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optics basics

Can anyone confirm the ans ? We are supposed to find the velocity of image
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CHEMISTRY

Chemical bonding
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application of derivatives (maxima minima)

Asked to find the least value of a€R for which 4ax²+1/x≥1, for all x>0

Aldehydes Doubt

Can anyone help? I don't get the approach for this.
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MOI

what is the moi of a uniform cube about an axis which passes through centre my thinking: a rod's moi about centroidal axis is (ml^2)/12 a square plate is just integration of multiple rods of same moi therefore moi of square plate about x or y axis is also (ml^2)/12 ...

Integration graph

Is there any method by which we can know that the area is going to be zero without actually integrating (que 3)
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chem equilibrium

can this be explained without organic?
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Sequence n Series

I am unable to find my mistake. Answer given is 120, i get 15.
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electrostatics dipole

If we make gaussian surface around a dipole, net charge inside the surface will be zero so electric field should be zero, but dipole has an electric field.....

THERMODYNAMICS

actually i want to study thermodynamics in deep out of Bruce H. mahan , Peter Atkins and Mc murry -fay what should i choose for deep understanding (self study via book reading :)) my style )...

PnC

How many 4 digits numbers can be formed by 0,1,2,3,4,5,6 without repetition which are divisible by 4