JEE Exam > JEE Notes > Mathematics (Maths) for JEE Main & Advanced > Solved Example: Application of Derivative
Solved Example: Application of Derivative | Mathematics (Maths) for JEE Main & Advanced PDF Download
| Download, print and study this document offline |
Please wait while the PDF view is loading
Page 1
JEE Solved Example on Application of Derivative
JEE Mains
Q1: The angle at which the curve ?? = ?? ?? ????
intersects the ?? -axis is
(A) ?????? ?? ??? ??
(B) ?????? ?? ?(?? ?? )
(C) ?????? ?? ?(v?? + ?? ?? )
(D) None
Ans: (B) ?? = ?? ?? ????
? ?? '
= ?? 2
?? ????
? ?? = ?? ,?? = 0
y
'
= k
2
?? tan??? =
1
k
2
? cot??? = k
2
?? ?? = cot
-1
?k
2
Q2: The angle between the tangent lines to the graph of the function ?? (?? )= ?
?? ?? ?(?? ?? - ?? )???? at the
point where the graph cuts the ?? -axis is -
(A) ?? /??
(B) ?? /??
(C) ?? /??
(D) ?? /??
Ans: (D) ?? (?? )= ? ?
?? 2
?(2?? - 5)= ?? 2
- 5?? |
2
?? = ?? 2
- 5?? - 4 + 10
?= ?? 2
- 5?? + 6 = (?? - 2)(?? - 3)
?? 1
(?? )= 2?? - 5
[?? = 2,?? (?? )= 0]?? '
(?? )= -1
[?? = 3,?? (?? )= 0]?? '
(?? )= 1
Angle between the 2 tangents is 90
°
(as m
1
m
2
= -1 )
Q3: If a variable tangent to the curve ?? ?? ?? = ?? ?? makes intercepts ?? ,?? on ?? and ?? axis respectively
then the value of ?? ?? ?? is
(A) ???? ?? ??
(B)
?? ????
?? ??
(C)
????
?? ?? ??
(D)
?? ?? ?? ??
Ans: (C) ?? 2
?? = ?? 3
Page 2
JEE Solved Example on Application of Derivative
JEE Mains
Q1: The angle at which the curve ?? = ?? ?? ????
intersects the ?? -axis is
(A) ?????? ?? ??? ??
(B) ?????? ?? ?(?? ?? )
(C) ?????? ?? ?(v?? + ?? ?? )
(D) None
Ans: (B) ?? = ?? ?? ????
? ?? '
= ?? 2
?? ????
? ?? = ?? ,?? = 0
y
'
= k
2
?? tan??? =
1
k
2
? cot??? = k
2
?? ?? = cot
-1
?k
2
Q2: The angle between the tangent lines to the graph of the function ?? (?? )= ?
?? ?? ?(?? ?? - ?? )???? at the
point where the graph cuts the ?? -axis is -
(A) ?? /??
(B) ?? /??
(C) ?? /??
(D) ?? /??
Ans: (D) ?? (?? )= ? ?
?? 2
?(2?? - 5)= ?? 2
- 5?? |
2
?? = ?? 2
- 5?? - 4 + 10
?= ?? 2
- 5?? + 6 = (?? - 2)(?? - 3)
?? 1
(?? )= 2?? - 5
[?? = 2,?? (?? )= 0]?? '
(?? )= -1
[?? = 3,?? (?? )= 0]?? '
(?? )= 1
Angle between the 2 tangents is 90
°
(as m
1
m
2
= -1 )
Q3: If a variable tangent to the curve ?? ?? ?? = ?? ?? makes intercepts ?? ,?? on ?? and ?? axis respectively
then the value of ?? ?? ?? is
(A) ???? ?? ??
(B)
?? ????
?? ??
(C)
????
?? ?? ??
(D)
?? ?? ?? ??
Ans: (C) ?? 2
?? = ?? 3
?? =
?? 3
?? 2
? ?? '
=
-2?? 3
?? 3
?? -
?? 3
?? 2
= -
2?? 3
?? 3
(?? - ?? )[?? = ???? =
?? 3
?? 2
]
?? intercept =
3?? 2
= ???? intercept
?=
3?? 3
?? 2
= ?? ? ?? 2
?? =
9?? 2
4
×
3?? 3
?? 2
=
27?? 3
4
[?? ]
Q4: Consider the function ?? (?? )= {
?? ?????? ?
?? ?? for ?? > ?? ?? for ?? = ?? then the number of points in (?? ,?? )
where the derivative ?? '
(?? ) vanishes, is
(A) 0
(B) 1
(C) 2
(D) infinite
Ans: (D) ?? (?? )= {
?? sin?(
?? ?? ) ?? > 0
0 ?? = 0
?? '
(?? )= ?? cos ?(
?? ?? )(
-?? ?? 2
)+ sin?
?? ?? = 0
?? ?? = tan?(
?? ?? )
?? ? [0,1] infinite solution
Q5: The tangent to the graph of the function ?? = ?? (?? ) at the point with abscissa ?? = ?? forms with
the ?? -axis an angle of ?? /?? and at the point with abscissa ?? = ?? at an angle of ?? /?? , then the value
of the integral, ?
?? ?? ??? '
(?? ).?? ''
(?? )???? is equal to
(A) 1
(B) 0
(C) -v??
(D) -1
[assume ?? '
(?? ) to be continuous]
Ans: (D) ?? = ?? (?? )? ?
?? ?? ??? 1
'
(?? )?? ?
''
(?? )
?? ?? = ?? '
(?? )?
?? ?? ??? ''
(?? )- ?
?? ?? ??? ''
(?? )?? '
(?? )
?? 2?? = [?? '
(?? )]
2
?? 2?? = [?? '
?? ]
2
[?? '
?? ]
2
?? 2?? = -2 ? ?? = -1
Page 3
JEE Solved Example on Application of Derivative
JEE Mains
Q1: The angle at which the curve ?? = ?? ?? ????
intersects the ?? -axis is
(A) ?????? ?? ??? ??
(B) ?????? ?? ?(?? ?? )
(C) ?????? ?? ?(v?? + ?? ?? )
(D) None
Ans: (B) ?? = ?? ?? ????
? ?? '
= ?? 2
?? ????
? ?? = ?? ,?? = 0
y
'
= k
2
?? tan??? =
1
k
2
? cot??? = k
2
?? ?? = cot
-1
?k
2
Q2: The angle between the tangent lines to the graph of the function ?? (?? )= ?
?? ?? ?(?? ?? - ?? )???? at the
point where the graph cuts the ?? -axis is -
(A) ?? /??
(B) ?? /??
(C) ?? /??
(D) ?? /??
Ans: (D) ?? (?? )= ? ?
?? 2
?(2?? - 5)= ?? 2
- 5?? |
2
?? = ?? 2
- 5?? - 4 + 10
?= ?? 2
- 5?? + 6 = (?? - 2)(?? - 3)
?? 1
(?? )= 2?? - 5
[?? = 2,?? (?? )= 0]?? '
(?? )= -1
[?? = 3,?? (?? )= 0]?? '
(?? )= 1
Angle between the 2 tangents is 90
°
(as m
1
m
2
= -1 )
Q3: If a variable tangent to the curve ?? ?? ?? = ?? ?? makes intercepts ?? ,?? on ?? and ?? axis respectively
then the value of ?? ?? ?? is
(A) ???? ?? ??
(B)
?? ????
?? ??
(C)
????
?? ?? ??
(D)
?? ?? ?? ??
Ans: (C) ?? 2
?? = ?? 3
?? =
?? 3
?? 2
? ?? '
=
-2?? 3
?? 3
?? -
?? 3
?? 2
= -
2?? 3
?? 3
(?? - ?? )[?? = ???? =
?? 3
?? 2
]
?? intercept =
3?? 2
= ???? intercept
?=
3?? 3
?? 2
= ?? ? ?? 2
?? =
9?? 2
4
×
3?? 3
?? 2
=
27?? 3
4
[?? ]
Q4: Consider the function ?? (?? )= {
?? ?????? ?
?? ?? for ?? > ?? ?? for ?? = ?? then the number of points in (?? ,?? )
where the derivative ?? '
(?? ) vanishes, is
(A) 0
(B) 1
(C) 2
(D) infinite
Ans: (D) ?? (?? )= {
?? sin?(
?? ?? ) ?? > 0
0 ?? = 0
?? '
(?? )= ?? cos ?(
?? ?? )(
-?? ?? 2
)+ sin?
?? ?? = 0
?? ?? = tan?(
?? ?? )
?? ? [0,1] infinite solution
Q5: The tangent to the graph of the function ?? = ?? (?? ) at the point with abscissa ?? = ?? forms with
the ?? -axis an angle of ?? /?? and at the point with abscissa ?? = ?? at an angle of ?? /?? , then the value
of the integral, ?
?? ?? ??? '
(?? ).?? ''
(?? )???? is equal to
(A) 1
(B) 0
(C) -v??
(D) -1
[assume ?? '
(?? ) to be continuous]
Ans: (D) ?? = ?? (?? )? ?
?? ?? ??? 1
'
(?? )?? ?
''
(?? )
?? ?? = ?? '
(?? )?
?? ?? ??? ''
(?? )- ?
?? ?? ??? ''
(?? )?? '
(?? )
?? 2?? = [?? '
(?? )]
2
?? 2?? = [?? '
?? ]
2
[?? '
?? ]
2
?? 2?? = -2 ? ?? = -1
Q6: The subnormal at any point on the curve ????
?? = ?? ?? ·?? is constant for:
(A) ?? = ??
(B) ?? = ??
(C) ?? = -??
(D) No value of ??
Ans: (C) Subnormal = ?? ????
????
???? ?? ?? -1
?? '
+ ?? ?? = 0
?? '
=
-?? ????
|?? ????
????
| =
?? 2
????
it is constant for ?
?? 2+?? ?? ?? +1
??
Constant for n = -2
Q7: Equation of the line through the point (?? /?? ,?? ) and tangent to the parabola ?? =
?? ?? ?? + ?? and
secant to the curve ?? = v?? - ?? ?? is
(A) ?? ?? + ?? ?? - ?? = ??
(B) ?? ?? + ?? ?? - ?? = ??
(C) ?? - ?? = ??
(D) None of these
Ans: (A) ?? = -
?? 2
2
+ 2
?? '
= -??
??
?? - 2
?? -
1
2
= ?? ?? ?? - 2 = ?? (?? -
1
2
) ?
-?? 2
2
=
2????
2
-
?? 2
?? ?? 2
+ 2???? - ?? = 0
?? ?? =
-2?? ± v4?? 2
+ 4?? 2
= 0
For ?? = 0
?? 4?? 2
+ 4?? = 0 ? ?? = 0,-1
?? ?? - 2 = -?? +
1
2
?? ?? + ?? =
5
2
Page 4
JEE Solved Example on Application of Derivative
JEE Mains
Q1: The angle at which the curve ?? = ?? ?? ????
intersects the ?? -axis is
(A) ?????? ?? ??? ??
(B) ?????? ?? ?(?? ?? )
(C) ?????? ?? ?(v?? + ?? ?? )
(D) None
Ans: (B) ?? = ?? ?? ????
? ?? '
= ?? 2
?? ????
? ?? = ?? ,?? = 0
y
'
= k
2
?? tan??? =
1
k
2
? cot??? = k
2
?? ?? = cot
-1
?k
2
Q2: The angle between the tangent lines to the graph of the function ?? (?? )= ?
?? ?? ?(?? ?? - ?? )???? at the
point where the graph cuts the ?? -axis is -
(A) ?? /??
(B) ?? /??
(C) ?? /??
(D) ?? /??
Ans: (D) ?? (?? )= ? ?
?? 2
?(2?? - 5)= ?? 2
- 5?? |
2
?? = ?? 2
- 5?? - 4 + 10
?= ?? 2
- 5?? + 6 = (?? - 2)(?? - 3)
?? 1
(?? )= 2?? - 5
[?? = 2,?? (?? )= 0]?? '
(?? )= -1
[?? = 3,?? (?? )= 0]?? '
(?? )= 1
Angle between the 2 tangents is 90
°
(as m
1
m
2
= -1 )
Q3: If a variable tangent to the curve ?? ?? ?? = ?? ?? makes intercepts ?? ,?? on ?? and ?? axis respectively
then the value of ?? ?? ?? is
(A) ???? ?? ??
(B)
?? ????
?? ??
(C)
????
?? ?? ??
(D)
?? ?? ?? ??
Ans: (C) ?? 2
?? = ?? 3
?? =
?? 3
?? 2
? ?? '
=
-2?? 3
?? 3
?? -
?? 3
?? 2
= -
2?? 3
?? 3
(?? - ?? )[?? = ???? =
?? 3
?? 2
]
?? intercept =
3?? 2
= ???? intercept
?=
3?? 3
?? 2
= ?? ? ?? 2
?? =
9?? 2
4
×
3?? 3
?? 2
=
27?? 3
4
[?? ]
Q4: Consider the function ?? (?? )= {
?? ?????? ?
?? ?? for ?? > ?? ?? for ?? = ?? then the number of points in (?? ,?? )
where the derivative ?? '
(?? ) vanishes, is
(A) 0
(B) 1
(C) 2
(D) infinite
Ans: (D) ?? (?? )= {
?? sin?(
?? ?? ) ?? > 0
0 ?? = 0
?? '
(?? )= ?? cos ?(
?? ?? )(
-?? ?? 2
)+ sin?
?? ?? = 0
?? ?? = tan?(
?? ?? )
?? ? [0,1] infinite solution
Q5: The tangent to the graph of the function ?? = ?? (?? ) at the point with abscissa ?? = ?? forms with
the ?? -axis an angle of ?? /?? and at the point with abscissa ?? = ?? at an angle of ?? /?? , then the value
of the integral, ?
?? ?? ??? '
(?? ).?? ''
(?? )???? is equal to
(A) 1
(B) 0
(C) -v??
(D) -1
[assume ?? '
(?? ) to be continuous]
Ans: (D) ?? = ?? (?? )? ?
?? ?? ??? 1
'
(?? )?? ?
''
(?? )
?? ?? = ?? '
(?? )?
?? ?? ??? ''
(?? )- ?
?? ?? ??? ''
(?? )?? '
(?? )
?? 2?? = [?? '
(?? )]
2
?? 2?? = [?? '
?? ]
2
[?? '
?? ]
2
?? 2?? = -2 ? ?? = -1
Q6: The subnormal at any point on the curve ????
?? = ?? ?? ·?? is constant for:
(A) ?? = ??
(B) ?? = ??
(C) ?? = -??
(D) No value of ??
Ans: (C) Subnormal = ?? ????
????
???? ?? ?? -1
?? '
+ ?? ?? = 0
?? '
=
-?? ????
|?? ????
????
| =
?? 2
????
it is constant for ?
?? 2+?? ?? ?? +1
??
Constant for n = -2
Q7: Equation of the line through the point (?? /?? ,?? ) and tangent to the parabola ?? =
?? ?? ?? + ?? and
secant to the curve ?? = v?? - ?? ?? is
(A) ?? ?? + ?? ?? - ?? = ??
(B) ?? ?? + ?? ?? - ?? = ??
(C) ?? - ?? = ??
(D) None of these
Ans: (A) ?? = -
?? 2
2
+ 2
?? '
= -??
??
?? - 2
?? -
1
2
= ?? ?? ?? - 2 = ?? (?? -
1
2
) ?
-?? 2
2
=
2????
2
-
?? 2
?? ?? 2
+ 2???? - ?? = 0
?? ?? =
-2?? ± v4?? 2
+ 4?? 2
= 0
For ?? = 0
?? 4?? 2
+ 4?? = 0 ? ?? = 0,-1
?? ?? - 2 = -?? +
1
2
?? ?? + ?? =
5
2
Q8: Two curves ?? ?? :?? = ?? ?? - ?? and ?? ?? :?? = ?? ?? ?? ,?? ? ?? intersect each other at two different point.
The tangent drawn to ?? ?? at one of the point of intersection ?? = (?? , ?? ?? ),(?? > ?? ) meets ?? ?? again
at ?? (?? ,?? ?? )(?? ?? ? ?? ?? ) . The value of ' ?? ' is
(A) 4
(B) 3
(C) 2
(D) 1
Ans: (D) ?? 1
?? = ?? 2
- 3 and ?? 2
?? = ?? ?? 2
?? ?? ?? 2
= ?? 2
- 3
?? ?? = ±
v
3
1 - ?? = ?? ? ?? =
3
1 - ?? - 3 =
3?? 1 - ?? ??
?? - ?? 1
?? - ?? = 2???? ? ?? - ?? 1
= 2???? (?? - ?? )
?? ?? 2
- 3 - ?? 1
= 2???? (?? - ?? )
?? -2 - ?? 1
= 2???? (1 - ?? )
?? 2
= -2
?? 1
= ?? ?? 2
?? -2 - ?? ?? 2
= 2???? - 2?? ?? 2
?? ?? ?? 2
- 2???? - 2 = 0
?? ?? (
3
1 - ?? )- 2 = 2?? v
3
1 - ?? ?
5?? - 2
v1 - ?? = 2?? v3
?? 5?? - 2 = 2?? v3 - 3?? ?? =
2
3
,?? = 1
Q9: Number of roots of the equation ?? ?? · ?? ?? |?? |
= ?? is:
(A) 2
(B) 4
(C) 6
(D) Zero
Ans: (B) ?? 2
= ?? |?? -2
No. of roots are 4
Page 5
JEE Solved Example on Application of Derivative
JEE Mains
Q1: The angle at which the curve ?? = ?? ?? ????
intersects the ?? -axis is
(A) ?????? ?? ??? ??
(B) ?????? ?? ?(?? ?? )
(C) ?????? ?? ?(v?? + ?? ?? )
(D) None
Ans: (B) ?? = ?? ?? ????
? ?? '
= ?? 2
?? ????
? ?? = ?? ,?? = 0
y
'
= k
2
?? tan??? =
1
k
2
? cot??? = k
2
?? ?? = cot
-1
?k
2
Q2: The angle between the tangent lines to the graph of the function ?? (?? )= ?
?? ?? ?(?? ?? - ?? )???? at the
point where the graph cuts the ?? -axis is -
(A) ?? /??
(B) ?? /??
(C) ?? /??
(D) ?? /??
Ans: (D) ?? (?? )= ? ?
?? 2
?(2?? - 5)= ?? 2
- 5?? |
2
?? = ?? 2
- 5?? - 4 + 10
?= ?? 2
- 5?? + 6 = (?? - 2)(?? - 3)
?? 1
(?? )= 2?? - 5
[?? = 2,?? (?? )= 0]?? '
(?? )= -1
[?? = 3,?? (?? )= 0]?? '
(?? )= 1
Angle between the 2 tangents is 90
°
(as m
1
m
2
= -1 )
Q3: If a variable tangent to the curve ?? ?? ?? = ?? ?? makes intercepts ?? ,?? on ?? and ?? axis respectively
then the value of ?? ?? ?? is
(A) ???? ?? ??
(B)
?? ????
?? ??
(C)
????
?? ?? ??
(D)
?? ?? ?? ??
Ans: (C) ?? 2
?? = ?? 3
?? =
?? 3
?? 2
? ?? '
=
-2?? 3
?? 3
?? -
?? 3
?? 2
= -
2?? 3
?? 3
(?? - ?? )[?? = ???? =
?? 3
?? 2
]
?? intercept =
3?? 2
= ???? intercept
?=
3?? 3
?? 2
= ?? ? ?? 2
?? =
9?? 2
4
×
3?? 3
?? 2
=
27?? 3
4
[?? ]
Q4: Consider the function ?? (?? )= {
?? ?????? ?
?? ?? for ?? > ?? ?? for ?? = ?? then the number of points in (?? ,?? )
where the derivative ?? '
(?? ) vanishes, is
(A) 0
(B) 1
(C) 2
(D) infinite
Ans: (D) ?? (?? )= {
?? sin?(
?? ?? ) ?? > 0
0 ?? = 0
?? '
(?? )= ?? cos ?(
?? ?? )(
-?? ?? 2
)+ sin?
?? ?? = 0
?? ?? = tan?(
?? ?? )
?? ? [0,1] infinite solution
Q5: The tangent to the graph of the function ?? = ?? (?? ) at the point with abscissa ?? = ?? forms with
the ?? -axis an angle of ?? /?? and at the point with abscissa ?? = ?? at an angle of ?? /?? , then the value
of the integral, ?
?? ?? ??? '
(?? ).?? ''
(?? )???? is equal to
(A) 1
(B) 0
(C) -v??
(D) -1
[assume ?? '
(?? ) to be continuous]
Ans: (D) ?? = ?? (?? )? ?
?? ?? ??? 1
'
(?? )?? ?
''
(?? )
?? ?? = ?? '
(?? )?
?? ?? ??? ''
(?? )- ?
?? ?? ??? ''
(?? )?? '
(?? )
?? 2?? = [?? '
(?? )]
2
?? 2?? = [?? '
?? ]
2
[?? '
?? ]
2
?? 2?? = -2 ? ?? = -1
Q6: The subnormal at any point on the curve ????
?? = ?? ?? ·?? is constant for:
(A) ?? = ??
(B) ?? = ??
(C) ?? = -??
(D) No value of ??
Ans: (C) Subnormal = ?? ????
????
???? ?? ?? -1
?? '
+ ?? ?? = 0
?? '
=
-?? ????
|?? ????
????
| =
?? 2
????
it is constant for ?
?? 2+?? ?? ?? +1
??
Constant for n = -2
Q7: Equation of the line through the point (?? /?? ,?? ) and tangent to the parabola ?? =
?? ?? ?? + ?? and
secant to the curve ?? = v?? - ?? ?? is
(A) ?? ?? + ?? ?? - ?? = ??
(B) ?? ?? + ?? ?? - ?? = ??
(C) ?? - ?? = ??
(D) None of these
Ans: (A) ?? = -
?? 2
2
+ 2
?? '
= -??
??
?? - 2
?? -
1
2
= ?? ?? ?? - 2 = ?? (?? -
1
2
) ?
-?? 2
2
=
2????
2
-
?? 2
?? ?? 2
+ 2???? - ?? = 0
?? ?? =
-2?? ± v4?? 2
+ 4?? 2
= 0
For ?? = 0
?? 4?? 2
+ 4?? = 0 ? ?? = 0,-1
?? ?? - 2 = -?? +
1
2
?? ?? + ?? =
5
2
Q8: Two curves ?? ?? :?? = ?? ?? - ?? and ?? ?? :?? = ?? ?? ?? ,?? ? ?? intersect each other at two different point.
The tangent drawn to ?? ?? at one of the point of intersection ?? = (?? , ?? ?? ),(?? > ?? ) meets ?? ?? again
at ?? (?? ,?? ?? )(?? ?? ? ?? ?? ) . The value of ' ?? ' is
(A) 4
(B) 3
(C) 2
(D) 1
Ans: (D) ?? 1
?? = ?? 2
- 3 and ?? 2
?? = ?? ?? 2
?? ?? ?? 2
= ?? 2
- 3
?? ?? = ±
v
3
1 - ?? = ?? ? ?? =
3
1 - ?? - 3 =
3?? 1 - ?? ??
?? - ?? 1
?? - ?? = 2???? ? ?? - ?? 1
= 2???? (?? - ?? )
?? ?? 2
- 3 - ?? 1
= 2???? (?? - ?? )
?? -2 - ?? 1
= 2???? (1 - ?? )
?? 2
= -2
?? 1
= ?? ?? 2
?? -2 - ?? ?? 2
= 2???? - 2?? ?? 2
?? ?? ?? 2
- 2???? - 2 = 0
?? ?? (
3
1 - ?? )- 2 = 2?? v
3
1 - ?? ?
5?? - 2
v1 - ?? = 2?? v3
?? 5?? - 2 = 2?? v3 - 3?? ?? =
2
3
,?? = 1
Q9: Number of roots of the equation ?? ?? · ?? ?? |?? |
= ?? is:
(A) 2
(B) 4
(C) 6
(D) Zero
Ans: (B) ?? 2
= ?? |?? -2
No. of roots are 4
Q10: The ?? -intercept of the tangent at any arbitrary point of the curve
?? ?? ?? +
?? ?? ?? = ?? is proportional
to
(A) Square of the abscissa of the point of tangency
(B) Square root of the abscissa of the point of tangency
(C) Cube of the abscissa of the point of tangency
(D) Cube root of the abscissa of the point of tangency
Ans: (C) -
?? ?? 3
-
?? ?? 3
?? '
= 0 at any general point
?? ?? intercept
?? - ?? (?? 2
- ?? )+ ?? ????
=
?? ?? 3
????
=
?? 3
?? = [?? ]
Q11: The line which is parallel to ?? -axis and crosses the curve ?? = v?? at an angle of
?? ?? is
(A) ?? = -?? /??
(B) ?? = ?? /??
(C) ?? = ?? /??
(D) ?? = ?? /??
Ans: (D) ?? = 0
?? = ?? ?? = v?? ?? 1
=
1
2v?? = 1;??? =
1
4
?? =
1
2
= ??
Q12: The lines tangent to the curves ?? ?? - ?? ?? ?? + ?? ?? - ?? ?? = ?? and ?? ?? - ?? ?? ?? ?? + ?? ?? + ?? ?? = ?? at
the origin intersect at an angle ?? equal to
(A) ?? /??
(B) ?? /??
(C) ?? /??
(D) ?? /??
Ans: (D) ?? 3
- ?? 2
?? + 5?? - 2?? = 0
Read More
|
209 videos|443 docs|143 tests
|
Related Exams
About this Document
|
Nov 22, 2024 Last updated |
Document Description: Solved Example: Application of Derivative for JEE 2024 is part of Mathematics (Maths) for JEE Main & Advanced preparation.
The notes and questions for Solved Example: Application of Derivative have been prepared according to the JEE exam syllabus. Information about Solved Example: Application of Derivative covers topics
like and Solved Example: Application of Derivative Example, for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for Solved Example: Application of Derivative.
Introduction of Solved Example: Application of Derivative in English is available as part of our Mathematics (Maths) for JEE Main & Advanced
for JEE & Solved Example: Application of Derivative in Hindi for Mathematics (Maths) for JEE Main & Advanced course.
Download more important topics related with notes, lectures and mock test series for JEE
Exam by signing up for free. JEE: Solved Example: Application of Derivative | Mathematics (Maths) for JEE Main & Advanced
Description
Full syllabus notes, lecture & questions for Solved Example: Application of Derivative | Mathematics (Maths) for JEE Main & Advanced - JEE | Plus excerises question with solution to help you revise complete syllabus for Mathematics (Maths) for JEE Main & Advanced | Best notes, free PDF download
Information about Solved Example: Application of Derivative
In this doc you can find the meaning of Solved Example: Application of Derivative defined & explained in the simplest way possible. Besides explaining types of
Solved Example: Application of Derivative theory, EduRev gives you an ample number of questions to practice Solved Example: Application of Derivative tests, examples and also practice JEE
tests
|
209 videos|443 docs|143 tests
|
Download as PDF
|
Explore Courses for JEE exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
Related Searches
Solved Example: Application of Derivative | Mathematics (Maths) for JEE Main & Advanced
,shortcuts and tricks
,ppt
,Viva Questions
,Semester Notes
,Solved Example: Application of Derivative | Mathematics (Maths) for JEE Main & Advanced
,Sample Paper
,past year papers
,Solved Example: Application of Derivative | Mathematics (Maths) for JEE Main & Advanced
,mock tests for examination
,practice quizzes
,Important questions
,Exam
,MCQs
,Free
,study material
,Previous Year Questions with Solutions
,Extra Questions
,Objective type Questions
,video lectures
,Summary
;
Additional Information about Solved Example: Application of Derivative for JEE Preparation
Solved Example: Application of Derivative Free PDF Download
The Solved Example: Application of Derivative is an invaluable resource that delves deep into the core of the JEE exam.
These study notes are curated by experts and cover all the essential topics and concepts, making your preparation more efficient and effective.
With the help of these notes, you can grasp complex subjects quickly, revise important points easily,
and reinforce your understanding of key concepts. The study notes are presented in a concise and easy-to-understand manner,
allowing you to optimize your learning process. Whether you're looking for best-recommended books, sample papers, study material,
or toppers' notes, this PDF has got you covered. Download the Solved Example: Application of Derivative now and kickstart your journey towards success in the JEE exam.
Importance of Solved Example: Application of Derivative
The importance of Solved Example: Application of Derivative cannot be overstated, especially for JEE aspirants.
This document holds the key to success in the JEE exam.
It offers a detailed understanding of the concept, providing invaluable insights into the topic.
By knowing the concepts well in advance, students can plan their preparation effectively.
Utilize this indispensable guide for a well-rounded preparation and achieve your desired results.
Solved Example: Application of Derivative Notes
Solved Example: Application of Derivative Notes offer in-depth insights into the specific topic to help you master it with ease.
This comprehensive document covers all aspects related to Solved Example: Application of Derivative.
It includes detailed information about the exam syllabus, recommended books, and study materials for a well-rounded preparation.
Practice papers and question papers enable you to assess your progress effectively.
Additionally, the paper analysis provides valuable tips for tackling the exam strategically.
Access to Toppers' notes gives you an edge in understanding complex concepts.
Whether you're a beginner or aiming for advanced proficiency, Solved Example: Application of Derivative Notes on EduRev are your ultimate resource for success.
Solved Example: Application of Derivative JEE Questions
The "Solved Example: Application of Derivative JEE Questions" guide is a valuable resource for all aspiring students preparing for the
JEE exam. It focuses on providing a wide range of practice questions to help students gauge
their understanding of the exam topics. These questions cover the entire syllabus, ensuring comprehensive preparation.
The guide includes previous years' question papers for students to familiarize themselves with the exam's format and difficulty level.
Additionally, it offers subject-specific question banks, allowing students to focus on weak areas and improve their performance.
Study Solved Example: Application of Derivative on the App
Students of JEE can study Solved Example: Application of Derivative alongwith tests & analysis from the EduRev app,
which will help them while preparing for their exam. Apart from the Solved Example: Application of Derivative,
students can also utilize the EduRev App for other study materials such as previous year question papers, syllabus, important questions, etc.
The EduRev App will make your learning easier as you can access it from anywhere you want.
The content of Solved Example: Application of Derivative is prepared as per the latest JEE syllabus.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup