Good questions for JEE (A) 2022

Please share some good questions which are not tough, lengthy, or calculative but are a bit conceptual, “new” (if you know what I mean). I have found a few from PCM each. Will post them below. You guys also contribute.


Maths

Share some good questions which are not tough, lengthy, or calculative but are a bit conceptual. Multiple concept problems are also welcomed.


Physics

Tricky questions? Cheeky aplication of a concept? Jo dikhta hh vo hota nahi, jo hota h vo dikhta nahi.


Chemistry

Shocking exceptions defying the normal behavior (well that’s the def. of exception).


Questions can be found in post number -
2, 3, 6, 16, 18, 23, 31, 32, 38, 47, 60, 77

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Q.1: If A^3 - 2A^2 - A + 2I = O then find A, where A is a square matrix.

Hint: A cubic with 5 solutions? Check again! 4 solutions? Yes!
(Source: Blackbook)

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Q.2 : Find solutions of sinx = 2.

Hint: Complex Numbers & Euler’s representation.

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Hint: Stirlings approximation

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K = 1/e

Yea correct. Using what method?

I don’t know by name…

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Answer (D)

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I’ve done this one before, nice ques…it is from Allen right!!
Fiitjee gave this Allen’s test to us in January.

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Now I’m feeling good cuz I solved this in the paper… probably wasted a lot of time in the paper

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But this what the paper setter’s trap…
Bcz such ques seem doable but suck lot of time…which could have been invested to do 2 - ques

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Can anyone understand this question and tell me , the commas in end are confusing since its correspond to three vectors respectively.

How did you do it? I tried via contact forces between rod and block and got equation which was not proceeding further

(abx) (bcy) and (caz) are each coplanar (the three vectors in parenthesis)

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Ok got it! Priniting confused me,
What about that rotation one

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You did right , thats why teachers tell to leave rotation and do it at end.

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Oh wait a min !! I think i got the rotation one using WPE

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use energy equations
change in PE of rod = (1/2)*mv²(of block) + (1/2)Iw²(of rod)
find the relation between w and v by using constraint at the point of contact → relative velocity=0 along perpendicular direction of rod

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Yeah got it just now.
It just looked hard , was simple 2 equations.

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