Exam (elaborations)
JEE MAIN QUESTION AND ANSWER
- Course
- Institution
I HAVE UPLOAD HERE JEE MAIN QUESTION PAPER OF 2022 YEAR WITH SOLN OF BATCH 1 AND 2
[Show more]
Seller
Follow
achintyarai
Content preview
JEE (Main)-2022 : Phase-2 (25-07-2022)-EveningMATHEMATICS
SECTION - A = 92 – 9 | | – 43
= 9 | |2 – 9 | | – 43
Multiple Choice Questions: This section contains 20
= 0 for 2 values of | | out of which one is –ve
multiple choice questions. Each question has 4 choices
and other is +ve
(1), (2), (3) and (4), out of which ONLY ONE is correct.
So, 2 values of satisfy the system of equations to
Choose the correct answer : obtain no solution
3. The number of bijective functions f : {1, 3, 5, 7, …,
1. For z if the minimum value of
99} → {2, 4, 6, 8, ….., 100} such that
( z − 3 2 + z − p 2i ) is 5 2, then a value of p
f ( 3 ) f ( 9 ) f (15 ) f ( 21) .... f ( 99 ) , is_____.
is _________.
50 50
7 (A) P17 (B) P33
(A) 3 (B)
2 50!
(C) 33! 17! (D)
9 2
(C) 4 (D)
2 Answer (B)
Answer (C) Sol. As function is one-one and onto, out of 50 elements
Sol. of domain set 17 elements are following restriction
f(3) > f(9) > f(15) ….. > f(99)
So number of ways =50 C17 · 1 · 33!
50
= P33
It is sum of distance of z from (3 2, 0 ) and
4. The remainder when (11)1011 + (1011)11 is divided
by 9 is
( 0, p 2 ) (A) 1 (B) 4
(C) 6 (D) 8
For minimising, z should lie on AB and AB = 5 2
Answer (D)
( AB ) 2
= 18 + 2 p 2
(11)1011 + (1011)11 1011 + 311
p = 4 Sol. Re = Re 2
9 9
2. The number of real values of , such that the
system of linear equations 21011
For Re
2x – 3y + 5z = 9 9
x + 3y – z = –18
21011 = ( 9 − 1) C0 9337 ( −1)
337 337 0
=
3x – y + (2 – | |)z = 16
C19336 ( −1)
337 1
has no solutions, is +
C2 9335 ( −1) + ......
337 2
(A) 0 (B) 1 +
(C) 2 (D) 4
C337 90 ( −1)
337 337
+
Answer (C)
2 −3 5 so, remainder is 8
Sol.
= 1 3 −1 (
= 2 3 2 − 3 | | −1) 311
and Re =0
3 −1 2 − | | +3 ( − | | +3 )
2 9
+5 ( −1 − 9 ) So, remainder is 8
- 16 -
, JEE (Main)-2022 : Phase-2 (25-07-2022)-Evening
21
3
5. The sum ( 4n − 1)( 4n + 3 ) is equal to
1
1 1 1 1
n =1 Sol. I = lim n + + + ..... +
n → 2
1 2 3 2 n
− 1
7 7 1 − n 1− n 1− n 1 − n
(A) (B) 2 2 2 2
87 29
14 21 Let 2n = t and if n → then t →
(C) (D)
87 29
1 t −1 1
Answer (B) l = lim
n → t
r =1 r
21
3 3 21 1 1 1−
Sol. ( 4n − 1)( 4n + 3 ) = 4 4n − 1 − 4n + 3 t
n =1 n =1
1
dx
1
dx a a
3 1 1 1 1 1 1 l= = f ( x ) dx = f ( a − x ) dx
= − + − + ..... + − 0 1− x 0 x 0 0
4 3 7 7 11 83 87
1
3 1 1 3 84 7 1
= − = = = 2 x 2 = 2
4 3 87 4 3.87 29 0
8 2 − ( cos x + sin x )
7
8. If A and B are two events such that
6. lim is equal to
x→
2 − 2 sin2x 1 1 1
4
P ( A ) = , P ( B ) = and P ( A B ) = , then
3 5 2
(A) 14 (B) 7
P ( A B ) + P ( B A ) is equal to
(C) 14 2 (D) 7 2
Answer (A) 3 5
(A) (B)
4 8
8 2 − ( cos x + sin x )
7
0
Sol. lim 0 form
x→
4
2 − 2 sin2 x (C)
5
(D)
7
4 8
−7 ( cos x + sin x ) ( − sin x + cos x )
6
= lim using L–H Answer (B)
x→
−2 2 cos2x
4
1 1 1
Rule Sol. P ( A ) = , P ( B ) = and P ( A B ) =
3 5 2
56 ( cos x − sin x ) 0
= lim 0 P (A B) =
1 1 1 1
+ − =
x→
4
2 2 cos2x 3 5 2 30
−56 ( sin x + cos x )
= lim using L–H Rule
x→
4
−4 2 sin2x
= 7 2 2 = 14
1 1 1 1 1
7. lim + + + ..... +
n → 2n
1 2 3 2 n
− 1
1 − n 1− n 1− n 1 − n
2 2 2 2
P ( A B ) P ( B A )
is equal to Now, P ( A B ) + P ( B A ) = +
P ( B ) P ( A )
1
(A) (B) 1 9 5
2
5
(C) 2 (D) –2 = 30 + 30 =
4 2 8
Answer (C) 5 3
- 17 -
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller achintyarai. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $8.49. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
76462 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now