Paper Code : 1001CT103516017 CLASSROOM CONTACT PROGRAMME (Academic Session : 2016 - 2017) ENGLISH JEE (Main + Advanced) : LEADER COURSE DO NOT BREAK THE SEALS WITHOUT BEING INSTRUCTED TO DO SO BY THE INVIGILATOR PHASE-III to VII (SCORE-I) Test Type : PART TEST Test Pattern : JEE-Advanced TEST DATE : 11 - 03 - 2017 Time : 3 Hours PAPER – 1 Maximum Marks : 195 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. 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 20 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. Please see the last page of this booklet for rest of the instructions
Target : JEE (Main + Advanced) 2017/11-03-2017/Paper-1 Atomic No. SOME USEFUL CONSTANTS Atomic masses : 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, 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 Coulomb's law constant 1 = 9 ×109 Universal gravitational constant 4 0 Speed of light in vacuum Stefan–Boltzmann constant G = 6.67259 × 10–11 N–m2 kg–2 Wien's displacement law constant c = 3 × 108 ms–1 Permeability of vacuum = 5.67 × 10–8 Wm–2–K–4 b = 2.89 × 10–3 m–K Permittivity of vacuum µ0 = 4 × 10–7 NA–2 Planck constant 1 0 = 0c2 h = 6.63 × 10–34 J–s Space for Rough Work E-2/36 1001CT103516017
Leader Course/Phase-III to VII/Score-I/11-03-2017/Paper-1 HAVE CONTROL HAVE PATIENCE HAVE CONFIDENCE 100% SUCCESS BEWARE OF NEGATIVE MARKING PHYSICS PART-1 : PHYSICS SECTION–I(i) : (Maximum Marks : 24) This section contains EIGHT questions. Each question has FOUR options (A), (B), (C) and (D). ONE OR MORE THAN ONE of these four option(s) is (are) correct. For each question, darken the bubble(s) corresponding to all the correct option(s) in the ORS For each question, marks will be awarded in one of the following categories : Full Marks : +3 If only the bubble(s) corresponding to all the correct option(s) is (are) darkened. Zero Marks : 0 In all other cases. 1. A projectile is projected on a horizontal ground at an angle of projection of 40°. After some time it lands on the horizontal ground. During its motion :- (A) Its distance from point of projection always increases. (B) Its distance from point of projection first increases then decreases. (C) Velocity vector of projectile at some instant makes an angle 78° with its initial direction of motion. (D) Velocity vector of projectile at some instant makes an angle 92° with its initial direction of motion. Space for Rough Work 1001CT103516017 E-3/36
PHYSICS Target : JEE (Main + Advanced) 2017/11-03-2017/Paper-1 2. A man weighing W stands on a horizontal beam (hinged on a wall) of negligible weight at point C and holds a massless rope passing over two smooth pulleys. The rope is attached to point B on the beam as shown. If the system is in equilibrium, then :- A 2m B C 2m (A) If W = 600 N, tension in string is 400 N (B) If W = 600 N hinge force at A is 200 N (C) Hinge force at A is always in vertically downward direction, irrespective of value of W (D) Hinge force at A is always in vertically upward direction, irrespective of value of W 3. Three rollers of different shapes are made to roll on a horizontal circular tracks (rails). The shapes of rollers are as shown. Mark the INCORRECT option :- (1) (2) (3) (A) Only roller 1 will be able to go all over the track (B) All the rollers will be able to go all over the track (C) Only roller 2 will be able to go all over the track (D) No roller will be able to go all over the track Space for Rough Work E-4/36 1001CT103516017
Leader Course/Phase-III to VII/Score-I/11-03-2017/Paper-1 4. An uniform rod of mass m and length is pivoted at top and it can perform angular SHM in PHYSICS vertical plane according to equation = 0 sin t. At time t 2 a point mass m (at rest) sticks to lowest end of rod. g (A) New time period of rod will be 2 times of the time period before collision. 3 (B) New angular amplitude is 0 12 (C) New angular amplitude is 0 4 (D) There will always be loss of kinetic energy of rod, irrespective of time at which mass sticks to rod. Space for Rough Work 1001CT103516017 E-5/36
PHYSICS Target : JEE (Main + Advanced) 2017/11-03-2017/Paper-1 5. A non conducting uniformly charged sphere of radius a is surrounded by a conducting shell of inner radius b and outer radius c. Inner sphere carries a charge q. Radius of inner surface of conducting shell is fixed while radius of outer surface can be changed :- qC ba (A) If conducting shell has a total charge +q then energy stored in the system will be independent of change in radius (B) If conducting shell has a total charge –q then energy stored in the system will be independent of change in radius (C) Energy stored in the region a r b will be independent of charge on conducting shell and radius of outer surface of shell. (D) If a certain volume of material is scooped out from the bulk of conducting shell keeping, its inner and outer radii fixed, then energy of system remains unchanged. 6. Two discs having uniform charge densities 1 and 2 are placed parallel to each other with their axis coinciding as shown. Flux of electric field linked with disc 1 is 1 and flux of electric field linked with disc 2 is 2. Then :- 1 2 (A) 1 = 2 (B) 1 2 2 1 (C) 1 1 2 2 (D) For any set of 1 and 2, the relation 11 = 22 is always true. Space for Rough Work E-6/36 1001CT103516017
Leader Course/Phase-III to VII/Score-I/11-03-2017/Paper-1 PHYSICS 7. Four large conducting plates are placed parallel to each other at equal separation between consequtive plates. These plates carry charges –2Q, Q, 4Q and –3Q respectively as shown. Point A is located to the left of plate 1 and B is located to the right of plate 4 :- –2Q Q 4Q –3Q AB 1234 (A) Potential difference between points A and B does not depend on location of A and B. (B) Potential difference between points A and B is zero. (C) If plates 2 and 3 are joined and combined plate is placed exactly in the middle of plate 1 and 4, then potential difference between A and B will remain zero. (D) If total charge combined together on all the plates is zero, no charge will appear on the left surface of plate 1 and on the right surface of plate 4. 8. A large number of bulbs have same voltage ratings but different power ratings i.e. (P1, V), (P2, V), (P3, V)......... etc. These bulbs have to be used either in series or in parallel combination in a circuit. (A) If bulbs are used in series then bulb with lowest power rating will glow maximum. (B) If bulbs are used in series then bulb with highest power rating will glow maximum. (C) If bulbs are used in parallel then bulb with lowest power rating will glow maximum. (D) If bulbs are used in parallel then bulb with lowest power rating will glow minimum. Space for Rough Work 1001CT103516017 E-7/36
Target : JEE (Main + Advanced) 2017/11-03-2017/Paper-1 SECTION–I(ii) : (Maximum Marks : 12) PHYSICS This section contains TWO paragraphs. Based on each paragraph, there are TWO questions. Each question has FOUR options (A), (B), (C) and (D) ONLY ONE of these four options is correct. For each question, darken the bubble corresponding to the correct option in the ORS. For each question, marks will be awarded in one of the following categories : Full Marks : +3 If only the bubble corresponding to the correct answer is darkened. Zero Marks : 0 If none of the bubbles is darkened. Negative Marks : –1 In all other cases Paragraph for Questions 9 and 10 Let us consider a two particles elastic collision in a plane and analyse it graphically. A convenient way to do so is to analyse it in CM frame. Let V1 and V2 are velocities of colliding particle before collision and V1' and V2' are the values after collision. In CM frame let these velocities are V1C , V2C , V1C' , V2C' respectively. We know that in an elastic collision the magnitude of velocities of each particle remains unchanged in CM frame, however direction of velocity for each particle changes by angle CM, as shown in figure. V1'C CM V2C V1C CM V2'C If we wish to calculate by what angle lab does particles scatter in lab (ground) frame, then it can be done by adding VCM in V1C' and V2C' . V1' = V1C' M + VCM , V2' = V2'CM + VCM Space for Rough Work E-8/36 1001CT103516017
Leader Course/Phase-III to VII/Score-I/11-03-2017/Paper-1 V1' PHYSICS V1C' lab CM VCM V1C V1 In a particular case if particle 2 was at rest before collision, then , VCM m1V1 V1C m2 V1 m1 m2 m1 m2 This gives a very interesting conclusion, that if m2 > m1, all values of lab are possible, however if m1 > m2 then lab can not be greater than a particular value max. 9. In a head-on elastic collision, the value of CM is :- (A) 0° (B) 90° (C) 180° (D) All angles are possible 10. A carom striker and a carom coin have masses 25 gm and 15 gm. When the striker, hits a stationary coin elastically, the angle that it (striker) can be deflected from original direction is :- (A) between zero to 53° (B) between zero to 37° (C) between 37° to 53° (D) All angles are possible Space for Rough Work 1001CT103516017 E-9/36
PHYSICS Target : JEE (Main + Advanced) 2017/11-03-2017/Paper-1 Paragraph for Questions 11 and 12 Motion of a spinning top is quite intriguing. When a spinning top is placed on the floor and its tip held in one position, it starts to precess about a vertical axis as shown. L Let us take the mass of top as m, its moment of inertia about spinning axis as I, distance of its centre of mass from pivot point is , and its spinning rate is S. The rate of precession, that is angular speed at which the top starts to rotate about vertical is . Generally is much smaller than , so in our present discussion we will assume that does not contribute to angular momentum L and it arises only due to S alone. So L . As the top precess, horizontal IS component of its angular momentum changes. This change is brought by the torque due to weight of top, about the pivot. If top precess with a steady rate, then dL dt ext Rate of change of horizontal component of L can be calculate easily, as described below Lsin (Lsind d Lsin dLH L sin d dt dt 11. If the top described in the problem is precessing uniformly, then its rate of precession is given by :- mg mg tan mg sin mg cos (A) IS (B) IS (C) IS (D) IS 12. Sometimes when a ceiling fan is fitted loosely on the ceiling, it performs a conical pendulum like motion with frequency , while running. If a fan is running at 100 rpm, find the value of assuming it to be much smaller as compared to spinning frequency. Take mass of fan 5kg, its moment of inertia about spinning axis is 2kg–m2 and distance of centre of mass of system from point of hanging is 0.5 m. (g = 10 m/s2) :- (A) 3.14 rev/min (B) 6 rev/min (C) 9.2 rev/min (D) 11.4 rev/min Space for Rough Work E-10/36 1001CT103516017
Leader Course/Phase-III to VII/Score-I/11-03-2017/Paper-1 SECTION–I(iii) : (Maximum Marks : 9) This section contains THREE questions. PHYSICS 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 bubble corresponding to the correct option is darkened. Zero Marks : 0 If none of the bubbles is darkened. Negative Marks : –1 In all other cases 13. Four galvenometers and two resistors, all having same resistance are to be arranged in different configurations, to work like a voltmeter. Each of the galvenometer has range 0 – 10V. In list–I are given different configurations and in list-II are given range for combination. Match the entries in list-I with entries in list-II :- List-I List–II G (P) G G G (1) 0 – 10 volt G (2) 0 – 60 volt (Q) G (3) 0 – 90 volt G 100 (4) 0 – volt G 3 G G G S (R) 1 4 G 4 1 G Space for Rough Work (S) G G G Codes :- Q R P 3 2 2 1 (A) 4 2 3 (B) 3 3 4 (C) 1 (D) 2 1001CT103516017 E-11/36
PHYSICS Target : JEE (Main + Advanced) 2017/11-03-2017/Paper-1 14. Various currents through different branches in presence of E1 and E2 are as shown in the circuit. If E1 is opened then total current in the circuit is 9A. Match List-I with List-II. I E1 bR E2 c a 8A 3A 4 3 5A d List–I List–II (1) 36 (P) Current I (in ampere) is (2) 2 (3) 9 (Q) EMF E1 (in volt) is (4) 54 (R) EMF E2 (in volt) is (S) Resistance R (in ) is S 3 Code :- Q R 2 P 1 2 3 1 4 4 (A) 4 1 4 (B) 3 2 3 Space for Rough Work (C) 2 (D) 1 E-12/36 1001CT103516017
Leader Course/Phase-III to VII/Score-I/11-03-2017/Paper-1 15. In all the situatins shown in list-I blocks are connected with ideal spring of constant K. Initially they are at rest and spring is unstretched (Netlect friction). Match the corresponding options PHYSICS in list-II. List-I List–II (P) F m 2m F (1) Maximum elongation in the spring is 4F/3K (Q) F m 2m 2F (2) Magnitude of acceleration of centre of mass of two (R) 2F m 2m 2F F block system is (S) m 2m 2F 3m (3) Relative velocity of block is maximum when F elongation in the spring K . (4) Maximum magnitude of relative velocity between F 6m the blocks is m K Code :- PQ R S (A) 1 2 3 4 (B) 2 4 1 3 (C) 3 2 4 1 (D) 4 1 2 3 Space for Rough Work SECTION –II : Matrix-Match Type & SECTION –III : Integer Value Correct Type No question will be asked in section II and III 1001CT103516017 E-13/36
Target : JEE (Main + Advanced) 2017/11-03-2017/Paper-1 SECTION–IV : (Maximum Marks : 20) PHYSICS This section contains FIVE questions. The answer to each question is a SINGLE DIGIT INTEGER ranging from 0 to 9, both inclusive. For each question, darken the bubble corresponding to the correct integer in the ORS. For each question, marks will be awarded in one of the following categories : Full Marks : +4 If only the bubble corresponding to the correct answer is darkened. Zero Marks : 0 In all other cases. 1. A bicycle wheel (ring) of mass 1kg and radius 2m is attached at the end of a long rod of mass 1kg and length 3m, with the axis of wheel perpendicular to the rod. The rod is rotating counter clockwise as seen from above, about its other end with an angular speed 0.5 rad/s. If wheel is also rotating about its axis with same angular speed in counter clock wise sense as seen from above. Find angular momentum of the system (in kg–m2/s) about the axis passing through one end of rod. (Neglect mass of spokes and mass of rod connecting end of rod of length 3m and centre of ring) 2m 3m 2. Find the time constant (in second) of circuit shown. 0.5µF 1M 3M 0.5µF Space for Rough Work E-14/36 1001CT103516017
Leader Course/Phase-III to VII/Score-I/11-03-2017/Paper-1 PHYSICS 3. In the circuit shown, switch S is initially closed. Find loss in energy (in joule) of system, after the switch is opened. S 2µF 2µF 10V 4. A potentiometer wire AB of uniform cross-section and resisitivity has a resistance 10. It is used in a circuit as shown below. If jockey is touched in the middle of potentiometer wire, find current (in ampere) through galvenometer. (Neglect resistance of galvenometer). 40V 5 A J 10 B G 5V 5 5. India plans to place geostationary satellites, in equatorial orbit at a height 36000 km from surface of earth. Each of these satellites are arranged equispaced in same orbit and should be able to see (exchange signals directly with each other) at any instant of time. If maximum number of such geostationary satellites is 2N + 1, then find the value of N. (Radius of earth = 6400 km, sin–1(0.15) = 0.15 radian) Space for Rough Work 1001CT103516017 E-15/36
Target : JEE (Main + Advanced) 2017/11-03-2017/Paper-1 CHEMISTRY PART-2 : CHEMISTRY SECTION–I(i) : (Maximum Marks : 24) This section contains EIGHT questions. Each question has FOUR options (A), (B), (C) and (D). ONE OR MORE THAN ONE of these four option(s) is (are) correct. For each question, darken the bubble(s) corresponding to all the correct option(s) in the ORS For each question, marks will be awarded in one of the following categories : Full Marks : +3 If only the bubble(s) corresponding to all the correct option(s) is (are) darkened. Zero Marks : 0 In all other cases. 1. Which of the following processes are spontaneous (A) melting of ice at 2 atm and 273 K (B) Melting point of ice at 1/2 atm and 273 K (C) Boiling of water at 1/2 atm and 373 K (D) Boiling of water at 2 atm and 373 K 2. Consider the following reaction : 2Fe2O3(s) + 3C(s) 4Fe(s) + 3CO2(g) Hfº of Fe2O3 & CO2 are –820 kJ/mol and –390 kJ/mol respectively. The reaction is - (A) Endothermic (B) Exothermic (C) Spontaneous at high temperature (D) Spontaneous at low temperature 3. Which of the following ions give coloured aqueous solutions :- (A) Ni+2 (B) Fe+2 (C) Sc+3 (D) Cu+2 4. Which of the following statement is/are INCORRECT :- (A) Reducing nature of hydrides of oxygen family increases down the group (B) With the ammonia solution (excess) Cd salt and Zn salt can be easily distinguished (C) Nitrogen gas is produced by the action of NaOH on ammonium salt. (D) down the group b.pt and m.pt of inert gases decreases Space for Rough Work E-16/36 1001CT103516017
Leader Course/Phase-III to VII/Score-I/11-03-2017/Paper-1 CHEMISTRY 5. Na air' X ' air Y Choose the CORRECT satement(s) :- (A) Oxidation state of oxygen is higher in 'X' as compared to 'Y' (B) Both 'X' and 'Y' are diamagnetic (C) 'Y' on reaction with water produces H2O2 (D) 'X' on reaction with CO2 produces Na2CO3 6. Which of the following represents correct product formation ? COOH OH O (B) B2H6 THF (A) O Zn (Hg) HCl O O COOC2H5 CH2OH + C2H5OH (C) H Red P/HI (D) DIBAL-H OH Toluene, –78ºC O H2O Space for Rough Work 1001CT103516017 E-17/36
Target : JEE (Main + Advanced) 2017/11-03-2017/Paper-1 CHEMISTRY7. Which of the following will give(s) CO2 gas with aq. NaHCO3 which contains –COOH group ? (A) Tartaric acid (B) Picric acid (C) Aspirin (D) Aspartic acid 8. Major product (S) of following sequence is : Br Alc. KOH P (i) O3 Q (NH4)2CO3 R Pd / C S (ii) Zn, H2O (A) (B) NH N NH (C) (D) N N Space for Rough Work E-18/36 1001CT103516017
Leader Course/Phase-III to VII/Score-I/11-03-2017/Paper-1 SECTION–I(ii) : (Maximum Marks : 12) CHEMISTRY This section contains TWO paragraphs. Based on each paragraph, there are TWO questions. Each question has FOUR options (A), (B), (C) and (D) ONLY ONE of these four options is correct. For each question, darken the bubble corresponding to the correct option in the ORS. For each question, marks will be awarded in one of the following categories : Full Marks : +3 If only the bubble corresponding to the correct answer is darkened. Zero Marks : 0 If none of the bubbles is darkened. Negative Marks : –1 In all other cases Paragraph for Questions 9 and 10 8 gm weak acid HX (molecular mass = 80) is dissolved is 100 ml water. (Ka = 10–4) 9. Find pH of solution (A) 3.3 (B) 2 (C) 2.3 (D) 3 10. If it is titrated with 0.25 M NaOH find pH at equivalence point (log5 = 0.7) (A) 9.15 (B) 8.65 (C) 4.65 (D) 4.85 Paragraph for Questions 11 and 12 (X) BaCl2 White ppt. (aq.) KI(aq.) (aq.) NH3(aq.) Bright yellow NaOH(aq.) Colourless ppt. solution (Y) Brown/Black ppt.(Z) 11. The compound (X) is :- (A) Pb(NO3)2 (B) CaCrO4 (C) Hg(NO3)2 (D) AgNO3 12. ppt. (Y) will be insoluble in :- (A) aq. NaCN (excess) (B) Na2S2O3 solution (excess) (C) NH3 solution (D) None of these Space for Rough Work 1001CT103516017 E-19/36
Target : JEE (Main + Advanced) 2017/11-03-2017/Paper-1 CHEMISTRY SECTION–I(iii) : (Maximum Marks : 9) This section contains THREE 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 bubble corresponding to the correct option is darkened. Zero Marks : 0 If none of the bubbles is darkened. Negative Marks : –1 In all other cases 13. Match the following for a reaction A + B P, the rate law is given as : r = K[A]1[B]0. Match the correct graph accordingly - List-I List-II (P) (1) [B] v/s time d[A] (Q) (2) v/s [A] dt (R) (3) log [A] v/s time (S) (4) [P] v/s t Codes : P QR S (A) 4 3 4 1 (B) 2 3 1 4 (C) 1 2 3 4 (D) 3 2 1 4 Space for Rough Work E-20/36 1001CT103516017
14. Match the list :- Leader Course/Phase-III to VII/Score-I/11-03-2017/Paper-1 CHEMISTRY List - I (Compound) List - II (Uses) (1) Remove temporary hardness (P) Na6P6O18 (2) A neutron moderator (Q) Ca(OH)2 (3) Remove permanent hardness (R) Mixture of (CO + H2) (4) Make hydrocarbons (S) Heavy water Code : S 2 PQR 1 (A) 3 1 4 3 (B) 2 4 3 3 (C) 4 2 1 (D) 2 4 1 Space for Rough Work 1001CT103516017 E-21/36
CHEMISTRY15. List-I Target : JEE (Main + Advanced) 2017/11-03-2017/Paper-1 (Reaction) List-II (Type of reaction) (P) + 3Cl2 hv (1) Elimination reaction (Q) CH3–CH=CH2 NBS (2) Substitution reaction (R) Br–CH2–CH2–Br Zn (3) Addition reaction (S) CH3–COOH Red P (4) Rearrangment reaction Cl2 S Code : 3 4 P QR 3 2 (A) 2 2 1 Space for Rough Work (B) 3 2 1 (C) 4 2 1 (D) 3 2 1 SECTION –II : Matrix-Match Type & SECTION –III : Integer Value Correct Type No question will be asked in section II and III E-22/36 1001CT103516017
Leader Course/Phase-III to VII/Score-I/11-03-2017/Paper-1 SECTION–IV : (Maximum Marks : 20) CHEMISTRY This section contains FIVE questions. The answer to each question is a SINGLE DIGIT INTEGER ranging from 0 to 9, both inclusive. For each question, darken the bubble corresponding to the correct integer in the ORS. For each question, marks will be awarded in one of the following categories : Full Marks : +4 If only the bubble corresponding to the correct answer is darkened. Zero Marks : 0 In all other cases. 1. Consider two Ist order reations at 25ºC with same initial concentrations of 1M I. A t1/2 40 min product (temperature coefficient = 2) II. B t1/2 30 min product (temperature coefficient = 3) If both reaction are carried out at 35ºC. Find ratio of concentrations of A & B after one hour. 2. PCl5 dissociates into PCl3 & Cl2. At equilibrium pressure of 3 atm, all three gases were found to have equal number of moles in a vessel. In another vessel, equimolar mixture of PCl5, PCl3 & Cl2 are taken at the same temperature but at an initial pressure of 9 atm then find the partial pressure of Cl2 (in atm) at equilibrium in second vessel. Space for Rough Work 1001CT103516017 E-23/36
CHEMISTRY Target : JEE (Main + Advanced) 2017/11-03-2017/Paper-1 3. Find the total number of coloured species out of following :- Cl2, NO2 , NH3 , CdS , N2O4 , Cu2[Fe(CN)6] 4. Total number of stereoisomers of following compound which contains plane of symmetry is : OH OH CH3–CH–CH=CH–CH–CH3 5. Degree of unsaturation of major product obtained in following reaction is : O (i) 2 HCHO / NaOH, heat Ph (ii) HCHO / H+ (catalytic amount) Space for Rough Work E-24/36 1001CT103516017
Leader Course/Phase-III to VII/Score-I/11-03-2017/Paper-1 PART-3 : MATHEMATICS MATHEMATICS SECTION–I(i) : (Maximum Marks : 24) This section contains EIGHT questions. Each question has FOUR options (A), (B), (C) and (D). ONE OR MORE THAN ONE of these four option(s) is (are) correct. For each question, darken the bubble(s) corresponding to all the correct option(s) in the ORS For each question, marks will be awarded in one of the following categories : Full Marks : +3 If only the bubble(s) corresponding to all the correct option(s) is (are) darkened. Zero Marks : 0 In all other cases. 1. If 5 cos22x + 4(cos4x + sin4x + cos6x + sin6x) = 8, then (A) sin2 2x 3 (B) tan2 2x 2017 4 (C) cos22x < cot22x (D) (tan2 2x)cos2 2x (cot2 2x)sin2 2x 2. Let ƒ(x) = sin–1 2x 1 x2 , then - 1 (A) ƒ(x) is continuous and differentiable at x = . 2 (B) ƒ(x) is continuous and differentiable at x 4. (C) ƒ(x) is continuous and differentiable at x . 6 (D) ƒ(x) is continuous but non-differentiable at x 1 2 3. If the equation in x, x4 + px3 + qx2 = 16(2x – 1), where p, q R has all positive roots, then (A) q : |p| = 3 : 2 (B) p > 8 (C) q > 4 (D) p < 0 < q < 8 Space for Rough Work 1001CT103516017 E-25/36
Target : JEE (Main + Advanced) 2017/11-03-2017/Paper-1 MATHEMATICS4. If cot1 4 2 cot1 4 6 cot1 4 12 ..... tan1 a , where a and b are relatively 4 4 4 b prime, then - (A) a > b (B) a3 + b3 = 9 sec1 a cosec1 b 10 2 cos1 bi i 1 (C) (D) 5 2 sin1 bj j1 5. Which of the following statement(s) is(are) correct ? (A) Number of solutions of the equation cos(tanx) = sin(tanx) in x 0, are infinite. 2 (B) If the equation in x, sinx + cos(k + x) + cos(k – x) = 2 has real solution, then |sin k| 1 . 2 (C) The equation 4sin2x + cosx = 5 has no real solution. (D) Number of solutions of the equation sinx.cos4x.sin5x = 1 in x , 3 are two. 2 2 Space for Rough Work E-26/36 1001CT103516017
Leader Course/Phase-III to VII/Score-I/11-03-2017/Paper-1 MATHEMATICS 6. If the function ƒ satisfies (ƒ(x) – 1)(x2 + x + 1)2 – (ƒ(x) + 1)(x4 + x2 + 1) = 0 for all x R – {0}, then (A) |ƒ(x)| > 2 for all x R – {0} (B) ƒ(x) has local maximum at x = –1. (C) ƒ(x) has local minimum at x = 1 (D) (cos x).ƒ(x)dx 0 7. Let a1, a2, a3, a4, ....... be an arithmetic progression and g1, g2, g3, g4, ..... be a geometric progression. If a1 + g1 = 1, a2 + g2 = 4, a3 + g3 = 15 and a4 + g4 = 2, then (A) the common ratio of geometric progression is equal to –2. (B) the common ratio of geometric progression is equal to –3. 20 (C) ak 960 k 1 20 (D) ak 480 k 1 8. Let y = ƒ(x) defined on R satisfies (1 + x2) dy 2xy 2x and ƒ(0) = 2, then dx (A) ƒ(x) is neither even nor odd function. (B) ƒ(x) increasing on (–, 0) and decreases on (0, ) 1 (C) the x-intercept of normal on graph of y = ƒ(x) at x = 1 equals . 4 (D) the area bounded by y = ƒ(x) with x-axis between ordinates at x = 0 and x = 1 equals 1 4 (square units). Space for Rough Work 1001CT103516017 E-27/36
Target : JEE (Main + Advanced) 2017/11-03-2017/Paper-1 MATHEMATICS SECTION–I(ii) : (Maximum Marks : 12) This section contains TWO paragraphs. Based on each paragraph, there are TWO questions. Each question has FOUR options (A), (B), (C) and (D) ONLY ONE of these four options is correct. For each question, darken the bubble corresponding to the correct option in the ORS. For each question, marks will be awarded in one of the following categories : Full Marks : +3 If only the bubble corresponding to the correct answer is darkened. Zero Marks : 0 If none of the bubbles is darkened. Negative Marks : –1 In all other cases Paragraph for Questions 9 and 10 x Consider two functions defined on R as g(x) (1 t t2 t3 t4 )dt and ƒ(x) = g'(x). 0 9. The sum of real roots of the equation ƒ(x) = 0 lies in - (A) (0, 1) (B) (–1, 0) (C) (–2, –1) (D) (1, 2) 10. The number of distinct real roots of the equation x2ƒ''(x) + 3xƒ'(x) + ƒ(x) = 0 is equal to - (A) 1 (B) 2 (C) 3 (D) 0 Space for Rough Work E-28/36 1001CT103516017
Leader Course/Phase-III to VII/Score-I/11-03-2017/Paper-1 MATHEMATICS Paragraph for Questions 11 and 12 Let k be the non-zero real number such that the quadratic equation kx2 + 2x + k = 0 has two distinct real roots and ( ). 11. If 2 , then 2, 2 2 2 , (A) k 3 3 (B) k , 3 3 2 2 , 1 (D) k 1, 1 (C) k 1, 3 3 12. If < 2 and > 5, then (A) k 4 , 5 (B) k 1, 4 5 , 1 5 13 5 13 (C) k 5 , 0 (D) (–1, 1) 13 Space for Rough Work 1001CT103516017 E-29/36
Target : JEE (Main + Advanced) 2017/11-03-2017/Paper-1 MATHEMATICS SECTION–I(iii) : (Maximum Marks : 9) This section contains THREE 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 bubble corresponding to the correct option is darkened. Zero Marks : 0 If none of the bubbles is darkened. Negative Marks : –1 In all other cases 13. Consider three functions, ƒ(x) = x3 + x2 + x + 1, g(x) 2x and = x2 1 h(x) = sin–1x – cos–1x + tan–1x – cot–1x. Match List-I with List-II and select the correct answer using the code given below the list. List-I List-II (P) If range of ƒ(g(x)) is [a, b], then (a + b) is equal to (1) 1 (Q) The number of integers in the range of g(ƒ(x)) is (2) 3 equal to (3) 4 (R) The maximum value of g(h(x)) is equal to k (4) 5 (S) If the minimum value of h(g(ƒ(x))) is 2 , then |k| is equal to Codes : P QR S (A) 2 3 1 4 (B) 3 2 4 1 (C) 3 2 1 4 (D) 2 3 4 1 Space for Rough Work E-30/36 1001CT103516017
Leader Course/Phase-III to VII/Score-I/11-03-2017/Paper-1 x MATHEMATICS 14. a ƒ(t) dt b, x0 ƒ(x) 0 , Let ƒ be a differentiable function on R defined as x2 4x 1, x 0 where a, b (0,) and tangent drawn to the graph of ƒ(x) at x = 1 is y = mx + c. Match List-I with List-II and select the correct answer using the code given below the list. List-I List-II (P) a = (1) –3 (Q) b = (2) 1 (R) c = (3) 4 (S) m = (4) 12 Codes : Space for Rough Work P QRS (A) 2 3 4 1 (B) 2 3 1 4 (C) 3 2 4 1 (D) 3 2 1 4 1001CT103516017 E-31/36
Target : JEE (Main + Advanced) 2017/11-03-2017/Paper-1 MATHEMATICS15. Match List-I with List-II and select the correct answer using the code given below the list. List-I List-II 5 1 (1) 0 (P) The value of sin(x2 3)dx sin(x2 12x 33)dx 4 2 is equal to (Q) If the function g(x) = (1 x)7 x2 1 , then g'(0) is equal to (2) 4 (x2 x 1)6 (R) If 5 j a , where a and b are coprime, (3) 5 11 b (4) 13 cos2 j1 then (a – b) is equal to (S) Number of integral values of p satisfying |9 – p2| + |p2 – 4| = 5, is equal to Codes : P QR S (A) 1 4 2 3 (B) 1 4 3 2 (C) 4 1 2 3 (D) 4 1 3 2 Space for Rough Work SECTION –II : Matrix-Match Type & SECTION –III : Integer Value Correct Type No question will be asked in section II and III E-32/36 1001CT103516017
Leader Course/Phase-III to VII/Score-I/11-03-2017/Paper-1 SECTION–IV : (Maximum Marks : 20) MATHEMATICS This section contains FIVE questions. The answer to each question is a SINGLE DIGIT INTEGER ranging from 0 to 9, both inclusive. For each question, darken the bubble corresponding to the correct integer in the ORS. For each question, marks will be awarded in one of the following categories : Full Marks : +4 If only the bubble corresponding to the correct answer is darkened. Zero Marks : 0 In all other cases. 1. Let the function ƒ : [0, 2] [0, ) satisfies ƒ3(x)ƒ''(x) = –1 for all x (0, 2) and ƒ'(1) + ƒ(1) = ƒ(1) – ƒ'(1) = 1. If the area bounded by ƒ(x) with x-axis is S, then 8 S is equal to x 2. Let the function ƒ : (0, 2) R be defined as ƒ(x) sin x.esin 2x esin2t (sin t cos t)dt . If m and 0 n be the number of points of local maximum and local minimum of ƒ(x) respectively, then (m + n) is equal to Space for Rough Work 1001CT103516017 E-33/36
Target : JEE (Main + Advanced) 2017/11-03-2017/Paper-1 MATHEMATICS t2 1x dx , then g(5) is equal to If the function g(t) = cot1 3. 2t (1 t)2 x g(3) 4. Consider two functions defined on R as ƒ(x) = 2 + |x – 1| and g(x) = min(ƒ(t)) where x < t < x2 + x + 1. If n1 denotes number of points of discontinuity of g(x) and n2 denotes number of points where g(x) is non-differentiable, then (n1 + n2) is equal to 50 50 j2 j 5. Let <an> be an arithmetic sequence such that a2i1 50 , then (1) 2 a2j1 is equal to i1 j1 Space for Rough Work E-34/36 1001CT103516017
Leader Course/Phase-III to VII/Score-I/11-03-2017/Paper-1 Space for Rough Work 1001CT103516017 E-35/36
Target : JEE (Main + Advanced) 2017/11-03-2017/Paper-1 QUESTION PAPER FORMAT AND MARKING SCHEME : 16. The question paper has three parts : Physics, Chemistry and Mathematics. 17. Each part has two sections as detailed in the following table. Que. No. Category-wise Marks for Each Question Maximum Section Type of Full Partial Zero Negative Marks of the Que. Marks Marks Marks Marks section +3 0 In all One or more If only the bubble(s) other cases I(i) correct 8 corresponding — — 24 option(s) to all the correct — 0 12 If none –1 9 option(s) is(are) of the In all bubbles is other darkened darkened cases Paragraph +3 –1 In all Based If only the bubble other cases I(ii) (Single 4 corresponding to correct the correct option option) is darkened Matching +3 0 Lists Type If only the bubble If none I(iii) (Single 3 corresponding to — of the correct the correct option bubbles is option) is darkened darkened +4 0 Single digit If only the bubble In all IV Integer 5 corresponding — other — 20 (0-9) to correct answer cases is darkened NAME OF THE CANDIDATE ................................................................................................ FORM NO. ............................................. I have read all the instructions I have verified the identity, name and Form and shall abide by them. number of the candidate, and that question paper and ORS codes are the same. ____________________________ ____________________________ Signature of the Candidate Signature of the invigilator Corporate Office : CAREER INSTITUTE, “SANKALP”, CP-6, Indra Vihar, Kota (Rajasthan)-324005 +91-744-5156100 [email protected] www.allen.ac.in E-36/36 Your Target is to secure Good Rank in JEE 2017 1001CT103516017
Paper Code : 1001CT103516017 CLASSROOM CONTACT PROGRAMME (Academic Session : 2016 - 2017) HINDI JEE (Main + Advanced) : LEADER COURSE PHASE-III to VII (SCORE-I) Test Type : PART TEST Test Pattern : JEE-Advanced TEST DATE : 11 - 03 - 2017 Time : 3 Hours PAPER – 1 Maximum Marks : 195 1. 2. (ORS) 3. 4. 5. 3620 6. 7. 8. 9. : 10. 11. 12. : 13. 14. 15. g = 10 m/s2
Target : JEE (Main + Advanced) 2017/11-03-2017/Paper-1 SOME USEFUL CONSTANTS Atomic No. H = 1, B = 5, C = 6, N = 7, O = 8, F = 9, Al = 13, P = 15, S = 16, Atomic masses : Cl = 17, Br = 35, Xe = 54, Ce = 58, 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 Coulomb's law constant 1 = 9 ×109 4 0 Universal gravitational constant Speed of light in vacuum G = 6.67259 × 10–11 N–m2 kg–2 Stefan–Boltzmann constant c = 3 × 108 ms–1 Wien's displacement law constant = 5.67 × 10–8 Wm–2–K–4 Permeability of vacuum b = 2.89 × 10–3 m–K µ0 = 4 × 10–7 NA–2 Permittivity of vacuum 1 Planck constant 0 = 0c2 h = 6.63 × 10–34 J–s H-2/36 1001CT103516017
Leader Course/Phase-III to VII/Score-I/11-03-2017/Paper-1PHYSICS HAVE CONTROL HAVE PATIENCE HAVE CONFIDENCE 100% SUCCESS BEWARE OF NEGATIVE MARKING -1: –I(i) : ( : 24) (A), (B), (C) (D) : +3 : 0 1. 40° (A) (B) (C) 78° (D) 92° 1001CT103516017 H-3/36
PHYSICS Target : JEE (Main + Advanced) 2017/11-03-2017/Paper-1 2. WC B A 2m B C 2m (A) W = 600 N 400N (B) W = 600 N A2 00 N (C) A W (D) A W 3. (1) (2) (3) (A) 1 (B) (C) 2 (D) H-4/36 1001CT103516017
Leader Course/Phase-III to VII/Score-I/11-03-2017/Paper-1PHYSICS 4. m=0sint t 2 m g (A) 2 3 (B) 0 12 (C) 0 4 (D) 1001CT103516017 H-5/36
PHYSICS Target : JEE (Main + Advanced) 2017/11-03-2017/Paper-1 5. ab c q qC ba (A) +q (B) –q (C) ar b (D) 6. 1 2 1212 1 2 (A) 1 = 2 (B) 1 2 2 1 (C) 1 1 2 2 (D) 1 2 11 = 22 H-6/36 1001CT103516017
Leader Course/Phase-III to VII/Score-I/11-03-2017/Paper-1PHYSICS 7. –2Q, Q, 4Q –3Q A,1B, 4 –2Q Q 4Q –3Q AB 1234 (A) A B AB (B) A B (C) 23 14AB (D) 14 8. (P1, V), (P2,V), (P3, V)......... (A) (B) (C) (D) 1001CT103516017 H-7/36
Target : JEE (Main + Advanced) 2017/11-03-2017/Paper-1 PHYSICS –I(ii) : ( : 12) (A), (B), (C) (D ) : +3 : 0 : –1 9 10 V1 V1'V2' V1C,V2C, V2 V1C' V2C' CM V1'C CM V2C V1C CM V2'C lab V1C' V2C' VCM V1' = V1C' M + VCM , V2' = V2'CM + VCM H-8/36 1001CT103516017
Leader Course/Phase-III to VII/Score-I/11-03-2017/Paper-1 V1' PHYSICS V1C' lab CM VCM V1C V1 2 , VCM m1V1 V1C m2 V1 m1 m2 m1 m2 m2>m1 labm1 >m2 labmax 9. CM (A) 0° (B) 90° (C) 180° (D) 10. 25gm15gm (A) 53° (B) 37° (C) 37° 53° (D) 1001CT103516017 H-9/36
PHYSICS Target : JEE (Main + Advanced) 2017/11-03-2017/Paper-1 11 12 precess L mI S L S L IS dL dt ext L Lsin (Lsind d Lsin dLH L sin d dt dt 11. mg mg tan mg sin mg cos (A) IS (B) IS (C) IS (D) IS 12. 100rpm 5kg2kg–m2 0.5m(g= 10 m/s2) :- (A) 3.14 rev/min (B) 6 rev/min (C) 9.2 rev/min (D) 11.4 rev/min H-10/36 1001CT103516017
Leader Course/Phase-III to VII/Score-I/11-03-2017/Paper-1 –I(iii) : ( : 9) PHYSICS (A), (B), (C)(D ) : +3 : 0 : –1 13. 0–10V–I -II -I -II G (P) G G G (1) 0 – 10 volt G (2) 0 – 60 volt (Q) G (3) 0 – 90 volt 100 G (4) 0 – 3 volt G G G G (R) G G (S) G G G Codes :- PQ R S (A) 4 3 2 1 (B) 3 2 1 4 (C) 1 2 3 4 (D) 2 3 4 1 1001CT103516017 H-11/36
PHYSICS Target : JEE (Main + Advanced) 2017/11-03-2017/Paper-1 14. E1E2 E1 9A-I -II I E1 bR E2 c a 8A 3A 4 3 5A d –I –II (P) I() (Q) E 1 () (1) 36 (R) E2 () (2) 2 (S) R( (3) 9 (4) 54 Codes :- PQ R S (A) 4 1 2 3 (B) 3 1 4 2 (C) 2 1 4 3 (D) 1 2 3 4 H-12/36 1001CT103516017
Leader Course/Phase-III to VII/Score-I/11-03-2017/Paper-1 15. -I KPHYSICS -II -I –II (P) F m 2m F (1) 4F/3K (Q) F m 2m 2F (2) F (R) 2F m 2m 2F 3m (3) KF (S) m 2m 2F (4) mF6Km Codes :- Q RS P 2 34 4 13 (A) 1 2 41 (B) 2 1 23 (C) 3 (D) 4 – II : & – III : II III 1001CT103516017 H-13/36
PHYSICS Target : JEE (Main + Advanced) 2017/11-03-2017/Paper-1 –IV : ( : 20) 09 : +4 : 0 1. 1kg 2m 1kg3m 0.5 rad/s (kg–m2/s )3m ) 2m 3m 2. 0.5µF 1M 3M 0.5µF H-14/36 1001CT103516017
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