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All questions of JEE Advanced 2012 for JEE Exam

Two solid cylinders P and Q of same mass and same radius start rolling down a fixed inclined plane from the same height at the same time. Cylinder P has most of its mass concentrated near its surface, while Q has most of its mass concentrated near the axis. Which statement(s) is(are) correct?
  • a)
    Both cylinders P and Q reach the ground at the same time.
  • b)
    Cylinders P has larger linear acceleration than cylinder Q.
  • c)
    Both cylinders reach the ground with same translational kinetic energy.
  • d)
    Cylinder Q reaches the ground with larger angular speed.
Correct answer is option 'D'. Can you explain this answer?

Dev Kumar answered
A=g sintheta × MR^2 / MR^2 + I .... so a is inversely proportional to moment of inertia I .... mass of P is concentrated at the surface so it's moment of inertia is more and mass of Q is near the axis so it's moment of inertia is less... so the body with less moment of inertia will have more acceleration as the relationship is inverse... so the body Q will have more acceleration and will reach the bottom with greater angular speed.. so the option D is correct..

With respect to graphite and diamond, which of the statement(s) given below is (are) correct?
  • a)
    Graphite is harder than diamond.
  • b)
    Graphite has higher electrical conductivity than diamond.
  • c)
    Graphite has higher thermal conductivity than diamond.
  • d)
    Graphite has higher C–C bond order than diamond.
Correct answer is option 'B,D'. Can you explain this answer?

Nandini Patel answered
Graphite can conduct electricity because of the delocalised (free) electrons in its structure. These arise because each carbon atom is only bonded to 3 other carbon atoms. ... However, in diamond, all 4 outer electrons on each carbon atom are used in covalent bonding, so there are no delocalised electrons.

graphite and graphene, diamond is the best thermal conductor around room temperature, having thermal conductivity of more than 2,000 watts per meter per Kelvin, which is five times higher than the best metals such as copper.

SECTION I : Single Correct Answer Type
This section contains 8 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of
which ONLY ONE is correct.
Q. Let a1, a2, a3, ….. be in harmonic progression with a1 = 5 and a20 = 25. The least positive integer n for
which an < 0
  • a)
    22
  • b)
    23
  • c)
    24
  • d)
    25
Correct answer is option 'D'. Can you explain this answer?

Understanding Harmonic Progression
Harmonic progression (HP) means that the reciprocals of the terms form an arithmetic progression (AP). Given that a1 = 5 and a20 = 25, we can derive the necessary values.
Finding the Reciprocals
- The terms in HP are:
a1 = 5, a2, a3, ...
The reciprocals are:
1/a1 = 1/5, 1/a2, 1/a3, ..., 1/a20 = 1/25
- Since these reciprocals are in AP, we can denote:
d = common difference of the AP.
Setting Up the Equations
1. The first term of the AP is 1/5.
2. The 20th term can be expressed as:
1/a20 = 1/5 + 19d = 1/25
- From this, we can solve for d:
1/5 + 19d = 1/25
19d = 1/25 - 1/5
19d = 1/25 - 5/25
19d = -4/25
d = -4/(25*19) = -4/475
Finding the General Term
- The n-th term of the reciprocals in AP is given by:
1/an = 1/5 + (n-1)(-4/475)
= 1/5 - 4(n-1)/475
- Therefore, the n-th term can be expressed as:
an = 1 / (1/5 - 4(n-1)/475)
Finding When an < />
- Setting an < 0:="" />
1/5 - 4(n-1)/475 < 0="" />
-4(n-1)/475 < -1/5="" />
4(n-1)/475 > 1/5
n - 1 > (475/4) * (1/5)
n - 1 > 23.75
n > 24.75
- Therefore, the least positive integer n is 25.
Thus, the answer is option D: 25.

SECTION III : Multiple Correct Answer(s) Type
The section contains 6 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE are correct.
Q. The reversible expansion of an ideal gas under adiabatic and isothermal conditions is shown in the figure.
Which of the following statement(s) is (are) correct?
  • a)
    T1 = T2
  • b)
    T3 > T1
  • c)
    wisothermal > wadiabatic
  • d)
    ΔUisothermal > ΔUadiabatic
Correct answer is option 'A,C,D'. Can you explain this answer?

Anjali Sharma answered
T1 = T2 because process is isothermal.
Work done in adiabatic process is less than in isothermal process because area covered by isothermal curve is more than the area co vered by the adiabatic curve.
In adiabatic process expansion occurs by using internal energy hence it decreases while in isothermal process temperature remains constant that’s why no change in internal energy.

The given graphs / data I, II, III and IV represent general trends observed for different physisorption and
chemisorption processes under mild conditions of temperature and pressure. Which of the following
choice(s) about I, II, III and IV is (are) correct?
  • a)
    I is physisorption and II is chemisorption
  • b)
    I is physisorption and III is chemisorption
  • c)
    IV is chemisorption and II is chemisorption
  • d)
    IV is chemisorption and III is chemisorption
Correct answer is option 'A,C'. Can you explain this answer?

Ashutosh Shah answered
Graph (I) and (III) represent physiosorption because, in physiosorption, the amount of adsorption decreases with the increase of temperature and increases with the increase of pressure.
Graph (II) represent chemisorption, because in chemisorption amount of adsorption increase with the increase of temperature. Graph (IV) is showing the formation of a chemical bond, hence chemisorption.

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