JEE Advanced 2022 Paper 1 PDF

General Instructions 1. The question paper consists of 3 Subject (Subject I: Physics, Subject II: Chemistry, Subject III: Mathematics). Each Part has three sections (Section 1, Section 2 & Section 3). 2. Section 1 contains 6 Multiple Choice Questi...

General Instructions 1. The question paper consists of 3 Subject (Subject I: Physics, Subject II: Chemistry, Subject III: Mathematics). Each Part has three sections (Section 1, Section 2 & Section 3). 2. Section 1 contains 6 Multiple Choice Questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE CHOICE is correct. Section 2 contains 6 Multiple Correct Answers Type Questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONE OR MORE THAN ONE CHOICE is correct. Section 3 contains 6 Numerical Value Type Questions. The answer to each question is a NUMERICAL VALUE. For each question, enter the correct numerical value of the answer. If the answer is a decimal numerical value, then round-off the value to TWO decimal places. If the answer is an Integer value, then do not add zero in the decimal places. In the OMR, do not bubble the  sign for positive values. However, for negative values, Θ sign should be bubbled. (Example: 6, 81, 1.50, 3.25, 0.08) 3. For answering a question, an ANSWER SHEET (OMR SHEET) is provided separately. Please fill your Test Code, Roll No. and Group properly in the space given in the ANSWER SHEET.  Vidyamandir Classes: Innovating For Your Success MARKING SCHEME SECTION - 1 (Maximum Marks: 18)  This section contains SIX (06) Multiple Choice Questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE CHOICE is correct.  Answer to each question will be evaluated according to the following marking scheme: Full Marks: +3 If only (all) the correct option(s) is(are) chosen Zero Mark: 0 if none of the options is chosen (i.e. the question is unanswered) Negative Marks: –1 In all other cases. SECTION - 2 (Maximum Marks: 24)  This section consists of SIX (06) Questions. Each question has FOUR options. ONE OR MORE THAN ONE of these four option(s) is(are) 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 Mark: 0 if none of the options is chosen (i.e. the question is unanswered) Negative Marks: –2 In all other cases. SECTION – 3 (Maximum Marks: 24)  This section contains 6 Numerical Value Type Questions. The answer to each question is a NUMERICAL VALUE. For each question, enter the correct numerical value of the answer. If the answer is a decimal numerical value, then round-off the value to TWO decimal places. If the answer is an Integer value, then do not add zero in the decimal places. In the OMR, do not bubble the  sign for positive values. However, for negative values, Θ sign should be bubbled. (Example: 6, 81, 1.50, 3.25, 0.08)  Answer to each question will be evaluated according to the following marking scheme: Full Marks: +4 If ONLY the correct Integer value is entered. There is NO negative marking. Zero Marks: 0 In all other cases. VMC | JEE-2022 | Paper-1 2 JEE Advanced-3 | Code A  Vidyamandir Classes: Innovating For Your Success SUBJECT I : PHYSICS 66 MARKS SECTION 1 SINGLE CORRECT ANSWERS TYPE This section contains 06 Multiple Choice Questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE CHOICE is correct. 1. A part of a larger circuit is shown in the figure. Both batteries shown have internal resistance 1  each. If the points A and B are equipotential and a current 2 A flows from A towards B, then the emf E (in Volts) is: (A) 14 (B) 16 (C) 18 (D) 22 2. In the circuit shown, the battery is ideal, and both capacitors are initially uncharged. If the switch S is closed, the current through the switch immediately afterwards, and the current through it after a long time is respectively: V 3V 3V V 3V 3V (A) , (B) , (C) , zero (D) zero, 3R R R 3R R R 3. A small dipole is fixed at the origin with its moment pointing in the +X direction. Consider two identical circular disc shaped imaginary surfaces with their centres at two points A and B on the X- axis equidistant from the origin, shown in the figure. The surfaces are perpendicular to the X-axis. The electric flux through the surfaces is  A and  B respectively. The sign of flux is taken positive if it crosses a surface towards the +X direction and taken negative if it crosses a surface towards the –X direction. Which of these options is correct? (A)  A  0 and  B  0 (B)  A  0 and  B  0 (C)  A  0 and  B  0 (D)  A  0 and  B  0 VMC | JEE-2022 | Paper-1 3 JEE Advanced-3 | Code A  Vidyamandir Classes: Innovating For Your Success 4. In the given circuit, all three capacitors are initially uncharged. If a battery of emf E is connected between the points A and B, the potential difference across the capacitor of capacitance 2C at steady state becomes: E 2E 3E 3E (A) (B) (C) (D) 4 5 5 4 5. A non-conducting ball carrying a charge Q is placed on a smooth horizontal non-conducting table and tied to a spring of spring constant k whose other end is fixed. Initially the spring is unstretched. Now, another identical ball, also carrying charge Q , is slowly moved closer from a very large initial distance directly towards the first ball until it reaches the position initially occupied by the first ball. If the work done in the process is proportional to QM k N , then: (The balls are small enough that the electrostatic force between them can be calculated by assuming that they are point charges) 4 2 1 2 4 1 (A) M  2, N  (B) M ,N  (C) M  , N 1 (D) M  ,N  3 3 3 3 3 3 R 6. The region r  of a non-conducting sphere (r denotes the distance from the centre of the sphere) is 2 R r uncharged, and the region  r  R is charged with charge density   r   0   , where  0 is a 2 R R constant. In the region  r  R , the electric field E  r  varies as: 2   R4    R4  (A) E r   0  r2  2  (B) E r   0  r2   40 R  4 r  40 R  16 r 2  0  3 R 4  0  3 R 4  (C) E r    r   (D) E  r   r   160 R 2  4 r  160 R 2  16 r  SPACE FOR ROUGH WORK VMC | JEE-2022 | Paper-1 4 JEE Advanced-3 | Code A  Vidyamandir Classes: Innovating For Your Success SECTION 2 MULTIPLE CORRECT ANSWERS TYPE This section consists of 06 Questions. Each question has FOUR options. ONE OR MORE THAN ONE of these four option(s) is(are) correct answer(s). 7. Two thin conducting spherical shells of radii R and 3R are fixed concentrically, and given total charge –Q and +Q respectively. Which of these options is/are correct? (A) The electric field at a point at a distance 2R from the their common centre has magnitude Q and is directed radially inward 16πε0 R 2 (B) The electric field inside the inner shell is zero Q (C) The potential at their common centre is  6πε0 R (D) The potential of the outer shell is zero 8. The separation between the plates of an uncharged capacitor of capacitance C is d. Initially, there is air (dielectric constant 1) between the plates. A slab of a material of dielectric constant 2 and d thickness is introduced inside the capacitor as shown. Now, the capacitor is connected across the 2 terminals of a battery of emf V. After the capacitor is completely charged: 4V (A) The electric field inside the slab is 3d 2V (B) The electric field inside the slab is 3d 2 (C) The potential energy stored in the capacitor is CV 2 3 1 (D) The potential energy stored in the capacitor is CV 2 3 9. Two small balls carrying charge +q each are fixed to the bottom of an empty non-conducting vessel, separated by a distance a as shown. A third small ball of density  0 , mass m and carrying the same 3 charge +q floats in equilibrium on the perpendicular bisector of the other two balls at a height a 2 above them, with all three balls being in the same vertical plane. Now, the vessel is filled with a liquid of density  and dielectric constant . If the floating ball remains in equilibrium at the same position as before while being fully submerged inside the liquid, which of these options is/are correct? VMC | JEE-2022 | Paper-1 5 JEE Advanced-3 | Code A  Vidyamandir Classes: Innovating For Your Success 3 q2 3 q2 20 0 (A) mg  (B) mg  (C)  (D)  160 a 2 40 a2 0   0   10. An insulating hemispherical shell of radius R is fixed and charged uniformly over its curved surface with charge per unit area . The flat, circular base of the shell is uncharged. Let O be the centre of the circular base. Which of these options is/are correct? (A) The circular base is an equipotential surface (B) The electric field at O is zero (C) The work done in moving a point charge +q from Rq infinity to O is 2 0 (D) The electric potential at a point in the same plane as the circular base, and at a distance 2R R from O, is 4 0 11. Three identical uncharged capacitors, each of capacitance C, are connected in a circuit with an ideal battery and an ammeter of resistance R as shown. Initially both the switches S1 and S2 are open. Now, S1 is closed. After the current in the ammeter has become negligible, S2 is closed while keeping S1 closed. Which of these options is/are correct? V (A) The current in the ammeter immediately after S1 is closed is 4R 1 (B) The work done by the battery during the time S1 is closed and S2 is open is CV 2 2 V (C) The current in the ammeter immediately after S2 is closed is 14 R 1 (D) The work done by the battery over a long time after S2 is closed is CV 2 6 12. Three ideal batteries of emf E1 , E2 and E3 and three resistances r1 , r2 and r3 are connected as shown. Currents I1 , I 2 and I 3 flow in the three branches along the directions indicated. Which of these options is/are correct? [Given : E1  4V , E2  4V , E3  2V , r1  1, r2  2 , r3  2  ] (A) I 3  0.75 A (B) VP  VQ  4V (C) VP  VQ  3.5V (D) I1  0.5V VMC | JEE-2022 | Paper-1 6 JEE Advanced-3 | Code A  Vidyamandir Classes: Innovating For Your Success SECTION 3 NUMERICAL VALUE TYPE QUESTIONS This section has 06 Questions. The answer to each question is a NUMERICAL VALUE. For each question, enter the correct numerical value of the answer. If the answer is a decimal numerical value, then round-off the value to TWO decimal places. If the answer is an Integer value, then do not add zero in the decimal places. In the OMR, do not bubble the  sign for positive values. However, for negative values, Θ sign should be bubbled. (Example: 6, 81, 1.50, 3.25) 13. The battery and the voltmeter in the given circuit are ideal. The voltmenter reads –1 V. The resistance R is equal to ___________ . 14. All capacitors in the network shown are initially uncharged. If a battery of emf E is connected between the points M and O, and the potential difference between the points N and P at steady state is V VNP , the ratio NP is _______________. E 15. A capacitor of capacitance C is charged to a potential difference V0 and then connected to two resistances R and 4R as shown. The total resistance of the branch containing the capacitor is negligible. After the switch is closed, the total heat energy dissipated in the resistance R until the   capacitor is completely discharged is X CV02. The value of X is ____________. 16. Two thin circular rings A and B, both of radius R, are fixed coaxially with a distance 3R between their centres and charged uniformly with total charge +Q and –Q respectively. A particle of mass m carrying charge +q is released from the centre of the ring A. If the particle reaches the centre of ring B 1/2   Q q  with velocity  X    , then X is ________________.   40 R m   VMC | JEE-2022 | Paper-1 7 JEE Advanced-3 | Code A  Vidyamandir Classes: Innovating For Your Success 17. Suppose we have an unlimited number of identical bulbs. Each bulb consumes power 4 W if it is operated at a potential difference 40 V. We also have a battery of emf 60 V and internal resistance 8 . The minimum number of bulbs that must be connected in parallel across this battery such that each bulb consumes power less than 4 W is ___________. 18. An insulating sphere of radius R is fixed with its centre at the origin of coordinates and charged such R that the region r  (r denotes the distance from the centre of the sphere) has uniform charge 2 R density 2 and the region  r  R has uniform charge density . A small dipole of dipole moment p 2  3R  is initially located at the point A  ,0  on the X-axis with its moment vector pointing in the +X  2   3R  direction. If the work done in slowly taking the dipole to the point B  0,   along a circular path  2  centred at the origin, such that the dipole moment vector always points in the +X direction, 1  pR  is   , then N is ________. N  0  SPACE FOR ROUGH WORK VMC | JEE-2022 | Paper-1 8 JEE Advanced-3 | Code A  Vidyamandir Classes: Innovating For Your Success SUBJECT II : CHEMISTRY 66 MARKS SECTION 1 SINGLE CORRECT ANSWERS TYPE This section contains 06 Multiple Choice Questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE CHOICE is correct. 1. Which of the following concentration profile is valid for the given sequential chemical reactions ? X  Y  Z 1 k 2 k k1  0.5min 1 ; k 2  0.05min 1 (A) (B) (C) (D) 2. Which of the following figure correctly represent fractional distillation of a mixture of ethanol and propanol ? (A) (B) (C) (D) VMC | JEE-2022 | Paper-1 9 JEE Advanced-3 | Code A  Vidyamandir Classes: Innovating For Your Success 3. Which of the following is NOT correctly matched ? (A) Buckminster fullerene (C-60 molecule) Truncated icosahedron (B) B-12 molecule Icosahedron (C) ZnS-cubic Zinc blende arrangement (D) Diamond-cubic B.C.C arrangement 4. Gas phase thermal decomposition of di-tert-butyl peroxide is obeying first order kinetics. (CH3 )3 C  O  O  C(CH3 )3 (g)  2(CH3 )2 C  O(g)  C2H6 (g) Total pressure at completion of the reaction is 360 torr and it is 240 torr after 10 minutes from start of the reaction, then rate of disappearance of (CH3 )3 C  O  O  C(CH 3 )3 after 30 min is : [in torr / min] (A) 1.04 (B) 2.87 (C) 6.93 102 (D) 0.14 5. Vapour pressure of pure water at 25°C is 80 torr and that of an aqueous solution is 75 torr at the same temperature. If K f for water is 1.86K kg mol1 then freezing point of the solution is : (A)  6.48C (B)  6.88C (C)  6.99C (D)  6.27C 6. What would be percentage packing efficiency of the smaller cubes, formed within a F.C.C arrangement by joining centres of the tetrahedral voids ? [Take (0.225)3  0.0114, (0.414)3  0.0710, (0.732)3  0.392, (1.414)3  2.83,  / 3  1.05] (A) 12.22% (B) 48.02% (C) 58.07% (D) 23.58% SPACE FOR ROUGH WORK SECTION 2 MULTIPLE CORRECT ANSWERS TYPE This section consists of 06 Questions. Each question has FOUR options. ONE OR MORE THAN ONE of these four option(s) is(are) correct answer(s). k1 k3 7. A B C at 25°C k2 k4 k1  2.5min 1, k 2  5.5min 1, k3  10.8min 1 and k 4  4.7min 1 The Arrhenius factor is 1012 min 1 for each reaction then : (A) A  B is an endothermic process (B) B  C is an endothermic process (C) Activation energy for the conversion B  A is higher than the activation energy for the conversion B  C (D) Overall order of the reaction is 1 VMC | JEE-2022 | Paper-1 10 JEE Advanced-3 | Code A  Vidyamandir Classes: Innovating For Your Success 8. Select the correct statements regarding colligative properties of ideal aqueous solutions : (A) Colligative properties are driven by entropy factor (B) Colligative properties increases with mole fraction of water (C) Colligative properties are independent of amount of the solution (D) Colligative properties are independent of degree on ionization of the solute dissolved in water 9. Which of the following is/are correct for a F.C.C unit cell ? (A) It has effectively four constituent particle per unit cell (B) It has effectively three voids per particle per unit cell (C) Packing efficiency is 0.74 (D) It has tetrahedral, octahedral and cubic voids 10. Acid catalysed hydrolysis of (+) sucrose is a first order reaction. It gives a mixture of (+) glucose and () fructose as the product of hydrolysis. If angle of rotation of the solution for a plane polarised light is  32 at t  0 and it is 12 at t   and  20 at t  50 minutes then : [Take log10 2  0.30, log10 5  0.70, log10 11  1.05, log10 3  0.48] (A) Half life of the reaction is 100 minutes (B) The reaction involve inversion of optical nature of the solution (C) Solution will be optically inactive after 190 minutes (D) After first half life solution is dextrorotatory 11. Boiling point of an aqueous solution of benzoic acid is 101°C. A solution of equal molality was prepared by dissolving benzoic acid in benzene. Then identify correct statements from the following: [Given that for water Kb  0.83k kg mol1, Kf  1.86k kg mol1 and for benzene Kb  2.0k kg mol1 and boiling point is 75°C] (A) Freezing point of the aqueous solution of benzoic acid is  2.24C (B) Boiling point of the solution of benzoic acid in benzene is 77.4°C (C) Observed molar mass of benzoic acid in water is equal to its value in presence of benzene as the solvent (D) Observed molar mass of benzoic acid in water is less than to its value in presence of benzene as the solvent 12. INCORRECT statements regarding defects in crystalline solids are : (A) Frenkel and Schottky defect are stoichiometric defects (B) Metal excess defect always cause decrease in density of the ionic solid and increase in its electrical conductivity (C) Metal deficiency defects always cause increase in density and electrical conductivity of the ionic solids (D) Impurity defects creates cationic vacancies in the ionic solids SPACE FOR ROUGH WORK VMC | JEE-2022 | Paper-1 11 JEE Advanced-3 | Code A  Vidyamandir Classes: Innovating For Your Success SECTION 3 NUMERICAL VALUE TYPE QUESTIONS This section has 06 Questions. The answer to each question is a NUMERICAL VALUE. For each question, enter the correct numerical value of the answer. If the answer is a decimal numerical value, then round-off the value to TWO decimal places. If the answer is an Integer value, then do not add zero in the decimal places. In the OMR, do not bubble the  sign for positive values. However, for negative values, Θ sign should be bubbled. (Example: 6, 81, 1.50, 3.25) 13. Thermal decomposition of gaseous HI obey following rate law 2HI(g)  H2 (g)  I2 (g) k Rate  k PHI 2 (g) If the reaction starts with PHI(g)  150 torr then total pressure at half-life of the reaction will be : [in torr] 14. Boiling point of a liquid X is 127°C at 1 atm pressure. Enthalpy of vapourisation of the liquid is 40kJ / mole. On addition of 50 grams of a non volatile and non dissociative solid Y to 1 L of the liquid X (density = 2 g/ml), the solution obtained will boil at T°C. Value of T is : [Take : Universal gas constant R  8J/mol Kelvin; Molar mass of X ( )  100g mol1 , Y(s)  80g mol1 ] 15. In diamond cubic structure, effective number of constituent per unit cell are p and number of voids per unit cell occupied by carbon atoms are q. Find value of (p  q). 16. First order gas phase thermal decomposition of N 2 O 5 occur as follows : 1 N2O5 (g)  2NO2 (g)  O2 (g) 2 If total pressure varies with time as given in the figure then half life of the reaction is : (in minutes) [Take log10 2  0.30, log10 5  0.70] 17. 0.2 M NaOH was gradually added to 200 mL, 0.1 M HCl solution. After complete neutralisation of the HCl, addition of NaOH was stopped and 1.7 L of water was further added to dilute the final mixture. What would be osmotic pressure (in atm) of the diluted mixture at 35°C. [Given that degree of dissociation of NaCl is 98% in water] [Take : R  0.0821 atm - L / mol - L] 18. Titanium oxide having formula Ti 2x O3[x  1] has metal deficiency defect due to which it consist of two different oxidation states of the metal i.e. Ti3 and Ti4. If ratio of number of the metal ions i.e. Ti4 : Ti 3 is 1 : 24 then value of 19x is : SPACE FOR ROUGH WORK VMC | JEE-2022 | Paper-1 12 JEE Advanced-3 | Code A  Vidyamandir Classes: Innovating For Your Success SUBJECT III : MATHEMATICS 66 MARKS SECTION 1 SINGLE CORRECT ANSWERS TYPE This section contains 06 Multiple Choice Questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE CHOICE is correct. 1. If a function f :[2, ) R is such that f ( x)  x 2  4 x  x 2  4 , then range of f ( x) is: (A) (, ) (B) [6, 12] (C) [6, ) (D) [6, 4] 3  3m  2. If m is the slope of a line which is tangent to y 3  x 4 & a normal to x 2  2 x  y 2  0 , then   is  4  equal to (m  0) 4 3 (A) 3 (B) (C) 4 (D) 3 4 3. Let f :[0, ) [2, ) be a differentiable increasing and onto function satisfying f ( x)  2 f 2 ( x)  2 f ( x)  x  f 2 ( y)  2 f ( y)  y. The value of lim is equal to: x 0 x 1 1 1 (A) (B) (C) (D) 0 2 2 3 4. Let f :[0, ) [2, ) be a differentiable increasing and onto function satisfying f 2 ( x)  2 f ( x)  x  f 2 ( y)  2 f ( y)  y. If g ( x) be the inverse of f ( x) , then g '(4) is equal to: 1 1 (A) 16 (B) (C) 96 (D) 16 96 5. If P( x)  a0  a1 x 2  a2 x 4 ....  an x 2 n be a polynomial in x  R with 0  a1  a2 .......  an , then P( x) has: (A) exactly one maximum (B) exactly one minimum (C) one maximum and one minimum (D) None of these 6. The normal to the curve 2 x 2  y 2  12 at the point (2, 2) cuts the curve again at:  22 2   22 2  (A)  ,   (B)  ,  (C) (–2, –2) (D) None of these  9 9  9 9 SPACE FOR ROUGH WORK VMC | JEE-2022 | Paper-1 13 JEE Advanced-3 | Code A  Vidyamandir Classes: Innovating For Your Success SECTION 2 MULTIPLE CORRECT ANSWERS TYPE This section consists of 06 Questions. Each question has FOUR options. ONE OR MORE THAN ONE of these four option(s) is(are) correct answer(s). 7. For the function f ( x)  4 x 2  4 x  2  x which of the following holds good: 3 1 (A) The least value of the function is 2 2 3 1 (B) The least possible value of function is 2 3 3 (C) The function takes its least value at x  6 (D) Function has exactly one point of minima 3  8. If complete set of values of ‘a’ for which f ( x)  log a (4ax  x 2 ) is strictly increasing in  , 2 , then 2  possible value(s) of a: 5 1 (A) (B) (C) 2 (D) 3 8 4 9. Let f ( x)  ( x  1) p  ( x  2) q where p  1, q  1. Each critical point of f ( x) is a point of extremum when: (A) p  3, q  4 (B) p  4, q  2 (C) p  2, q  3 (D) p  2, q  4     10. If f ( x)   tan 2  x    where [ x] is the greatest integer function, then:   4   (A) f ( x) is continuous at x  0 (B) f ( x) is differentiable at x  2     (C) f ( x) is continuous in  0,  (D) f ( x) is differentiable in  0,   2  2 sin x  cos x 11. If  (sin x  cos x) dx  cos ec 1  g  x    c  x  R , then: sin x cos x  sin x cos x 2 2 (A) g ( x)  1  sin 2 x (B) g ( x)  1  sin 2 x (C) g ( x)  0 (D) 1  g ( x)  1  ax 2  b, x  1   12. If Rolle’s theorem is applicable to the function f defined by f ( x)  1, x  1 for x  [2, 2] ,   x 1  x then: 3 (A) a  b 1 (B)  ab (C) b (D) 3a  b  0 2 SPACE FOR ROUGH WORK VMC | JEE-2022 | Paper-1 14 JEE Advanced-3 | Code A  Vidyamandir Classes: Innovating For Your Success SECTION 3 NUMERICAL VALUE TYPE QUESTIONS This section has 06 Questions. The answer to each question is a NUMERICAL VALUE. For each question, enter the correct numerical value of the answer. If the answer is a decimal numerical value, then round-off the value to TWO decimal places. If the answer is an Integer value, then do not add zero in the decimal places. In the OMR, do not bubble the  sign for positive values. However, for negative values, Θ sign should be bubbled. (Example: 6, 81, 1.50, 3.25) axe x  b log(1  x)  c  x  e x a  4b 13. Find a, b, c such that lim  2. The value is _____. x 0 x  sin x 2 c sin x  sin x  x sin x 14. Value of lim   is n. The value of [n 3 ] is ____. {where [.] denotes greatest integer x 0  x  function} 15. If f (2 x  1)  4 x 2  14 x , then find the sum of the squares of roots of the equation f ( x)  0. 16. Find the value of ab if y  a log | x | bx 2  x has its extreme values at x  1 and x  2 17. For how many integral values of k where k  (15, 15) does the function y  x3  3(7  k ) x 2  3(9  k 2 ) x  2, x  0 have a point of maximum? 2 f ( x)  3 f (2 x)  f (4 x) 18. If f ( x) is twice differentiable and f "(0)  p , then lim is kp. The value of x 0 x2 k is ______. SPACE FOR ROUGH WORK    End of JEE Advanced-3 | PAPER-1 | JEE-2022    VMC | JEE-2022 | Paper-1 15 JEE Advanced-3 | Code A