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iit jee
| 2006
Solutions for all the questions from iit jee
of year 2006
EXAM
board examination
iit jee
jee advanced
jee main
neet
YEAR
All
2006
SUBJECT
maths
class 11
Maths
Co-ordinate Geometry
Parabola
The equations of the common tangents to the parabola
$y=x_{2}andy=−(x−2)_{2}$
is/are :
class 11
Maths
Calculus
Limits And Derivatives
For
$x>0,x→0lim (sinx)_{x1}+(x1 )_{sinx}$
is equal to
class 11
Maths
Trigonometry
Solution And Properties Of Triangle
Internal bisector of
$∠A$
of triangle ABC meets side BC at D. A line drawn through D perpendicular to AD intersects the side AC at E and the side AB at F. If a, b, c represent sides of
$ΔABC$
, then
class 12
Maths
Co-ordinate Geometry
Hyperbola
If
$a$
hyperbola passes through the foci of the ellipse
$25x_{2} +16y_{2} =1$
. Its transverse and conjugate axes coincide respectively with the major and minor axes of the ellipse and if the product of eccentricities of hyperbola and ellipse is 1 then the equation of a. hyperbola is
$9x_{2} −16y_{2} =1$
b. the equation of hyperbola is
$9x_{2} −25y_{2} =1$
c. focus of hyperbola is (5, 0) d. focus of hyperbola is
$(53 ,0)$
class 12
Maths
Calculus
Functions
If
$f_{x}=−f(x)$
and
$g(x)=f_{prime}(x)$
and
$F(x)=(f(2x ))_{2}+(g(2x ))_{2}$
and given that
$F(5)=5,$
then
$F(10)$
is equal to5 (b) 10 (c) 0 (d) 15
class 11
Maths
Co-ordinate Geometry
Parabola
The axis of a parabola is along the line
$y=x$
and the distance of its vertex and focus from the origin are
$2 $
and
$22 $
, respectively. If vertex and focus both lie in the first quadrant, then the equation of the parabola is
$(x+y)_{2}=(x−y−2)$
$(x−y)_{2}=(x+y−2)$
$(x−y)_{2}=4(x+y−2)$
$(x−y)_{2}=8(x+y−2)$
class 12
Maths
Calculus
Indefinite Integrals
$∫x_{3}2x_{4}−2x_{2}+1 x_{2}−1 dxisequa<o$
$x_{3}2x_{4}−2x_{2}+1 +C$
(b)
$x2x_{4}−2x_{2}+1 +C$
$x_{2}2x_{4}−2x_{2}+1 +C$
(d)
$2x_{2}2x_{4}−2x_{2}+1 +C$
class 11
Maths
Algebra
Fundamental Of Mathematics
lf
$r,s,t$
are prime numbers and
$p,q$
are the positive integers such that their LCM of
$p,q$
is
$r_{2}t_{4}s_{2},$
then the numbers of ordered pair of
$(p,q)$
is (A)
$252$
(B)
$254$
(C)
$225$
(D)
$224$
class 12
Maths
Calculus
Application Of Derivatives
$f(x)$
is cubic polynomial with
$f(x)=18andf(1)=−1$
. Also
$f(x)$
has local maxima at
$x=−1andf_{prime}(x)$
has local minima at
$x=0$
, thenthe distance between
$(−1,2)and(af(a)),$
where
$x=a$
is the point of local minima is
$25 $
$f(x)$
is increasing for
$x∈[1,25 )$
$f(x)$
has local minima at
$x=1$
the value of
$f(0)=15$
class 11
Maths
Algebra
Fundamental Of Mathematics
There are n urns each containing (n+1) balls such that ith urn contains i white balls and (n+1-i) red balls.
1
2
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iit jee
| 2006
Solutions for all the questions from iit jee
of year 2006
Filter Results
EXAM
board examination
iit jee
jee advanced
jee main
neet
YEAR
All
2006
SUBJECT
maths
class 11
Maths
Co-ordinate Geometry
Parabola
The equations of the common tangents to the parabola
$y=x_{2}andy=−(x−2)_{2}$
is/are :
class 11
Maths
Calculus
Limits And Derivatives
For
$x>0,x→0lim (sinx)_{x1}+(x1 )_{sinx}$
is equal to
class 11
Maths
Trigonometry
Solution And Properties Of Triangle
Internal bisector of
$∠A$
of triangle ABC meets side BC at D. A line drawn through D perpendicular to AD intersects the side AC at E and the side AB at F. If a, b, c represent sides of
$ΔABC$
, then
class 12
Maths
Co-ordinate Geometry
Hyperbola
If
$a$
hyperbola passes through the foci of the ellipse
$25x_{2} +16y_{2} =1$
. Its transverse and conjugate axes coincide respectively with the major and minor axes of the ellipse and if the product of eccentricities of hyperbola and ellipse is 1 then the equation of a. hyperbola is
$9x_{2} −16y_{2} =1$
b. the equation of hyperbola is
$9x_{2} −25y_{2} =1$
c. focus of hyperbola is (5, 0) d. focus of hyperbola is
$(53 ,0)$
class 12
Maths
Calculus
Functions
If
$f_{x}=−f(x)$
and
$g(x)=f_{prime}(x)$
and
$F(x)=(f(2x ))_{2}+(g(2x ))_{2}$
and given that
$F(5)=5,$
then
$F(10)$
is equal to5 (b) 10 (c) 0 (d) 15
class 11
Maths
Co-ordinate Geometry
Parabola
The axis of a parabola is along the line
$y=x$
and the distance of its vertex and focus from the origin are
$2 $
and
$22 $
, respectively. If vertex and focus both lie in the first quadrant, then the equation of the parabola is
$(x+y)_{2}=(x−y−2)$
$(x−y)_{2}=(x+y−2)$
$(x−y)_{2}=4(x+y−2)$
$(x−y)_{2}=8(x+y−2)$
class 12
Maths
Calculus
Indefinite Integrals
$∫x_{3}2x_{4}−2x_{2}+1 x_{2}−1 dxisequa<o$
$x_{3}2x_{4}−2x_{2}+1 +C$
(b)
$x2x_{4}−2x_{2}+1 +C$
$x_{2}2x_{4}−2x_{2}+1 +C$
(d)
$2x_{2}2x_{4}−2x_{2}+1 +C$
class 11
Maths
Algebra
Fundamental Of Mathematics
lf
$r,s,t$
are prime numbers and
$p,q$
are the positive integers such that their LCM of
$p,q$
is
$r_{2}t_{4}s_{2},$
then the numbers of ordered pair of
$(p,q)$
is (A)
$252$
(B)
$254$
(C)
$225$
(D)
$224$
class 12
Maths
Calculus
Application Of Derivatives
$f(x)$
is cubic polynomial with
$f(x)=18andf(1)=−1$
. Also
$f(x)$
has local maxima at
$x=−1andf_{prime}(x)$
has local minima at
$x=0$
, thenthe distance between
$(−1,2)and(af(a)),$
where
$x=a$
is the point of local minima is
$25 $
$f(x)$
is increasing for
$x∈[1,25 )$
$f(x)$
has local minima at
$x=1$
the value of
$f(0)=15$
class 11
Maths
Algebra
Fundamental Of Mathematics
There are n urns each containing (n+1) balls such that ith urn contains i white balls and (n+1-i) red balls.
1
2
Previous
page
1 / 1
You're on page
1
Next
page
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