JEE Advanced 2012 Paper 2

Q: How many questions does this paper have?

53 questions are reproduced here in full.

Question 1

Question 1 (figure/table included)

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

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Question 2

Question 2

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, I B | as a function of the radial distance r from the axis is best represented by.

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Question 3

Question 3

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 Pc is the relative density of the material of the shell with respect to water, then the correct statement is that the shell is

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Question 4

Question 4

In the given circuit, a charge of +80 C is given to the upper plate of the4 F capacitor. Then in the steady state, the charge on the upper plate of the 3 F capacitor is +80 C 4 F 2 F 3 F

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Question 5

Question 5

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)

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Question 6

Question 6 (figure/table included)

Consider a disc rotating in the horizontal plane with a constant angular speed 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 towardsR. 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 completed rotation, (ii) their range is less than half the disc radius, and (iii) remains constant throughout. Then R Q O

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Question 7

Question 7

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

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Question 8

Question 8 (figure/table included)

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

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Question 9

Question 9

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

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Question 10

Question 10

Choose the correct statement.

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Question 11

Question 11

What is the maximum energy of the anti-neutrino?

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Question 12

Question 12 (figure/table included)

If the anti-neutrino had a mass of 3 eV/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?

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Question 13

Question 13

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

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Question 14

Question 14

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

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Question 15

Question 15

In the given circuit, the AC source has = 100 rad/s. Considering the inductor and capacitor to be ideal, the correct choice(s) is(are) 100 F 100 0.5H 50 9 W 20 V

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Question 16

Question 16

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)

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Question 17

Question 17 (figure/table included)

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 K =- 4Eo L2 6+ P A S T D +2q 0 2q R B +q b-

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Question 18

Question 18

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 ?

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Question 19

Question 20 (figure/table included)

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 and (ii) an inner disc of radius frictionless ball bearings. The system is in the x-z plane. The point P on the inner disc is at a distance R from the origin, where OP makes an angle of 30 with the horizontal. Then with respect to the horizontal surface, Z 4 Ka2 3R P R30 >x 0 2R

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Question 20

Question 21

NiCl,{P(C,Hs),(C,Hs)}, exhibits temperature dependent magnetic behaviour (paramagnetic / diamagnetic). The coordination geometries of Ni* in the paramagnetic and diamagnetic states. are respectively

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Question 21

Question 22

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

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Question 22

Question 23

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

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Question 23

Question 24

The shape of XeO,F, molecule is

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Question 24

Question 25

For a dilute solution containing 2.5 g of a non-volatile non-electrolyte solute in100 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 K, = 0.76 K kg mol⁻¹)

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Question 25

Question 26

The compound that undergoes 'decarboxylation most readily under mild condition is.

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Question 26

Question 27

Using the data provided, calculate the multiple bond energy (kJ mol') of a C=C bond in C,H₂. That energy is (take the bond energy of a C-H bond as 350 kJ mol '.). 2C(s) + H₂(g) > C2H₂(g) A H = 225 kJ mol⁻¹ 2C(s) >2C(g) A H = 1410 kJ mol-' H₂(g) > 2H(g) AH = 330 kJ mol'

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Question 27

Question 28

The major product H of the given reaction sequence is OCN G_9 95%H₂SO₄ yH CH - CH - CO - CH₃ Heat

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Question 28

Question 29 (figure/table included)

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

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Question 29

Question 31

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

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Question 30

Question 32

The value of G (kJ mol-') for the given cell is (take 1F = 96500 C mol-l)

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Question 31

Question 33

The compound I is

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Question 32

Question 34

The compound K is

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Question 33

Question 35 (figure/table included)

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?. (P),V;,Tj) isothermal P adiabatic *(P2,V2,T2) o(P3,V2,T3) V

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Question 34

Question 37

For the given aqueous reactions, which of the statement(s) is (are) true ? dilute HSO4 excess KI + Kz[Fe(CN)6] brownish-yellow solution ZnSO4 white precipitate + brownish-yellow filtrate Na2S2O3 colourless solution

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Question 35

Question 38

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

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Question 36

Question 39

With reference to the scheme given, which of the given statment(s) about T, U, V and W is (are) correct ?. H3C T LiAIH4 excess (CH3CO)2O >w

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Question 37

Question 40

Which of the given statement(s) about N, O, P and Q with respect to M is (are) correct ? CI HO H HO H CH₃ CH₃ H CI CH₃ OH H HO HO H HO H H OH HO H HO H HO H CH₃ CI CH₃ CI CI m N 0 P Q

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Question 38

Question 41

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

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Question 39

Question 43

If a and b are vectors suchthata +b= 29 and a x (2i +3j +4k) = (2i +3j + 4k) b, then a possible value of (a+ b).(-7i +2j +3k) is

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Question 40

Question 44

If P is a 3 x 3 matrix such that PT= 2P + I, where pTis the transpose of P andI is the 3 x 3 x] [0] identity matrix, then there exists a column matrix X = y # 0 such that [o] [o]

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Question 41

Question 45

Let a(a) and (a) be the roots of the equation 1+a-1)x2+(1+a-1)x+(V1+a-1)=0 where a>-1. Then lim a-0+a(a) and lim na-o+(a) are

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Question 42

Question 46

Four fair dice D,, D2, D, andD4, each having six faces numbered 1, 2, 3, 4, 5 and 6, are rolled simultaneously. The probability that D, shows a number appearing on one of Dj, D, and D,is 91 108 125 127

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Question 43

Question 49

The value of b, is

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Question 44

Question 50

Which of the following is correct?.

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Question 45

Question 51

Which of the following is true?.

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Question 46

Question 52

Consider the statements :. P : There exists some x E IR such that f (x) + 2x = 2(1 + x2) Q : There exists some x E IR such that 2f (x) + 1= 2x(1 + x) Then

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Question 47

Question 53

A possible equation of L is

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Question 48

Question 54

A common tangent of the two circles is

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Question 49

Question 56

If f(x)= (t -2)(t-3) dt for all xE (0,), then

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Question 50

Question 57

If the straight lines x-1 _ y+1. and 2 5 2 K containing these two lines is(are)

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Question 51

Question 58

Let X and Y be two events such that P(X |Y) = 1 P(Y|x)=] and P(X nY)=1 2 3 6 Which of the following is (are) correct?. 2|3

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Question 52

Question 59

If the adjoint of a 3x3 matrix P is 2 1 7 then the possible value(s) of the 1 1 3 determinant of P is (are)

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Question 53

Question 60

Let f: (-1, 1)->IR be such that f(cos 40) = 2 - sec? e the value(s) of f is (are) 3 23 23

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JEE Advanced 2012 Paper 2