Paper Code : 100 1CT103516011 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 Test Type : MINOR PHASE : III, IV & V Test Pattern : JEE-Advanced TEST DATE : 18 - 12 - 2016 Time : 3 Hours PAPER – 1 Maximum Marks : 234 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 32 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) 2017/18-12-2016/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-2/32 1001CT103516011
Leader Course/Phase-III, IV & V/18-12-2016/Paper-1 HAVE CONTROL HAVE PATIENCE HAVE CONFIDENCE 100% SUCCESS PHYSICS BEWARE OF NEGATIVE MARKING PART-1 : PHYSICS SECTION–I(i) : (Maximum Marks : 32) 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 : +4 If only the bubble(s) corresponding to all the correct option(s) is (are) darkened. Partial Marks : +1 For darkening a bubble corresponding to each correct option, Provided NO incorrect option is darkened. Zero Marks : 0 If none of the bubbles is darkened. Negative Marks : –1 In all other cases. for example, if (A), (C) and (D) are all the correct options for a question, darkening all these three will result in +4 marks; darkening only (A) and (D) will result in +2 marks; and darkening (A) and (B) will result in –1 marks, as a wrong option is also darkened 1. Which of the following statements is CORRECT about reference frames. (A) In a non-inertial reference frame, an isolated particle does not retain a constant velocity. (B) A reference frame travelling with acceleration relative to an inertial reference is a non- inertial reference frame (C) In an inertial reference frame, velocity vector of an isolated particle changes neither in direction nor in magnitude, with time. (D) If a block is stationary in an elevator then reference frame fixed to elevator must be inertial. 2. Consider a car starting from rest and reaches a kinetic energy k by accelerating without skidding along a horizontal road. Neglect air resistance. Mark the CORRECT statements :- (A) Net work done by external forces an car is zero (B) Net work done by forces exerted tires by the road is zero. (C) Change in kinetic energy of car is decrease in internal energy of car (D) Change in kinetic energy of car is increase in internal energy of car Space for Rough Work 1001CT103516011 E-3/32
PHYSICS Target : JEE (Main + Advanced) 2017/18-12-2016/Paper-1 3. A disc of mass M radius R moves under gravity while unwinding string under non slip condition. Mark the correct statement(s): y x RM z 2g (A) Acceleration of the disc is 3 L dL (B) Rate of change of angular momentum of disc dt about a point along string is in kˆ direction. (C) Angular momentum of disc is conserved about centre of mass. dL (D) Rate of change of angular momentum dt of disc about center of mass is in kˆ direction. Space for Rough Work E-4/32 1001CT103516011
Leader Course/Phase-III, IV & V/18-12-2016/Paper-1 PHYSICS 4. Hard rods form right triangle with base angle , which rotates at a constant angular velocity about a vertical axis AB (see figure). On the rod AC a spring with stiffness k = m2 and unstretched length is coiled. One end of the spring is hinged to A and the other end of spring is attached to a sleeve of mass 'm'. B C m A (A) For 1 g cos sin the mass 'm' be in equilibrium with the spring remaining undeformed. (B) For option (A) the equilibrium will be stable. (C) For option (A) the equilibrium will be unstable. (D) For small oscillation, 'm' will perform SHM. Space for Rough Work 1001CT103516011 E-5/32
PHYSICS Target : JEE (Main + Advanced) 2017/18-12-2016/Paper-1 5. A closed conducting loop, having resistance R, is being rotated about an axis perpendicular to the magnetic field. Magnetic flux through the closed conducting loop is continuously changing according to the graph shown in the adjacent figure. Then, which of the following statement(s) is/are correct? Flux (in T-m2) 10 0 1 2 3 4 5 6 time t(in sec) -10 (A) The electric current through the loop is minimum (zero) at t = 1 s, 3s and 5s. (B) The electric current through the loop is minimum (zero) at t = 0 s, 2s and 6s. (C) Total charge flown through any cross-section of a closed conducting loop between 0 and 6 s is zero (D) Total work done in rotating the loop in the magnetic field is zero 6. A uniform conducting rectangular loop of sides , b and mass m carrying current i is hanging horizontally with the help of two vertical strings. There exists a uniform horizontal magnetic field B which is parallel to the longer side of loop. Choose the CORRECT option(s) :- T1 T2 b B mg (B) The value of T1 = mg 2ibB (A) The value of T1 = T2 = 2 2 (C) The value of T2 = mg 2ibB (D) The value of T1 < value of T2 2 Space for Rough Work E-6/32 1001CT103516011
Leader Course/Phase-III, IV & V/18-12-2016/Paper-1 7. A uniform rod AB of mass M is attached to a hinge at one end A, and released from rest from the PHYSICS horizontal position. The rod rotates about A, and when it reaches the vertical position the rod strikes a sphere of mass m and radius r initially at rest on the smooth horizontal surface as shown in the adjacent figure. The impact is along the horizontal direction and perfectly elastic. At the moment of impact the lowest end of the rod is very close to the smooth horizontal surface. After the impact, the sphere moves along the horizontal and the rod, subsequently rises to a maximum of 60° with the vertical. Choose the correct statement(s) from the following, taking into account the information given above. The length of the rod equals 2r . 62 r 10 m Initial final position A position m A m 60° rr B B M3 (A) The ratio m is 2 M2 (B) The ratio is m3 (C) The speed of the sphere just after collision is 6 m/s (D) The speed of the sphere just after collision is 3 m/s 8. A system is shown in the figure, which is released from rest. There is no friction between ground and mass 5m. The coefficient of friction between mass 5m and mass 2m is µ. The coefficient of friction between mass 5m and mass m is also µ. Choose the CORRECT statement(s) :- m 2m 5m 60° (A) The acceleration of centre of mass of system is zero for any value of µ. (B) The magnitude of acceleration of mass 5m is zero if µ = 0 (C) The tension in the string is 4mg if 1 33 3 (D) The magnitude of acceleration of mass 5m is zero if 1 3 Space for Rough Work 1001CT103516011 E-7/32
Target : JEE (Main + Advanced) 2017/18-12-2016/Paper-1 PHYSICS SECTION–I(ii) : (Maximum Marks : 18) This section contains THREE 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 A person wants to roll a solid non-conducting spherical ball of mass m and radius r on a surface whose coefficient of static friction is µ. He placed the ball on the surface wrapped with n turns of closely packed conducting coils of negligible mass at the diameter. By some arrangement he is able to pass a current i through the coils either in the clockwise direction or in the anticlockwise direction. A constant horizontal magnetic field B is present throughout the space as shown in the figure. (Assume µ is large enough to help rolling motion) y iB x 9. If current i is passed through the coils the maximum torque in the coil due to magnetic field is :- (A) –nir2B kˆ (B) nir2B ˆj (C) nir2Bˆj (D) nir2Bkˆ 10. The angular velocity of the ball when it has rotated through an angle is ( < 180°) is :- (A) 10 niB sin (B) 5 niB sin (C) 5 niB cos (D) 5 niB sin 7m 14 m 14 m 7m Space for Rough Work E-8/32 1001CT103516011
Leader Course/Phase-III, IV & V/18-12-2016/Paper-1 PHYSICS Paragraph for Questions 11 and 12 Figure shows a massless wheel of radius R and massless spokes with five charges each of charge Q and mass m. System is placed in a field created by two large fixed plates having charges +Q0 and –Q0 respectively. Entire assembly lies in a smooth horizontal plane. Wheel is placed in horizontal plane and constrained to move in horizontal plane. Initally spokes are released along x & y axis as shown in figure. (A = surface area of plate) +Q0 –Q0 y +Q B x –Q A C +Q +Q D –Q 11. Mark the CORRECT statement : QQ0 (A) Acceleration of centre of mass is 5 0 mA (B) Acceleration of centre of mass is QQ0 10 0 mA QQ0 (C) Instantaneous angular acceleration of system is 4 0 AmR (D) Instantaneous angular acceleration of system is QQ0 5 0 AmR 12. Mark the CORRECT statement : (A) When released from rest system executes periodic motion in the reference frame-fixed to centre of mass. (B) When released from rest system executes simple harmonic motion in the reference frame- fixed to centre of mass. (C) Acceleration of point A immediately after release is 5 QQ0 ˆi 2 QQ0 ˆj . 0 mA 0 Am (D) Acceleration of point A immediately after release is QQ0 ˆi 5 QQ0 ˆj . 5 0 mA 0 Am Space for Rough Work 1001CT103516011 E-9/32
Target : JEE (Main + Advanced) 2017/18-12-2016/Paper-1 Paragraph for Questions 13 and 14 PHYSICS A massless square loop of side a is kept in xz plane as shown. Magnetic field in space is non uniform given by B B0 y kˆ . The loop is rotated about x-axis with constant angular velocity . a y B x a z 13. e.m.f. induced in the loop as function of time is equal to :- (A) B0a2 sin 2t (B) B0a2 1 sin 2t (C) 2B0a2 cos t (D) B0a2 cos2t 2 2 14. Torque required to rotate the loop with constant angular velocity (as a function of time). Take resistance of loop = R. (A) B02a4 1 sin 2t2 (B) B02a4 sin2 2t 4R 4R (C) 4B20a4 cos2 t (D) B20a4 cos4 t R R Space for Rough Work E-10/32 1001CT103516011
Leader Course/Phase-III, IV & V/18-12-2016/Paper-1 PHYSICS SECTION–II : (Maximum Marks : 8) This section contains ONE question. Each question contains two columns, Column-I and Column-II. Column-I has four entries (A), (B), (C) and (D) Column-II has five entries (P), (Q), (R), (S) and (T) Match the entries in Column-I with the entries in column-II. One or more entries in Column-I may match with one or more entries in Column-II. The ORS contains a 4 × 5 matrix whose layout will be similar to the one shown below : (A) (P) (Q) (R) (S) (T) (B) (P) (Q) (R) (S) (T) (C) (P) (Q) (R) (S) (T) (D) (P) (Q) (R) (S) (T) For each entry in column-I, darken the bubbles of all the matching entries. For example, if entry (A) in Column-I matches with entries (Q), (R) and (T), then darken these three bubbles in the ORS. Similarly, for entries (B), (C) and (D). For each question, marks will be awarded in one of the following categories : For each entry in Column-I Full Marks : +2 If only the bubble(s) corresponding to all the correct match(es) is (are) Zero Marks darkened : 0 In all other cases 1001CT103516011 E-11/32
Target : JEE (Main + Advanced) 2017/18-12-2016/Paper-1 1. Column-I Column-II PHYSICS (A) Electric field increases as r increases. (P) A single dipole is kept on a axis at x = r such that it is oriented in positive x-direction. We find electric field at a point on +y axis (not origin) (B) Electric field decreases as r increases. (Q) A conductor of radius r & length is connected to battery whose other end is earthed as shown. The volume of conductor is kept constant as r increases or decreases. Electric field is inside the conductor. f y (C) Electric field has downward (R) An ideal solenoid has current i (or negative y) component and radius r.Current is decreasing with time. Point P remains outside the solenoid. Electric field at point P is being investigated y P xr (D) Electric field has upward (S) Parallel plate capacitor is connected (or positive y) component to a battery. The distance between plates is d and radius of plates is r. y Electric field is in between the capacitor plates. (T) A point positive charge is kept at origin. Electric field is being found at (r, r, 0), where r > 0. SECTION–III : Integer Value Correct Type No question will be asked in section III E-12/32 1001CT103516011
Leader Course/Phase-III, IV & V/18-12-2016/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 solid uniform cylinder of mass m performs small oscillations due to the action of two springs combined stiffness equal to k (figure). The period of these oscillations in the absence of sliding is T xm Then find x : 2k . R m 2. Two particle of mass m each are fixed to a massless rod of length 2. The rod is smoothly hinged at one end to a ceiling. It performs oscillation of small angle in vertical plane. The length x of the equivalent simple pendulum is 3 . Then find x : m m Space for Rough Work 1001CT103516011 E-13/32
PHYSICS Target : JEE (Main + Advanced) 2017/18-12-2016/Paper-1 3. The magnetic field of a cylindrical magnet that has a pole-face radius 2.8 cm can be varied sinusoidally between minimum value 16.8 T and maximum value 17.2 T at a frequency of 60 Hz. Cross section of the magnetic field created by the magnet is shown. At a radial distance of 2cm from the axis if the amplitude of the electric field (in mN/C) induced by the magnetic field variation is 40 xmN/C. Then find the value of x. XXX X X XX X X X 2.8cm X X X X X X 4. Consider the E versus x graph. What is the minimum velocity that should be given to a point charge –Q of mass M at x = 3L so that it can reach the origin? Take Q = 1 C, mass of the charge as 1g, E0 = 5 N/C and L = 5m. E0 x 3L L 2L –E0 Space for Rough Work E-14/32 1001CT103516011
Leader Course/Phase-III, IV & V/18-12-2016/Paper-1 PHYSICS 5. A uniform solid sphere of mass m = 400 gm and radius R = 2cm is released from rest from a point A of a rough slide AB. Initially, the centre O of the sphere is at the horizontal level of A. At the lower end B, the slide passes to smooth horizontal plane. A spring is attached to a wall on the horizontal plane. Find the maximum compression (in cm) of the spring in the process of motion of the sphere. (Take g = 10 m/s2) A R = 2cm O m = 400 gm 0.3m Smooth K = 1000 N/m B light strip 2cm Sufficient Smooth Horizontal rough floor Space for Rough Work 1001CT103516011 E-15/32
Target : JEE (Main + Advanced) 2017/18-12-2016/Paper-1 CHEMISTRY PART-2 : CHEMISTRY SECTION–I(i) : (Maximum Marks : 32) 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 : +4 If only the bubble(s) corresponding to all the correct option(s) is (are) darkened. Partial Marks : +1 For darkening a bubble corresponding to each correct option, Provided NO incorrect option is darkened. Zero Marks : 0 If none of the bubbles is darkened. Negative Marks : –1 In all other cases. for example, if (A), (C) and (D) are all the correct options for a question, darkening all these three will result in +4 marks; darkening only (A) and (D) will result in +2 marks; and darkening (A) and (B) will result in –1 marks, as a wrong option is also darkened 1. For a given reaction, rate = k[A] [B]2/3. Correct option(s) is/are :- (A) Units of k = mol–5/3 L5/3 sec–1 (B) Units of k = mol–2/3 L2/3 sec–1 (C) on diluting the solution 8 times rate will become 32 times the initial rate (D) Reaction is a complex reaction 2. Select the correct option(s): (A) H o [H2O(l)] is zero at 25°C f (B) Sfo [O2(g)] is zero at 25°C (C) S°[O2(g)] is zero at 25°C (D) Entropies of aqueous ions can be negative or positive 3. For [Cr(H2O)6]3+ and [Co(H2O)6]3+, which of the following statement(s) is/are CORRECT ? (A) Differ in hybridisation (B) Differ in magnetic properties (C) Same number of atoms are in same plane (D) No one can show any type of isomerism Space for Rough Work E-16/32 1001CT103516011
Leader Course/Phase-III, IV & V/18-12-2016/Paper-1 4. Which of the following is/are related to extraction of metal from silver glance :- CHEMISTRY (A) Formation of complex from NaCN solution (B) Air acts as oxidising agent (C) Thermal decomposition of cyanide complex (D) Zn - dust acts as reducing agent 5. On the complete hydrolysis, which of the given compound(s) is/are producing hydrogen peroxide as one of the product ? (A) H4P2O6 (B) H3PO5 (C) H2S2O6 (D) H2S2O8 6. Red P + HI can be used to carry out which of the following conversion : (A) Propanoic acid Ethane (B) Butanal n-butane (C) Glucose n-hexane (D) Acetophenone Ethyl benzene 7. Following transformation can be carried by using : CH3–CH2–CH=CH2 CH3–CH=CH–CH3 (Major) (A) (i) HBr / H2O2 ; (ii) Aq. KOH ; (iii) Conc. H2SO4 , (B) (i) H2, Ni ; (ii) Br2, hv ; (iii) Alc. KOH , (C) (i) Dil. H2SO4 ; (ii) SOCl2 ; (iii) (CH3)3C–ONa (D) (i) Br2, H2O ; (ii) HBr ; (iii) NaI / Acetone 8. For the following sequence, choose the incorrect option(s) ? CH3–CH2–Br KCN P (i) LiAlH4 Q NaNO2 R (i) CH3MgBr S Aq. EtOH (ii) H2O HCl (ii) H2O Major (A) IUPAC name of (P) is \"ethanenitrile\" (B) Common name of (S) is \"acetaldehyde\" (C) (Q) is more basic than (P) (D) (R) can give immediate turbidity with lucas reagent Space for Rough Work 1001CT103516011 E-17/32
Target : JEE (Main + Advanced) 2017/18-12-2016/Paper-1 CHEMISTRY SECTION–I(ii) : (Maximum Marks : 18) This section contains THREE 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 The solubility of sparingly soluble salt increases in presence of complexating agents while it decreases in presence of common ions. AgCl is a sparingly soluble salt (ksp = 10–10). The solubility of AgCl decreases in AgNO3 and NaCl solution while it increases when taken in aqueous ammonia. The formation constant kf for [Ag(NH3)2]+ is 108. (Given : MAgCl = 143.5 g/mole) 9. What is the solubility of AgCl in (mg) in 10 mL of 0.1 M AgNO3 solution. (A) 9.25 × 10–9 (B) 1.43 × 10–6 (C) 6.96 × 10–9 (D) 1.43 × 10–9 10. How many mole of NH must be added to dissolve 0.01 mole of AgCl in 1 L H O. 32 (A) 0.5 M (B) 0.12 M (C) 0.2 M (D) 0.15 M Space for Rough Work E-18/32 1001CT103516011
Leader Course/Phase-III, IV & V/18-12-2016/Paper-1 CHEMISTRY Paragraph for Questions 11 and 12 White phosphorus + SOCl2 (A) On (B) Trigonal Complete Oxy acid hydrolysis pyramidal (A) + (D) structure Greenish White phosphorus + SO2Cl2 (C) On yellow gas heating Trigonal bipyramidal structure On partial (E) On (F) hydrolysis Complete hydrolysis Oxy acid If anhydride of (B) and (F), both have same number of P–O–P linkage and acts as strong dehydrating agent then. 11. The chemical formula of (E) is :- (A) PCl3 (B) PCl5 (C) POCl3 (D) H3PO3 12. If the basicity of oxyacid (B) is 'x' and basicity of oxyacid (F) is 'y' then the value of x + y is :- (A) 3 (B) 4 (C) 5 (D) 6 Paragraph for Questions 13 and 14 Primary alkyl halide C4H9Br (P) reacted with alcoholic KOH to give compound (Q). Compound (Q) is reacted with HBr to give (R) which is an isomer of (P). (R) on reaction with water produces optically active alcohol (S). 13. Compound (P) in above sequence is : Br (A) Br (B) (C) (D) Br Br 14. Compound (Q) on reaction with NBS produces (X) monobromo derivative then (X) is : (A) 2 (B) 3 (C) 4 (D) 1 Space for Rough Work 1001CT103516011 E-19/32
CHEMISTRY Target : JEE (Main + Advanced) 2017/18-12-2016/Paper-1 SECTION–II : (Maximum Marks : 8) This section contains ONE question. Each question contains two columns, Column-I and Column-II. Column-I has four entries (A), (B), (C) and (D) Column-II has five entries (P), (Q), (R), (S) and (T) Match the entries in Column-I with the entries in column-II. One or more entries in Column-I may match with one or more entries in Column-II. The ORS contains a 4 × 5 matrix whose layout will be similar to the one shown below : (A) (P) (Q) (R) (S) (T) (B) (P) (Q) (R) (S) (T) (C) (P) (Q) (R) (S) (T) (D) (P) (Q) (R) (S) (T) For each entry in column-I, darken the bubbles of all the matching entries. For example, if entry (A) in Column-I matches with entries (Q), (R) and (T), then darken these three bubbles in the ORS. Similarly, for entries (B), (C) and (D). For each question, marks will be awarded in one of the following categories : For each entry in Column-I Full Marks : +2 If only the bubble(s) corresponding to all the correct match(es) is (are) darkened Zero Marks : 0 In all other cases 1. Match the column- Column-I Column-II (A) 0.01 M RNH2 (kb = 10–10M) (P) pH = 4 (B) 0.1M H2A (Q) pH = 6 (ka1 = 10–7M ; ka2 = 10–10M) (R) pH = 8.5 (C) 10–2M HA (ka = 10–15M) (D) when equal volumes of (S) pH = 8 0.1 M HA(ka = 10–7M) and (T) degree of dissociation is 10–2M HB (ka= 10–6M) are mixed negligible Space for Rough Work SECTION–III : Integer Value Correct Type No question will be asked in section III E-20/32 1001CT103516011
Leader Course/Phase-III, IV & V/18-12-2016/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. The compressibility factor (Z) vs P for one mole of a real gas is plotted at constant temperature 300K. If the slope of the graph at very high pressure is 1 atm–1. Find Vander Waal constant b in 10 litre mol–1. Given R = 0.08 atm litre/mol K. First multiply your answer with 10. Then fill your answer as sum of digits (excluding decimal places) till you get the single digit answer. 2. For the conversion of ore into their oxide, roasting process is used for how many given ores ? Sphalerite , Chalcocite , Fluorspar , Calamine , Azurite , Anglesite , Limonite , Cinnabar , Galena , Pyrolusite , Fool's gold Space for Rough Work 1001CT103516011 E-21/32
CHEMISTRY Target : JEE (Main + Advanced) 2017/18-12-2016/Paper-1 3. Total number of geometrical isomers are possible for [Co(NH3)3(H2O)2(NO3)]2+ is :- 4. In the following monobromination reaction, the number of possible chiral product is/are Br Br2 (1.0 mole) 300º C (1.0 mole) 5. Consider all possible isomeric ketones including stereoisomers of molecular formula 'C5H10O' , All these isomers are independently reacted with LiAlH4 (NOTE : stereoisomers are also reacted separately) The, total number of ketones that give a racemic product(s) is/are. Space for Rough Work E-22/32 1001CT103516011
Leader Course/Phase-III, IV & V/18-12-2016/Paper-1 PART-3 : MATHEMATICS MATHEMATICS SECTION–I(i) : (Maximum Marks : 32) 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 : +4 If only the bubble(s) corresponding to all the correct option(s) is (are) darkened. Partial Marks : +1 For darkening a bubble corresponding to each correct option, Provided NO incorrect option is darkened. Zero Marks : 0 If none of the bubbles is darkened. Negative Marks : –1 In all other cases. for example, if (A), (C) and (D) are all the correct options for a question, darkening all these three will result in +4 marks; darkening only (A) and (D) will result in +2 marks; and darkening (A) and (B) will result in –1 marks, as a wrong option is also darkened 1. Let S1 & S2 are two circles of same radius 2 and their centres C1 & C2 lie on line y = x. Line 4x – 3y = 5 is one common tangent of two circles which touches S1 at point A & S2 at point B. Identify the correct statements - (A) AB 28 (B) C1C2 = 10 (C) Area of ABC1 is 28 sq. units (D) Area of quadrilateral AC2BC1 = 42 sq. units 2. If sec2 x 3 dx n ƒ(x) 4 ƒ2(x) 3 sin1 k.g(x) C , where C is an integration 2 constant, then (A) value of k is equal to 3 (B) g(x) ƒ(x) 1 ƒ2(x) 2 (D) g2(x)ƒ2(x) = ƒ2(x) – g2(x) (C) g2(x) 1 ƒ2 (x) 1 Space for Rough Work 1001CT103516011 E-23/32
MATHEMATICS Target : JEE (Main + Advanced) 2017/18-12-2016/Paper-1 3. Consider ƒ() = 2sin2 – cos2 + 1, where R, then which is/are correct - 3 (A) If [0, 1], then maximum value of ƒ() is 4 (B) If [0, 1], then maximum value of ƒ() is 3 (C) If > 0 and ƒ() 2 2 , then n ,n Z 24 (D) If < 0 and ƒ() 32 4 2 , then 2 2 4. P(x) is a least degree polynomial such that (P(x) – 1) is divisible by (x – 1)2 & (P(x) – 3) is divisible by (x + 1)2 , then (A) graph of y = P(x) is symmetric about origin (B) y = P(x) has two points of extrema (C) P(x)dx 0 for exactly one value of . 4 (D) P(x)dx 0 for exactly two values of . 4 ƒ( x ) 1 / x 1 2x3 e3 5. Let ƒ(x) be a biquadratic function of x such that lim , then- x0 (A) the value of |ƒ(1)| is 8. (B) the value of |ƒ'(1)| is 30. (C) absolute value of lim ƒ(x) is 6. (D) the value of ƒ(1) is 8. x4 x Space for Rough Work E-24/32 1001CT103516011
Leader Course/Phase-III, IV & V/18-12-2016/Paper-1 2 3 n MATHEMATICS 3 .... n 6.e1/n 2 e1 / n e1/ n e1 / n n2 lim is less than- n (A) 0 (B) 1 (C) 2 (D) 3 7. Let y = ƒ(x) be a non negative function such that area of quadrilateral formed by tangent at any point P on the curve, co-ordinate axes & ordinate of point P is equal to abscissa of point P. If ƒ(1) = 2, then (A) ƒ(x) is a bounded function (B) area bounded by y = ƒ(x) & (y – 1)2 = 6x is 2 sq. units (C) tangents drawn to y = ƒ(x) from point 1, 3 are mutually perpendicular 4 (D) function g(x) = |ƒ(x) – x2| is non differentiable at two points. 8. Consider three distinct lines x + y + 6 = 0 2x + y – 3 = 0 x + 2y + 5 = 0 let m denotes number of possible values of for which given lines are concurrent and n denotes number of possible values of for which given lines do not form a triangle, then (A) m = 2 (B) m = 3 (C) n = 6 (D) n = 7 Space for Rough Work 1001CT103516011 E-25/32
Target : JEE (Main + Advanced) 2017/18-12-2016/Paper-1 MATHEMATICS SECTION–I(ii) : (Maximum Marks : 18) This section contains THREE 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 Question 9 and 10 Consider set S = {(a,b) : (a + 3)t2 = 3 – a and bt2 – 4t + b = 0}, where t is are real parameter. Let C is curve which is formed by all elements of set S where (a,b) is a point in R2. Tangents are drawn from the point P(3,4) to the curve C touching the curve C at point Q and R. 9. The circumcentre of triangle PQR is (), then value of + 3 is- (A) 3 (B) 5 (C) 7 (D) 9 10. Curve E is equation of ellipse whose foci are Q,R and curve E is passing through point P, then eccentricity of ellipse E is- 2 10 3 10 3 10 2 10 (A) (B) (C) (D) 53 5 54 5 45 5 3 5 10 Space for Rough Work E-26/32 1001CT103516011
Leader Course/Phase-III, IV & V/18-12-2016/Paper-1 MATHEMATICS Paragraph for Questions 11 and 12 If ƒ(x,y) = 0 be the solution of differential equation (2y cosec2x + ncoty)dx + (ntanx – 2xcosec2y)dy = 0 such that ƒ , 0 , then 4 2 11. ƒ(x,y) is- (B) (tanx)y(coty)x (A) (tanx)x(coty)y (C) tan xx2 cot yy2 (D) tan xy2 cot yx2 ƒ 5 , 2017 cos x 1 3/2 4 4 2 , then 0x 12. dx If 0x dx 1 sin2 x is equal to- (D) (A) 6 (B) 4 (C) 2 Paragraph for Questions 13 and 14 Normals are drawn from a point P(h,k) with slopes m1, m2, m3 to the parabola C1 : y2 = 4x. 13. If curve C is the locus of point P with m1m2 = 2, then number of common tangents to curve C1 and curve C is - (A) 1 (B) 2 (C) 4 (D) infinite 89 22 (m1 ) (m2 ) (m3 ) 0 0 0 If 14. , where |mi| < 1 i = 1, 2, 3, then value of 67h – 89k is - (A) 139 (B) 157 (C) 173 (D) 191 Space for Rough Work 1001CT103516011 E-27/32
MATHEMATICS Target : JEE (Main + Advanced) 2017/18-12-2016/Paper-1 SECTION–II : (Maximum Marks : 8) This section contains ONE question. Each question contains two columns, Column-I and Column-II. Column-I has four entries (A), (B), (C) and (D) Column-II has five entries (P), (Q), (R), (S) and (T) Match the entries in Column-I with the entries in column-II. One or more entries in Column-I may match with one or more entries in Column-II. The ORS contains a 4 × 5 matrix whose layout will be similar to the one shown below : (A) (P) (Q) (R) (S) (T) (B) (P) (Q) (R) (S) (T) (C) (P) (Q) (R) (S) (T) (D) (P) (Q) (R) (S) (T) For each entry in column-I, darken the bubbles of all the matching entries. For example, if entry (A) in Column-I matches with entries (Q), (R) and (T), then darken these three bubbles in the ORS. Similarly, for entries (B), (C) and (D). For each question, marks will be awarded in one of the following categories : For each entry in Column-I Full Marks : +2 If only the bubble(s) corresponding to all the correct match(es) is (are) Zero Marks darkened : 0 In all other cases 1. Column-I Column-II (A) The eccenticity of ellipse x2 y2 2 1 be (P) 0 2 1 2 1 4 , then 2is (Q) 1 3 . If its latus rectum is (R) 3 (B) Least prime value of K, such that K||x|n|x||= 1 (S) an even integer (T) an odd integer has exactly 6 distinct solutions, is (C) If A(cos, sin), B(sin, – cos) and C(2,1) are the vertices of ABC. If centre of locus of centroid is () then + is (D) If xyx x , x,y R+ then slope of tangent at point y (e,1) on the curve is Space for Rough Work SECTION–III : Integer Value Correct Type No question will be asked in section III E-28/32 1001CT103516011
Leader Course/Phase-III, IV & V/18-12-2016/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. Number of solution(s) of equation x [0,] (cos5x) + (sinx) (cos4x) – (sin4x) + (sin3x) + (cosx) (sin2x) – (cos2x) = 0 is 2. An insect moves around the circle x2 + y2 = 1 in circular orbits of different radii such that circle subtends an angle to the insect where , . Let S1 & S2 are circles with minimum and 2 maximum radii of such orbits respectively, then the radius of locus of a point whose chord of contact to S2 touches S1, is Space for Rough Work 1001CT103516011 E-29/32
MATHEMATICS Target : JEE (Main + Advanced) 2017/18-12-2016/Paper-1 xx 3. Let ƒ be a continuous function satisfying the equation ƒ(t)dt tƒ(x t)dt ex 1 , then value 00 of |ƒ(0)| is 4. The sum of integral values of k for which the equation sin–1x + tan–1x = sin–1(sinx) + 2k – 1, has a real solution is 5. If x,y R, x2 + y2 + xy = 1, then minimum value of x3y + xy3 + 7 is Space for Rough Work E-30/32 1001CT103516011
Leader Course/Phase-III, IV & V/18-12-2016/Paper-1 Space for Rough Work 1001CT103516011 E-31/32
Target : JEE (Main + Advanced) 2017/18-12-2016/Paper-1 QUESTION PAPER FORMAT AND MARKING SCHEME : 16. The question paper has three parts : Physics, Chemistry and Mathematics. 17. Each part has three 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 +4 +1 0 –1 One or more If only the bubble(s) For darkening a bubble If none In all I(i) correct 8 corresponding corresponding to each of the other 32 option(s) to all the correct correct option, provided bubbles is cases option(s) is(are) NO incorrect option darkened darkened darkened Paragraph +3 0 –1 Based If only the bubble If none In all of the other I(ii) (Single 6 corresponding to — 18 correct the correct option bubbles is cases option) is darkened darkened +8 +2 0 II Matrix If only the bubble(s) For darkeninga bubble In all Match Type 1 corresponding to corresponding to each other — 8 — 20 all the correct correct match is cases match(es) is(are) darkened darkened +4 0 Single digit If only the bubble In all IV Integer 5 corresponding — other (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-32/32 Your Target is to secure Good Rank in JEE 2017 1001CT103516011
Paper Code : 1001CT103516011 CLASSROOM CONTACT PROGRAMME (Academic Session : 2016 - 2017) HINDI JEE (Main + Advanced) : LEADER COURSE Test Type : MINOR PHASE : III, IV & V Test Pattern : JEE-Advanced TEST DATE : 18 - 12 - 2016 Time : 3 Hours PAPER – 1 Maximum Marks : 234 1. 2. (ORS) 3. 4. 5. 3220 6. 7. 8. 9. : 10. 11. 12. : 13. 14. 15. g = 10 m/s2
Target : JEE (Main + Advanced) 2017/18-12-2016/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 H-2/32 1001CT103516011
Leader Course/Phase-III, IV & V/18-12-2016/Paper-1PHYSICS HAVE CONTROL HAVE PATIENCE HAVE CONFIDENCE 100% SUCCESS BEWARE OF NEGATIVE MARKING -1: –I(i) : ( : 32) (A), (B), (C) (D) : +4 : +1 : 0 : –1 (A),(C) (D ) +4 (A)(D ) +2(A ) (B) –1 1. (A) (B) (C) (D) 2. k (A) (B) (C) (D) 1001CT103516011 H-3/32
PHYSICS Target : JEE (Main + Advanced) 2017/18-12-2016/Paper-1 3. MR y x RM z (A) 23g (B) LddLt, kˆ (C) (D) ddLt,kˆ H-4/32 1001CT103516011
Leader Course/Phase-III, IV & V/18-12-2016/Paper-1PHYSICS 4. AB ACk= m2 A'm' BC m A 1 g cos 'm' (A) sin (B) (A) (C) (A) (D) 'm' 1001CT103516011 H-5/32
PHYSICS Target : JEE (Main + Advanced) 2017/18-12-2016/Paper-1 5. R Flux (in T-m2) 10 0 1 2 3 4 5 6 time t(in sec) -10 (A) t = 1 s, 3s 5s (B) t = 0 s, 2s 6s (C) 6s (D) 6. , bm i B T1 T2 b B mg (B) T1 m g 2ibB (A) T1 = T2 = 2 2 (C) T2 m g 2ibB (D) T1 < T2 2 H-6/32 1001CT103516011
Leader Course/Phase-III, IV & V/18-12-2016/Paper-1 7. AB MA PHYSICS A mr 60° 2rr 62 10 m Initial position A final m position m A 60° rr B B (A) Mm 32 (B) Mm 23 (C) 6m/s (D) 3m/s 8. 5m5m 2m µ5mmµ m 2m 5m 60° (A) µ (B) 5m µ=0 (C) 43m3g 1 3 (D) 5m 13 1001CT103516011 H-7/32
PHYSICS Target : JEE (Main + Advanced) 2017/18-12-2016/Paper-1 –I(ii) : ( :18) (A), (B), (C) (D ) : +3 : 0 : –1 9 10 m rµ n i B µ y iB x 9. i (A) –nir2B kˆ (B) nir2B ˆj (C) nir2Bˆj (D) nir2Bkˆ 10. (< 180°) (A) 10 niB sin (B) 5 niB sin (C) 5 niB cos (D) 5 niB sin 7m 14 m 14 m 7m H-8/32 1001CT103516011
Leader Course/Phase-III, IV & V/18-12-2016/Paper-1PHYSICS 11 12 RQ m +Q0 –Q0 xy (A = ) +Q0 –Q0 y +Q B x –Q A C +Q +Q D –Q 11. : (A) 5Q0Qm0A (B) 10Q0Qm0 A (C) 4Q0QAm0R (D) 5Q0QAm0R 12. (A) (B) (C) A5Q0Qm0 Aˆi QQ0 ˆj 2 0 Am (D) A5Q0Qm0 Aiˆ 5 QQ0 ˆj 0 Am 1001CT103516011 H-9/32
PHYSICS Target : JEE (Main + Advanced) 2017/18-12-2016/Paper-1 13 14 axzBB0ykˆ a x- y B x a z 13. (A) B0a2 sin 2t (B) B0a2 1 sin 2t (C) 2B0a2 cos t (D) B0a2 cos2t 2 2 14. (=R) (A) B20a4 1 sin 2t2 (B) B20a4 sin2 2t 4R 4R (C) 4B20a4 cos2 t (D) B02a4 cos4 t R R H-10/32 1001CT103516011
Leader Course/Phase-III, IV & V/18-12-2016/Paper-1PHYSICS –II : ( : 8) -I-II -I (A), (B), (C) (D) -II (P), (Q), (R), (S) (T) -I -II -I -II 4 ×5 : (A) (P) (Q) (R) (S) (T) (B) (P) (Q) (R) (S) (T) (C) (P) (Q) (R) (S) (T) (D) (P) (Q) (R) (S) (T) -I -I(A) (Q),(R) (T) (B), (C)(D) : -I : +2 : 0 1001CT103516011 H-11/32
Target : JEE (Main + Advanced) 2017/18-12-2016/Paper-1 1. -I -II PHYSICS (A) r (P) x=r x- +y (B) r (Q) r r f y (C) (R) i r ( y) P (D) P (y) y P xr (S) dr y (T) (r, r, 0) r> 0 –III : III H-12/32 1001CT103516011
Leader Course/Phase-III, IV & V/18-12-2016/Paper-1PHYSICS –IV : (: 20) 09 : +4 : 0 1. mk Tx2mkx R m 2. m 2 x3 x m m 1001CT103516011 H-13/32
PHYSICS Target : JEE (Main + Advanced) 2017/18-12-2016/Paper-1 3. 2.8 cm 60Hz16.8T 17.2 T 2cm 40xmN/Cx XXX X X XX X X X 2.8cm X X X X X X 4. E-x x=3L M –Q Q=1C , 1g,E 0 = 5 N/C L = 5m E0 3L x L 2L –E0 H-14/32 1001CT103516011
Leader Course/Phase-III, IV & V/18-12-2016/Paper-1PHYSICS 5. m = 400 gm R=2cm ABA O,A B (cm )(g= 10 m/s2) A R = 2cm O m = 400 gm 0.3m Smooth K = 1000 N/m B light strip 2cm Sufficient Smooth Horizontal rough floor 1001CT103516011 H-15/32
Target : JEE (Main + Advanced) 2017/18-12-2016/Paper-1 CHEMISTRY -2: –I(i) : ( : 32) (A), (B), (C) (D) : +4 : +1 : 0 : –1 (A),(C) (D ) +4 (A)(D ) +2(A ) (B) –1 1. = k[A] [B]2/3 :- (A) k =m ol–5/3 L5/3 sec–1 (B) k =m ol–2/3 L2/3 sec–1 (C) 8 32 (D) 2. : (A) 25°C H o [H2O(l)] f (B) 25°C Sfo [O2(g)] (C) 25°C S°[O2(g)] (D) 3. [Cr(H2O)6]3+ [Co(H2O)6]3+ , ? (A) (B) (C) (D) H-16/32 1001CT103516011
Leader Course/Phase-III, IV & V/18-12-2016/Paper-1 4. :- CHEMISTRY (A) NaCN (B) (C) (D) Zn - (dust) 5. ? (A) H4P2O6 (B) H3PO5 (C) H2S2O6 (D) H2S2O8 6. P+HI (A) (B) n- (C) n- (D) 7. CH3–CH2–CH=CH2 CH3–CH=CH–CH3 (A) (i) HBr / H2O2 ; (ii) KOH ; (iii) H2SO4 , (B) (i) H2, Ni ; (ii) Br2, hv ; (iii) KOH , (C) (i) Dil. H2SO4 ; (ii) SOCl2 ; (iii) (CH3)3C–ONa (D) (i) Br2, H2O ; (ii) HBr ; (iii) NaI / 8. CH3–CH2–Br KCN P (i) LiAlH4 Q NaNO2 R (i) CH3MgBr S Aq. EtOH (ii) H2O HCl (ii) H2O Major (A) (P) IUPAC \" \" (B) (S) \"\" (C) (P) (Q) (D) (R), 1001CT103516011 H-17/32
Target : JEE (Main + Advanced) 2017/18-12-2016/Paper-1 CHEMISTRY –I(ii) : ( :18) (A), (B), (C) (D ) : +3 : 0 : –1 9 10 AgCl (ksp = 10–10) AgCl AgNO3 NaCl [Ag(NH3)2]+ kf=108 (:M AgCl = 143.5 g/mole) 9. 10 ml 0.1 M AgNO3 AgCl (m g) (A) 9.25 × 10–9 (B) 1.43 × 10–6 (C) 6.96 × 10–9 (D) 1.43 × 10–9 10. 1 L H O0.01 AgCl NH 23 (A) 0.5 M (B) 0.12 M (C) 0.2 M (D) 0.15 M H-18/32 1001CT103516011
Search
