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jee advanced
| 2014
Solutions for all the questions from jee advanced
of year 2014
EXAM
board examination
iit jee
jee advanced
jee main
neet
rtb
YEAR
All
2014
SUBJECT
math
30
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30
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class 12
Math
Algebra
Matrices
Let
$M$
be a
$2×2$
symmetric matrix with integer entries. Then
$M$
is invertible ifThe first column of
$M$
is the transpose of the second row of
$M$
The second row of
$M$
is the transpose of the first column of
$M$
$M$
is a diagonal matrix with non-zero entries in the main diagonalThe product of entries in the main diagonal of
$M$
is not the square of an integer
class 12
Math
Calculus
Determinants
Let
$MandN$
be two
$3×3$
matrices such that
$MN=NM˙$
Further, if
$M=N_{2}andM_{2}=N_{4},$
then Determinant of
$(M_{2}+MN_{2})$
is 0 There is a
$3×3$
non-zeero matrix
$U$
such tht
$(M_{2}+MN_{2})U$
is the zero matrix Determinant of
$(M_{2}+MN_{2})≥1$
For a
$3×3$
matrix
$U,if(M_{2}+MN_{2})U$
equal the zero mattix then
$U$
is the zero matrix
class 12
Math
3D Geometry
Three Dimensional Geometry
From a point
$P(λ,λ,λ)$
, perpendicular PQ and PR are drawn respectively on the lines
$y=x,z=1$
and
$y=−x,z=−1$
.If P is such that
$∠QPR$
is a right angle, then the possible value(s) of
$λ$
is/(are)
class 11
Math
Algebra
Quadratic Equations
The quadratic equation
$p(x)=0$
with real coefficients has purely imaginary roots. Then the equation
$p(p(x))=0$
has A. only purely imaginary roots B. all real roots C. two real and purely imaginary roots D. neither real nor purely imaginary roots
class 12
Math
Calculus
Definite Integral
The following integral
$∫_{4π}(2cosecx)_{17}dx$
is equal to
$(a)∫_{0}2(e_{u}+e_{−u})_{16}du$
$(b)∫_{0}2(e_{u}+e_{−u})_{17}du$
$(c)∫_{0}2(e_{u}−e_{−u})_{17}du$
$(d)∫_{0}2(e_{u}−e_{−u})_{16}du$
class 12
Math
Calculus
Application Of Derivatives
Late
$a∈R$
and let
$f:R$
be given by
$f(x)=x_{5}−5x+a,$
then
$f(x)$
has three real roots if
$a>4$
$f(x)$
has only one real roots if
$a>4$
$f(x)$
has three real roots if
$a<−4$
$f(x)$
has three real roots if
$−4<a<4$
class 12
Math
Calculus
Application Of Integrals
For a point
$P$
in the plane, let
$d_{1}(P)andd_{2}(P)$
be the distances of the point
$P$
from the lines
$x−y=0andx+y=0$
respectively. The area of the region
$R$
consisting of all points
$P$
lying in the first quadrant of the plane and satisfying
$2≤d_{1}(P)+d_{2}(P)≤4,$
is
class 11
Math
Algebra
Sequences And Series
Let a,b ,c be positive integers such that
$ab $
is an integer. If a,b,c are in GP and the arithmetic mean of a,b,c, is b+2 then the value of
$a+1a_{2}+a−14 $
is
class 12
Math
Calculus
Continuity And Differentiability
Let
$f:R→Randg:R→R$
be respectively given by
$f(x)=∣x∣+1andg(x)=x_{2}+1$
. Define
$h:R→R$
by
$h(x)={max{f(x),g(x)},ifx≤0andmin{f(x),g(x)},ifx>0$
.The number of points at which
$h(x)$
is not differentiable is
class 11
Math
All topics
Trigonometric Equation
For
$x∈(0,π),$
the equation
$sinx+2$
sin
$x−sin3x=3$
has (A)infinitely many solutions (B)three solutions (C)one solution (D)no solution
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jee advanced
| 2014
Solutions for all the questions from jee advanced
of year 2014
30
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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
2014
SUBJECT
math
class 12
Math
Algebra
Matrices
Let
$M$
be a
$2×2$
symmetric matrix with integer entries. Then
$M$
is invertible ifThe first column of
$M$
is the transpose of the second row of
$M$
The second row of
$M$
is the transpose of the first column of
$M$
$M$
is a diagonal matrix with non-zero entries in the main diagonalThe product of entries in the main diagonal of
$M$
is not the square of an integer
class 12
Math
Calculus
Determinants
Let
$MandN$
be two
$3×3$
matrices such that
$MN=NM˙$
Further, if
$M=N_{2}andM_{2}=N_{4},$
then Determinant of
$(M_{2}+MN_{2})$
is 0 There is a
$3×3$
non-zeero matrix
$U$
such tht
$(M_{2}+MN_{2})U$
is the zero matrix Determinant of
$(M_{2}+MN_{2})≥1$
For a
$3×3$
matrix
$U,if(M_{2}+MN_{2})U$
equal the zero mattix then
$U$
is the zero matrix
class 12
Math
3D Geometry
Three Dimensional Geometry
From a point
$P(λ,λ,λ)$
, perpendicular PQ and PR are drawn respectively on the lines
$y=x,z=1$
and
$y=−x,z=−1$
.If P is such that
$∠QPR$
is a right angle, then the possible value(s) of
$λ$
is/(are)
class 11
Math
Algebra
Quadratic Equations
The quadratic equation
$p(x)=0$
with real coefficients has purely imaginary roots. Then the equation
$p(p(x))=0$
has A. only purely imaginary roots B. all real roots C. two real and purely imaginary roots D. neither real nor purely imaginary roots
class 12
Math
Calculus
Definite Integral
The following integral
$∫_{4π}(2cosecx)_{17}dx$
is equal to
$(a)∫_{0}2(e_{u}+e_{−u})_{16}du$
$(b)∫_{0}2(e_{u}+e_{−u})_{17}du$
$(c)∫_{0}2(e_{u}−e_{−u})_{17}du$
$(d)∫_{0}2(e_{u}−e_{−u})_{16}du$
class 12
Math
Calculus
Application Of Derivatives
Late
$a∈R$
and let
$f:R$
be given by
$f(x)=x_{5}−5x+a,$
then
$f(x)$
has three real roots if
$a>4$
$f(x)$
has only one real roots if
$a>4$
$f(x)$
has three real roots if
$a<−4$
$f(x)$
has three real roots if
$−4<a<4$
class 12
Math
Calculus
Application Of Integrals
For a point
$P$
in the plane, let
$d_{1}(P)andd_{2}(P)$
be the distances of the point
$P$
from the lines
$x−y=0andx+y=0$
respectively. The area of the region
$R$
consisting of all points
$P$
lying in the first quadrant of the plane and satisfying
$2≤d_{1}(P)+d_{2}(P)≤4,$
is
class 11
Math
Algebra
Sequences And Series
Let a,b ,c be positive integers such that
$ab $
is an integer. If a,b,c are in GP and the arithmetic mean of a,b,c, is b+2 then the value of
$a+1a_{2}+a−14 $
is
class 12
Math
Calculus
Continuity And Differentiability
Let
$f:R→Randg:R→R$
be respectively given by
$f(x)=∣x∣+1andg(x)=x_{2}+1$
. Define
$h:R→R$
by
$h(x)={max{f(x),g(x)},ifx≤0andmin{f(x),g(x)},ifx>0$
.The number of points at which
$h(x)$
is not differentiable is
class 11
Math
All topics
Trigonometric Equation
For
$x∈(0,π),$
the equation
$sinx+2$
sin
$x−sin3x=3$
has (A)infinitely many solutions (B)three solutions (C)one solution (D)no solution
1
2
3
4
5
6
7
8
Previous
page
1 / 1
You're on page
1
Next
page
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