m
e
(
α
)
=
0
class 11
Maths
Algebra
Complex Numbers
For a non-zero complex number
z
, let
a
r
g
(
z
)
denote theprincipal argument with
π
<
a
r
g
(
z
)
≤
π
Then, whichof the following statement(s) is (are) FALSE?
a
r
g
(
−
1
,
−
i
)
=
4
π
,
where
i
=
−
1
(b) The function
f
:
R
→
(
−
π
,
π
]
,
defined by
f
(
t
)
=
a
r
g
(
−
1
+
i
t
)
for all
t
∈
R
, iscontinuous at all points of
R
, where
i
=
−
1
(c) For any two non-zero complex numbers
z
1
and
z
2
,
a
r
g
(
z
2
z
1
)
−
a
r
g
(
z
1
)
+
a
r
g
(
z
2
)
is an integer multiple of
2
π
(d) For any three given distinct complex numbers
z
1
,
z
2
and
z
3
, the locus of the point
z
satisfying the condition
a
r
g
(
(
z
−
z
3
)
(
z
2
−
z
1
)
(
z
−
z
1
)
(
z
2
−
z
3
)
)
=
π
, lies on a straight line
class 11
Maths
Calculus
Limits And Derivatives
For each positive integer
n
, let
y
n
=
n
1
(
(
n
+
1
)
(
n
+
2
)
n
+
n
˙
)
n
1
For
x
∈
R
let
[
x
]
be the greatest integer less than or equal to
x
. If
(
lim
)
n
→
∞
y
n
=
L
, then the value of
[
L
]
is ______.
class 12
Maths
Calculus
Application Of Integrals
Let
f
:
[
0
,
∞
)
→
R
be a continuous function such that
f
(
x
)
=
1
−
2
x
+
∫
0
x
e
x
−
t
f
(
t
)
d
t
for all
x
∈
[
0
,
∞
)
. Then, which of the following statement(s) is (are) TRUE?The curve
y
=
f
(
x
)
passes through the point
(
1
,
2
)
(b) The curve
y
=
f
(
x
)
passes through the point
(
2
,
−
1
)
(c) The area of the region
{
(
x
,
y
)
∈
[
0
,
1
]
×
R
:
f
(
x
)
≤
y
≤
1
−
x
2
}
is
4
π
−
2
(d) The area of the region
{
(
x
,
y
)
∈
[
0
,
1
]
×
R
:
f
(
x
)
≤
y
≤
1
−
x
2
}
is
4
π
−
1
class 11
Maths
Algebra
Permutations And Combinations
Let
X
be the set consisting of the first 2018 terms of the arithmetic progression
1
,
6
,
1
1
,
,
¨
and
Y
be the set consisting of the first 2018 terms of the arithmetic progression
9
,
1
6
,
2
3
,
¨
. Then, the number of elements in the set
X
∪
Y
is _____.
1
2
3
4
5
6
7
8
9
Previous
page
1 / 1
You're on page
1
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page
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