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IIT JEE Exam 2025 : Main : Prac paper

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ALLENO Topic : Cireular Motion, Centreof Mass (1.0 To 3.4) PHYSICS SECTION-I: (Maximum Marks: 80) This section contains 20 questions. Each question has 4 options for correct answer. 3. with constant angular velocity o on a horizontal Multiple-Choice frictionless tablethen the ratio of tensions Questions (MCQs)Only one option is corect. For each question, marks will be awarded as Full Marks Zero Marks (ciren follows: selected. +4 If correct answer is Negative Marks ) (0) : -11If wrong option is selected. T. A particle is projected with velocity u at an angle 9 with the horizontal., Find the radius of curvature at O? m; T, m, (A) m (B) m2 (C) u 4 (A) u (B) g cos 0 g sin 0 (C) 2 T :01f n ne of the option is selected. 1. The whole sct up shown in the figurc is rotating (D u'cos e A body of m kg slides from rest along the curve of vertical circle from point A to B in friction (m1 + 2m) 2m2 m2 m+3mT (D) m 3m A smooth wire is bent into a vertical circle of radius a. A bead P can slide smoothly on the wire. The circle is rotated about vertical diameter AB as axis with a constant speed o as shown in figure. The bead P is at rest w.r.t. the wire in the position shown. Then o is equal to: less path. The velocity of the body at B is: (Vertical Circle) 2 (given, R=14 m, g= 10 m/s and v2 = 1.4) (A) 19.8 m/s (B) 21.9 m/s (C) 16.7 m/s (D) 10.6 m/s B (A) 2g Nurture I|T-JEE(M+A) NURTURE PHASE-182 IT-6 (MOR+AFTN) :SET Page 2/18 #A Space for Rough Work V:utat (B) 2g av3 (C) V a (D) 2a gv3 6001CJA10100124011| English / 15092024 ALLENE 5 A stone tied to the end of a string 100 cm long is whirled in a horizontal circle with a constant 8. identical massless strings of length 16cm each 3 speed. If the stone makes 30 revolution in 60 s, the magnitude of acceleration is : 6 (A) 20 ms2 (B) 12 m/s? (C) 9,9 ms (D) 8 ns2 A small block is connected to one end of two with their other ends fixed to a vertical rod. If the ratio of tensions T, /T, be 4: 1, then what will be the angular velocity o of the block A body of mass 'm' is tied to one end of a spring and whirled round in ahorizontal plane with a constant angular velocity. The elongation in the spring is lcm. If the angular velocity is doubled, 7. (A) 16 cm (B) 15 cm (C) 12 cm (D) 10 cm T, 600 the elongation in the spring is 5 cm. The original length of the spring is: (A) J4 Tad (B) 16ad Consider a roller coaster with a circular loop. A sec roller coaster car starts from rest from the top of a hill which is 5m higher than the top of the (C) 24Tad (D)28Tad Sec sec loop. It rolls down the hill and through the loop. What must the radius of the loop be so that the passengers of the car will feel at highest point, as if they have their normal weight? Sm. (A) 5 m (B) 10 m (C) 15 m (D) 20 m 9. sec A coin placed on a rotating turn table just slips if it is at a distance of 20 cm from the centre. If the angular velocity of the turntable is doubled, it will just slip at a distance of (A) 10 cm (B) 20 cm (C) 15 cm (D) 5 cm Nurture -IIT-JEE(M+A) NURTURE PHASE-1&2 IT-6 (MOR+AFTN) :SET #A Space for Rough Work English /15092024 6001CJA10100124011 Page 3/18 ALLEN A particle is attached with a string of length which is fixed at point O on an inclined plane what minimum velocity should be given to the particle along the incline (at P) so that it nmay complete a circle on inclined plane (plane resting 10. 12. In the figure shown a lift goes downwards with a constant retardation. An observer in the lie observers a conical pendulum the lift, revolving in a horizontal circle with time period 2 seconds. The distance between the centre of the circle and the point of suspension is 2.0 m. Find the retardation of the lift in m/s? on the inclined plane.) (use T? = 10 and g= 10m/s) (B) /Sgt V2 (A) V5gt (C) 5V3gl (D) 4ge 2 11. A stone of mass 1kg tied to a light inextensible string of length L = 10/3 metre is whirling in a circular path of radius L, in a vertical plane. If (B) 20 (A) 10 13. (C) 15 (D) 5 A turn of radius 20m is banked for the vehicles the ratio of the maximum tension in the string to going at a speed of 36 km/h. If the co-efficient of the minimum tension is 4 and if g is taken to be static friction between the road & the tyre is 0.4 10 metre per sec, the speed of the stone at the highest point of the circle is then what is the maximum speed with which car (A) 20 metre per sec (A) 10 m/s (B) 15 m/s (C) 20 m/s (D) 25 m/s can negotiate the turn safely? (g = 10 m/s) )0, (B) 10v3metre per sec 14. (C) 10v2 metre per sec A stone tied to a string of length L is whirled in a vertical circle with the other end of the string at (D) 10 metre per sec the centre. At a certain instant of time, the stone is at its lowest position, and has a speed u. The magnitude of the change in its velocity as it Tmin reaches a position where the string is horizontal is: 1-ngy wS0 m - 10cos 186 (A) /u-2gL (B) V2glL (C) (D) /2(u-gL) u- gL 6001CJA10100124011 Nurture I|T-JEE(M+A) NURTURE PHASE-1&2 IT-6 (MOR+AFTN) :SET # A Space for Rough Work Page 4/18 |4 14 3 English /15092024 ALLEN& 15. The centre of mass of a system of two particles divides the distance between them (A) In inverse ratio of square of masses of 18 two particles. If the particles move under the mutual attraction of each other, then the position particles of centre of mass at t (B) In direct ratio of square of masses of particles isc () of radus 'a' as shown in Jm/ Ikg Ikq xSm K2m (D) In direct ratio of masses of particles A cinular hole of radus 1s is Sm/ (C) In inverse ratio of masses of particles 16. The figure shows the positions and velocities of is cut out of a cincular figure. The centroid of the remaining cinular portion with espect to point O' 19. will be: (A) x= 5m (B) x 6m (C) x = 7m (D) x= 2m A man (mass = 50 kg) and his son (mass = 20 kg) are standing on a frictionless surface facing cach other. The man pushes his son so that he starts moving at speed of 0.70 ms with respect to the man. The speed of the man with respect to the surface is: (A) (B) 10 20. (D) 17. (A) 0.26 ms (B) 0.14 ms (C) 0.47 ms! (D) 0.20 ms Two particles A and B initially at rest, move towards each other under the mutual force of A wedge of mass M = 2 m lies on a frictionless attraction. At the instant when the speed of A is plane. A particle of mass m approaches the wedge with speed v. There is no friction between the particle and the plane or between the particle Vand the speed of B is 2v, the speed of the (A) 3v (B) v and the wedge. The maximum height climbed by the particle on the wedge is given by: (C) 1.5v (D) Zero centre of mass of the system is: m 2m (A) 2v' 7g (B) 3g (C) 2v2 5g (D) 2g Nurture I|T-JEE(M+A) NURTURE PHASE-182 IT-6 (MOR+AFTN) :SET #A English /15092024 Space for Rough Work 6001CJA10100124011| Page 5/18 ALLENO SECTION-M: (Maximum Marks: 20) 1. This section contains 10 questions Candidates have A circular table is rotating with an angular velocity of o rad/s about its axis (sce figure). There is a smooth groove along aradial direction on the table. A steel ball is gently placed at a distance of Im on the groove. All the surface are smooth. If the radius of the table is 3m, the radial velocity of the ball w.r.t the table at the time ball to attempt any 5questions out of 10. If more than 5 questions are attempted, then only first 5 attempted questions will be evaluated. The answer to cach question is a Numerical Value Type questions. leaves the table is xv20 m/s, where the value of For each question, enter the correct numerical x is value (in decimal notation, truncated/rounded off to the second decimal place; e.g. 6.25, 7.00, -0.33, -.30, 30.27, -127.30, if answer is then 11.36777.... 999 e0o both 11.370 will be l11.36 0and 9 0 correct) Im 3m 2. A small block slides down from the top of hemisphere of radius R = 3m as shown in the figure. The height 'h' at which the block will lose contact with the surface of the sphere is m. (Assume there is no friction between the block and the hemisphere) 8 Answer to each question will be evaluated according tothe following marking scheme: Full Marks Zero Marks Negative Marks +4 If correct answer is 0 If the question is entered. R unanswered. : -1 If wrong answer is (R-h) entered. 3. Starting from rest, a particle rotates a circle of radius R= V2m with an angular acceleration a = rad/sec". Calculate the magnitude of 4 average velocity of the particle over the time it rotates quarter circle. (in ms) Nurture -I|T-JEE(M+A) NURTURE PHASE-182 |T-6 (MOR+AFTN) :SET Page 6/18 #A Space for Rough Work 6001CJA10100124011 English / 15092024 ALLEN& 4. A small block of mass 1kg is released from rest at 8. the top of a rough track. The track is a circular arc of radius 30 m. The block slides along the track without toppling and a frictional force acts on it in the direction opposite the instantancous velocity. The work done in overcoming the friction up to the point Q, as shown in the figure below, is 22 J. (Take the acceleration due to gravity, g= 10 ms) The speed of the block when it reaches the point Q m/s. Two particles A and B of masses I kg and 2 kg respectively are projected in the same vertical line as shown in figure with speeds uA = 200 m/s and ug = 8Sm/s respectively. Initially they were 90 m apart. Find he maximum height attained by the centre of mass of the system of particles A and B, from the initial position of centre of mass of the system. Assume that none of these particles collides with the ground that duration Take g= 10 m/s'.(Ans should be in metre) B -R. 90m R A 5. A fly wheel is accelerated unifommly from rest and rotates through 4 rad in the first second. The angle rotated by the fly wheel in the next second, will be rad. 6. A railroad car of mass M is at rest on a 9 A ball of mass lg is released down an inclined plane, just describes a circle of radius 10 cm in the vertical plane, on reaching the bottom, the minimum Cm. height of the inclined plane is frictionless track with a man of mass m standing at its edge. If the man jumps off from the car 10cm towards right with an initial velocity u, with respect to the car, find the velocity of the car after its jump. (in m/s) (m =40kg, M=60 kg, u =10 m/s) 7. The centre of mass of a solid cone of height 12cm is X cm from its base.Then value of x is 10. A particle is performing circular motion of radius 2.25m. Its speed is v= (3t) m/s. The magnitude of its acceleration at t= 1s. is m/s'. |Nurture - I|T-JEE(M+A) NURTURE PHASE-182 IT-6 (MOR+AFTN) :SET #A English / 15092024 Space for Rough Work 6001CJA10100124011 Page 7/18 ALLEN Topic: Thermodynamics (Only) (1.0 to 14.0) CHEMISTRY SECTION-I: (Maximum Marks: 80) 3. This section contains 20 questions. Each question has 4 options for correct answer. Multiple-Choice Questions (MCQs) Only one option is correct. For each question, marks will be awarded as follows: Full Marks +4 If correct answer is selected. Zero Marks : 0If none of the option is done (w) on the final volume (V) is: 1. For (A) : -1 lf wrong option is 2. (B) 4 (C) 5 (D) 6 T; selected. In V of an ideal gas into vacuum, among the following how many are zero (A) 7 T2 (B) isothermal expansion AU, AH, AT, q. Pext, ASsystem , |wl| T selected. Negative Marks Consider the reversible isothermal expansion of an ideal gas in a closed system at two different temperatures T and T; (T, < T). The correct graphical depiction of the dependence of work Iwl| ASuniverse T2 system, the process is (A) cyclic (B) isothermal (C) adiabatic (D) isolated T2 Iwl| T1 (C) If the internal energy of an ideal gas decreases by the same amount as the work done by the InV T (D) In V 4. In V Which one of the following equations does not correctly represent the first law of thermodynamics for the given process involving an ideal gas ? (Assume non expansion work is zero) (A) Cyclic process: q = w (B) Adiabatic process : AU=q (C) Isochoric process : AU=q (D) Isothermal process :q =-wX Nurture - I|T-JEE(M+A) NURTURE Page 8/18 PHASE-1&2 IT-6 (MOR+AFTN) :SET # A Space for Rough Work 6001CJA10100124011 English / 15092024 5. An ideal gas shown in figure undergoes A ALLENO a cyclic process as 7. Which of the following statements is correct ? (A) AS for one mole of ideal gas : Reversible Isothermal expansion > Reversible adiabatic expansion B P (B) Slope of the adiabatic P-Vcurve will be same as that in isothermal one. (C) Magnitude of slope of adiabatic P-V cuve V willbe larger than in isothermal one. AURe =-5OkJmoll qAB = 20kJmol! (D) Both (A) and (C) WAB =-50kJmol 8. A cyclic process is shown in the P-T diagram WCA = 30kJmol-! B Heat absorbed by the system during process CA is [in kJ/mol] (A) 180 6. (B) +50 (-50 P (D) -180 Which one of the following statements is false (A) Work is a state function A T Which of the curves show the same process on V-T diagram? (B) Temperature is a state function (C) Change in the state is comnpletely defined when the initial and final states are (B) specified DY Work appears at the boundary of the T T system C 4 V A 0 PHASE-1&2 IT-6 (MOR+AFTN) :SET #A Nurture - I|T-JEE(M+A) NURTURE English /15092024 Space for Rough Work V (D) B I 6001CJA10100124011 Page 9/18 5 An ideal gas shown in figure undergoes a ALLENO cyclic process as 7 Which of the following statements is correct ? (A) AS for one mole of ideal gas : Reversible Isothermal expansion > Reversible adiabatic expansion P (B) Slope of the adiabatic P-V curve will be same as that in isothermal one. (C) Magnitude of slope of adiabatic P-V cuve will be larger than in isothermal one. AUgc =-50kJmoll (D) Both (A) and (C) QAB =20kJmol! WAB =-50kJmol WCA = 3OkJmol Heat absorbed by the system during process CA is [in kJ/mol] (A) 180 6. (B) +50 (9-s0 8. Acyclic process is shown in the P-T diagram (D) -180 Which one of the following statements is false (A) Work is a state function T Which of the curves show the same process on V-T diagram? (B) Temperature is a state function B (C) Change in the state is completely defined when the initial and final states are specified 7 V (A) (B) A DY Work appears at the boundary of the C T system T C V (C) D) A I Nurture -|T-JEE(M+A) NURTURE PHASE-182 IT-6 (MOR+AFTN) :SET #A Space for Rough Work English / 15092024 6001CJA10100124011 | Page 9/18 ALLEN 9. In themodynamics, a process is calld reversible when - 12. A heat enginc carries one mole of an ideal diatomic gas around the cycle as show in the figure, thc amount of heat added the proccss (A) Surroundings and system change into cach other AB & heat removed in the process CA are (B) There is no boundary between system and surroundings 9) The surroundings are always in cquilibrium with the system (D) The system changes into the Which property is n t intensive (A) Temperature P surroundings spontaneously 10. B(Ta=600K) A (TA=300K) (Te=400K) propcrty. (A) qaB =750R & qCA =-450R (B) Molarity 11. C (C) Refractive index (B) QAB =650R & qCA =-350R D Heat capacity (C) qaB=750R &qcA =-350R If (D) qAB -650R & gcA -450R w),W), W; and w4 are magnitude of work done in isothermal, adiabatic, isochoric reversible process, (for expansion) will be isobaric and 13 the correct order In case of an adiabatic irreversible process the following must be correct (A) ATsys=0 (C) ASsys <0 (A) W; > W, > W; > W4 (B) W3 > W> W > W4 14. (C) W3 > W) > W4 >W1 (D) w; >W >W) > W4 (D) Asur <0 When one mole of an ideal gas is compressed to half of its initial volume and simultaneously heated to twice its temperature, the change in entropy of system is (A) Cym In2 (B) Cpm In2 (C) R In2 (D) (Cym - R) In2, Nurture - T-JEE(M+A) NURTURE PHASE-182 IT-6 (MOR+AFTN) :SET #A Page 10/18 B As urr=0 Space for Rough Work 6001CJA10100124011 English / 15092024 15. Mixing of accompanied by non-reacting ideal gases is ALLENO 18, gener a l y in (A) Decrease entropy (B) Increase in entropy (C) Change in enthalpy D) Change in atomicity of gases Carnot's engine's absolute temperature ofeftheficiency depends on the 19. (B) Sink (C) Both 11. A process source nor sink A B where e.u. is AS (AC)=50 e.u. AS D)=30 eu. B D= entropy unit. (A B)entisropy change AS for the Then the AAY+100 eu. (C) -100 e.u. (A) B is ASIC for NH3 (D) None of these Cy directly instead it dif icult to 0ccur Successive steps : takes place in three C D (C) CA< CB (B) CA >Cp contributision Vibrational degree'including s of freedom source and sink (D) Neither the two processes then 16. The (4Y Source Work done by a sample of an ideal gas in a process A is double of the work done in another process B. The temperature rises through the same amount in the two lf CA and Cp prOcesses. be the molar heat capacities for (B) -60 e.u. (D) +60 e.u. 20 eu. process (C) 20. fromn where (B) 10 9 6 (D) 3 Calof NH4 culate the work done in 12 Joules when 1.0 mole decomposed against a pressure of 1.0 atm at 27 C (R=8.314 J mol k 3N,H, () 4NH, (g) + (A) 4988.4 (C) 9976.8 2N, (e) (B) 9976.8 (D) 498.84 24 at m R-8.314 Nurture - -JEEIM+A) NURTURE English \IIT15092024 PHASE-182 IT-6 30ale ALLEN 2. SECTION-I: (Maximum Marks: 20) This section contains 10 questions Candidates have to attempt any 5 questions out of 10. Ifmore than5 questions are attempted, then only first 5 attempted questions willbe evaluated. (c) Molar entropy (d) Volume (g) Molality 3. For a perfectly crystalline solid, Cp,m aT , (a = constant) if Cm is 0.42 JK mol-l at 10 K, molar entropy at 20 K (in JK ' mol) is value (in decimal notation, truncated/rounded off to the second decimal place; e.g. 6.25, 7.00, -0.33, -30, 30.27, -127.30, if answer is 11.36777.. then both 11.36 and 11.37 will be correct) () Boiling point (e) Density The answer to each question is a Numerical Value Type questions. For each question, enter the correct numerical properties What is the total number of intensive in the given list ? (a) Internal energy (b)Pressure 4. An ideal gas (y = 1.5) undergoes an irreversible process in which the volume of gas decreases by 75%. If the final and initial entropy of the system is same, then the ratio of final and initial temperature of gas is 4 8 5. -0 (r) ideal gas 8 Answer to each question will be evaluated according to the following marking scheme: Full Marks Zero Marks +4 If correct answer is entered. : 0If the question is unanswered. Negative Marks : -1If wrong answer is entered. 1. Calculate the entropy change of system when two moles of an ideal gas are subjected to a reversible adiabatic change from state (1 atm, 10 litre) to 14 atm. [Take : Cy m= 3R] Nurture - IlT-JEE(M+A) NURTURE Page 12/18 If one mole of a PHASE-1&2IT-6 (MOR+AFTN) :SET #A mixture 6. monoatomic ideal gas is mixed with 1mole of a diatomic (-) The value of y for the 1 mole of an ideal gas is allowed to expand at isothermally 27 C till its volume is tripled . If the expansion is carried out reversibly then the ASuniverSe Will be? 23t2) + 7 One mole of an ideal ALLEN monoatomic expanded |9. imreversibly in two stage expansion. State-1 (8.0 bar, 4.0 L, 300 K) State-2 (2.0 bar, 16 L, 300 K) State-3 (1.0 bar, 32 L, 300 K) Total heat absorbed by the gas in the process is : (in J) gas Use (1 Liter- atm =100J) 8 Eor 1mole of mono atomic ideal gas, work done. Calculate 10, How many of the following are state function : (i) Internal energy (ii) Heat (iii) Enthalpy (iv) Entropy (v) Pressure (vi) Temp. (vii) Volume (vii) Work (ix)Specific heat capacity (x) Molar heat capacity When a polyatomic gas undergoes an adiabatic process, its temperature and volume are related by the equation TV n= constant, then what is the P. value of n? **** 300K 400K [Given, poisson's ratioy= 1.33] T -PV Av:300 3 400 Nurture -IT-JEE(M+A) NURTURE PHASE-182 IT-6 (MOR+AFTN) :SET #A English / 15092024 Space for Rough Work 6001CJA10100124011 Page 13/18

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