Joint Entrance Examination (JEE) is an all India common engineering entrance examination. It is one of the most difficult exams to crack. Only the aspirants who qualify JEE-Mains can appear for JEE-Advanced examination. There is no better way to prepare for JEE advance examination then solving Model papers and sample papers because the sample papers are the similar to the actual exam prepare.

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Q-1) A light source, which emits two wavelengths 𝜆𝜆1 = 400 𝑛𝑛𝑛𝑛 and 𝜆𝜆2 = 600 𝑛𝑛𝑛𝑛, is used in a Young’s double slit experiment. If recorded fringe widths for 𝜆𝜆1 and𝜆𝜆2 are𝛽𝛽1 and𝛽𝛽2 © number of fringes for them within a distance yon one side of the central maximum are m1 and m2, respectively, then
1.    𝛽𝛽2 > 𝛽𝛽1
2.    𝑚𝑚1 > 𝑚𝑚2
3.    From the central maximum, 3rdmaximum of λ2 overlaps with 5th minimum of λ1
4.    The angular separation of fringes for λ1 is greater than λ2
Ans.) 1, 2 and 3

Q-2) One end of a taut string of length 3m along the x axis is fixed at x=0.The speed of the waves in the string is 100 𝑚𝑚𝑠𝑠−1. The other end of the string is vibrating in the y direction so that stationary waves are set up in the string. The possible waveform(s) of these stationary waves is(are)
1.    𝑦𝑦(𝑡𝑡) = 𝐴𝐴 sin 𝜋𝜋𝜋𝜋 6 cos 50𝜋𝜋𝜋𝜋 3
2.    𝑦𝑦(𝑡𝑡) = 𝐴𝐴 sin 𝜋𝜋𝜋𝜋 3 cos 100𝜋𝜋𝜋𝜋 3
3.    𝑦𝑦(𝑡𝑡) = 𝐴𝐴 sin5𝜋𝜋𝜋𝜋 6 cos 250𝜋𝜋𝜋𝜋 3
4.    𝑦𝑦(𝑡𝑡) = 𝐴𝐴 sin5𝜋𝜋𝜋𝜋 2 cos 250𝜋𝜋
Ans.) 1,3 and 4

Q-3) Let𝐸𝐸1(𝑟𝑟), 𝐸𝐸2(𝑟𝑟) and 𝐸𝐸3(𝑟𝑟) be the respective electric fields at a distance r from a point charge Q, an infinitely long wire with constant linear charge density λ, and an infinite plane with uniform surface charge density σ. If 𝐸𝐸1(𝑟𝑟0) = 𝐸𝐸2(𝑟𝑟0) = 𝐸𝐸3(𝑟𝑟0) at a given distance r0, then
1.    𝑄𝑄 = 4𝜎𝜎𝜎𝜎𝑟𝑟0 2
2.    𝑟𝑟0 = 𝜆𝜆 2𝜋𝜋𝜋𝜋
3.    𝐸𝐸1(𝑟𝑟0⁄2)= 2𝐸𝐸2(𝑟𝑟0⁄2)
4.    𝐸𝐸2(𝑟𝑟0⁄2)=4𝐸𝐸3(𝑟𝑟0⁄2)
Ans.) 3

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Q-4) Heater of an electric kettle is made of a wire of length L and diameter d. It takes 4 minutes to raise the temperature of 0.5kgwater by 40K. This heater is replaced by a new heater having two wires of the same material, each of length L and diameter 2d.The way these wires are connected is given in the options. How much time in minutes will it take to raise the temperature of the same amount of water by 40 K?
1.    4 if wires are in parallel
2.    2 if wires are in series
3.    1 if wires are in series
4.    0.5 if wires are in parallel
Ans.) 2 and 4

Q-5) A transparent thin film of uniform thickness and refractive index n1= 1.4 is coated on theconvex spherical surface of radius Rat one end of a long solid glass cylinder of refractive index n2 = 1.5, as shown in the figure. Rays of light parallel to the axis of the cylinder traversing through the film from air to glass get focused at distance f1 from the film, while rays of light traversing from glass to air get focused at distance f2 from the film. Then

1.    |𝑓𝑓1| =3R
2.    |𝑓𝑓1| = 2.8R
3.    |𝑓𝑓2| =2R
4.    |𝑓𝑓2| = 1.4R
Ans) 1and 3

Q-6) Two ideal batteries of emfV1 and V2 and three resistancesR1, R2 andR3 are connected as shown in the figure. The current in resistanceR2 would be zero if
1.    𝑉𝑉1 = 𝑉𝑉2and𝑅𝑅1 = 𝑅𝑅2 = 𝑅𝑅3
2.    𝑉𝑉1 = 𝑉��2and𝑅𝑅1 = 2𝑅𝑅2 = 𝑅𝑅3
3.    𝑉𝑉1 = 2𝑉𝑉2and 2𝑅𝑅1 = 2𝑅𝑅2 = 𝑅𝑅3
4.    2𝑉𝑉1 = 𝑉𝑉2and2𝑅𝑅1 = 𝑅𝑅2 = 𝑅𝑅3

Ans.) 1, 2 and 4

This section contains 5 questions. Each question, when worked out will result in one integer from 0 to 9 (both inclusive).

Q-7) Airplanes A and B are flying with constant velocity in the same vertical plane at angles 30° and 60° with respect to the horizontal respectively as shown in figure. The speed of A is 100√3 𝑚s−1. At time 𝑡= 0 𝑠, an observer in A finds B at a distance of 500 m. This observer sees B moving with a constant velocity perpendicular to the line of motion of A. If at 𝑡 = 𝑡0, A just escapes being hit by B, 𝑡0 in seconds is
Ans.) 5

Q-8) During Searle’s experiment, zero of the Vernier scale lies between 3.20 × 10−2 𝑚𝑚 and 3.25 × 10−2 𝑚𝑚 of the main scale. The 20th division of the Vernier scale exactly coincides with one of the main scale divisions. When an additional load of 2 kg is applied to the wire, the zero of the Vernier scale still lies between 3.20 × 10−2 𝑚𝑚 and 3.25 × 10−2 𝑚𝑚 of the main scale but now the 45th division of Vernier scale coincides with one of the main scale divisions. The length of the thin metallic wire is 2 m and its cross-sectional area is 8 × 10−7𝑚𝑚2. The least count of the Vernier scale is 1.0 × 10−5 𝑚𝑚. The maximum percentage error in the Young’s modulus of the wire is
Ans.) 4

Q-9) A uniform circular disc of mass 1.5 kg and radius 0.5 m is initially at rest on a horizontal frictionless surface. Three forces of equal magnitude F = 0.5 N are applied simultaneously along the three sides of an equilateral triangle XYZ with its vertices on the perimeter of the disc (see figure). One second after applying the forces, the angular speed of the disc in rads−1 is
Ans.) 2

Q-10) Two parallel wires in the plane of the paper are distance X0 apart. A point charge is moving with speed u between the wires in the same plane at a distance X1 from one of the wires. When the wires carry current of magnitude I in the same direction, the radius of curvature of the path of the point charge is R1. In contrast, if the currents I in the two wires have directions opposite to each other, the radius of curvature of the path is R2. If 𝑋0/ 𝑋1 = 3, the value of 𝑅1/ 𝑅2 is
Ans.) 3

Q-11) To find the distance d over which a signal can be seen clearly in foggy conditions, a railways engineer uses dimensional analysis and assumes that the distance depends on the mass density ρ of the fog, intensity (power/area) 𝑆𝑆 of the light from the signal and its frequency f. The engineer finds that 𝑑 is proportional to 𝑆1⁄ . The value of 𝑛 is
Ans.) 3

Q-12 An ideal gas in a thermally insulated vessel at internal pressure = P1, volume = V1 and absolute temperature = T1 expands irreversibly against zero external pressure, as shown in the diagram. The final internal pressure, volume and absolute temperature of the gas are P2, V2 and T2, respectively. For this expansion,

1.    q = 0
2.    T2 = T1
3.    P2V2 = P1V1
4.    P2V2 γ = P1V1y
Ans.) 1, 2 and 3

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Q-13) Hydrogen bonding plays a central role in the following phenomena:
1.    Ice floats in water.
2.    Higher Lewis basicity of primary amines than tertiary amines in aqueous solutions.
3.    Formic acid is more acidic than acetic acid.
4.    Dimerisation of acetic acid in benzene
Ans.) 1,2,4

Q-14) In a galvanic cell, the salt bridge
1.    does not participate chemically in the cell reaction
2.    stops the diffusion of ions from one electrode to another
3.    is necessary for the occurrence of the cell reaction
4.    ensures mixing of the two electrolytic solutions.
Ans.) 1, 3 or only 1

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Q-15) Upon heating with Cu2S, the reagent(s) that give copper metal is/are
1.    CuFeS2
2.    CuO
3.    Cu2O
4.    CuSO4
Ans.) 2,3 and 4

Q-16) The correct statement(s) for orthoboric acid is/are
1.    It behaves as a weak acid in water due to self ionization
2.    Acidity of its aqueous solution increases upon addition of ethylene glycol
3.    It has a three dimensional structure due to hydrogen bonding
4.    It is a weak electrolyte in water.
Ans.) 2 and 4

Q-17) The pair(s) of reagents that yield paramagnetic species is/are
1.    Na and excess of NH3
2.    K and excess of O2
3.    Cu and dilute HNO3
4.    O2 and 2-ethylanthraquinol
Ans.) 1, 2 and 3

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Q-18) Among PbS, CuS, HgS, MnS, Ag2S, NiS, CoS, Bi2S3 and SnS2, the total number of BLACK coloured sulfides is
Ans.) 6 or 7

Q-19) Consider the following list of reagents:
Acidified K2Cr2O7, alkaline KMnO4, CuSO4, H2O2, Cl2, O3, FeCl3, HNO3 and Na2S2O3. The total number of reagents that can oxidise aqueous iodide to iodine is
Ans.) 7

Q-20) MX2 dissociates into M2+ and X ions in an aqueous solution, with a degree of dissociation (α) of 0.5. The ratio of the observed depression of freezing point of the aqueous solution to the value of the depression of freezing point in the absence of ionic dissociation is
Ans.) 2