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jee advanced
| 2013
Solutions for all the questions from jee advanced
of year 2013
EXAM
board examination
iit jee
jee advanced
jee main
neet
rtb
YEAR
All
2013
SUBJECT
math
30
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class 11
Math
Algebra
Complex Numbers
Let w = (
$3 +2ι )$
and
$P={w_{n}:n=1,2,3,…..},$
Further
$H_{1}={z∈C:Re(z)>21 }andH_{2}={z∈c:Re(z)<−21 }$
Where C is set of all complex numbers. If
$z_{1}∈P∩H_{1},z_{2}∈P∩H_{2}$
and O represent the origin, then
$∠Z_{1}OZ_{2}$
=
class 11
Math
Co-ordinate Geometry
Ellipse
A vertical line passing through the point
$(h,0)$
intersects the ellipse
$4x_{2} +3y_{2} =1$
at the points
$P$
and
$Q$
.Let the tangents to the ellipse at P and Q meet at
$R$
. If
$δ(h)$
Area of triangle
$δPQR$
, and
$δ_{1}21 ≤h≤1max δ(h)$
A further
$δ_{2}21 ≤h≤1min δ(h)$
Then
$5 8 δ_{1}−8δ_{2}$
class 12
Math
Calculus
Definite Integral
For
$a∈R$
(the set of all real numbers),
$a=−1),$
$(lim)_{n→∞}((n+1)_{a−1}[(na+1)+(na+2)+……(na+n)]1_{a}+2_{a}++n_{a} =60.1 $
Then
$a=$
(a)
$5$
(b) 7 (c)
$2−15 $
(d)
$2−17 $
class 11
Math
Algebra
Sequences And Series
Let
$S_{n}=k=1∑4n (−1)2k(k+1) k_{2}˙$
Then
$S_{n}$
can take value (s)
$1056$
b.
$1088$
c.
$1120$
d.
$1332$
class 11
Math
Co-ordinate Geometry
Circles
Circle(s) touching x-axis at a distance 3 from the origin and having an intercept of length
$27 $
on y-axis is (are)
class 11
Math
Trigonometry
Solution And Properties Of Triangle
In a triangle PQR, P is the largest angle and
$cosP=31 $
. Further the incircle of the triangle touches the sides PQ, QR and RP at N, L and M respectively, such that the lengths of PN, QL and RM are consecutive even integers. Then possible length(s) of the side(s) of the triangle is (are)
class 11
Math
Co-ordinate Geometry
Circles
Circle(s) touching x-axis at a distance 3 from the origin and having an intercept of length
$27 $
on y-axis is (are)
class 11
Math
Co-ordinate Geometry
Parabola
Let PQ be a focal chord of the parabola
$y_{2}=4ax$
The tangents to the parabola at P and Q meet at a point lying on the line
$y=2x+a,a>0$
. Length of chord PQ is
class 12
Math
Calculus
Application Of Derivatives
The function
$f(x)=2∣x∣+∣x+2∣=∣∣x∣2∣−2∣x∣∣$
has a local minimum or a local maximum at
$x=$
$−2$
(b)
$−32 $
(c) 2 (d)
$32 $
class 12
Math
Calculus
Application Of Derivatives
Let
$f[0,1]→R$
(the set of all real numbers be a function.Suppose the function f is twice differentiable,
$f(0)=f(1)=0$
,and satisfies
$f_{′}(x)–2f_{′}(x)+f(x)≤e_{x},x∈[0,1]$
.Which of the following is true for
$0<x<1?$
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jee advanced
| 2013
Solutions for all the questions from jee advanced
of year 2013
30
JEE MAINS
Crash Course
●LIVE
Classes starting
15
^{th}
June 2021
30 Students | 90 Days | 24x7 Video Doubt Support
₹16000
₹8000
KNOW MORE
30
JEE MAINS
Crash Course
●LIVE
Classes starting
15
^{th}
June 2021
30 Students | 90 Days | 24x7 Video Doubt Support
₹16000
₹8000
KNOW MORE
Filter Results
EXAM
board examination
iit jee
jee advanced
jee main
neet
rtb
YEAR
All
2013
SUBJECT
math
class 11
Math
Algebra
Complex Numbers
Let w = (
$3 +2ι )$
and
$P={w_{n}:n=1,2,3,…..},$
Further
$H_{1}={z∈C:Re(z)>21 }andH_{2}={z∈c:Re(z)<−21 }$
Where C is set of all complex numbers. If
$z_{1}∈P∩H_{1},z_{2}∈P∩H_{2}$
and O represent the origin, then
$∠Z_{1}OZ_{2}$
=
class 11
Math
Co-ordinate Geometry
Ellipse
A vertical line passing through the point
$(h,0)$
intersects the ellipse
$4x_{2} +3y_{2} =1$
at the points
$P$
and
$Q$
.Let the tangents to the ellipse at P and Q meet at
$R$
. If
$δ(h)$
Area of triangle
$δPQR$
, and
$δ_{1}21 ≤h≤1max δ(h)$
A further
$δ_{2}21 ≤h≤1min δ(h)$
Then
$5 8 δ_{1}−8δ_{2}$
class 12
Math
Calculus
Definite Integral
For
$a∈R$
(the set of all real numbers),
$a=−1),$
$(lim)_{n→∞}((n+1)_{a−1}[(na+1)+(na+2)+……(na+n)]1_{a}+2_{a}++n_{a} =60.1 $
Then
$a=$
(a)
$5$
(b) 7 (c)
$2−15 $
(d)
$2−17 $
class 11
Math
Algebra
Sequences And Series
Let
$S_{n}=k=1∑4n (−1)2k(k+1) k_{2}˙$
Then
$S_{n}$
can take value (s)
$1056$
b.
$1088$
c.
$1120$
d.
$1332$
class 11
Math
Co-ordinate Geometry
Circles
Circle(s) touching x-axis at a distance 3 from the origin and having an intercept of length
$27 $
on y-axis is (are)
class 11
Math
Trigonometry
Solution And Properties Of Triangle
In a triangle PQR, P is the largest angle and
$cosP=31 $
. Further the incircle of the triangle touches the sides PQ, QR and RP at N, L and M respectively, such that the lengths of PN, QL and RM are consecutive even integers. Then possible length(s) of the side(s) of the triangle is (are)
class 11
Math
Co-ordinate Geometry
Circles
Circle(s) touching x-axis at a distance 3 from the origin and having an intercept of length
$27 $
on y-axis is (are)
class 11
Math
Co-ordinate Geometry
Parabola
Let PQ be a focal chord of the parabola
$y_{2}=4ax$
The tangents to the parabola at P and Q meet at a point lying on the line
$y=2x+a,a>0$
. Length of chord PQ is
class 12
Math
Calculus
Application Of Derivatives
The function
$f(x)=2∣x∣+∣x+2∣=∣∣x∣2∣−2∣x∣∣$
has a local minimum or a local maximum at
$x=$
$−2$
(b)
$−32 $
(c) 2 (d)
$32 $
class 12
Math
Calculus
Application Of Derivatives
Let
$f[0,1]→R$
(the set of all real numbers be a function.Suppose the function f is twice differentiable,
$f(0)=f(1)=0$
,and satisfies
$f_{′}(x)–2f_{′}(x)+f(x)≤e_{x},x∈[0,1]$
.Which of the following is true for
$0<x<1?$
1
2
3
4
5
6
7
8
9
10
Previous
page
1 / 1
You're on page
1
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