JEE Advanced 2011 Paper 1

Q: How many questions does this paper have?

64 questions are reproduced here in full.

Question 1

Question 1

Extra pure N, can be obtained by heating.

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Question 2

Question 2

Geometrical shapes of the complexes formed by the reaction of Ni?* with C1, CN~ and. H,O, respectively, are

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Question 3

Question 3

Bombardment of aluminum by a-particle leads to its artificia! disintegration in two ways,. (ii) and (ii) as shown. Products X, Y and Z respectively are, (ii) 27 I + 13A1 15 (i) 30 si 30g + x Si + Z 14 14

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Question 4

Question 4

Dissolving 120 g of urea (mol. wt. 60) in 1000 g of water gave a solution of density 1.15 g/mL. The molarity of the solution is.

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Question 5

Question 5

AgNOs (aq.) was added to an aqueous KCl solution gradually and the conductivity of the solution was measured. The plot of conductance

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Question 6

Question 6

Among the following compounds, the most acidic is

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Question 7

Question 7

The major product of the following reaction is (i) KOH NH (ii) Br CH,Cl

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Question 8

Question 8

Extraction of metal from the ore cassiterite involves

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Question 9

Question 9

The correct statement(s) pertaining to the adsorption of a gas on a solid surface is (are)

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Question 10

Question 10

According to kinetic theory of gases.

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Question 11

Question 11

Amongst the given options, the compound(s) in which all the atoms are in one plane in all the possible conformations (if any), is (are). H H H

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Question 12

Question 12

The metal rod M is

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Question 13

Question 13

The compound N is

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Question 14

Question 14

The final solution contains

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Question 15

Question 15

The structure of compound P is

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Question 16

Question 16

The structure of the compound Q is 5&H OH H3C OH

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Question 17

Question 17

The difference in the oxidation numbers of the two types of sulphur atoms in Na,S,O, is ANSWER : 5

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Question 18

Question 18

Reaction of Br, with Na,CO, in aqueous solution gives sodium bromide and sodium. bromate with evolution of CO, gas. The number of sodium bromide molecules involved. in the balanced chemical equation is ANSWER : 5

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Question 19

Question 19

The maximum number of electrons that can have principal quantum number, n = 3, and spin quantum number, m = --1/2, is ANSWER : 9 CHEMISTRY

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Question 20

Question 20

The work function ($) of some metals is listed below. The number of metals which will. show photoelectric effect when light of 300 nm wavelength falls on the metal is. Metal Li Na K Mg Cu Ag Fe Pt w $ (eV) 2.4 2.3 2.2 3.7 4.8 4.3 4.7 6.3 4.75 ANSWER : 4

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Question 21

Question 21

To an evacuated vessel with movable piston under external pressure of 1 atm., 0.1 mol of He and 1.0 mol of an unknown compound (vapour pressure 0.68 atm. at 0 C) are. introduced. Considering the ideal gas behaviour, the total volume (in litre) of the gases at. 0 C is close to ANSWER : 7

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Question 22

Question 22

The total number of alkenes possible by dehydrobromination of 3-bromo-. 3-cyclopentylhexane using alcoholic KOH is. ANSWER : 5

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Question 23

Question 23

A decapeptide (Mol. Wt. 796) on complete hydrolysis gives glycine (Mol. Wt. 75), alanine and phenylalanine. Glycine contributes 47.0 % to the total weight of the hydrolysed products. The number of glycine units present in the decapeptide is. ANSWER : 6 PART II : PHYSICS SECTION - I (Total Marks : 21) (Single Correct Answer Type) This section contains 7 multiple choice questions. Each question has four choices.

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Question 24

Question 24

A police car with a siren of frequency 8 kHz is moving with uniform velocity 36 km/hr. towards a tall building which reflects the sound waves. The speed of sound in air is

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Question 25

Question 26 (figure/table included)

Consider an electric fieldE - E, x, where E, is a constant. The flux through the shaded area (as shown in the figure) due to this field is z (a,0,a) (a,a,a) (0,0,0) (0,a,0) Ega?

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Question 26

Question 27

The wavelength of the first spectral line in the Balmer series of hydrogen atom is 6561 A The wavelength of the second spectral line in the Balmer series of singly-ionized helium atom is

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Question 27

Question 28

A ball of mass (m) 0.5 kg is attached to the end of a string having length (L) 0.5 m. The ball is rotated on a horizontal circular path about vertical axis. The maximum tension that the string can bear is 324 N. The maximum possible value of angular velocity of ball (in radian/s) is L m

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Question 28

Question 29

A meter bridge is set-up as shown, to determine an unknown resistance 'X' using a standard 10 ohm resistor. The galvanometer shows null point when tapping-key is at 52 cm mark. The end-corrections are 1 cm and 2 cm respectively for the ends A and B. The determined value of 'X' is x 10 M A B

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Question 29

Question 31

A spherical metal shell A of radius R, and a solid metal sphere B of radius Rg (< R) are kept far apart and each is given charge '+Q'. Now they are connected by a thin metal wire. Then

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Question 30

Question 32

An electron and a proton are moving on straight parallel paths with same velocity. They of the following statement(s) is/are true?

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Question 31

Question 33 (figure/table included)

A composite block is made of slabs A, B, C, D and E of different thermal conductivities. (given in terms of a constant K) and sizes (given in terms of length, L) as shown in the. figure. All slabs are of same width. Heat 'Q' flows only from left to right through the. blocks. Then in steady state 0 1L 5L 6L heat A B 3K E 1L 2K c 4K 6K 3L D 5K 4L

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Question 32

Question 34 (figure/table included)

A metal rod of length 'L' and mass 'm' is pivoted at one end. A thin disk of mass 'M' and. radius 'R' (< L) is attached at its center to the free end of the rod. Consider two ways the disc is free to rotate about its center. The rod-disc system performs SHM in vertical plane after being released from the same displaced position. Which of the following statement(s) is (are) true?

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Question 33

Question 35

The phase space diagram for a ball thrown vertically up from ground is Momentum Momentum

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Question 34

Question 36 (figure/table included)

The phase space diagram for simple Momentum harmonic motion is a circle centered at the origin. In the figure, the two circles represent the same oscillator but for different initial E1 conditions, and E1 and E2 are the total E2 mechanical energies respectively. Then. 2a

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Question 35

Question 37 (figure/table included)

Consider the spring-mass system, with the mass submerged in water, as shown in the figure. The phase space diagram for one cycle of this system is. Momentum Momentum Position Position

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Question 36

Question 38

Taking the electronic charge as 'e' and the permittivity as 'so', use dimensional analysis to determine the correct expression for @p. Ne mEo Ne2 mE0

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Question 37

Question 39

Estimate the wavelength at which plasma reflection will occur for a metal having the quantities are in proper SI units.

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Question 38

Question 40 (figure/table included)

A boy is pushing a ring of mass 2 kg and radius 0.5 m with a stick as shown in the figure. The stick applies a force of 2 N on the ring and rolls it without slipping with an acceleration of 0.3 m/s'. The coefficient of friction between the ground and the ring is large enough that rolling always occurs and the coefficient of friction between the stick and the ring is (P/10). The value of P is Stick Ground ANSWER: 4

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Question 39

Question 41

A block is moving on an inclined plane making an angle 45' with the horizontal and the coefficient of friction is . The force required to just push it up the inclined plane is 3 times the force required to just prevent it from sliding down. If we define N = 10 , then N is ANSWER : 5 PHYSICS

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Question 40

Question 42

Four point charges, each of +q, are rigidly fixed at the four corners of a square planar soap film of side 'a ' The surface tension of the soap film is y. The system of charges and. 1/ N planar film are in equilibrium, and a =k , where 'k'is a constant. Then Nis ANSWER : 3

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Question 41

Question 43

Steel wire of length 'L' at 40'C is suspended from the ceiling and then a mass 'm' is hung. from its free end. The wire is cooled down from 40'C to 30'C to regain its original length. 'L'. The coefficient of linear thermal expansion of the steel is 10-b / C, Young's modulus. of steel is 10 ' N/m~ and radius of the wire is 1 mm. Assume that L >> diameter of the wire. Then the value of 'm' in kg is nearly ANSWER : 3

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Question 42

Question 44

The activity of a freshly prepared radioactive sample is 1o'o disintegrations per second,. whose mean life is 10's. The mass of an atom of this radioisotope is 10-25 kg. The mass. (in mg) of the radioactive sample is ANSWER : 1 PHYSICS

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Question 43

Question 45

A long circular tube of length 10 m and radius 0.3 m carries a current 1 along its curved surface as shown. A wire-loop of resistance 0.005 ohm and of radius 0.1 m is placed inside the tube with its axis coinciding with the axis of the tube. The current varies as N , I, sin (300 t), then 'N' is ANSWER : 6

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Question 44

Question 46

Four solid spheres each of diameter 5 cm and mass 0.5 kg are placed with their centers at the corners of a square of side 4 cm. The moment of inertia of the system about the diagonal of the square is N x 10* kg-m", then N is ANSWER : 9 PART III : MATHEMATICS SECTION - I (Total Marks : 21) (Single Correct Answer Type) This section contains 7 multiple choice questions. Each question has four choices

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Question 45

Question 47

Let (xo, yo) be the solution of the following equations. (2x)2=(3y)n3 3lnx = 2lny. Then x, is 11

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Question 46

Question 48

The value of dx is Vm² sinx +sin(ln6-x2)

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Question 47

Question 49

Let a=i+ j+k, b=i- j+k and c=i-j-k be three vectors. A vector in the plane of a and b, whose projection on c is 1 3, is given by 3

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Question 48

Question 50

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Question 49

Question 51

Let the straight line x=b divide the area enclosed byy=(1-x)?, y=0, and x=0 into 4 31 1|2 1|3 1|4

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Question 50

Question 52

Let and be the roots of x2-6x-2=0, with a> . If a, =a" -n for n1, then the value ot 0 - 24s is 2a9

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Question 51

Question 53

A straight line L through the point (3,-2) is inclined at an angle 60 to the line 3x + y =1. If L also intersects the x-axis, then the equation of L is

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Question 52

Question 55

Let M and N be two 3x3 non-singular skew-symmetric matrices such that MN = NM . If p' denotes the transpose of P, then M?N₂ (M'N)' (Mn-')' is equal to.

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Question 53

Question 56

Let the eccentricity of the hyperbola. =1 be reciprocal to that of the ellipse a ba x' +4y' = 4. If the hyperbola passes through a focus of the ellipse, then. x2 y?

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Question 54

Question 58

If the point P(a, b, c), with reference to (E), lies on the plane 2x+ y+ z =1, then the value of 7a+b+c is

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Question 55

Question 59

Let w be a solution of x3-1=0 with Im(w)>0. If a=2 with b and c satisfying (E), then the value of 3 1 3 W" wb is equal to

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Question 56

Question 60

Let b =6, with a and c satisfying (E). If a and are the roots of the quadratic equation. ax' + bx +c =0, then (+9) is 6|7

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Question 57

Question 61

The probability of the drawn ball from U, being white is 13 23 19

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Question 58

Question 62

Given that the drawn ball from U, is white, the probability that head appeared on the coin is 17 11 15 12

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Question 59

Question 64

Let ay, a, 4z, ., 4oo be an arithmetic progression with a = 3 and s, = a, 1 p 100.. 1=1 Sn ANSWER : 3, 9, 3 & 9 BOTH

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Question 60

Question 65

The positive integer value of n > 3 satisfying the equation. T 2n 3n sin sin sin n is ANSWER : 7 MATHEMATICS

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Question 61

Question 66

Let f : [1, ) --> [2, ) be a differentiable function such that f(1) = 2. If 6J f(t)dt=3x f(x)-x3 for all x 1, then the value of f(2) is ANSWER : MARKS TO ALL

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Question 62

Question 67

If z is any complex number satisfying z-3-2i|2, then the minimum value of I2z-6+5i| is ANSWER : 5

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Question 63

Question 68

The minimum value of the sum of real numbers a-, a-4, 3a-', 1,a and alo with a>0 is ANSWER : 8

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Question 64

Question 69

Let f(0) = sin tan-1 sin 0 where cos 20 4 4 is ANSWER : 1

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JEE Advanced 2011 Paper 1