ALLEN JEE (Main + Advanced) 2023 03-04-2022 Paper-1 PDF

Test Pattern (1001CJA102922014) )1001CJA102922014) English CLASSROOM CONTACT PROGRAMME JEE(Advanced) UNIT TEST...

Test Pattern (1001CJA102922014) )1001CJA102922014) English CLASSROOM CONTACT PROGRAMME JEE(Advanced) UNIT TEST (Academic Session : 2022 - 2023) 03-04-2022 JEE(Main+Advanced) : ENTHUSIAST COURSE [PHASE : TOAS, TNAS & TAAS] Time : 3 Hours PAPER-1 Maximum Marks : 186 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. 3. Blank spaces are provided within this booklet for rough work. DO NOT BREAK THE SEALS WITHOUT BEING INSTRUCTED TO DO SO BY THE INVIGILATOR 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 36 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) 2023/03-04-2022/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 · Boltzmann constant k = 1.38 × 10–23 JK–1 1 · Coulomb's law constant = 9 ×10 9 4 pe0 · Universal gravitational constant G = 6.67259 × 10–11 N–m2 kg–2 · Speed of light in vacuum c = 3 × 108 ms–1 · Stefan–Boltzmann constant s = 5.67 × 10–8 Wm–2–K–4 · Wien's displacement law constant b = 2.89 × 10–3 m–K · Permeability of vacuum µ0 = 4p × 10–7 NA–2 1 · Permittivity of vacuum Î0 = m0 c2 · Planck constant h = 6.63 × 10–34 J–s Space for Rough Work E-2/36 1001CJA102922014  Enthusiast Course/Phase-TOAS, TNAS & TAAS/03-04-2022/Paper-1 ALLEN BEWARE OF NEGATIVE MARKING PART-1 : PHYSICS SECTION-I (i) : (Maximum Marks: 32) This section contains EIGHT (08) 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 : –1 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 –1 marks. 1. Table shown in figure is rotating about its vertical axis with an angular speed ω = 2 rad/sec. Blocks A and B have masses 45 kg and 22.5 kg respectively. String connecting them is light and passes through a small hole in the table. Pulley shown in massless. Coefficient of friction at the contacts of A and B with the table is 0.4. dimensions of two blocks are small and distance of B from rotation axis is 0.6 m. If block A remains stationary relative to the table at a distance 'x' from the rotation axis then (Take : g = 10 m/s2) (A) Minimum possible value of x is 0.13 m (B) Minimum possible value of x is 0.26 m (C) Maximum possible value of x is 2.37 m (D) Maximum possible value of x is 1.37 m Space for Rough Work 1001CJA102922014 E-3/36  Target : JEE (Main + Advanced) 2023/03-04-2022/Paper-1 ALLEN 2. A ball of mass M is swing around in a circle in a horizontal plane. On end of spring (spring constant k) is fixed and other end is connected to the ball as shown in figure. The ball describes a horizontal circle a distance h above the horizontal floor with constant speed. The stretched spring has a length ℓ and makes an angle 60° with the vertical. Neglect air resistance. (A) Magnitude of force exerted by spring on block is 2 Mg 2Mg (B) Natural length of spring is (ℓ + ). k − −−− 3gℓ (C) Speed of the ball is √ 2 (D) At some instant of time, if spring breaks, the ball moves a horizontal distance √−−− 3hℓ , before it hits the floor. Space for Rough Work E-4/36 1001CJA102922014  Enthusiast Course/Phase-TOAS, TNAS & TAAS/03-04-2022/Paper-1 ALLEN 3. A small toy car of mass m slides with negligible friction on a loop track as shown in figure. The toy car starts from rest at a point H = 4R above the lowest point of the track. (Acceleration due to gravity is g and radius of circular part is R). − −−− (A) Speed of toy car at point B is √4gR (B) Normal force exerted by track on the toy car at point B is 9 mg. (C) Normal force exerted by track on the toy car at position C is 6 mg. (D) Toy car looses contact with track at a point between C and D. Space for Rough Work 1001CJA102922014 E-5/36  Target : JEE (Main + Advanced) 2023/03-04-2022/Paper-1 ALLEN 4. A small block slides down a hill (starting from rest) of height H. The part of the hill near its end B is horizontal. The block flies off the hill at B to hit the ground at C. Hill is smooth. If y is height of end B of hill from ground and x is horizontal displacement of block before hitting the ground after loosing contact with track, then : (A) For x to be maximum, y is H H (B) For x to be maximum y is. 2 H (C) Maximum possible value of x is. 2 (D) Maximum possible value of x is H. Space for Rough Work E-6/36 1001CJA102922014  Enthusiast Course/Phase-TOAS, TNAS & TAAS/03-04-2022/Paper-1 ALLEN 5. A thin non conducting ring of radius R has linear charge density λ varying as λ = λ0 cosθ, where λ0 is a positive constant and θ is angle measured from positive x-direction as shown. Consider centre of ring is at origin. (A) Resultant electric field at origin is towards positive y-axis. (B) Resultant electric field at origin is towards negative x-axis. λ0 (C) Magnitude of resultant electric field at origin is 8ε 0 R. λ0 (D) Magnitude of resultant electric field at origin is. 4ε 0 R Space for Rough Work 1001CJA102922014 E-7/36  Target : JEE (Main + Advanced) 2023/03-04-2022/Paper-1 ALLEN 6. A fixed smooth inclined plane making an angle θ with the horizontal is placed in a uniform horizontal electric field E0 as shown in figure. A small block of mass m having charge +q is released on inclined plane. (Acceleration due to gravity is 'g') (A) Normal contact force applied by inclined plane on block is (mg cosθ + qE0sinθ) (B) Normal contact force force applied by inclined plane on block is (mg cosθ – qE0sinθ) 1 qE 0 (C) If acceleration of block is zero then θ = tan − ( ). mg 1 mg (D) If acceleration of block is zero then θ = tan − ( ). qE 0 7. A long cylindrical tube containing water is closed by an equiconvex lens of focal length 10 cm in air. A point object 'O' is placed along the axis of the tube outside it at a distance of 21 cm from the lens. 4 Refractive index of material of lens is 1.5 and that of water is. 3 (A) Final image is virtual in nature. (B) Final image is real in nature. (C) Final image is located at a distance 70 cm from lens inside the tube. (D) Final image is located at a distance 30 cm from lens inside the tube. Space for Rough Work E-8/36 1001CJA102922014  Enthusiast Course/Phase-TOAS, TNAS & TAAS/03-04-2022/Paper-1 ALLEN − − 8. A prism with prism angle 60° and refractive index √ 7 is given. 3 (A) Minimum possible angle of incidence so that the light ray is refracted from the second surface is 30°. (B) Minimum possible angle of incidence, so that the light ray is refracted from the second surface is 60°. (C) Maximum possible deviation produced by prism is 30°. (D) Maximum possible deviation produced by prism is 60°. Space for Rough Work 1001CJA102922014 E-9/36  Target : JEE (Main + Advanced) 2023/03-04-2022/Paper-1 ALLEN SECTION-I (ii) : (Maximum Marks: 12) This section contains TWO (02) List-Match sets. Each List-Match set has TWO Multiple Choice Questions. Each List-Match set has two lists : List-I and List-II List-I has Four entries (I), (II), (III) and (IV) and List-II has Six entries (P), (Q), (R), (S), (T) and (U) Four options are given in each Multiple Choice Question based on List-I and List-II and ONLY ONE of these four options satisfies the condition asked in the Multiple Choice Question. Answer to each question will be evaluated according to the following marking scheme : Full Marks : +3 If ONLY the option corresponding to the correct combination 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 9. A particle is performing SHM x = A sin (ωt + ϕ) whose time period is T. List-I contains events related to the motion of particle and List-II contains the minimum time after which that event happen. Choose the correct match from option if ϕ = 0° List–I List–II (I) Particle comes to rest (P) T/4 (II) Velocity is maximum (Q) T/6 (III) Kinetic energy = Potential energy (R) 3T/8 (IV) Velocity is half of maximum velocity (S) T/24 (T) T/2 (U) T/8 (A) I → P;II → T;III → U;IV → Q (B) I → Q;II → P;III → R;IV → S (C) I → R;II → U;III → U;IV → Q (D) I → S;II → Q;III → R;IV → S Space for Rough Work E-10/36 1001CJA102922014  Enthusiast Course/Phase-TOAS, TNAS & TAAS/03-04-2022/Paper-1 ALLEN 10. A particle is performing SHM x = A sin (ωt + ϕ) whose time period is T. List-I contains events related to the motion of particle and List-II contains the minimum time after which that event happen. Choose the correct match from option if ϕ = π/4 List–I List–II (I) Particle comes to rest (P) T/4 (II) Velocity is maximum (Q) T/6 (III) Kinetic energy = Potential energy (R) 3T/8 (IV) Velocity is half of maximum velocity (S) T/24 (T) T/2 (U) T/8 (A) I → P;II → T;III → U;IV → Q (B) I → U;II → R;III → P;IV → S (C) I → R;II → Q;III → S;IV → T (D) I → S;II → Q;III → R;IV → T Space for Rough Work 1001CJA102922014 E-11/36  Target : JEE (Main + Advanced) 2023/03-04-2022/Paper-1 ALLEN 11. ABC is a right-angled prism kept in air. A ray (1) is incident on the face AB along the normal. Refractive index of the material of prism is the minimum value that will be required so that ray (1) undergoes total internal reflection at the face AC. Another ray (2) is incident on the face AB such that it emerges from face AC along the normal to AC. A third ray (3) falls on the face BC and emerges from face AC such that its angle of emergence is the same as that of incidence. Assuming light (1), (2) and (3) have the same wavelength, then match the following. List-I List-II (I) Refractive index of the material of prism is (P) 120 (II) Angle of incidence in degree of ray (2) is (Q) 90 (III) Deviation in degree suffered by ray (2) is (R) 2 (IV) Deviation in degree suffered by ray (3) is (S) 60 (T) 1.5 (U) 4 (A) I → U;II → Q;III → S;IV → P (B) I → R;II → P;III → S;IV → P (C) I → U;II → S;III → P;IV → T (D) I → R;II → Q;III → S;IV → P Space for Rough Work E-12/36 1001CJA102922014  Enthusiast Course/Phase-TOAS, TNAS & TAAS/03-04-2022/Paper-1 ALLEN 12. ABC is a right-angled prism kept in air. A ray (1) is incident on the face AB along the normal. Refractive index of the material of prism is the minimum value that will be required so that ray (1) undergoes total internal reflection at the face AC. Another ray (2) is incident on the face AB such that it emerges from face AC along the normal to AC. A third ray (3) falls on the face BC and emerges from face AC such that its angle of emergence is the same as that of incidence. Assuming light (1), (2) and (3) have the same wavelength, then match the following. [Take : sin–1 (0.29) ≈ 17°, sin 15° = 0.258] List-I List-II (I) Refractive index of the material of prism is (P) 120 (II) Angle of incidence in degree of ray (2) is (Q) 90 (III) Deviation in degree suffered by ray (2) is (R) 2 (IV) Deviation in degree suffered by ray (3) is (S) 30 (T) 1.15 (U) 4 (A) I → U;II → Q;III → S;IV → P (B) I → T;II → Q;III → S;IV → U (C) I → U;II → S;III → P;IV → T (D) I → R;II → Q;III → S;IV → P Space for Rough Work 1001CJA102922014 E-13/36  Target : JEE (Main + Advanced) 2023/03-04-2022/Paper-1 ALLEN SECTION-II : (Maximum Marks: 18) This section contains SIX (06) 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 uniform chain of mass M and length L rests on a rough horizontal table such that one of its ends hangs over the edge. The chain begins to slide if length of overhanging part is at least equal to two third of the total length of the chain. Chain is released and starts its motion from a position where two third of its total length is overhanging. If work done by friction force acting on the chain by the moment it completely − μMgL slides off the table is given by then find the value of N. Coefficient of friction between chain N and rough horizontal surface is µ and acceleration due to gravity is g. Space for Rough Work E-14/36 1001CJA102922014  Enthusiast Course/Phase-TOAS, TNAS & TAAS/03-04-2022/Paper-1 ALLEN 2. The ends of a spring are attached to two blocks of masses 5 kg and 3 kg as shown in figure. The 5 kg block rests on a horizontal surface and the 3 kg block which is vertically above it is in equilibrium with the spring compressed by 1 cm. The 3 kg block is pushed down further by x cm and released. Find the minimum value of x so that the 5 kg block may be lifted off the ground during the subsequent motion. 3. A thin plano convex lens A has material of refractive index µA = 1.8 and it's curved surface has radius of curvature R. A thin layer of transparent material B is laid over the curved surface of A. The refractive R index of B is 1.2 and the curved surface of B that is not touching A has radius of curvature. This 2 surface of B is silvered. A point object 'O' is kept at a distance of 10cm on the principal axis of the system (above the plane surface) and it's image is formed at a distance of 40 cm above the plane surface. Find R (in cm). Space for Rough Work 1001CJA102922014 E-15/36  Target : JEE (Main + Advanced) 2023/03-04-2022/Paper-1 ALLEN 4. A convex lens of focal length 20 cm and another plano-convex lens of focal length 40 cm are placed co-axially. The plane surface of the plano convex lens is silvered. An object O is kept on the principal axis at a distance of 10 cm from the convex lens as shown in figure. Find the distance d (in cm) between two lenses so that final image is formed on object itself. 5. Four small particles charged with equal positive charge +Q each are arranged at the four corners of a horizontal square of side a. A particle having charge +q and mass m is placed at a height h above the centre of the square. Condition under which particle at height h is in equilibrium is given by Qqh m= N2. Fill the value of (N1 + N2). (Acceleration due to gravity is 'g') 2 a2 gπε 0 (h + N1 ) 6. A particle performs SHM along x-axis according to the relation x = 3 sin (100t) + 8 cos2 (50t) where 'x' is in cm and 't' is in second. Find the maximum possible distance (in cm) of the particle from origin during its motion. Space for Rough Work E-16/36 1001CJA102922014  Enthusiast Course/Phase-TOAS, TNAS & TAAS/03-04-2022/Paper-1 ALLEN PART-2 : CHEMISTRY SECTION-I (i) : (Maximum Marks: 32) This section contains EIGHT (08) 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 : –1 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 –1 marks. 1. Which of the following is/are correctly match with their equilibrium constant (Keq) (A) (B) (C) (D) Space for Rough Work 1001CJA102922014 E-17/36  Target : JEE (Main + Advanced) 2023/03-04-2022/Paper-1 ALLEN 2. Which of the following reaction result the formation of a pair of diastereomers? Hg(OAc) 2 H2O (A) −−→ (B) −−−−−−− → NaBH 4 , ŌH KCN Br 2 (C) −−−− → (D) −−−→ DMSO CCl4 3. H 3 P O4 / Δ −−−−−− → A + B Identify relation between A and B. If both A and B give Bromine water test (A) Stereoisomers (B) Structural isomers (C) Enantiomers (D) Diastereomers 4. Choose the correct statement among the following : (A) Primitive cubic unit cell involves two dimensional hexagonal closed packed array of atoms (B) Four hexagonal closed packed two dimensional layers of atoms are involved in one FCC unit cell (C) Three hexagonal close packed two dimensional layers of atoms are involved in one HCP unit cell (D) Four square close packed two dimensional layers of atoms are involved in one BCC unit cell Space for Rough Work E-18/36 1001CJA102922014  Enthusiast Course/Phase-TOAS, TNAS & TAAS/03-04-2022/Paper-1 ALLEN 600 5. Hydrocarbon contains % by mass carbon and its one molecule weighs 93.33 × 10–24 g. 7 Which of the following statement(s) is/are correct [NA = 6.0 × 1023] (A) Empirical formula is CH (B) Empirical formula is CH2 (C) Molecular formula of C3H8 (D) Molecular formula is C4H8 6. Which of the following given order is CORRECT with respect to bond angle? (A) (In SeOCl2) (B) (In SbF4–) (C) (In SbF4–) (D) (In SeOCl2) 7. Which of the following species is/are planar and polar? (A) NO2 (B) ClO2 (C) XeF 5 − (D) ClF3 8. Choose the INCORRECT order of the indicated property given in the options. Clathrate compound formation (A) He < Ne < Kr < Ar : tendency order (B) NaO2 < KO2 < RbO2 < CsO2 : Thermal stability order (C) BeF2 < BaF2 : Solubility order (D) LiF > LiCl > LiI : Melting point order Space for Rough Work 1001CJA102922014 E-19/36  Target : JEE (Main + Advanced) 2023/03-04-2022/Paper-1 ALLEN SECTION-I (ii) : (Maximum Marks: 12) This section contains TWO (02) List-Match sets. Each List-Match set has TWO Multiple Choice Questions. Each List-Match set has two lists : List-I and List-II List-I has Four entries (I), (II), (III) and (IV) and List-II has Six entries (P), (Q), (R), (S), (T) and (U) Four options are given in each Multiple Choice Question based on List-I and List-II and ONLY ONE of these four options satisfies the condition asked in the Multiple Choice Question. Answer to each question will be evaluated according to the following marking scheme : Full Marks : +3 If ONLY the option corresponding to the correct combination 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 9. Answer the following by approximately matching the lists based on the information given in the paragraph. For an nth order reaction A → products, dC A − The rate law is = kC An. Where CA = concentration of A at time 't'. Let C A0 is initial concentration dt of A and and α = degree of dissociation of reactant 'A' List-I List-II C A0 − CA (I) n=0 (P) α= C A0 1 (II) n= (Q) α = 1 – e–kt 2 kt (III) n=1 (R) α= CA 0 C A0 kt (IV) n=2 (S) α= (1 + C A0 kt) α = independent of initial (T) concentration of reactant Graph between 'α' and 't' is a (U) straight line passing through origin Which of the following options has the correct combination considering List-I and List-II ? (A) II → P, R (B) I → P,R,T (C) III → P,Q,U (D) III → P,Q,T Space for Rough Work E-20/36 1001CJA102922014  Enthusiast Course/Phase-TOAS, TNAS & TAAS/03-04-2022/Paper-1 ALLEN 10. Answer the following by approximately matching the lists based on the information given in the paragraph. For an nth order reaction A → products, dC A − The rate law is = kC An. Where CA = concentration of A at time 't'. Let C A0 is initial dt concentration of A and and α = degree of dissociation of reactant 'A' List-I List-II C A0 − CA (I) n = 0 (P) α= C A0 1 (II) n = (Q) α = 1 – e–kt 2 kt (III) n = 1 (R) α= CA 0 C A0 kt (IV) n = 2 (S) α= ( 1 + C A0 kt) (T) α = independent of initial concentration of reactant (U) Graph between 'α' and 't' is a straight line passing through origin Which of the following options has the correct combination considering List-I and List-II ? (A) I → P,Q (B) IV → S,T (C) IV → P,S (D) III → Q,U Space for Rough Work 1001CJA102922014 E-21/36  Target : JEE (Main + Advanced) 2023/03-04-2022/Paper-1 ALLEN 11. List-I List-II Dimerization/polymerization by (I) 3c - 2e– (P) BeX2 (II) Co-ordinate bond (Q) AlX3 (III) Odd e– (R) CX3 (IV) No dimerization (S) BX3 (T) IX3 (U) ClO3 Select correct match when X = F. (A) II → R (B) I → Q (C) III → U (D) IV → S 12. List-I List-II Dimerization/polymerization by (I) 3c - 2e– (P) BeX2 (II) Co-ordinate bond (Q) AlX3 (III) Odd e– (R) CX3 (IV) No dimerization (S) BX3 (T) IX3 (U) ClO3 Select correct match when X = Cl (A) I → P (B) III → R (C) II → Q (D) IV → T Space for Rough Work E-22/36 1001CJA102922014  Enthusiast Course/Phase-TOAS, TNAS & TAAS/03-04-2022/Paper-1 ALLEN SECTION-II : (Maximum Marks: 18) This section contains SIX (06) 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. Number of following compounds which can't be synthesised in good yield by Williamson's reaction (i) (ii) Me–O–Ph (iii) (iv) Ph–O–Ph (v) (vi) (vii) 2. Number of compounds which are more reactive than by SN2 mechanism? ; ; ; ; ; H3C—Cl ; ; Space for Rough Work 1001CJA102922014 E-23/36  Target : JEE (Main + Advanced) 2023/03-04-2022/Paper-1 ALLEN 3. How many of the following substrate can give E2 elimination reaction on treatment with base / Δ (i) Ph–Cl (ii) Me3C–Br (iii) (iv) CH3–Cl (v) (vi) (vii) (viii) (ix) Ph3C–Cl 4. What should be the minimum pressure (in atm) applied on 0.1 M glucose solution, filled in semi-permiable membrane, so as to filter away 750 mL water, leaving 250 mL of glucose solution at 300 K. [Given : R = 0.08 atm LK – 1 mol – 1 ] 5. An aq. solution of 0.5M KMnO4 is divided into two parts. One part of it requires 125 ml of 1.5M aq. solution of oxalate ions in acidic medium, while another part requires 270 ml of 0.5M aq. solution of iodide ions in neutral medium which are converted into I2 only. Calcualte total volume (mL) of the initial KMnO4 solution. 6. If s and p-orbital mixing (s-p mixing) is operative for all species given, then how many following species is/are paramagnetic in nature ? O 2 , N2, C2, CN–, B2, O 22 − + Space for Rough Work E-24/36 1001CJA102922014  Enthusiast Course/Phase-TOAS, TNAS & TAAS/03-04-2022/Paper-1 ALLEN PART-3 : MATHEMATICS SECTION-I (i) : (Maximum Marks: 32) This section contains EIGHT (08) 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 : –1 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 –1 marks. 1. Consider ƒ : R → R satisfying the equation ƒ(x + y) = ƒ(x – y) + ƒ(x).ƒ(y) ∀ x, y ∈ R. Identify the correct statement(s) (A) ƒ(2014) + ƒ(2015) = ƒ(2016) π (B) sin–1(ƒ(2)) + cos–1(ƒ(3)) = 2 (C) ƒ(2014) – ƒ(2015) = ƒ(2016) π (D) sin–1(ƒ(3)) + cos–1(ƒ(2)) = 2 Space for Rough Work 1001CJA102922014 E-25/36  Target : JEE (Main + Advanced) 2023/03-04-2022/Paper-1 ALLEN 2. ABC is a triangle in which ∠C = 2∠B. D is a point on BC such that AD bisects ∠BAC and AC = BD. Then which of the following is/are true – √5 (A) cosB + cosC = 2 1 (B) cos B − cos C = 2 sin A (C) = 1 sin C – sin A √ 5+1 (D) = sin C 4 3. m For the figure given below if tan α = , where m and n are relatively prime positive integers then n (A) m + n = 463 (B) n – m = 122 (C) 2m – n = 41 (D) m + n = 465 Space for Rough Work E-26/36 1001CJA102922014  Enthusiast Course/Phase-TOAS, TNAS & TAAS/03-04-2022/Paper-1 ALLEN 4. ∞ tr The value of lim (1 − t) ∑ is t→1 − r 1 1 + tr = (A) ℓn2 (B) ℓn3 2e 1 (C) ℓn ( ) (D) 1+e 2 5. Which of the following are even functions in their domain ( 2 sin x − 1) (sin 2 x − 1) (A) y(x) = 2 sin x − 1) ( (B) y(x) = ƒogoh(x) (where ƒ is neither even nor odd, g is even and h is an odd function, all functions are defined for all x ∈ R) (C) y(x) is defined for all real x and y(x) =|x – 1| for x ∈ [0,2], and y(x) is periodic with period 2. 1 + ex − 1 cos(1 − x) + cos(1 + x)) + e2x ( (D) y (x) = ex Space for Rough Work 1001CJA102922014 E-27/36  Target : JEE (Main + Advanced) 2023/03-04-2022/Paper-1 ALLEN 1 x2 − 1 1 2x 1 2x 2π 6. For the equation cos − ( ) + sin − ( ) + tan − ( ) = , x2 + 1 x2 + 1 x2 − 1 3 which of the following is/are correct. (A) The number of solution is 2 (B) It has at least one irrational solution (C) The sum of solution is positive (D) The sum of solution is negative 7. In the diagram shown, AB and AC are equal sides of an isosceles triangle ABC. The equilateral triangle DEF is inscribed. If ∠ADF be α, ∠BED be β and ∠CFE be γ, then CORRECT relation is/are α+γ β+γ α−γ β−γ (A) β= (B) α= (C) β= (D) α= 2 2 2 2 8. If α (α > 0) is a root of x11 – x10 + x8 – x7 + x5 – x4 + x2 – x – 20 = 0 then α12 is greater than (A) 59 (B) 61 (C) 58 (D) 57 Space for Rough Work E-28/36 1001CJA102922014  Enthusiast Course/Phase-TOAS, TNAS & TAAS/03-04-2022/Paper-1 ALLEN SECTION-I (ii) : (Maximum Marks: 12) This section contains TWO (02) List-Match sets. Each List-Match set has TWO Multiple Choice Questions. Each List-Match set has two lists : List-I and List-II List-I has Four entries (I), (II), (III) and (IV) and List-II has Six entries (P), (Q), (R), (S), (T) and (U) Four options are given in each Multiple Choice Question based on List-I and List-II and ONLY ONE of these four options satisfies the condition asked in the Multiple Choice Question. Answer to each question will be evaluated according to the following marking scheme : Full Marks : +3 If ONLY the option corresponding to the correct combination 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 9. Match List-I with List-II and select the correct answer using the code given below the list. List-I List-II Equations No. of solutions π 3π (I) x2tanx = 1 x∈( , ) (P) 5 2 2 (II) 2cosx = |sinx|, x ∈ [0, 2π] (Q) 1 If ƒ(x) is a polynomial of degree 5 with real coefficients such (III) (R) 3 that ƒ(|x|) = 0 has 8 real roots then, roots of ƒ(x) = 0 (IV) 7|x| (|5 – |x||) = 1 (S) 4 (T) 0 (U) 10 Which of the following is the only CORRECT combination ? (A) I → P (B) II → Q (C) III → R (D) IV → S Space for Rough Work 1001CJA102922014 E-29/36  Target : JEE (Main + Advanced) 2023/03-04-2022/Paper-1 ALLEN 10. Match List-I with List-II and select the correct answer using the code given below the list. List-I List-II Equations No. of solutions π 3π (I) x2tanx = 1 x∈( , ) (P) 5 2 2 (II) 2cosx = |sinx|, x ∈ [0, 2π] (Q) 1 If ƒ(x) is a polynomial of degree 5 with real coefficients such (III) (R) 3 that ƒ(|x|) = 0 has 8 real roots then, roots of ƒ(x) = 0 (IV) 7|x| (|5 – |x||) = 1 (S) 4 (T) 0 (U) 10 Which of the following is the only INCORRECT combination ? (A) I → R (B) II → S (C) III → P (D) IV → Q Space for Rough Work E-30/36 1001CJA102922014  Enthusiast Course/Phase-TOAS, TNAS & TAAS/03-04-2022/Paper-1 ALLEN 11. Match List-I with List-II and select the correct answer using the code given below the list. List-I List-II (I) Number of solutions of 4(sin6θ + cos6θ) = 10 – 18sinθcosθ in [0, 3π], is (P) 1 Number of possible pairs (x, y) satisfying x2 – 6x + 10 – sin2y = 0, (II) (Q) 2 where y ∈ [0, 2π] and x ∈ R, is 1 (III) Number of integral values of x satisfying sin x < in [0, 2π], is (R) 3 2 (IV) Number of solutions satisfying tanx + secx = 2cosx in [0, 4π], is (S) 4 (T) 5 (U) 6 Which of the following is the only CORRECT combination ? (A) I → Q (B) I → R (C) II → P (D) II → R Space for Rough Work 1001CJA102922014 E-31/36  Target : JEE (Main + Advanced) 2023/03-04-2022/Paper-1 ALLEN 12. Match List-I with List-II and select the correct answer using the code given below the list. List-I List-II (I) Number of solutions of 4(sin6θ + cos6θ) = 10 – 18sinθcosθ in [0, 3π], is (P) 1 Number of possible pairs (x, y) satisfying x2 – 6x + 10 – sin2y = 0, (II) (Q) 2 where y ∈ [0, 2π] and x ∈ R, is 1 (III) Number of integral values of x satisfying sin x < in [0, 2π], is (R) 3 2 (IV) Number of solutions satisfying tanx + secx = 2cosx in [0, 4π], is (S) 4 (T) 5 (U) 6 Which of the following is the only CORRECT combination ? (A) III → S (B) III → U (C) IV → T (D) IV → S Space for Rough Work E-32/36 1001CJA102922014  Enthusiast Course/Phase-TOAS, TNAS & TAAS/03-04-2022/Paper-1 ALLEN SECTION-II : (Maximum Marks: 18) This section contains SIX (06) 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. n 1 49 1. Let S n ∑ tan − then cot(nlim S ) is equal to →∞ n = k=0 49k2 + 63k + 57 π π 2. In a triangle ABC, medians AD and CE are drawn. If AD=5, ∠DAC = and ∠ACE = then the 8 4 area of the triangle ABC is equal to ⎛ sin 2 x ⎞ sin(sin x) − sin x π2 − 3. If lim × =. Then value of b + c is x→0 + ⎝[ x x2 ⎠ ax 5 + bx 3 + c 12 π ]+ π2 (Where [.] denotes greatest integer function) Space for Rough Work 1001CJA102922014 E-33/36  Target : JEE (Main + Advanced) 2023/03-04-2022/Paper-1 ALLEN −−−−− π 4. If the value of xlim x 2 tan(ℓn (√cos )) is equal to −kπ 2 , then k is equal to →∞ x 1 10 10 10 5. Let f (θ) = 9 ((1 + tan θ) + (2 + tan θ) +.... (20 + tan θ) ) − 20 tan θ. The value of tan θ lim f (θ) is θ→ π 2 − 6. The number of solution of equation 2sin 2x + sinx (1 – 2cos 2x) – 4 = 0 in the interval (0, π) : Space for Rough Work E-34/36 1001CJA102922014  Enthusiast Course/Phase-TOAS, TNAS & TAAS/03-04-2022/Paper-1 ALLEN Space for Rough Work 1001CJA102922014 E-35/36  Target : JEE (Main + Advanced) 2023/03-04-2022/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 Space for Rough Work Corporate Office : ALLEN CAREER INSTITUTE, “SANKALP”, CP-6, Indra Vihar, Kota (Rajasthan) INDIA 324005 +91-744-2757575 [email protected] www.allen.ac.in E-36/36 Your Target is to secure Good Rank in JEE 2023 1001CJA102922014