JEE Advanced 2011 Paper 1
Q. 1 Extra pure N₂ can be obtained by heating
A. A
B. B
C. C
D. D
Q. 2 Geometrical shapes of the complexes formed by the reaction of Ni₂+ with Cl- , CN- and H₂0, respectively, are
A. octahedral, tetrahedral and square planar
B. tetrahedral, square planar and octahedral
C. square planar, tetrahedral and octahedral
D. octahedral, square planar and octahedral
Q. 3 Bombardment of aluminum by α-particle leads to its artificial disintegration in two ways, (i) and (ii) as shown. Products X, Y and 2 respectively are
A. proton, neutron, positron
B. neutron, positron, proton
C. proton, positron, neutron
D. positron, proton, neutron
Q. 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
A. 1.78 M
B. 2.00 M
C. 2.05 M
D. 2.22 M
Q. 5 AgNO₃ (aq.) was added to an aqueous KCl solution gradually and the conductivity of the solution was measured. The plot of conductance (A) versus the volume of AgNO₃ is
A. (P)
B. (Q)
C. (R)
D. (S)
Q. 6 Among the following compounds, the most acidic is
A. p-nitrophenol
B. p-hydroxybenzoic acid
C. o-hydroxybenzoic acid
D. p-toluic acid
Q. 7 The major product of the following reaction is
A. A
B. B
C. C
D. D
Q. 8 Extraction of metal from the ore cassiterite involves
A. carbon reduction of an oxide ore
B. self-reduction of a sulphide ore
C. removal of copper impurity
D. removal of iron impurity
Q. 9 The correct statement(s) pertaining to the adsorption of a gas on a solid surface is (are)
A. Adsorption is always exothermic.
B. Physisorption may transform into chemisorption at high temperature.
C. Physisorption increases with increasing temperature but chemisorption decreases
with increasing temperature.
D. Chemisorption is more exothermic than physisorption, however it is very slow due to higher energy of activation.
Q. 10 According to kinetic theory of gases
A. collisions are always elastic.
B. heavier molecules transfer more momentum to the wall of the container.
C. only a small number of molecules have very high velocity.
D. between collisions, the molecules move in straight lines with constant velocities.
Q. 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)
A. A
B. B
C. C
D. D
Questions: 12 – 14
When a metal rod M is dipped into an aqueous colourless concentrated solution of compound N, the solution turns light blue. Addition of aqueous NaCl to the blue solution gives a white precipitate 0. Addition of aqueous NH₃ dissolves O and gives an intense blue solution
Q. 12 The metal rod M is
A. Fe
B. Cu
C. Ni
D. Co
Q. 13 The compound N is
A. AgNO₃
B. Zn(NO₃)₂
C. Al(NO₃)₂
D. Pb(NO₃)₂
Q. 14 The final solution contains
A. [Pb(NH₃)₄]₂- and [CoCl₄]₂⁻
B. [Al(NH₃)₄]₃+ and [Cu(NH₃)₄]₂⁺
C. [Ag(NH₃)₂]⁺ and [Cu(NH₃)₄]₂⁺
D. [Ag(NH₃)₂]⁺ and [Ni(NH₃)₆]₂⁺
Questions: 15 – 16
An acyclic hydrocarbon P, having molecular formula CsHm, gave acetone as the only organic product through the following sequence of reactions, in which Q is an intermediate organic compound.
Q. 15 Choose the correct option
A. A
B. B
C. C
D. D
Q. 16 Choose the correct option
A. A
B. B
C. C
D. D
Q. 17 The difference in the oxidation numbers of the two types of sulphur atoms in Na₂S₄O₆ is
Q. 18 Reaction of Br₂ with Na₂CO₃ in aqueous solution gives sodium bromide and sodium bromate with evolution of CO₂ gas. The number of sodium bromide molecules involved in the balanced chemical equation is
Q. 19 The maximum number of electrons that can have principal quantum number, n = 3, and spin quantum number, ms = -1/2, is
Q. 20 The work function (Φ) 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
Q. 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
Q. 22 The total number of alkenes possible by dehydrobromination of 3-bromo-3-
cyclopentylhexane using alcoholic KOH is
Q. 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 hydrolysis products. The number of glycine units present in the decapeptide is
Q. 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 320 m/s. The frequency of the siren heard by the car driver is
A. 8.50 kHz
B. 8.25 kHz
C. 7.75 kHz
D. 7.50 kHz
Q. 25 5.6 liter of helium gas at STP is adiabatically compressed to 0.7 liter. Taking the initial temperature to be T1, the work done in the process is
A. 9/8 RT1
B. 3/2 RT1
C. 15/8 RT1
D. 9/2 RT1
Q. 26 Consider an electric field E̅ = Eo x̂, where Eo is a constant. The flux through the shaded area (as shown in the figure) due to this field is
A. 2Eo a²
B. √2Eo a²
C. Eo a²
D. Eo a²/√2
Q. 27 The wavelength of the first spectral line in the Balmer series of hydrogen atom is 6561 Å. The wavelength of the second spectral line in the Balmer series of singly-ionized helium atom is
A. 1215 Å
B. 1640 Å
C. 2430 Å
D. 4687 Å
Q. 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
A. 9
B. 18
C. 27
D. 36
Q. 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
A. 10.2 ohm
B. 10.6 ohm
C. 10.8 ohm
D. 11.1 ohm
Q. 30 A 2 μF capacitor is charged as shown in figure. The percentage of its stored energy dissipated after the switch 8 is turned to position 2 is
A. 0 %
B. 20 %
C. 75 %
D. 80 %
Q. 31 A spherical metal shell A of radius RA and a solid metal sphere B of radius RB (< RA) are kept far apart and each is given charge ‘+Q’. Now they are connected by a thin metal wire. Then
A. A
B. B
C. C
D. D
Q. 32 An electron and a proton are moving on straight parallel paths with same velocity. They enter a semi-infinite region of uniform magnetic field perpendicular to the velocity. Which of the following statement(s) is/are true?
A. They will never come out of the magnetic field region.
B. They will come out travelling along parallel paths.
C. They will come out at the same time.
D. They will come out at different times.
Q. 33 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
A. heat flow through A and E slabs are same.
B. heat flow through slab E is maximum.
C. temperature difference across slab E is smallest.
D. heat flow through C = heat flow through B + heat flow through D.
Q. 34 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 attached: (case A) The disc is not free to rotate about its center and (case B) 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?
A. Restoring torque in case A = Restoring torque in case B
B. Restoring torque in case A < Restoring torque in case B
C. Angular frequency for case A > Angular frequency for case B.
D. Angular frequency for case A < Angular frequency for case B.
Questions: 35 – 37
Phase space diagrams are useful tools in analyzing all kinds of dynamical problems. They are especially useful in studying the changes in motion as initial position and momentum are changed. Here we consider some simple dynamical systems in one-dimension. For such systems, phase space is a plane in which position is plotted along horizontal axis and momentum is plotted along vertical axis. The phase space diagram is x(t) vs. p(t) curve in this plane. The arrow on the curve indicates the time flow. For example, the phase space diagram for a particle moving with constant velocity is a straight line as shown in the figure. We use the sign convention in which position or momentum upwards (or to right) is positive and downwards (or to left) is negative.
Q. 35 Choose the correct option
A. A
B. B
C. C
D. D
Q. 36 Choose the correct option
A. A
B. B
C. C
D. D
Q. 37 Choose the correct option
A. A
B. B
C. C
D. D
Questions: 38 – 39
A dense collection of equal number of electrons and positive ions is called neutral plasma. Certain solids containing fixed positive ions surrounded by free electrons can be treated as neutral plasma. Let ‘N’ be the number density of free electrons, each of mass ‘m’. When the electrons are subjected to an electric field, they are displaced relatively away from the heavy positive ions. if the electric field becomes zero, the electrons begin to oscillate about the positive ions with a natural angular frequency ‘ωp’, which is called the plasma frequency. To sustain the oscillations, a time varying electric field needs to be applied that has an angular frequency ω, where a part of the energy is absorbed and a part of it is reflected. As ω approaches ωp, all the free electrons are set to resonance together and all the energy is reflected. This is the explanation of high reflectivity of metals.
Q. 38 Taking the electronic charge as ‘e’ and the permittivity as ‘εo’, use dimensional analysis to determine the correct expression for ωp.
A. √(Ne/mεo)
B. √(mεo/Ne)
C. √(Ne²/mεo)
D. √(mεo/Ne²)
Q. 39 Estimate the wavelength at which plasma reflection will occur for a metal having the density of electrons N ≈ 4 x 10²⁷ m-³. Take ε0 ≈ 10⁻¹¹ and m ≈ 10⁻³⁰, where these quantities are in proper SI units.
A. 800 nm
B. 600 nm
C. 300 nm
D. 200 nm
Q. 40 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/s². 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
Q. 41 A block is moving on an inclined plane making an angle 45° with the horizontal and the coefficient of friction is μ. 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 μ, then N is
Q. 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 γ. The system of charges and planar film are in equilibrium, (value of a given in the figure, where ‘k’ is a constant. Then N is
Q. 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 10⁻⁵/ °C, Young’s modulus of steel is 10¹¹ N/m² and radius of the wire is 1 mm. Assume that L >> diameter of the wire. Then the value of ‘m’ in kg is nearly
Q. 44 The activity of a freshly prepared radioactive sample is 10¹⁰ disintegrations per second, whose mean life is 10⁹ s. The mass of an atom of this radioisotope is 10⁻²⁵ kg. The mass (in mg) of the radioactive sample is
Q. 45 A long circular tube of length 10 m and radius 0.3 m carries a current I 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 I = Io cos (300 t) where Io is constant. It the magnetic moment of the loop is N μo Io sin (300 t) , then ‘N’ is
Q. 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 10⁻⁴ kg-m² , then N is
Q. 47 Let (x₀, y₀) be the solution of the following equations. Then x₀ is
A. 1/6
B. 1/3
C. 1/2
D. 6
Q. 48 Choose the correct option.
A. A
B. B
C. C
D. D
Q. 49 Let a̅ = î + ĵ + k̂ , b̅ = î – ĵ + k̂ and c̅ = î – ĵ – k̂ be three vectors. A vector v̅ in the plane of a̅ and b̅ , whose projection on c̅ is 1/√3, is given by,
A. î – 3ĵ + 3k̂
B. -3î – 3ĵ – 3k̂
C. 3î – ĵ + 3k̂
D. î + 3ĵ – 3k̂
Q. 50 Let P = {θ: sinθ – cosθ = √2 cosθ} and Q= {θ: sinθ + cosθ = √2 cosθ} be two sets. Then
A. P ⊂ Q and Q – P ≠ ∅
B. Q ⊄ P
C. P ⊄ Q
D. P = Q
Q. 51 Let the straight line x = b divide the area enclosed by y = (1 – x)², y=0 , and x = 0 into two parts R₁ (0 ≤ x ≤ b) and R₂ (b ≤ x ≤ 1) such that R₁ – R₂= 1/4. Then b equals
A. 3/4
B. 1/2
C. 1/3
D. 1/4
Q. 52 Let α and β be the roots of x² – 6x – 2 = 0 with α > β. If an = αⁿ – βⁿ, for n ≥ 1 , then the value of expression in the image is
A. 1
B. 2
C. 3
D. 4
Q. 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
A. y + √3x + 2 – 3√3 = 0
B. y – √3x + 2 + 3√3 = 0
C. √3y – x + 3 + 2√3 = 0
D. √3y + x – 3 + 2√3 = 0
Q. 54 The vector(s) which is/are coplanar with vectors î + ĵ + 2k̂ and î + 2ĵ + k̂ , and perpendicular to the vector î + ĵ + k̂ is/are
A. ĵ – k̂
B. -î + ĵ
C. î – ĵ
D. -ĵ + k̂
Q. 55 Let M and N be two 3×3 non-singular skew-symmetric matrices such that MN = NM. if Pᵗ denotes the transpose of P, then the value of the expression given in the image is?
A. M²
B. -N²
C. -M²
D. MN
Q. 56 Let the eccentricity of the hyperbola x²/a² – y²/b² = 1 be reciprocal to that of the ellipse x² + 4y² = 4.If the hyperbola passes through a focus of the ellipse, then
A. the equation of the hyperbola is x²/3 – y²/2 = 1
B. a focus of the hyperbola is (2, 0)
C. the eccentricity of the hyperbola is √5/3
D. the equation of the hyperbola is x² – 3y² = 3
Q. 57 Let f : ℝ → ℝ be a function such that f(x+y) = f(x) + f(y), Ɐx, y∈R If f (x) is differentiable at x = 0, then
A. (x) is differentiable only in a finite interval containing zero
B. f (x) is continuous Ɐx ∈ ℝ
C. f’(x) is constant Ɐx ∈ ℝ
D. f (x) is differentiable except at finitely many points
Questions: 58 – 60
Let a, b and c be three real numbers satisfying
Q. 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
A. 0
B. 12
C. 7
D. 6
Q. 59 Choose the correct option:
A. -2
B. 2
C. 3
D. -3
Q. 60 Choose the correct option:
A. 6
B. 7
C. 6/7
D. ∞
Questions: 61 – 62
Let U₁ and U₂ be two urns such that U₁ contains 3 white and 2 red balls, and U₂ contains only 1 white ball. A fair coin is tossed. If head appears then 1 ball is drawn at random from U₁ and put into U₂. However, if tail appears then 2 balls are drawn at random from U₁ and put into U₂. Now 1 ball is drawn at random from U₂.
Q. 61 The probability of the drawn ball from U₂ being white is
A. 13/30
B. 23/30
C. 19/30
D. 11/30
Q. 62 Given that the drawn ball from U₂ is white, the probability that head appeared on the coin is
A. 17/23
B. 11/23
C. 15/23
D. 12/23
Q. 63 Consider the parabola y² = 8x. Let Δ₁ be the area of the triangle formed by the end points of its Latus rectum and the point P(1/2, 2) on the parabola, and Δ₂ be the area of the triangle formed by drawing tangents at P and at the end points of the Latus rectum. Then Δ₁/Δ₂ is
Q. 64 Answer the following question:
Q. 65 The positive integer value of n > 3 satisfying the equation is
Q. 66 Let f : [1,∞) -> [2,∞) be a differentiable function such that f(1) = 2. If the expression in figure is true for all x ≥ , then the value of f(2) is
Q. 67 If z is any complex number satisfying |z – 3 – 2i| ≤ 2, then the minimum value of |2z – 6 + 5i|
Q. 68 Answer the following question:
Q. 69 Answer the following:
| Answer Sheet |
||||||||||
| Question | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Answer | D | B | A | C | D | C | A | ACD | ABD | ABCD |
| Question | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
| Answer | BC | B | A | C | D | B | 5 | 5 | 9 | 4 |
| Question | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 |
| Answer | 7 | 5 | 6 | A | A | C | A | D | B | D |
| Question | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 |
| Answer | ABCD | BCD | ACD | AD | D | C | B | C | B | 4 |
| Question | 41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 | 49 | 50 |
| Answer | 5 | 3 | 3 | 1 | 6 | 9 | C | A | C | D |
| Question | 51 | 52 | 53 | 54 | 55 | 56 | 57 | 58 | 59 | 60 |
| Answer | B | C | B | AD | ABCD | BD | BCD | D | A | B |
| Question | 61 | 62 | 63 | 64 | 65 | 66 | 67 | 68 | 69 | |
| Answer | B | D | 2 | 3 OR 9 | 7 | 6 | 5 | 8 | 1 |