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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
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Document Description: Solved Example: Application of Derivative for JEE 2025 is part of Mathematics (Maths) for JEE Main & Advanced preparation.
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