ALLEN JEE(Main+Advanced) 2025/25-02-2024 Paper-1 PDF

Test Pattern (1001CJA101005230018) )1001CJA101005230018) English CLASSROOM CONTACT PROGRAMME JEE(Advanced)...

Test Pattern (1001CJA101005230018) )1001CJA101005230018) English CLASSROOM CONTACT PROGRAMME JEE(Advanced) REVIEW TEST (Academic Session : 2023 - 2024) 25-02-2024 JEE(Main+Advanced) : NURTURE COURSE [PHASE : V & VI] Time : 3 Hours PAPER-1 (OPTIONAL) Maximum Marks : 180 IMPORTANT NOTE : Students having 8 digits Form No. must fill two zero before their Form No. in OMR. For example, if your Form No. is 12345678, then you have to fill 0012345678. READ THE INSTRUCTIONS CAREFULLY GENERAL : 1. This sealed booklet is your Question Paper. Do not break the seal till you are told to do so. 2. Use the Optical Response sheet (ORS) provided separately for answering the questions. DO NOT BREAK THE SEALS WITHOUT BEING INSTRUCTED TO DO SO BY THE INVIGILATOR 3. Blank spaces are provided within this booklet for rough work. 4. Write your name, form number and sign in the space provided on the back cover of this booklet. 5. After breaking the seal of the booklet, verify that the booklet contains 24 pages and that all the 18 questions in each subject and along with the options are legible. If not, contact the invigilator for replacement of the booklet. 6. You are allowed to take away the Question Paper at the end of the examination. OPTICAL RESPONSE SHEET : 7. The ORS will be collected by the invigilator at the end of the examination. 8. Do not tamper with or mutilate the ORS. Do not use the ORS for rough work. 9. Write your name, form number and sign with pen in the space provided for this purpose on the ORS. Do not write any of these details anywhere else on the ORS. Darken the appropriate bubble under each digit of your form number. DARKENING THE BUBBLES ON THE ORS : 10. Use a BLACK BALL POINT PEN to darken the bubbles on the ORS. 11. Darken the bubble COMPLETELY. 12. The correct way of darkening a bubble is as : 13. The ORS is machine-gradable. Ensure that the bubbles are darkened in the correct way. 14. Darken the bubbles ONLY IF you are sure of the answer. There is NO WAY to erase or "un-darken" a darkened bubble. 15. Take g = 10 m/s2 unless otherwise stated. QUESTION PAPER FORMAT : 16. The question paper has three parts : Physics, Chemistry and Mathematics. Please see the last page of this booklet for rest of the instructions  Target : JEE (Main + Advanced) 2025/25-02-2024/Paper-1 ALLEN ® SOME USEFUL CONSTANTS Atomic No. : H = 1, B = 5, C = 6, N = 7, O = 8, F = 9, Al = 13, P = 15, S = 16, Cl = 17, Br = 35, Xe = 54, Ce = 58 Atomic masses : H = 1, Li = 7, B = 11, C = 12, N = 14, O = 16, F = 19, Na = 23, Mg =24, Al = 27, P = 31, S = 32, Cl = 35.5, Ca=40, Fe = 56, Br = 80, I = 127, Xe = 131, Ba=137, Ce = 140, Cu = 63.5, Ne = 20, K = 39, Mn = 55 Space for Rough Work E-2/24 1001CJA101005230018  Nurture Course/Phase-V & VI/25-02-2024/Paper-1 BEWARE OF NEGATIVE MARKING PART-1 : PHYSICS SECTION-I (i) : (Maximum Marks: 24) This section contains SIX (06) questions. Each question has FOUR options. ONE OR MORE THAN ONE of these four option(s) is (are) correct answer(s). For each question, choose the option(s) corresponding to (all ) the correct answer(s) Answer to each question will be evaluated according to the following marking scheme: Full Marks : +4 If only (all) the correct option(s) is (are) chosen. Partial Marks : +3 If all the four options are correct but ONLY three options are chosen. Partial Marks : +2 If three or more options are correct but ONLY two options are chosen and both of which are correct. Partial Marks : +1 If two or more options are correct but ONLY one option is chosen and it is a correct option. Zero Marks : 0 If none of the options is chosen (i.e. the question is unanswered). Negative Marks : –2 In all other cases. For Example : If first, third and fourth are the ONLY three correct options for a question with second option being an incorrect option; selecting only all the three correct options will result in +4 marks. Selecting only two of the three correct options (e.g. the first and fourth options), without selecting any incorrect option (second option in this case), will result in +2 marks. Selecting only one of the three correct options (either first or third or fourth option), without selecting any incorrect option (second option in this case), will result in +1 marks. Selecting any incorrect option(s) (second option in this case), with or without selection of any correct option(s) will result in –2 marks. 1. For the equation x = AC sin (Bt) + D e(BCt), where x and t represent position and time respectively, which of the following is/are CORRECT? (A) Dimension of AC is LT –1. (B) Dimension of B is T –1. (C) Dimension of AC and D are same. (D) Dimension of C is T –1. 2. A particle is moving in three dimensional space with the position vector →r = x (t) ^i + y (t) ^j + z (t) k^ and velocity vector →v = vx (t) ^i + vy (t) ^j + vz (t) k^. If the particle is always moving towards origin, then :- vx vy v (A) = = z x y z vx vy vz (B) ( )( )( ) < 0 x y z (C) xvx + yvy + zvz < 0 vx vy (D) ( )( ) > 0 x y 1001CJA101005230018 E-3/24  Target : JEE (Main + Advanced) 2025/25-02-2024/Paper-1 3. A stone is projected from level ground at t = 0 sec such that its horizontal and vertical components of initial velocity are 10 m/s and 20 m/s respectively. Then the instant of time at which magnitude of tangential and magnitude of normal components of acceleration of stone are same is :- (neglect air resistance) g = 10 m/s2. (A) 1 (B) 1 sec sec 2 (C) 3 sec (D) 4 sec 4. In the figure shown, all strings are massless. Choose the correct option(s) out of the following. (A) T1 > T3 (B) T3 > T1 (C) T2 > T1 (D) T2 > T3 5. A particle is moving from point (1, 2, 3) to (4, 6, 8) with initial speed 5 2 m/s on a straight line. It √ experiences a force of (3i^ + 4j^)N throughout its journey. Choose the correct statement(s) :- ^ (A) Initial velocity vector of the particle is (3i^ + 4j^ + 5k) m/s (B) Work done by the given force in the journey is 25J (W = F→. →S) (C) Initial power delivered by the given force is 25 watt ( (P →.V =F → ), P is power and V is velocity) (D) If velocity of the particle doesn't change there must be some other force acting on the particle. 6. A billiard ball initially at rest is given a sharp blow by a cue stick. The impulse is horizontal and is applied at a distance 2R/3 below the centerline, as shown in figure. The initial speed of the ball is v0, and the coefficient of kinetic friction is μ k. (A) Initially kinetic friction acts in negative x direction. (B) Initially kinetic friction acts in positive x direction. (C) Ball instantaneously starts pure rolling. (D) Initial angular velocity of ball is 5v0. 3R E-4/24 1001CJA101005230018  Nurture Course/Phase-V & VI/25-02-2024/Paper-1 SECTION-I (ii) : (Maximum Marks: 12) This section contains FOUR (04) questions. Each question has matching lists. The codes for the lists have choices (A), (B), (C) and (D) out of which ONLY ONE is correct For each question, marks will be awarded in one of the following categories : Full Marks : +3 If ONLY the correct option is chosen. Zero Marks : 0 If none of the options is chosen (i.e. the question is unanswered) Negative Marks : –1 In all other cases 7. Figure shows particles each connected rigidly by massless thin rods. Mass of each particle is m. In each case calculate moment of inertia of assembly about axis shown in figure. List-I List-II edge length of cube = L (I) (P) 8 mL2 Axis passing through centre of upper and lower faces edge length of cube = L (II) (Q) 4 mL2 Axis passing through edge of cube radius of cylinder = L (III) (R) 3 mL2 Axis passing through symmetry axis of cylinder edge of tetrahedron = L (IV) (S) mL2 Axis passing through the centroid of base (T) mL2/2 (A) I → Q;II → S;III → P;IV → R (B) I → Q;II → R;III → P;IV → S (C) I → Q;II → P;III → P;IV → S (D) I → Q;II → P;III → P;IV → R 1001CJA101005230018 E-5/24  Target : JEE (Main + Advanced) 2025/25-02-2024/Paper-1 8. In List-I, certain situations are depicted where steam at 100°C is used to melt ice at 0°C by means of a conducting body which is insulated to prevent heat losses to surrounding. Match the numerical value of question asked in each entry to the corresponding entry in List-II. Symbols have usual meaning. List-I List-II (I) (P) 10 Find temperature of interface of two rods in °C. (II) (Q) 20 Find total rate of heat transfer through the two rods in SI units. (III) (R) 30 hollow sphere of k = 1 W/mK 32 π Find thermal resistance in SI units. (IV) (S) 40 Hollow cylinder of k = π W/mK 10 Find temperature gradients in SI units. (T) 50 (A) I → Q;II → R;III → S;IV → P (B) I → R;II → S;III → P;IV → Q (C) I → Q;II → R;III → P;IV → S (D) I → R;II → S;III → Q;IV → P E-6/24 1001CJA101005230018  Nurture Course/Phase-V & VI/25-02-2024/Paper-1 9. In the given figure. List-II List-I (values in appropriate SI unit) 1 (I) If F = 50 N, θ = 53° and μ = (P) ^ 6 3i then acceleration of block is If F = 100 N, θ = 37° and µ = 1.5 ^ (II) (Q) 2i then acceleration of block is If F = 200 N, θ = 53° and µ = 1.0 ^ ^ (III) (R) 12 i + 6 j then acceleration of block is If F = 110 N, θ = 90° and µ = 0.2 ^ (IV) (S) 1j then acceleration of block is ^ ^ (T) 12 i + 16 j (A) I → Q;II → S;III → P;IV → R,T (B) I → S;II → R;III → P;IV → Q (C) I → Q;II → Q;III → R;IV → S (D) I → R;II → Q,T;III → S;IV → P 1001CJA101005230018 E-7/24  Target : JEE (Main + Advanced) 2025/25-02-2024/Paper-1 10. Answer the following by appropriately matching the lists based on the information given in the paragraph. Consider a body rolling on a horizontal surface as shown in figure (Symbols have their usual meaning) List-I List-II (I) Velocity is zero (P) Point A (II) Speed in maximum (Q) Point B (III) 0 < speed < vcm (R) Point C (IV) 1.3 vcm < speed < 2 vcm (S) Point D (T) Point E (A) I → P,R;II → Q,S;III → Q;IV → R (B) I → Q,S;II → P,T;III → Q,S;IV → Q,R (C) I → Q,S;II → T;III → P;IV → R (D) I → R;II → P;III → T;IV → Q,S E-8/24 1001CJA101005230018  Nurture Course/Phase-V & VI/25-02-2024/Paper-1 SECTION-II : (Maximum Marks: 24) This section contains EIGHT (08) questions. The answer to each question is a NUMERICAL VALUE. For each question, enter the correct numerical value of the answer in the place designated to enter the answer. If the numerical value has more than two decimal places, truncate/round-off the value to Two decimal places; 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) Answer to each question will be evaluated according to the following marking scheme: Full Marks : +3 If ONLY the correct numerical value is entered. Zero Marks : 0 In all other cases. 1. A metal rod A of 25 cm length expands by 0.050 cm, when its temperature is raised from 0°C to 100°C. Another rod B of a different metal of length 40 cm expands by 0.04 cm for the same rise in temperature. A third rod C of 50 cm length is made up of pieces of rod A and B placed end to end expands by 0.03 cm on heating from 0°C to 50°C. Find the length (in cm) of the piece of rod A. 2. Find A if the natural frequency of oscillation of the system as shown in figure is f = A √ K. Pulleys are π m massless and frictionless. Spring and string are also massless. 3. A soap bubble is being blown on a tube of radius 1 cm. The surface tension of the soap solution is 0.05 N/m and the bubble makes an angle of 60° with the tube as shown. The excess of pressure (in Pa) over the atmospheric pressure in the tube is :- 1001CJA101005230018 E-9/24  Target : JEE (Main + Advanced) 2025/25-02-2024/Paper-1 4. A body is on a rough horizontal surface which is moving horizontally in S.H.M of frequency 2 Hz. The coefficient of static friction between the body and the surface is 0.5. The maximum value of the amplitude (in mm) for which the body will not slip along the surface is :- (Take π 2 = 10 & g = 10 m/s2) 5. There is a 1mm thick layer of glycerine between a flat plate of area 100 cm2 & a big fixed plate. If the coefficient of viscosity of glycerine is 1.0 kg/m-s then how much force (in N) is required to move the plate with a velocity of 7 cm/s? 6. One mole of an ideal gas at STP is heated in an insulated closed container until the average speed of its molecules is doubled. If its pressure will become N times then find N. 7. A large cylindrical tank of cross-sectional area 1m2 is filled with water. It has a small hole at a height of 1m from the bottom. A movable piston of mass 5 kg is fitted on the top of the tank such that it can slide in the tank freely. A load of 45 kg is applied on the top of water by piston, as shown in figure. Find the value of v (in m/s) when piston is 7m above the bottom :- (g = 10 m/s2) 8. 2 kg ice at – 20°C is mixed with 5 kg water at 20°C. Then final amount of water (in kg) in the mixture would be :- (Given specific heat of ice = 0.5cal/g°C, specific heat of water = 1 cal/g°C, Latent heat of fusion of ice = 80 cal/g.) E-10/24 1001CJA101005230018  Nurture Course/Phase-V & VI/25-02-2024/Paper-1 PART-2 : CHEMISTRY SECTION-I (i) : (Maximum Marks: 24) This section contains SIX (06) questions. Each question has FOUR options. ONE OR MORE THAN ONE of these four option(s) is (are) correct answer(s). For each question, choose the option(s) corresponding to (all ) the correct answer(s) Answer to each question will be evaluated according to the following marking scheme: Full Marks : +4 If only (all) the correct option(s) is (are) chosen. Partial Marks : +3 If all the four options are correct but ONLY three options are chosen. Partial Marks : +2 If three or more options are correct but ONLY two options are chosen and both of which are correct. Partial Marks : +1 If two or more options are correct but ONLY one option is chosen and it is a correct option. Zero Marks : 0 If none of the options is chosen (i.e. the question is unanswered). Negative Marks : –2 In all other cases. For Example : If first, third and fourth are the ONLY three correct options for a question with second option being an incorrect option; selecting only all the three correct options will result in +4 marks. Selecting only two of the three correct options (e.g. the first and fourth options), without selecting any incorrect option (second option in this case), will result in +2 marks. Selecting only one of the three correct options (either first or third or fourth option), without selecting any incorrect option (second option in this case), will result in +1 marks. Selecting any incorrect option(s) (second option in this case), with or without selection of any correct option(s) will result in –2 marks. 1. Select correct statements : (A) Low pressure is favourable for evaporation of H2O( ℓ ) (B) The degree of dissociation of CaCO3(s) decreased with increase in pressure (C) If the equilibrium constant for A2(g) + B2(g) ⇌ 2AB(g) is 25, then equilibrium constant for 1 1 AB(g) ⇌ A2(g) + B2(g) is 0.2 2 2 (D) If solid product is added to an equilibrium mixture, the equilibrium will be unaffected. 1001CJA101005230018 E-11/24  Target : JEE (Main + Advanced) 2025/25-02-2024/Paper-1 2. 3M, 2L of aq. solution of NaCl is mixed with 1M, 3L of AgNO3(aq.) solution, NaCl(aq.) + AgNO3(aq.) → AgCl(s)↓ + NaNO3(aq.) Which of the following is/are correct for resulting solution ? (A) [Na+] = 1.2M (B) [Ag+] = 0.6M (C) [NO−3 ] = 0.6M (D) [Cl – ] = 1.2M 3. Which of the following are true ? (A) SH6 and NCl5 do not exist (B) There are two p π – d π bonds in SO3 (C) SeF4 and CH4 are tetrahedral (D) I3 – is linear molecule with sp3d hybridisation 4. Which of the following is/are incorrect? (A) N < O < F < Cl (Electron affinity) (B) Li < Na < K < Rb (Ionisation energy) (C) Ca+2 > K ⊕ > S –2 > Cl – (Ionisation energy) (D) Al+3 > Mg+2 > Na+ (Ionic size) 5. Which of following has/have “Z” configuration : (A) (B) (C) (D) 6. Resonance energy will be maximum from the following : (A) (B) (C) (D) E-12/24 1001CJA101005230018  Nurture Course/Phase-V & VI/25-02-2024/Paper-1 SECTION-I (ii) : (Maximum Marks: 12) This section contains FOUR (04) questions. Each question has matching lists. The codes for the lists have choices (A), (B), (C) and (D) out of which ONLY ONE is correct For each question, marks will be awarded in one of the following categories : Full Marks : +3 If ONLY the correct option is chosen. Zero Marks : 0 If none of the options is chosen (i.e. the question is unanswered) Negative Marks : –1 In all other cases 7. Match the following: List-I List-II (P) Electron moving in 2nd orbit in He+ ion (1) Radius of orbit is 0.529 Å (Q) Electron moving in 3rd orbit in H-atom (2) Total energy of electron is ( – 13.6) × 9eV (R) Electron moving in 1st orbit in Li+2 ion (3) Velocity of electron is 2.188 × 106 m/sec 3 (S) Electron moving in 2nd orbit in Be+3 ion (4) De-Broglie wavelength of electron is 150 √ Å 13.6 (5) Momentum of an electron is 6.637 × 10 –25 kg ms –1 (A) P → 2;Q → 1,3;R → 5;S → 1 (B) P → 4;Q → 3,5;R → 2;S → 1 (C) P → 3;Q → 2,3;R → 4;S → 5 (D) P → 1;Q → 3,4;R → 2;S → 5 8. Select the correct match of shape as well as hybridisation for the species given in List-I. List-I List-II (P) XeF4 (1) sp3d2 (Q) XeF2 (2) Planar (R) CH3+ (3) Linear (S) BrF5 (4) sp2 (5) sp3d (A) P → 2,3;Q → 2,3,5;R → 1,2;S → 3,5 (B) P → 1,2;Q → 2,3,5;R → 2,4;S → 1 (C) P → 1,2;Q → 2,3,5;R → 1,5;S → 2,3 (D) P → 3;Q → 2,3;R → 1,2;S → 4,5 1001CJA101005230018 E-13/24  Target : JEE (Main + Advanced) 2025/25-02-2024/Paper-1 9. List-I List-II (compound) (pKa) (P) (1) 17 (Q) (2) 8.9 (R) (3) 10.7 (S) (4) 5 (5) 7 (A) P → 3;Q → 2;R → 1;S → 4 (B) P → 2;Q → 3;R → 4;S → 1 (C) P → 3;Q → 2;R → 4;S → 1 (D) P → 4;Q → 2;R → 3;S → 1 10. Answer the following by appropriately matching the lists based on the information given in the paragraph. List-I List-II (P) (1) Correct order of stability of alkene (Q) (2) Correct order of heat of combustion (R) (3) Correct order of heat of hydrogenation (S) (4) Correct order of C=C bond length (5) Correct order of no of α -H (A) P → 1,3;Q → 1,2,3;R → 2,3;S → 1,2,4 (B) P → 1,2,4,5;Q → 2,3;R → 1,2,4,5;S → 1,4 (C) P → 1,2;Q → 1,4;R → 2,3;S → 1,2,4 (D) P → 1,4;Q → 1,2,4;R → 2,3;S → 1,2,4 E-14/24 1001CJA101005230018  Nurture Course/Phase-V & VI/25-02-2024/Paper-1 SECTION-II : (Maximum Marks: 24) This section contains EIGHT (08) questions. The answer to each question is a NUMERICAL VALUE. For each question, enter the correct numerical value of the answer in the place designated to enter the answer. If the numerical value has more than two decimal places, truncate/round-off the value to Two decimal places; 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) Answer to each question will be evaluated according to the following marking scheme: Full Marks : +3 If ONLY the correct numerical value is entered. Zero Marks : 0 In all other cases. 1. For the reaction: A(g) + B(g) ⇌ C(g) the equilibrium partial pressures, pA = 0.15 atm, pB = 0.1 atm and pC = 0.3 atm. When the volume of the reaction vessel was reduced to such an extent, so that on re-establishing the equilibrium, partial pressure of A and B were found to be doubled. The new partial pressure of C would be x atm. What will be the value of x ? 0.2 2. The density of a mixture of O2 and N2 gases at 1 atm and 273K is 0.0013 gm/ml. If partial pressure of O2 in the mixture is A atm , then calculate value of 25A. (Take 273R = 22.4) 3. For any orbital Ψ (r) = K. e−Kr ( r4 + K1 r3 + K2 r2 ). The value of (n − ℓ ) is: 4. Find the number of oxy acids having peroxy linkage H4P2O6, H4P2O8, H4P2O7, H2SO5, H4P2O5, H3P3O9, H6P4O13, H2S2O7, H2S2O3, H2S2O5, HClO4 5. How many of the following have hydrogen bonding? NH3 , CH4 , H2O , HI, HF, HCOOH, B(OH)3 , CH3COOH 6. Find the number of electrons in dipositive zinc ion having n × ℓ × m = 0. 7. How many H atoms will be replaced by D atom when the following compound in kept in OD⊖ / D2O solution : OD Θ /D2 O −−−−−−→ 8. Total number of groups which can show – I effect when attached to benzene ring : (a) – OH (b) – NH2 (c) (d) – Cl (e) (f) – O – (g) – CH3 (h) (i) (j) – C ≡ N (k) 1001CJA101005230018 E-15/24  Target : JEE (Main + Advanced) 2025/25-02-2024/Paper-1 PART-3 : MATHEMATICS SECTION-I (i) : (Maximum Marks: 24) This section contains SIX (06) questions. Each question has FOUR options. ONE OR MORE THAN ONE of these four option(s) is (are) correct answer(s). For each question, choose the option(s) corresponding to (all ) the correct answer(s) Answer to each question will be evaluated according to the following marking scheme: Full Marks : +4 If only (all) the correct option(s) is (are) chosen. Partial Marks : +3 If all the four options are correct but ONLY three options are chosen. Partial Marks : +2 If three or more options are correct but ONLY two options are chosen and both of which are correct. Partial Marks : +1 If two or more options are correct but ONLY one option is chosen and it is a correct option. Zero Marks : 0 If none of the options is chosen (i.e. the question is unanswered). Negative Marks : –2 In all other cases. For Example : If first, third and fourth are the ONLY three correct options for a question with second option being an incorrect option; selecting only all the three correct options will result in +4 marks. Selecting only two of the three correct options (e.g. the first and fourth options), without selecting any incorrect option (second option in this case), will result in +2 marks. Selecting only one of the three correct options (either first or third or fourth option), without selecting any incorrect option (second option in this case), will result in +1 marks. Selecting any incorrect option(s) (second option in this case), with or without selection of any correct option(s) will result in –2 marks. 1. If 100! = 2 α 3 β..., then (A) α = 97 (B) β = 1 ( α − 1) 2 (C) β = 48 (D) α – β = 49 2. A person wants to invite one or more of his friends for a party. In how many ways can he do so if he has eight friends ? (A) 28 – 1 (B) 28 (C) 82 8 (D) C1 + 8 C2 +..... +8 C8 E-16/24 1001CJA101005230018  Nurture Course/Phase-V & VI/25-02-2024/Paper-1 n 3 x 3. If the 6th term in the expansion of ( + ) when x = 3 is numerically greatest then the possible 2 3 integral value(s) of n can be − (A) 11 (B) 12 (C) 13 (D) 14 8 x3 4. In the expansion of ( + 3 ) 3 x (A) coefficient of x independent term is 70 (B) coefficient of x independent term is 2268 (C) coefficient of middle term is 2268 (D) coefficient of middle term is 70 x2 y2 5. The value of m for which y = mx + 6 is a tangent to the hyperbola – = 1 is 100 49 (A) 17 (B) – 17 √( ) √( ) 20 20 (C) √( 20 (D) – √( 20 ) ) 17 17 6. If point P lies on the curve y2 = 8x then locus of mid point of line segment PA is (2y – 1)2 = λ (x – 1) where A(2, 1). Then λ is divisible by (A) 2 (B) 4 (C) 6 (D) 8 1001CJA101005230018 E-17/24  Target : JEE (Main + Advanced) 2025/25-02-2024/Paper-1 SECTION-I (ii) : (Maximum Marks: 12) This section contains FOUR (04) questions. Each question has matching lists. The codes for the lists have choices (A), (B), (C) and (D) out of which ONLY ONE is correct For each question, marks will be awarded in one of the following categories : Full Marks : +3 If ONLY the correct option is chosen. Zero Marks : 0 If none of the options is chosen (i.e. the question is unanswered) Negative Marks : –1 In all other cases 7. List-I List-II (I) 1 (P) has zero element {x ∈ [0, 2 π ] : sinx = } 2022 (II) {x 1 (Q) has one element ∈ [0, π ] : cosx = } 2022 ∈ [− π , π ] : tanx = − } (III) {x 1 (R) has two element 2 5 (IV) {x ∈ [0, 4 π ] : sinx = log25} (S) has three element (T) has four element (A) I → R;II → Q;III → R;IV → P (B) I → P;II → Q;III → P;IV → T (C) I → T;II → P;III → Q;IV → S (D) I → S;II → T;III → P;IV → Q E-18/24 1001CJA101005230018  Nurture Course/Phase-V & VI/25-02-2024/Paper-1 8. List-I List-II x2 y2 (I) Sum of distances of a point on the ellipse + =1 (P) 2 9 16 from the foci x2 y2 If the mid point of a chord of the ellipse + =1 (II) 16 25 (Q) 10 4k is (0, 3), then length of the chord is. Determine k. 5 The slope of common tangents to x2 + 4y2 = 4 (III) (R) 12 and x2 + y2 = 3 is 'm', then m2 is If 'e' is eccentricity and ℓ is the length of latus (IV) rectum of the ellipse 9x2 + 5y2 – 30y = 0, then 3(e + ℓ ) (S) 8 is (T) 5 (A) I → P;II → Q;III → S;IV → R (B) I → P;II → S;III → Q;IV → R (C) I → Q;II → R;III → S;IV → P (D) I → S;II → S;III → P;IV → R 1001CJA101005230018 E-19/24  Target : JEE (Main + Advanced) 2025/25-02-2024/Paper-1 9. In a high school, a committee has to be formed from a group of 6 boys M1, M2, M3, M4, M5, M6 and 5 girls G1, G2, G3, G4, G5. (i) Let α 1 be the total number of ways in which the committee can be formed such that the committee has 5 members, having exactly 3 boys and 2 girls. (ii) Let α 2 be the total number of ways in which the committee can be formed such that the committee has at least 2 members, and having an equal number of boys and girls. (iii) Let α 3 be the total number of ways in which the committee can be formed such that the committee has 5 members, at least 2 of them being girls. (iv) Let α 4 be the total number of ways in which the committee can be formed such that the committee has 4 members, having at least 2 girls and such that both M1 and G1 are NOT in the committee together. List-I List-II (I) The value of α 1 is (P) 461 (II) The value of α 2 is (Q) 189 (III) The value of α 3 is (R) 192 (IV) The value of α 4 is (S) 200 (T) 381 (A) I → S;II → R;III → Q;IV → P (B) I → P;II → S;III → Q;IV → R (C) I → S;II → P;III → T;IV → Q (D) I → R;II → Q;III → T;IV → S E-20/24 1001CJA101005230018  Nurture Course/Phase-V & VI/25-02-2024/Paper-1 10. List-I List-II (I) If ai are in A.P. and a1 + a7 = 8, then a4 is equal to (P) 2 (II) If a, b, c are in H.P., then b+a b+c (Q) 4 + is equal to b−a b−c If the sum of first 20 terms is same as the sum of first 10 terms in (III) an arithmetic progression then the sum of first 30 terms is equal (R) 0 to 3 5 7 199 a If sum of + +....+ is (where a (IV) 2 1.2 2 22.32 32.42 992.1002 b (S) 3 and b are coprime) the value of |b – a| is (T) 1 (A) I → Q;II → P;III → R;IV → T (B) I → P;II → Q;III → R;IV → S (C) I → T;II → S;III → P;IV → Q (D) I → R;II → S;III → P;IV → T 1001CJA101005230018 E-21/24  Target : JEE (Main + Advanced) 2025/25-02-2024/Paper-1 SECTION-II : (Maximum Marks: 24) This section contains EIGHT (08) questions. The answer to each question is a NUMERICAL VALUE. For each question, enter the correct numerical value of the answer in the place designated to enter the answer. If the numerical value has more than two decimal places, truncate/round-off the value to Two decimal places; 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) Answer to each question will be evaluated according to the following marking scheme: Full Marks : +3 If ONLY the correct numerical value is entered. Zero Marks : 0 In all other cases. 1. The coefficient of a2 b3 in (a + b)5 is - 2. If nC4, nC5 and nC6 are in A.P., then sum of values of n is: 3. If all the letters of the word “MANWAR” are arranged in all possible manner as they are in a dictionary, then the rank of the word MANWAR is____. 4. In how many ways can a person go from point A to point B if he can travel only to the right or upward along the lines. N 5. If N denotes the number of four-digit natural numbers formed by using only even digits. Then is 125 6. If the circles x2 + y2 – 2x – 4gy – 3 = 0 and x2 + y2 + 6gx – 8y – 4 = 0 intersect each other ∣ 11g ∣ orthogonally then ∣ ∣ is ∣ 7 ∣ 7. If the lines 3x – 5y + 9 = 0, 4x + ky – 28 = 0 and 13x – 8y – 1 = 0 are concurrent, then the value of k is : 8. Sum of all the solution(s) of the equation log10(x) + log10(x + 2) – log10(5x + 4) = 0 is E-22/24 1001CJA101005230018  Nurture Course/Phase-V & VI/25-02-2024/Paper-1 ALLEN ® Space for Rough Work 1001CJA101005230018 E-23/24  Target : JEE (Main + Advanced) 2025/25-02-2024/Paper-1 ALLEN ® NAME OF THE CANDIDATE................................................................................................ FORM NO.............................................. I have read all the instructions I have verified the identity, name and Form number of the candidate, and that question and shall abide by them. paper and ORS codes are the same. ____________________________ ____________________________ Signature of the Candidate Signature of the Invigilator ALLEN CAREER INSTITUTE Pvt. Ltd. Registered & Corporate Office : ‘SANKALP’, CP-6, Indra Vihar, Kota (Rajasthan) INDIA-324005 Ph. : +91-744-3556677, +91-744-2757575|E-mail : [email protected]|Website : www.allen.ac.in E-24/24 Your Hard Work Leads to Strong Foundation 1001CJA101005230018  Test Pattern (1001CJA101005230018) )1001CJA101005230018) Hindi CLASSROOM CONTACT PROGRAMME JEE(Advanced) REVIEW TEST (Academic Session : 2023 - 2024) 25-02-2024 JEE(Main+Advanced) : NURTURE COURSE [PHASE : V & VI] Time : 3 Hours PAPER-1 (OPTIONAL) Maximum Marks : 180 egRoiw.kZ funZs 'k % ftu fo|kfFkZ;ksa ds QkWeZ uEcj 8 vadksa ds gSa] mUgs OMR esa QkWeZ uEcj ds igys nks 'kwU; Hkjuk gSA tSls fd] ;fn vkidk QkWeZ uEcj 12345678 gS] rks vkidks 0012345678 Hkjuk gSA Ïi;k bu funsZ'kksa dks /;ku ls i