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Page 1
9
th
January 2020 (Shift 2), Mathematics Page | 1
Date: 9
th
January 2020 (Shift 2)
Time: 2:30 P.M. to 5:30 P.M.
Subject: Mathematics
1. If ?? (?? )= |
?? +?? ?? +2 ?? +1
?? +?? ?? +3 ?? +2
?? +?? ?? +4 ?? +3
| and ?? -2?? +?? =1 then
a. ?? (-50)=-1 b. ?? (50)= 1
c. ?? (50)=-501 d. ?? (50)= 501
Answer: (?? )
Solution:
Given ?? (?? )= |
?? +?? ?? +2 ?? +1
?? +?? ?? +3 ?? +2
?? +?? ?? +4 ?? +3
|
?? -2?? +?? =1
Applying ?? 1
??? 1
-2?? 2
+?? 3
?? (?? )= |
?? -2?? +?? 0 0
?? +?? ?? +3 ?? +2
?? +?? ?? +4 ?? +3
|
Using ?? -2?? +?? =1
??? (?? )= (?? +3)
2
-(?? +2)(?? +4)
??? (?? )=1
??? (50)=1
??? (-50)=1
2. If ?? (?? )=
{
?? 0<?? <
1
2
1
2
?? =
1
2
1-??
1
2
<?? <1
?? (?? )= (?? -
1
2
)
2
then find the area bounded by ?? (?? ) and ?? (?? ) from ?? =
1
2
to ?? =
v3
2
.
a.
v3
2
-
1
3
b.
v3
4
+
1
3
c. 2v3 d. 3v3
Page 2
9
th
January 2020 (Shift 2), Mathematics Page | 1
Date: 9
th
January 2020 (Shift 2)
Time: 2:30 P.M. to 5:30 P.M.
Subject: Mathematics
1. If ?? (?? )= |
?? +?? ?? +2 ?? +1
?? +?? ?? +3 ?? +2
?? +?? ?? +4 ?? +3
| and ?? -2?? +?? =1 then
a. ?? (-50)=-1 b. ?? (50)= 1
c. ?? (50)=-501 d. ?? (50)= 501
Answer: (?? )
Solution:
Given ?? (?? )= |
?? +?? ?? +2 ?? +1
?? +?? ?? +3 ?? +2
?? +?? ?? +4 ?? +3
|
?? -2?? +?? =1
Applying ?? 1
??? 1
-2?? 2
+?? 3
?? (?? )= |
?? -2?? +?? 0 0
?? +?? ?? +3 ?? +2
?? +?? ?? +4 ?? +3
|
Using ?? -2?? +?? =1
??? (?? )= (?? +3)
2
-(?? +2)(?? +4)
??? (?? )=1
??? (50)=1
??? (-50)=1
2. If ?? (?? )=
{
?? 0<?? <
1
2
1
2
?? =
1
2
1-??
1
2
<?? <1
?? (?? )= (?? -
1
2
)
2
then find the area bounded by ?? (?? ) and ?? (?? ) from ?? =
1
2
to ?? =
v3
2
.
a.
v3
2
-
1
3
b.
v3
4
+
1
3
c. 2v3 d. 3v3
9
th
January 2020 (Shift 2), Mathematics Page | 2
Answer: (?? )
Solution:
Given ?? (?? )=
{
?? 0<?? <
1
2
1
2
?? =
1
2
1-??
1
2
<?? <1
?? (?? )= (?? -
1
2
)
2
The area between ?? (?? ) and ?? (?? ) from ?? =
1
2
to =
v3
2
:
Points of intersection of ?? (?? ) and (?? ) :
1-?? = (?? -
1
2
)
2
??? =
v3
2
,-
v3
2
Required area =?
(?? (?? )-?? (?? ))????
v3
2
1
2
=? (1-?? - (?? -
1
2
)
2
)????
v3
2
1
2
=?? -
?? 2
2
-
1
3
(?? -
1
2
)
3
|
1
2
v3
2
=
v3
4
-
1
3
Page 3
9
th
January 2020 (Shift 2), Mathematics Page | 1
Date: 9
th
January 2020 (Shift 2)
Time: 2:30 P.M. to 5:30 P.M.
Subject: Mathematics
1. If ?? (?? )= |
?? +?? ?? +2 ?? +1
?? +?? ?? +3 ?? +2
?? +?? ?? +4 ?? +3
| and ?? -2?? +?? =1 then
a. ?? (-50)=-1 b. ?? (50)= 1
c. ?? (50)=-501 d. ?? (50)= 501
Answer: (?? )
Solution:
Given ?? (?? )= |
?? +?? ?? +2 ?? +1
?? +?? ?? +3 ?? +2
?? +?? ?? +4 ?? +3
|
?? -2?? +?? =1
Applying ?? 1
??? 1
-2?? 2
+?? 3
?? (?? )= |
?? -2?? +?? 0 0
?? +?? ?? +3 ?? +2
?? +?? ?? +4 ?? +3
|
Using ?? -2?? +?? =1
??? (?? )= (?? +3)
2
-(?? +2)(?? +4)
??? (?? )=1
??? (50)=1
??? (-50)=1
2. If ?? (?? )=
{
?? 0<?? <
1
2
1
2
?? =
1
2
1-??
1
2
<?? <1
?? (?? )= (?? -
1
2
)
2
then find the area bounded by ?? (?? ) and ?? (?? ) from ?? =
1
2
to ?? =
v3
2
.
a.
v3
2
-
1
3
b.
v3
4
+
1
3
c. 2v3 d. 3v3
9
th
January 2020 (Shift 2), Mathematics Page | 2
Answer: (?? )
Solution:
Given ?? (?? )=
{
?? 0<?? <
1
2
1
2
?? =
1
2
1-??
1
2
<?? <1
?? (?? )= (?? -
1
2
)
2
The area between ?? (?? ) and ?? (?? ) from ?? =
1
2
to =
v3
2
:
Points of intersection of ?? (?? ) and (?? ) :
1-?? = (?? -
1
2
)
2
??? =
v3
2
,-
v3
2
Required area =?
(?? (?? )-?? (?? ))????
v3
2
1
2
=? (1-?? - (?? -
1
2
)
2
)????
v3
2
1
2
=?? -
?? 2
2
-
1
3
(?? -
1
2
)
3
|
1
2
v3
2
=
v3
4
-
1
3
9
th
January 2020 (Shift 2), Mathematics Page | 3
3. If ?? ?(?? ?~ ?? ) is false. Truth value of ?? and ?? will be
a. TF b. FT
c. TT d. FF
Answer: (?? )
Solution:
Given ?? ?(?? ?~ ?? )
Truth table:
?? ?? ~?? (?? ?~ ?? ) ?? ?(?? ?~ ?? )
T T F F F
T F T T T
F T F F T
F F T F T
?? ?(?? ?~ ?? ) is false when ?? is true and ?? is true.
4. ?
????
cos
2
??
(sec2?? +tan2?? )
=?? tan?? +2log?? (?? )+?? then ordered pair (?? , ?? (?? )) is
a. (1,1+tan?? ) b. (1,1-tan?? )
c. (-1,1+tan?? ) d. (-1,1-tan?? )
Answer: (?? )
Solution:
Let ?? = ?
????
cos
2
?? (sec2?? +tan2?? )
?? = ?
sec
2
?? ????
(
1+tan
2
?? 1-tan
2
?? )+ (
2tan?? 1- tan
2
?? )
?? = ?
(1- tan
2
?? )(sec
2
?? )????
(1+tan?? )
2
Let tan?? =?? ? sec
2
?? ???? =d??
?? = ?
(1- ?? 2
)
(1+?? )
2
???? = ?
(1- ?? )
(1+?? )
????
?? = (
2
1+?? -1)????
?? =2ln|1+?? |-?? +??
?? =2ln|1+tan?? |-tan?? +??
Page 4
9
th
January 2020 (Shift 2), Mathematics Page | 1
Date: 9
th
January 2020 (Shift 2)
Time: 2:30 P.M. to 5:30 P.M.
Subject: Mathematics
1. If ?? (?? )= |
?? +?? ?? +2 ?? +1
?? +?? ?? +3 ?? +2
?? +?? ?? +4 ?? +3
| and ?? -2?? +?? =1 then
a. ?? (-50)=-1 b. ?? (50)= 1
c. ?? (50)=-501 d. ?? (50)= 501
Answer: (?? )
Solution:
Given ?? (?? )= |
?? +?? ?? +2 ?? +1
?? +?? ?? +3 ?? +2
?? +?? ?? +4 ?? +3
|
?? -2?? +?? =1
Applying ?? 1
??? 1
-2?? 2
+?? 3
?? (?? )= |
?? -2?? +?? 0 0
?? +?? ?? +3 ?? +2
?? +?? ?? +4 ?? +3
|
Using ?? -2?? +?? =1
??? (?? )= (?? +3)
2
-(?? +2)(?? +4)
??? (?? )=1
??? (50)=1
??? (-50)=1
2. If ?? (?? )=
{
?? 0<?? <
1
2
1
2
?? =
1
2
1-??
1
2
<?? <1
?? (?? )= (?? -
1
2
)
2
then find the area bounded by ?? (?? ) and ?? (?? ) from ?? =
1
2
to ?? =
v3
2
.
a.
v3
2
-
1
3
b.
v3
4
+
1
3
c. 2v3 d. 3v3
9
th
January 2020 (Shift 2), Mathematics Page | 2
Answer: (?? )
Solution:
Given ?? (?? )=
{
?? 0<?? <
1
2
1
2
?? =
1
2
1-??
1
2
<?? <1
?? (?? )= (?? -
1
2
)
2
The area between ?? (?? ) and ?? (?? ) from ?? =
1
2
to =
v3
2
:
Points of intersection of ?? (?? ) and (?? ) :
1-?? = (?? -
1
2
)
2
??? =
v3
2
,-
v3
2
Required area =?
(?? (?? )-?? (?? ))????
v3
2
1
2
=? (1-?? - (?? -
1
2
)
2
)????
v3
2
1
2
=?? -
?? 2
2
-
1
3
(?? -
1
2
)
3
|
1
2
v3
2
=
v3
4
-
1
3
9
th
January 2020 (Shift 2), Mathematics Page | 3
3. If ?? ?(?? ?~ ?? ) is false. Truth value of ?? and ?? will be
a. TF b. FT
c. TT d. FF
Answer: (?? )
Solution:
Given ?? ?(?? ?~ ?? )
Truth table:
?? ?? ~?? (?? ?~ ?? ) ?? ?(?? ?~ ?? )
T T F F F
T F T T T
F T F F T
F F T F T
?? ?(?? ?~ ?? ) is false when ?? is true and ?? is true.
4. ?
????
cos
2
??
(sec2?? +tan2?? )
=?? tan?? +2log?? (?? )+?? then ordered pair (?? , ?? (?? )) is
a. (1,1+tan?? ) b. (1,1-tan?? )
c. (-1,1+tan?? ) d. (-1,1-tan?? )
Answer: (?? )
Solution:
Let ?? = ?
????
cos
2
?? (sec2?? +tan2?? )
?? = ?
sec
2
?? ????
(
1+tan
2
?? 1-tan
2
?? )+ (
2tan?? 1- tan
2
?? )
?? = ?
(1- tan
2
?? )(sec
2
?? )????
(1+tan?? )
2
Let tan?? =?? ? sec
2
?? ???? =d??
?? = ?
(1- ?? 2
)
(1+?? )
2
???? = ?
(1- ?? )
(1+?? )
????
?? = (
2
1+?? -1)????
?? =2ln|1+?? |-?? +??
?? =2ln|1+tan?? |-tan?? +??
9
th
January 2020 (Shift 2), Mathematics Page | 4
Given ?? =?? tan?? +2log?? (?? )+??
??? = -1 , ?? (?? )=|1+???????? |
5. Let ?? ?? is a positive term of GP and ? ?? 2?? +1
=200
100
?? =1
, ? ?? 2?? =100
100
?? =1
, then the value of ? ?? ?? 200
?? =1
is
a. 150 b. 225
c. 300 d. 175
Answer: (?? )
Solution:
?? ?? is a positive term of GP.
Let GP be ?? ,???? ,????
2
,.....
? ?? 2?? +1
100
?? =1
=?? 3
+ ?? 5
+ .......+?? 201
200=????
2
+ ????
4
+ .......+ ????
201
200=
????
2
(?? 200
-1)
?? 2
-1
. . . (1)
Also, ? ?? 2?? 100
?? =1
=100
100=?? 2
+ ?? 4
+ ... .....+ ?? 200
100=???? + ????
3
+ ........+????
199
100=
???? (?? 200
-1)
?? 2
-1
. . . (2)
From (1) and (2), r = 2
And ? ?? 2?? +1
100
?? =1
+ ? ?? 2?? 100
?? =1
=300
? ?? 2
+ ?? 3
+ ?? 4
... .....+ ?? 200
+?? 201
=300
? ???? + ????
2
+ ????
3
+ .......+ ????
200
=300
??? (?? +???? + ?? ?? 2
+ .....+ ????
199
)=300
?2(?? 1
+ ?? 2
+ ?? 3
+ ......+ ?? 200
)=300
? ?? ?? 200
?? =1
=150
6. ?? is a complex number such that |Re(?? )|+|Im(?? )|=4, then |?? | cannot be equal to
a. v8 b. v7
c. v
17
2
d. v10
Page 5
9
th
January 2020 (Shift 2), Mathematics Page | 1
Date: 9
th
January 2020 (Shift 2)
Time: 2:30 P.M. to 5:30 P.M.
Subject: Mathematics
1. If ?? (?? )= |
?? +?? ?? +2 ?? +1
?? +?? ?? +3 ?? +2
?? +?? ?? +4 ?? +3
| and ?? -2?? +?? =1 then
a. ?? (-50)=-1 b. ?? (50)= 1
c. ?? (50)=-501 d. ?? (50)= 501
Answer: (?? )
Solution:
Given ?? (?? )= |
?? +?? ?? +2 ?? +1
?? +?? ?? +3 ?? +2
?? +?? ?? +4 ?? +3
|
?? -2?? +?? =1
Applying ?? 1
??? 1
-2?? 2
+?? 3
?? (?? )= |
?? -2?? +?? 0 0
?? +?? ?? +3 ?? +2
?? +?? ?? +4 ?? +3
|
Using ?? -2?? +?? =1
??? (?? )= (?? +3)
2
-(?? +2)(?? +4)
??? (?? )=1
??? (50)=1
??? (-50)=1
2. If ?? (?? )=
{
?? 0<?? <
1
2
1
2
?? =
1
2
1-??
1
2
<?? <1
?? (?? )= (?? -
1
2
)
2
then find the area bounded by ?? (?? ) and ?? (?? ) from ?? =
1
2
to ?? =
v3
2
.
a.
v3
2
-
1
3
b.
v3
4
+
1
3
c. 2v3 d. 3v3
9
th
January 2020 (Shift 2), Mathematics Page | 2
Answer: (?? )
Solution:
Given ?? (?? )=
{
?? 0<?? <
1
2
1
2
?? =
1
2
1-??
1
2
<?? <1
?? (?? )= (?? -
1
2
)
2
The area between ?? (?? ) and ?? (?? ) from ?? =
1
2
to =
v3
2
:
Points of intersection of ?? (?? ) and (?? ) :
1-?? = (?? -
1
2
)
2
??? =
v3
2
,-
v3
2
Required area =?
(?? (?? )-?? (?? ))????
v3
2
1
2
=? (1-?? - (?? -
1
2
)
2
)????
v3
2
1
2
=?? -
?? 2
2
-
1
3
(?? -
1
2
)
3
|
1
2
v3
2
=
v3
4
-
1
3
9
th
January 2020 (Shift 2), Mathematics Page | 3
3. If ?? ?(?? ?~ ?? ) is false. Truth value of ?? and ?? will be
a. TF b. FT
c. TT d. FF
Answer: (?? )
Solution:
Given ?? ?(?? ?~ ?? )
Truth table:
?? ?? ~?? (?? ?~ ?? ) ?? ?(?? ?~ ?? )
T T F F F
T F T T T
F T F F T
F F T F T
?? ?(?? ?~ ?? ) is false when ?? is true and ?? is true.
4. ?
????
cos
2
??
(sec2?? +tan2?? )
=?? tan?? +2log?? (?? )+?? then ordered pair (?? , ?? (?? )) is
a. (1,1+tan?? ) b. (1,1-tan?? )
c. (-1,1+tan?? ) d. (-1,1-tan?? )
Answer: (?? )
Solution:
Let ?? = ?
????
cos
2
?? (sec2?? +tan2?? )
?? = ?
sec
2
?? ????
(
1+tan
2
?? 1-tan
2
?? )+ (
2tan?? 1- tan
2
?? )
?? = ?
(1- tan
2
?? )(sec
2
?? )????
(1+tan?? )
2
Let tan?? =?? ? sec
2
?? ???? =d??
?? = ?
(1- ?? 2
)
(1+?? )
2
???? = ?
(1- ?? )
(1+?? )
????
?? = (
2
1+?? -1)????
?? =2ln|1+?? |-?? +??
?? =2ln|1+tan?? |-tan?? +??
9
th
January 2020 (Shift 2), Mathematics Page | 4
Given ?? =?? tan?? +2log?? (?? )+??
??? = -1 , ?? (?? )=|1+???????? |
5. Let ?? ?? is a positive term of GP and ? ?? 2?? +1
=200
100
?? =1
, ? ?? 2?? =100
100
?? =1
, then the value of ? ?? ?? 200
?? =1
is
a. 150 b. 225
c. 300 d. 175
Answer: (?? )
Solution:
?? ?? is a positive term of GP.
Let GP be ?? ,???? ,????
2
,.....
? ?? 2?? +1
100
?? =1
=?? 3
+ ?? 5
+ .......+?? 201
200=????
2
+ ????
4
+ .......+ ????
201
200=
????
2
(?? 200
-1)
?? 2
-1
. . . (1)
Also, ? ?? 2?? 100
?? =1
=100
100=?? 2
+ ?? 4
+ ... .....+ ?? 200
100=???? + ????
3
+ ........+????
199
100=
???? (?? 200
-1)
?? 2
-1
. . . (2)
From (1) and (2), r = 2
And ? ?? 2?? +1
100
?? =1
+ ? ?? 2?? 100
?? =1
=300
? ?? 2
+ ?? 3
+ ?? 4
... .....+ ?? 200
+?? 201
=300
? ???? + ????
2
+ ????
3
+ .......+ ????
200
=300
??? (?? +???? + ?? ?? 2
+ .....+ ????
199
)=300
?2(?? 1
+ ?? 2
+ ?? 3
+ ......+ ?? 200
)=300
? ?? ?? 200
?? =1
=150
6. ?? is a complex number such that |Re(?? )|+|Im(?? )|=4, then |?? | cannot be equal to
a. v8 b. v7
c. v
17
2
d. v10
9
th
January 2020 (Shift 2), Mathematics Page | 5
Answer: (?? )
Solution:
|Re(?? )|+|Im(?? )|=4
Let ?? =?? +????
?|?? |+|?? |=4
??? lies on the rhombus.
Maximum value of |?? |=4 when ?? =4,-4,4?? ,-4??
Minimum value of |?? |=2v2 when ?? =2±2??, ±2+2??
|?? |?[2v2 ,4]
|?? |?[v8 ,v16]
|?? |?v7
7. ?? (?? ):[0,5]??? ,?? (?? )=? ?? 2
?? (?? )???? ,?? (1)=3,
?? 0
?? (?? )=? ?? (?? )????
?? 1
then correct choice is
a. ?? (?? ) has no critical point
b. ?? (?? ) has local minimum at ?? =1
c. ?? (?? ) has local maximum at ?? =1
d. ?? (?? ) has point of inflection at ?? =1
Answer: (b)
Solution:
?? (?? )=?? 2
?? (?? )
Put ?? =1
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FAQs on JEE Main 2020 January 9 Question Paper Shift 2 - JEE Main & Advanced Previous Year Papers
| 1. क्या JEE Main 2020 January 9 Question Paper Shift 2 में किसी खास विषय पर प्रश्न पूछे गए थे? |  |
Ans. हां, JEE Main 2020 January 9 Question Paper Shift 2 में विभिन्न विषयों पर प्रश्न पूछे गए थे जैसे कि गणित, भौतिक विज्ञान और रसायन विज्ञान।
| 2. JEE Main 2020 January 9 Question Paper Shift 2 में कितने प्रश्न पूछे गए थे? | |
Ans. JEE Main 2020 January 9 Question Paper Shift 2 में कुल मिलाकर 75 प्रश्न पूछे गए थे।
| 3. क्या JEE Main 2020 January 9 Question Paper Shift 2 में किसी विषय पर अधिक प्रश्न पूछे गए थे? | |
Ans. हां, JEE Main 2020 January 9 Question Paper Shift 2 में गणित विषय पर अधिक प्रश्न पूछे गए थे।
| 4. JEE Main 2020 January 9 Question Paper Shift 2 की तैयारी के लिए सर्वश्रेष्ठ संदेश क्या होगा? | |
Ans. JEE Main 2020 January 9 Question Paper Shift 2 की तैयारी के लिए प्रैक्टिस सेट्स और मॉक टेस्ट करना बेहतर हो सकता है।
| 5. JEE Main 2020 January 9 Question Paper Shift 2 के नतीजे कब जारी होंगे? | |
Ans. JEE Main 2020 January 9 Question Paper Shift 2 के नतीजे जल्द ही ऑफिशियल वेबसाइट पर जारी किए जाएंगे।
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Dec 23, 2024 Last updated |
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Additional Information about JEE Main 2020 January 9 Question Paper Shift 2 for JEE Preparation
JEE Main 2020 January 9 Question Paper Shift 2 Free PDF Download
The JEE Main 2020 January 9 Question Paper Shift 2 is an invaluable resource that delves deep into the core of the JEE exam.
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JEE Main 2020 January 9 Question Paper Shift 2 Notes
JEE Main 2020 January 9 Question Paper Shift 2 Notes offer in-depth insights into the specific topic to help you master it with ease.
This comprehensive document covers all aspects related to JEE Main 2020 January 9 Question Paper Shift 2.
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JEE Main 2020 January 9 Question Paper Shift 2 JEE Questions
The "JEE Main 2020 January 9 Question Paper Shift 2 JEE Questions" guide is a valuable resource for all aspiring students preparing for the
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The guide includes previous years' question papers for students to familiarize themselves with the exam's format and difficulty level.
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The content of JEE Main 2020 January 9 Question Paper Shift 2 is prepared as per the latest JEE syllabus.
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