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JEE Advanced 2012 Paper -2 with Solutions


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JEE Advanced 2012 Paper -2 with Solutions - Question 1

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. Two identical discs of same radius R are rotating about their axes in opposite directions with the same constant angular speed ω. The discs are in the same horizontal plane. At time t = 0, the points P and Q are facing each other as shown in the figure. The relative speed between the two points P and Q is vr. In one time period (T) of rotation of the discs, vr as a function of time is best represented by

Detailed Solution for JEE Advanced 2012 Paper -2 with Solutions - Question 1

In each rotation relative speed becomes zero twice and becomes maximum twice.

JEE Advanced 2012 Paper -2 with Solutions - Question 2

A loop carrying current I lies in the x-y plane as shown in the figure. The unit vector is coming
out of the plane of the paper. The magnetic moment of the current loop is

Detailed Solution for JEE Advanced 2012 Paper -2 with Solutions - Question 2

JEE Advanced 2012 Paper -2 with Solutions - Question 3

An infinitely long hollow conducting cylinder with inner radius R/2 and outer radius R carries a uniform current density along its length. The magnitude of the magnetic field,  as a function of the radial distance r from the axis is best represented by

Detailed Solution for JEE Advanced 2012 Paper -2 with Solutions - Question 3

JEE Advanced 2012 Paper -2 with Solutions - Question 4

A thin uniform cylindrical shell, closed at both ends, is partially filled with water. It is floating vertically in water in half-submerged state. If ρc is the relative density of the material of the shell with respect to water, then the correct statement is that the shell is

Detailed Solution for JEE Advanced 2012 Paper -2 with Solutions - Question 4

JEE Advanced 2012 Paper -2 with Solutions - Question 5

In the given circuit, a charge of +80 μC is given to the upper plate of the 4 μF capacitor. Then in the steady state, the charge on the upper plate of the 3 μF capacitor is

Detailed Solution for JEE Advanced 2012 Paper -2 with Solutions - Question 5

Let ‘q’ be the final charge on 3μF capacitor then

JEE Advanced 2012 Paper -2 with Solutions - Question 6

Two moles of ideal helium gas are in a rubber balloon at 30°C. The balloon is fully expandable and can be assumed to require no energy in its expansion. The temperature of the gas in the balloon is slowly changed to 35°C. The amount of heat required in raising the temperature is nearly (take R = 8.31 J/mol.K)

Detailed Solution for JEE Advanced 2012 Paper -2 with Solutions - Question 6

JEE Advanced 2012 Paper -2 with Solutions - Question 7

Consider a disc rotating in the horizontal plane with a constant angular speed w about its centre O. The disc has a shaded region on one side of the diameter and an unshaded region on the other side as shown in the figure. When the disc is in the orientation as shown, two pebbles P and Q are simultaneously projected at an angle towards R. The velocity of projection is in the y-z plane and is same for both pebbles with respect to the disc. Assume that

(i) they land back on the disc before the disc has 1/8 completed  rotation,

(ii) their range is less than half the disc radius, and

(iii) ω remains constant throughout. Then

Detailed Solution for JEE Advanced 2012 Paper -2 with Solutions - Question 7

JEE Advanced 2012 Paper -2 with Solutions - Question 8

A student is performing the experiment of resonance Column. The diameter of the column tube is 4 cm. The frequency of the tuning fork is 512 Hz. The air temperature is 38°C in which the speed of sound is 336 m/s. The zero of the meter scale coincides with the top end of the Resonance Column tube. When the first resonance occurs, the reading of the water level in the column is

Detailed Solution for JEE Advanced 2012 Paper -2 with Solutions - Question 8

JEE Advanced 2012 Paper -2 with Solutions - Question 9

SECTION II : Paragraph Type

This section contains 6 multiple choice questions relating to three paragraphs with two questions on each
paragraph. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

Paragraph for Questions 9 and 10

The general motion of a rigid body can be considered to be a combination of (i) a motion of its centre of
mass about an axis, and (ii) its motion about an instantaneous axis passing through the centre of mass.
These axes need not be stationary. Consider, for example, a thin uniform disc welded (rigidly fixed)
horizontally at its rim to a massless stick, as shown in the figure. When the disc-stick system is rotated
about the origin on a horizontal frictionless plane with angular speed ω, the motion at any instant can be
taken as a combination of (i) a rotation of the centre of mass of the disc about the z-axis, and (ii) a rotation
of the disc through an instantaneous vertical axis passing through its centre of mass (as is seen from the
changed orientation of points P and Q). Both these motions have the same angular speed ω in this case


Now consider two similar systems as shown in the figure: Case(a) the disc with its face vertical and
parallel to x-z plane; Case (b) the disc with its face making an angle of 45° with x-y plane and its
horizontal diameter parallel to x-axis. In both the cases, the disc is welded at point P, and the systems are
rotated with constant angular speed ω about the z-axis.

  
Q. Which of the following statements about the instantaneous axis (passing through the centre of mass) is correct?

JEE Advanced 2012 Paper -2 with Solutions - Question 10

Paragraph for Questions 9 and 10

The general motion of a rigid body can be considered to be a combination of (i) a motion of its centre of
mass about an axis, and (ii) its motion about an instantaneous axis passing through the centre of mass.
These axes need not be stationary. Consider, for example, a thin uniform disc welded (rigidly fixed)
horizontally at its rim to a massless stick, as shown in the figure. When the disc-stick system is rotated
about the origin on a horizontal frictionless plane with angular speed ω, the motion at any instant can be
taken as a combination of (i) a rotation of the centre of mass of the disc about the z-axis, and (ii) a rotation
of the disc through an instantaneous vertical axis passing through its centre of mass (as is seen from the
changed orientation of points P and Q). Both these motions have the same angular speed ω in this case


Now consider two similar systems as shown in the figure: Case(a) the disc with its face vertical and
parallel to x-z plane; Case (b) the disc with its face making an angle of 45° with x-y plane and its
horizontal diameter parallel to x-axis. In both the cases, the disc is welded at point P, and the systems are
rotated with constant angular speed ω about the z-axis.

  

Q. Which of the following statements regarding the angular speed about the instantaneous axis (passing through the centre of mass) is correct?

JEE Advanced 2012 Paper -2 with Solutions - Question 11

Paragraph for Questions 11 and 12

The β-decay process, discovered around 1900, is basically the decay of a neutron (n). In the laboratory, a proton (p) and an electron (e) are observed as the decay products of the neutron. Therefore, considering the decay of a neutron as a two-body decay process, it was predicted theoretically that the kinetic energy of the electron should be a constant. But experimentally, it was observed that the electron kinetic energy has continuous spectrum. Considering a three-body decay process, i.e.
around 1930, Pauli explained the observed electron energy spectrum. Assuming the anti-neutrino to be massless and possessing negligible energy, and the neutron to be at rest, momentum and energy conservation principles are applied. From this calculation, the maximum kinetic energy of the electron is 0.8 × 106 eV. The kinetic energy carried by the proton is only the recoil energy.

Q. If the anti-neutrino had a mass of 3eV/c2 (where c is the speed of light) instead of zero mass, what
should be the range of the kinetic energy, K, of the electron?

JEE Advanced 2012 Paper -2 with Solutions - Question 12

Paragraph for Questions 11 and 12

The β-decay process, discovered around 1900, is basically the decay of a neutron (n). In the laboratory, a proton (p) and an electron (e) are observed as the decay products of the neutron. Therefore, considering the decay of a neutron as a two-body decay process, it was predicted theoretically that the kinetic energy of the electron should be a constant. But experimentally, it was observed that the electron kinetic energy has continuous spectrum. Considering a three-body decay process, i.e.
around 1930, Pauli explained the observed electron energy spectrum. Assuming the anti-neutrino to be massless and possessing negligible energy, and the neutron to be at rest, momentum and energy conservation principles are applied. From this calculation, the maximum kinetic energy of the electron is 0.8 × 106 eV. The kinetic energy carried by the proton is only the recoil energy.

Q. What is the maximum energy of the anti-neutrino?

JEE Advanced 2012 Paper -2 with Solutions - Question 13

Paragraph for Questions 13 and 14
Most materials have the refractive index, n > 1. So, when a light ray from air enters a naturally occurring
material, then by Snell’s law,  it is understood that the refracted ray bends towards the normal.
But it never emerges on the same side of the normal as the incident ray. According to electromagnetism,
the refractive index of the medium is given by the relation,  where c is the speed of
electromagnetic waves in vacuum, v its speed in the medium, εr and μr are the relative permittivity and
permeability of the medium respectively.

In normal materials, both εr and μr, are positive, implying positive n for the medium. When both εr and μare negative, one must choose the negative root of n. Such negative refractive index materials can now
be artificially prepared and are called meta-materials. They exhibit significantly different optical behavior,
without violating any physical laws. Since n is negative, it results in a change in the direction of
propagation of the refracted light. However, similar to normal materials, the frequency of light remains
unchanged upon refraction even in meta-materials.

Q. For light incident from air on a meta-material, the appropriate ray diagram is

JEE Advanced 2012 Paper -2 with Solutions - Question 14

Paragraph for Questions 13 and 14
Most materials have the refractive index, n > 1. So, when a light ray from air enters a naturally occurring
material, then by Snell’s law,  it is understood that the refracted ray bends towards the normal.
But it never emerges on the same side of the normal as the incident ray. According to electromagnetism,
the refractive index of the medium is given by the relation,  where c is the speed of
electromagnetic waves in vacuum, v its speed in the medium, εr and μr are the relative permittivity and
permeability of the medium respectively.

In normal materials, both εr and μr, are positive, implying positive n for the medium. When both εr and μare negative, one must choose the negative root of n. Such negative refractive index materials can now
be artificially prepared and are called meta-materials. They exhibit significantly different optical behavior,
without violating any physical laws. Since n is negative, it results in a change in the direction of
propagation of the refracted light. However, similar to normal materials, the frequency of light remains
unchanged upon refraction even in meta-materials.

Q. Choose the correct statement.

*Multiple options can be correct
JEE Advanced 2012 Paper -2 with Solutions - Question 15

SECTION III : Multiple Correct Answer(s) Type

This section contains 6 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of
which ONE or MORE are correct.

15. In the given circuit, the AC source has ω = 100 rad/s. Considering the inductor and capacitor to be ideal, the correct choice(s) is (are)

Detailed Solution for JEE Advanced 2012 Paper -2 with Solutions - Question 15

*Multiple options can be correct
JEE Advanced 2012 Paper -2 with Solutions - Question 16

Six point charges are kept at the vertices of a regular hexagon of side L and centre O, as shown
in the figure. Given that ,  which of the following statement(s) is (are) correct?

Detailed Solution for JEE Advanced 2012 Paper -2 with Solutions - Question 16

Line PR is perpendicular bisector of all
the dipoles.

*Multiple options can be correct
JEE Advanced 2012 Paper -2 with Solutions - Question 17

Two spherical planets P and Q have the same uniform density r, masses Mp and MQ and surface
areas A and 4A respectively. A spherical planet R also has uniform density ρ and its mass is (MP
+ MQ). The escape velocities from the planets P, Q and R are VP, VQ and VR, respectively. Then

Detailed Solution for JEE Advanced 2012 Paper -2 with Solutions - Question 17

By calculation, if Mass of P = m

and Radius of P = R

Then Mass of Q = 8M

and radius of Q = 2R

and Mass of R = 9M

and radius of R = 91/3R

*Multiple options can be correct
JEE Advanced 2012 Paper -2 with Solutions - Question 18

The figure shows a system consisting of (i) a ring of outer radius 3R rolling clockwise without slipping on a horizontal surface with angular speed ω and (ii) an inner disc of radius 2R rotating anti-clockwise with angular speed ω/2. The ring and disc are separated by frictionless ball bearings. The point P on the inner disc is at a distance R from the origin, where OP makes an angle of 300 with the horizontal. Then with respect to the horizontal surface,

Detailed Solution for JEE Advanced 2012 Paper -2 with Solutions - Question 18

*Multiple options can be correct
JEE Advanced 2012 Paper -2 with Solutions - Question 19

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?

Detailed Solution for JEE Advanced 2012 Paper -2 with Solutions - Question 19

*Multiple options can be correct
JEE Advanced 2012 Paper -2 with Solutions - Question 20

A current carrying infinitely long wire is kept along the diameter of a circular wire loop, without
touching it, the correct statement(s) is(are)

Detailed Solution for JEE Advanced 2012 Paper -2 with Solutions - Question 20

JEE Advanced 2012 Paper -2 with Solutions - Question 21

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. The major product H of the given reaction sequence is

Detailed Solution for JEE Advanced 2012 Paper -2 with Solutions - Question 21

JEE Advanced 2012 Paper -2 with Solutions - Question 22

NiCl2{P(C2H5)2(C6H5)}2 exhibits temperature dependent magnetic behaviour (paramagnetic/diamagnetic).
The coordination geometries of Ni2+ in the paramagnetic and diamagnetic states are respectively

Detailed Solution for JEE Advanced 2012 Paper -2 with Solutions - Question 22

In both complexes Ni exists as Ni2+.

In sp3 (tetrahedral)


In dsp2 (square planar geometry)

JEE Advanced 2012 Paper -2 with Solutions - Question 23

In the cyanide extraction process of silver from argentite ore, the oxidising and reducing agents used are

Detailed Solution for JEE Advanced 2012 Paper -2 with Solutions - Question 23

The reactions involved in cyanide extraction process are:

JEE Advanced 2012 Paper -2 with Solutions - Question 24

The reaction of white phosphorous with aqueous NaOH gives phosphine along with another phosphorous
containing compound. The reaction type; the oxidation states of phosphorus in phosphine and the other
product are respectively

Detailed Solution for JEE Advanced 2012 Paper -2 with Solutions - Question 24

The balanced disproportionation reaction involving white phosphorus with aq. NaOH is

JEE Advanced 2012 Paper -2 with Solutions - Question 25

The shape of XeO2F2 molecule is

Detailed Solution for JEE Advanced 2012 Paper -2 with Solutions - Question 25

Hybridization = sp3d
Shape = see – saw

JEE Advanced 2012 Paper -2 with Solutions - Question 26

For a dilute solution containing 2.5 g of a non–volatile non–electrolyte solute in 100 g of water, the elevation in boiling point at 1 atm pressure is 2°C. Assuming concentration of solute is much lower than the concentration of solvent, the vapour pressure (mm of Hg) of the solution is (take Kb = 0.76 K kg mol-1)

Detailed Solution for JEE Advanced 2012 Paper -2 with Solutions - Question 26

B → Solute; A → Solvent

WB = 2.5 g, WA = 100 g

JEE Advanced 2012 Paper -2 with Solutions - Question 27

The compound that undergoes decarboxylation most readily under mild condition is

Detailed Solution for JEE Advanced 2012 Paper -2 with Solutions - Question 27

JEE Advanced 2012 Paper -2 with Solutions - Question 28

Using the data provided, calculate the multiple bond energy (kJ mol-1) of a CºC bond in C2H2. That energy
is (take the bond energy of a C–H bond as 350 kJ mol-1)

Detailed Solution for JEE Advanced 2012 Paper -2 with Solutions - Question 28

JEE Advanced 2012 Paper -2 with Solutions - Question 29

SECTION II : Paragraph Type

This section contains 6 multiple choice questions relating to three paragraphs with two questions on each
paragraph. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

Paragraph for Questions 29 and 30

In the following reaction sequence, the compound J is an intermediate.

Q. The compound I is

JEE Advanced 2012 Paper -2 with Solutions - Question 30

SECTION II : Paragraph Type

This section contains 6 multiple choice questions relating to three paragraphs with two questions on each
paragraph. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

Paragraph for Questions 29 and 30

In the following reaction sequence, the compound J is an intermediate.

Q. The compound K is

Detailed Solution for JEE Advanced 2012 Paper -2 with Solutions - Question 30

29- 30

JEE Advanced 2012 Paper -2 with Solutions - Question 31

Paragraph for Questions 31 and 32

The electrochemical cell shown below is a concentration cell.

M|M2+ (saturated solution of a sparingly soluble salt, MX2) || M2+ (0.001 mol dm–3) | M

The emf of the cell depends on the difference in concentrations of M2+ ions at the two electrodes. The emf of the cell at 298 K is 0.059 V.

Q. The value of ΔG (kJ mol–1) for the given cell is (take 1F = 96500 C mol–1)

Detailed Solution for JEE Advanced 2012 Paper -2 with Solutions - Question 31

JEE Advanced 2012 Paper -2 with Solutions - Question 32

Paragraph for Questions 31 and 32

The electrochemical cell shown below is a concentration cell.

M|M2+ (saturated solution of a sparingly soluble salt, MX2) || M2+ (0.001 mol dm–3) | M

The emf of the cell depends on the difference in concentrations of M2+ ions at the two electrodes. The emf of the cell at 298 K is 0.059 V.

Q. The solubility product (Ksp; mol3 dm–9) of MX2 at 298 K based on the information available for the given
concentration cell is (take 2.303 x R x 298/F = 0.059 V)

Detailed Solution for JEE Advanced 2012 Paper -2 with Solutions - Question 32

JEE Advanced 2012 Paper -2 with Solutions - Question 33

Paragraph for Questions 33 and 34

Bleaching powder and bleach solution are produced on a large scale and used in several household products. The effectiveness of bleach solution is often measured by iodometry.

Q. Bleaching powder contains a salt of an oxoacid as one of its components. The anhydride of that oxoacid is

Detailed Solution for JEE Advanced 2012 Paper -2 with Solutions - Question 33

JEE Advanced 2012 Paper -2 with Solutions - Question 34

Paragraph for Questions 33 and 34

Bleaching powder and bleach solution are produced on a large scale and used in several household products. The effectiveness of bleach solution is often measured by iodometry.

Q. 25 mL of household solution was mixed with 30 mL of 0.50 M KI and 10 mL of 4 N acetic acid. In the
titration of the liberated iodine, 48 mL of 0.25 N Na2S2O3 was used to reach the end point. The molarity of
the household bleach solution is

Detailed Solution for JEE Advanced 2012 Paper -2 with Solutions - Question 34

*Multiple options can be correct
JEE Advanced 2012 Paper -2 with Solutions - Question 35

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?

Detailed Solution for JEE Advanced 2012 Paper -2 with Solutions - Question 35

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.

*Multiple options can be correct
JEE Advanced 2012 Paper -2 with Solutions - Question 36

For the given aqueous reactions, which of the statement(s) is (are) true?

Detailed Solution for JEE Advanced 2012 Paper -2 with Solutions - Question 36

*Multiple options can be correct
JEE Advanced 2012 Paper -2 with Solutions - Question 37

With reference to the scheme given, which of the given statement(s) about T, U, V and W is (are) correct?

Detailed Solution for JEE Advanced 2012 Paper -2 with Solutions - Question 37

*Multiple options can be correct
JEE Advanced 2012 Paper -2 with Solutions - Question 38

Which of the given statement(s) about N, O, P and Q with respect to M is (are) correct?

Detailed Solution for JEE Advanced 2012 Paper -2 with Solutions - Question 38

*Multiple options can be correct
JEE Advanced 2012 Paper -2 with Solutions - Question 39

With respect to graphite and diamond, which of the statement(s) given below is (are) correct?

Detailed Solution for JEE Advanced 2012 Paper -2 with Solutions - Question 39

⇒ Diamond is harder than graphite.

⇒ Graphite is good conductor of electricity as each carbon is attached to three C-atoms leaving one valency free, which is responsible for electrical conduction, while in diamond, all the four valencies of
carbon are satisfied, hence insulator.

⇒ Diamond is better thermal conductor than graphite. Whereas electrical conduction is due to availability of free electrons; thermal conduction is due to transfer of thermal vibrations from atom to atom. A compact and precisely aligned crystal like diamond thus facilitates fast movement of heat.

⇒ In graphite, C – C bond acquires double bond character, hence higher bond order than in diamond.

*Multiple options can be correct
JEE Advanced 2012 Paper -2 with Solutions - Question 40

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?

Detailed Solution for JEE Advanced 2012 Paper -2 with Solutions - Question 40

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.

JEE Advanced 2012 Paper -2 with Solutions - Question 41

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

Detailed Solution for JEE Advanced 2012 Paper -2 with Solutions - Question 41

JEE Advanced 2012 Paper -2 with Solutions - Question 42

The equation of a plane passing through the line of intersection of the planes x + 2y + 3z = 2 and x – y + z
= 3 and at a distance  from the point (3, 1, –1) is

Detailed Solution for JEE Advanced 2012 Paper -2 with Solutions - Question 42

-5x + 11y - z + 17 = 0.

JEE Advanced 2012 Paper -2 with Solutions - Question 43

Let PQR be a triangle of area  where a, b, and c are the lengths of the sides of the triangle opposite to the angles at P, Q and R respectively. Then  equals

Detailed Solution for JEE Advanced 2012 Paper -2 with Solutions - Question 43

JEE Advanced 2012 Paper -2 with Solutions - Question 44

If then a possible
value of

Detailed Solution for JEE Advanced 2012 Paper -2 with Solutions - Question 44

JEE Advanced 2012 Paper -2 with Solutions - Question 45

If P is a 3 × 3 matrix such that PT = 2P + I, where PT is the transpose of P and I is the 3 × 3 identity matrix,
then there exists a column matrix  such that

Detailed Solution for JEE Advanced 2012 Paper -2 with Solutions - Question 45

JEE Advanced 2012 Paper -2 with Solutions - Question 46

Let a (a) and b (a) be the roots of the equation where
a > – 1. Then are

Detailed Solution for JEE Advanced 2012 Paper -2 with Solutions - Question 46

JEE Advanced 2012 Paper -2 with Solutions - Question 47

Four fair dice D1, D2, D3 and D4, each having six faces numbered 1, 2, 3, 4, 5, and 6, are rolled simultaneously. The probability that D4 shows a number appearing on one of D1, D2 and D3 is

Detailed Solution for JEE Advanced 2012 Paper -2 with Solutions - Question 47

JEE Advanced 2012 Paper -2 with Solutions - Question 48

The value of the integral 

Detailed Solution for JEE Advanced 2012 Paper -2 with Solutions - Question 48

JEE Advanced 2012 Paper -2 with Solutions - Question 49

SECTION II : Paragraph Type

This section contains 6 multiple choice questions relating to three paragraphs with two questions on each
paragraph. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

Paragraph for Questions 49 and 50

A tangent PT is drawn to the circle x2 + y2 = 4 at the point . A straight line L, perpendicular to PT is a tangent to the circle (x -3)2 + y2 =1.

Q. A possible equation of L is

Detailed Solution for JEE Advanced 2012 Paper -2 with Solutions - Question 49

JEE Advanced 2012 Paper -2 with Solutions - Question 50

Paragraph for Questions 49 and 50

A tangent PT is drawn to the circle x2 + y2 = 4 at the point . A straight line L, perpendicular to PT is a tangent to the circle (x -3)2 + y2 =1.

Q. A common tangent of the two circles is

Detailed Solution for JEE Advanced 2012 Paper -2 with Solutions - Question 50

JEE Advanced 2012 Paper -2 with Solutions - Question 51

Paragraph for Questions 51 and 52

Q. Consider the statements:

P : There exists some x ε  such that f(x) + 2x = 2(1 + x2)

Q : There exists some x ε  such that 2f(x) + 1 = 2x(1 + x)
Then

Detailed Solution for JEE Advanced 2012 Paper -2 with Solutions - Question 51

JEE Advanced 2012 Paper -2 with Solutions - Question 52

Paragraph for Questions 51 and 52

Q. Which of the following is true?

Detailed Solution for JEE Advanced 2012 Paper -2 with Solutions - Question 52

JEE Advanced 2012 Paper -2 with Solutions - Question 53

Paragraph for Questions 53 and 54
Let an denote the number of all n–digit positive integers formed by the digits 0, 1 or both such that no consecutive digits in them are 0. Let bn = the number of such n–digit integers ending with digit 1 and cn = the number of such n–digit integers ending with digit 0.

Q. The value of b6 is

Detailed Solution for JEE Advanced 2012 Paper -2 with Solutions - Question 53

JEE Advanced 2012 Paper -2 with Solutions - Question 54

Paragraph for Questions 53 and 54
Let an denote the number of all n–digit positive integers formed by the digits 0, 1 or both such that no consecutive digits in them are 0. Let bn = the number of such n–digit integers ending with digit 1 and cn = the number of such n–digit integers ending with digit 0.

Q. Which of the following is correct?

Detailed Solution for JEE Advanced 2012 Paper -2 with Solutions - Question 54

*Multiple options can be correct
JEE Advanced 2012 Paper -2 with Solutions - Question 55

SECTION III : Multiple Correct Answer(s) Type

This section contains 6 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of
which ONE or MORE are correct.

55. For every integer n, let an and bn be real numbers. Let function f : IR → IR be given by
  for all integers n. If f is continuous, then which of the following hold(s) for all n?

Detailed Solution for JEE Advanced 2012 Paper -2 with Solutions - Question 55

*Multiple options can be correct
JEE Advanced 2012 Paper -2 with Solutions - Question 56

If the straight lines   are coplanar, then the plane(s) containing these two lines is(are)

Detailed Solution for JEE Advanced 2012 Paper -2 with Solutions - Question 56

For given lines to be coplanar, we get

*Multiple options can be correct
JEE Advanced 2012 Paper -2 with Solutions - Question 57

If the adjoint of a 3 × 3 matrix P is , then the possible value(s) of the determinant of P is (are)

Detailed Solution for JEE Advanced 2012 Paper -2 with Solutions - Question 57

*Multiple options can be correct
JEE Advanced 2012 Paper -2 with Solutions - Question 58

Detailed Solution for JEE Advanced 2012 Paper -2 with Solutions - Question 58

*Multiple options can be correct
JEE Advanced 2012 Paper -2 with Solutions - Question 59

Let X and Y be two events such that   

Which of the following is (are) correct?

Detailed Solution for JEE Advanced 2012 Paper -2 with Solutions - Question 59

*Multiple options can be correct
JEE Advanced 2012 Paper -2 with Solutions - Question 60

Detailed Solution for JEE Advanced 2012 Paper -2 with Solutions - Question 60

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