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Maths Sequence and Series ques

How to solve this question using Vn -Vn-1 method ?
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why does Earth rotate?

may ssem like a dumb doubt but i was fumbled that even my coaching topper couldnt answer. leave me. so why does it rotate? i tried finding answers on net but most of them are different and couldnt make it to a singke conclusion. please help

Vector Analysis-III

Shouldn't the answer to this be zero?
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Vector Analysis-II

Again I think this is more related to 3-d but anyhow...
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Vector Analysis

I tried breaking the middle term to somehow cancel out the first and last term. is this correct or am I way off?
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gravitation problem

Please help me solve this
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Minimum path diff.

△x = (n-1/2)β Is there + or - in between for condition for minimas...Somewhere - is used like in standard YDSE but in Lloyd's Mirror , for minimas it's + β:fringe width...

Spring mass problems

Please help me with this question.
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Path difference

In Lloyd's Mirror, Why we add this λ/2 or π in path difference?
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Application of cross product

Well if we take out area of parlellogram and equate it with 1/2(d1xd2) which we can write as 1/2|d1||d2|sintheta|, i get theta as root(7/9) while the actual answer is cos theta= root (3/10)
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Elasticity

my solution has taken the normal formula of U/v = 1/2 x stress x straint to cancel out the equal lengths with which i get the answer 2:1 but the solution they gave, they converted strain = stress/Y and cancelled out Y both sides which makes no sense cause the question says their length is equal and not their Y. Am i wrong or is the solution/answer by nta just incorrect?
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A.P.

I solved by first expanding the ap and then eliminating the terms divisible by 3 then i formed 2 different aps (one starting with 8 and the other with 13) each with cd = 15 and summed them up separately. but my answer is wrong whereas the solution given takes the sum of this normal ap first then subtracts it with sum of multiples of 3 in it. i want to understand why my method was wrong?
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Organic Reaction mechanism is needed for JEE Mains + Advanced as well?

As JEE mains 1 is approaching real soon!! I have nearly no much time left and doing syllabus completion as fast as possible, Do I need to study learn Organic reaction mechanisms for JEE mains?? Or it can be skipped is it fine ? I study that later and grind on pyqs for Oc cuz I have done direct reactions from Ncert itself till now pls reply.. 🙏

Sn1 Reaction

Chlorine also shows +M why isnt it 2nd why is Cholrobenzene more reactive towards SN1
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Why doesn't addition of inert gas at constant volume shift the rxn towards one direction

When adding an inert gas in a closed vessel , the total volume is constant so the total pressure has to increase. But change in total pressure should shift the rxn towards one end (if delta Ng isnt zero) But that doesnt happen. Please help me understand why this is the case...

EM Waves

shouldnt a and c both be correct B has to perpendicualr , no information given about direction of wave
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thermo doubt

in phase change, temp, pressure is constant...so wont delta h = ncpdt = 0 as dt = 0 and delta s = q /t = delta h /t which will again be zero