JEE (Main + Advanced) Review Test 10-07-2022 PDF

Test Pattern (1001CJA102922038) )1001CJA102922038) English CLASSROOM CONTACT PROGRAMME JEE(Advanced) REVIEW TEST...

Test Pattern (1001CJA102922038) )1001CJA102922038) English CLASSROOM CONTACT PROGRAMME JEE(Advanced) REVIEW TEST (Academic Session : 2022 - 2023) 10-07-2022 JEE(Main+Advanced) : ENTHUSIAST COURSE (PHASE : TOAS) Time : 3 Hours PAPER-1 Maximum Marks : 192 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 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) 2023/10-07-2022/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–m 2 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-2/24 1001CJA102922038  Enthusiast Course/Phase-TOAS/10-07-2022/Paper-1 ALLEN BEWARE OF NEGATIVE MARKING PART-1 : PHYSICS SECTION-I : (Maximum Marks: 40) This section contains TEN (10) 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. A charge particle q0 is kept at centre of 2 non conducting hemi spherical shell of radius R1 & R2. If E1 & E2 is electric field at surfaces of A & B then ϕ1 (A) Ratio of flux = 1. (B) E1 = E2 ϕ2 −−− R1 E2 (C) = √ (D) E1 ≠ E2 R2 E1 Space for Rough Work 1001CJA102922038 E-3/24  Target : JEE (Main + Advanced) 2023/10-07-2022/Paper-1 ALLEN 2. A ray of light tangentialy incident on outer sphere. (A) Net deviation suffered by ray is 240°. (B) Ray will never enter inside inner sphere. (C) Ray is incident tangentialy on inner sphere. (D) Angle made by ray with normal inside inner sphere is 30°. 3. Variation of magnification of convex lens vs image distance for real objects is shown. Choose correct statement. 1 (A) f is equal to intercept of V-axis. (B) f is equal to of graph. slope (C) f is equal to slope of graph (D) magnitude of intercept on m axis is 1. 4. Diagram shows a capacitor connected with a constant current source. Choose the correct option(s) : (A) the rate of change of voltage across the capacitor in the circuit of figure from top to bottom 166.7 V/s. (B) the rate of change of voltage across the capacitor in the circuit of figure from top to bottom –166.7 V/s. (C) the capacitor's voltage 10 milliseconds after power is switched on is 1.667V. (D) the capacitor's voltage 10 milliseconds after power is switched on is 2.667V. Space for Rough Work E-4/24 1001CJA102922038  Enthusiast Course/Phase-TOAS/10-07-2022/Paper-1 ALLEN 5. A long metallic pipe with internal diameter d is pointing directly downwards. Water is slowly dripping from a nozzle at its lower end, see fig. Water can be considered to be electrically conducting; its surface tension is σ and its density is ρ. A droplet of radius r hangs below the nozzle. The radius grows slowly in time until the droplet separates from the nozzle due to the free fall acceleration g. Always assume that d z (C) z > 120° (D) x > y cold CrO3 5. −−−−−−−− → A −−−→ B alkaline KnO4 H A and B are :- (A) (B) (C) (D) No formation of A and B 6. Products formed by P & Q can not be differentiated by: (A) 2, 4 DNP (B) Lucas reagent (ZnCl2) conc. HCl (C) NaHSO3 (D) Fehlings solution Space for Rough Work 1001CJA102922038 E-13/24  Target : JEE (Main + Advanced) 2023/10-07-2022/Paper-1 ALLEN 7. Which of the following reaction(s) produce aldehyde as a product : (A) (B) i SnCl2 ( ) / HCl (C) CH 3 − CN −−−−−−−−− → ii) H 3 O ( + H + / H2O (D) C H 3 MgBr + CH 3 − C ≡ N −−−−−− → 8. Which of the following compound can only form + HCHO on ozonolysis : (A) (B) (C) (D) Space for Rough Work E-14/24 1001CJA102922038  Enthusiast Course/Phase-TOAS/10-07-2022/Paper-1 ALLEN 9. Which of the following statement(s) is/are INCORRECT? (A) H2S when passed in sodium nitroprussiden solution then purple complex is formed (B) H2S reacts with H2SO3 solution and produce sulphur , in this reaction H2S acts as oxidizing agent (C) NaNO2 produce a basic gas on reaction with Zn dust + KOH solution (D) NaNO2 give red coloured product when treated with sulphanilic acid and dil. CH3COOH followed by the addition of 1-nepthylamine. 10. Light from a discharge tube containing hydrogen atom fall on the surface of a piece of sodium. The kinetic energy of a fastest photo electron emitted from sodium is 0.73 eV and work function for sodium is 1.82 eV. Collector plate is connected to +ve terminal of battery having voltage 2 volts. Which of the following are true regarding above experiment : (A) The energy of photon causing the photoelectric effect is 2.55 eV. (B) Hydrogen atoms electron undergoes a transition from n = 4 to n = 2 to show given photoelectric effect. (C) Change in angular momentum of the electron in the hydrogen atom will be h/π. (D) Kinetic energy of photoelectron at emitter plate will be 0.73 eV and at collector plate will be 2.73 eV. Space for Rough Work 1001CJA102922038 E-15/24  Target : JEE (Main + Advanced) 2023/10-07-2022/Paper-1 ALLEN 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. If the number of following chemical species which form N2O with dilute HNO3 is x. Then predict the values of x. Ag , Au , Fe+2 , Zn , S , BaSO3 , Hg , CaCO3 , I2 2. If the number of metal-metal bond, number of terminal CO ligand and number of bridging ligand in Co2(CO)8 (solid) are x, y & z respectively. Find (x + y + z). 3. A fish swims in water at 300 K. In the process fish released 3000 Joule energy to water. 2 If ΔSfish = − × 10 3 J /K − for every joule of energy released by fish, find ΔSuniverse in the process (in J/K) 3 4. Determine degree of dissociation (in %) of 0.05 M NH­3 at 25ºC in a solution of pH = 11. Space for Rough Work E-16/24 1001CJA102922038  Enthusiast Course/Phase-TOAS/10-07-2022/Paper-1 ALLEN 5. The vapour pressures of two pure liquids A and B which form an ideal solution are 300 and 800 Torr, respectively, at temperature T. A liquid solution of A and B for which the mole fraction of A is 0.60 is contained in a cylinder closed by a piston on which the pressure can be varied. The solution is slowly vapourized at temperature T by decreasing the applied pressure. Find total vapour pressure (in torr) when last drop of liquid is remaining ? 6. Find sum of the oxidation number of Iodine in (X) and (Z). KI + conc. H2SO4 → (X) iodine containing product + other product 7. 1 mole How many (x) moles of HI consumed in the given reaction ? 8. How many compounds will give positive Fehling test : (i) CH3CHO (ii) PhCHO (iii) (iv) (v) (vi) (vii) (viii) CH ≡ CH Space for Rough Work 1001CJA102922038 E-17/24  Target : JEE (Main + Advanced) 2023/10-07-2022/Paper-1 ALLEN PART-3 : MATHEMATICS SECTION-I : (Maximum Marks: 40) This section contains TEN (10) 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. Identify the correct statement(s) : (Where 'C' is constant of integration) 1/5 ( x 5 − x) 5 1 6/5 (A) ∫ dx = (1 − ) + C x6 24 x4 1/5 ( x 5 − x) 5 1 6/5 (B) ∫ dx = − (1 − ) + C x6 24 x4 ( tan x + 1) 2 (C) ∫ tan 3 x + tan 2 x + tan x + 1) dx = ( + C 2 1 2 (D) ∫ ( tan 3 x + tan 2 x + tan x + 1) dx = sec x + tan x + C 2 Space for Rough Work E-18/24 1001CJA102922038  Enthusiast Course/Phase-TOAS/10-07-2022/Paper-1 ALLEN 1 n 2. Given I n = ∫ ( 1 − x 2 ) dx (n = 0, 1, 2,...), then which of the following is/are true ? 0 In 1 + In 1 + 2n + 2 (A) is independent of n (B) = In In 2n + 3 k 2r (C) Ik = ∏( ),( k ∈ N) (D) there exist some n (n ∈ N) for which In ≥ 1 r=1 2r + 1 −−−−−−−− 3. ∫ √ 1 + cosecx dx equals - (where C is integration constant) 1 −−−− – 1 (A) 2sin − √ +sin x C (B) √ 2cos − √cos x −−−− + C (C) C − 2sin − 1 (1 − 2 sin x) (D) cos–1(1 – 2sinx) + C n−1 n−1 n n 4. Let An = ∑ and B n = ∑ for n = 1, 2, 3,..., then which k=0 k2 + n 2 +( n + 2)k + n + 1 k=0 n 2 + kn + k2 of the following is/are true ? π π (A) An < Bn (B) An > Bn (C) An < (D) Bn > 3 9 2x 2n + x + 2 5. If f (x) = nlim , then which of the following statement(s) holds good ? →∞ x 2n − x 2 + 3 (A) f(x) is continuous at x = 1 (B) f(x) is discontinuous at x = 1 (C) lim f (x) exists finitely (D) lim f (x) does not exist x→2 x→2 6. The function f(x) = [cosx] cosx in (0, 2π) - (A) is discontinuous at two points (B) is non differentiable at two points (C) has range (0, 1] (D) is such that f(f(x)) + 1 = 0 has no real roots Space for Rough Work 1001CJA102922038 E-19/24  Target : JEE (Main + Advanced) 2023/10-07-2022/Paper-1 ALLEN 7. Let line L is normal to parabola y2 = 4x and line L intersect the parabola at A and B. If point P(α, β) is point of intersection of tangents at A and B then which of the following is/are correct ? (A) Locus of point P is symmetric w.r.t. x axis (B) Locus of point P is symmetric w.r.t. y axis (C) If α, β ∈ I then total number of possible ordered pair (α, β) is 2 (D) If α, β ∈ I then total number of possible ordered pair (α, β) is 4 ex e − x Let f(x) = ax9 + bsinx + cx2 sgn(x) + − 8. be defined on set of real number (where a > 0, b, c ∈ R). ex +e − x If f(–5) = 5, f(–2) = –3, then the minimum number of zeroes of the equation f(x) = 0, is (A) 1 (B) 2 (C) 3 (D) 5 f ′′ (x) g′′ (x) 9. Given f and g are twice differentiable functions and f ′ ≠ 0, g ′ ≠ 0. If f(x) g(x) = 1, then − f ′ (x) g′ (x) is equal to : − 2g′ (x) g′ (x) 2f ′ (x) − f ′ (x) (A) (B) (C) (D) g(x) g(x) f (x) f (x) q 7 + 6x 13 p(1 − x 13 ) 3 10. If ∫ 3 −−−−−−− dx = − r + C where p, q, r ∈ N and C is the constant of integration, then √ 17 − x 30 x 2x 3 (A) p = 3 (B) p = 7 (C) r – q = 12 (D) r – q = 8 Space for Rough Work E-20/24 1001CJA102922038  Enthusiast Course/Phase-TOAS/10-07-2022/Paper-1 ALLEN 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 π ex dx 1. If ∫ −−−−− = A and ∫ e sin x ( | | + e | cos x| ) dx is equal to λA, then the value of λ is - 1 √ − 2x 0 0 1 3 −−− 3 −−−−− 2 −−−−−− 2. The value of ∫ √ 2x− 3x − + x 1 dx is - 0 ( 3x 2 + 2x)dx 1 1 3. If ∫ = tan − (g(x)) + C , then the value of (g(1) + g(0)) is x 6 + 2x 5 + x 4 + 2x 3 + 2x 2 + 5 2 f (5x) − 3f (3x) + 2f (2x) 4. Let f(x) be a twice differentiable function such that f ″(0) = 2, then the value of lim is x→0 x2 Space for Rough Work 1001CJA102922038 E-21/24  Target : JEE (Main + Advanced) 2023/10-07-2022/Paper-1 ALLEN 1 –2x 5. Let g : [ , 1] → (0, ∞) , g(x) = e f(x), where g(x) is non constant decreasing and differentiable function 2 and g ( 1 ) = 1. Then the value of is 2 e [where [x] denotes the greatest integer less than or equal to real number x] 6. The number of values of x, x ∈ [–2, 3] where f(x) = [x2] sin(πx) is discontinuous, is (where [.] denotes greatest integer function) - 7. 1x 1 1y 1 1z π 1 2 2 Let tan − = tan − = tan − = , then the value of (x + y + z 2 − x 2 y2 z 2 ) , is 2 3 7 2 2x 2 + 7x + 3 8. The maximum value of f (x) = , is 2x 2 + x + 1 Space for Rough Work E-22/24 1001CJA102922038  Enthusiast Course/Phase-TOAS/10-07-2022/Paper-1 ALLEN Space for Rough Work 1001CJA102922038 E-23/24  Target : JEE (Main + Advanced) 2023/10-07-2022/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-24/24 Your Target is to secure Good Rank in JEE 2023 1001CJA102922038