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JEE Advanced Mi...

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  • Question 1
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    When liquid medicine of density p is to be put in the eye it is done with the help of a dropper. As the bulb on the top of the dropper is pressed, a drop forms at the opening of the dropper. We wish to estimate the size of the drop. We first assume that the drop formed at the opening is spherical because that requires a minimum increase in its surface energy. To determine the size, we calculate the net vertical force due to the surface tension T when the radius of the drop is R. When this force becomes smaller than the weight of the drop, the drop gets detached from the dropper.

    If the radius of the opening of the dropper is r, the vertical force due to the surface tension on the drop of radius R (assuming r << R)

  • Question 2
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    Directions For Questions

    The nuclear charge (Ze) is non-uniformly distributed within a nucleus of radius R. The charge density p(r) [charge per unit volume] is dependent only on the radial distance r from the centre of the nucleus as shown in figure. The electric field is only along the radial direction.

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    For a = 0, the value of d (maximum value of p as shown in the figure) is

  • Question 3
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    Two small equally charged spheres, each of mass m, are suspended from the same point by silk threads of length l. The distance between the spheres x << l. Find the rate dq/dt with which the charge leaks off each sphere if their approach velocity varies as v = a/√x , where a is a constant.

  • Question 4
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    Directions For Questions

    Directions: The following question is based on the paragraph given below.

    The noble gases have closed-shell electronic configuration and are monatomic gases under normal conditions. The low boiling points of the lighter noble gases are due to weak dispersion forces between the atoms and the absence of other interatomic interactions.

    The direct reaction of xenon with fluorine leads to a series of compounds with oxidation numbers +2, +4 and +6. XeF4 reacts violently with water to give XeO3. The compound can also be prepared using XeF6 as the starting compound. The compounds of xenon exhibit rich stereochemistry and their geometries can be deduced considering the total number of electron pairs in the valence shell.

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    The chemical nature of the compounds XeF4 and XeF6 is expected to be

  • Question 5
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    (1R, 3S)-Cis-1-Bromo-3-methyl cyclohexane. The product formed in the reaction is

  • Question 6
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    What is the magnetic moment of coordination compound formed during brown ring test?

  • Question 7
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    The equilibrium constant K for the reaction 2HI(g) ⇌ H2 (g) + I2(g) at room temperature is 2.85 and that at 698 K is 1.4 × 10–2. This implies that -

  • Question 8
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  • Question 9
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    Out of 3n consecutive integers, three are selected at random. Find the probability that their sum is divisible by 3.

  • Question 10
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    If SK be the perpendicular from the focus S on the tangent at any point P on the ellipse  then locus of the foot of the perpendicular K is equal to

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