Paper Code : 100 1CT103516006 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 : 25 - 09 - 2016 Time : 3 Hours PAPER – 2 Maximum Marks : 240 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) 2017/25-09-2016/Paper-2 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 1001CT103516006
Leader Course/Phase-III, IV & V/25-09-2016/Paper-2 HAVE CONTROL HAVE PATIENCE HAVE CONFIDENCE 100% SUCCESS BEWARE OF NEGATIVE MARKING PHYSICS 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. Zero Marks : 0 If none of the bubbles is darkened. Negative Marks : –2 In all other cases. 1. As shown below, a boy is using the rope through a fixed pulley to move a box with constant speed v. The kinetic friction coefficient between the box and the ground is < 1; assume that the fixed pulley is massless and there is no friction between the rope and the fixed pulley. Then, while the box is moving on surface, which of the following statements is/are correct? ////////////////////////////////////////////////// //////////////////////////////////////////////////////// (A) The magnitude of the force on the rope is constant. (B) The magnitude of friction between the ground and the box is decreasing. (C) The magnitude of the normal force of the ground on the box is increasing. (D) The magnitude of the normal force of the ground on the box is decreasing Space for Rough Work 1001CT103516006 E-3/32
PHYSICS Target : JEE (Main + Advanced) 2017/25-09-2016/Paper-2 2. A massless bucket is initially at rest next to one end of a chain that lies in a straight line on the floor, as shown in Fig. The chain has uniform mass density (kg/m). You push on the bucket (so that it gathers up the chain) with the force F(t) that gives the bucket and whatever chain is inside, a constant acceleration a at all times. 't' is time. There is no friction between the bucket and the floor. bucket F(t) chain a (A) F(t) at time t is 3 a2t2 (B) work done by F(t) upto time t is 3 a3t4 2 8 (C) F(t) at time t is 3 a2t2 (D) work done by F(t) upto time t is 3 a3t4 4 4 3. A stick with length has both translational and rotational motion, as shown in figure. Both v and are positive in the direction shown. Taking clockwise angular momentum L to be positive, which one of the following statements is/are true? B v A (A) The L around point B is negative. (B) The L around point A can be positive or negative, depending on the value of v and . (C) The L around point A is positive (D) The L around point B can be positive or negative, depending on the value of v and . Space for Rough Work E-4/32 1001CT103516006
Leader Course/Phase-III, IV & V/25-09-2016/Paper-2 PHYSICS 4. One end of a stick with mass m and length is pivoted on a wall and the other end rests on a frictionless floor, as shown in figure. Let FL and FR be the vertical forces on the left and right ends of the stick, respectively. Then :- Pivot FR FL (A) FL= mg/2 (B) FL < FR (C) FL = FR (D) FL = FR = mg cos 5. Acceleration time graph of particle is as shown in figure. Initial velocity of particle is 8m/s. a 4 24 t (A) maximum velocity of particle is 16 m/s (B) displacement of particle from t = 2 sec to t = 4 sec is 92/3 (C) particle changes its direction of motion at t = 4 sec (D) velocity time graph is a parabola. Space for Rough Work 1001CT103516006 E-5/32
PHYSICS Target : JEE (Main + Advanced) 2017/25-09-2016/Paper-2 6. An apple falls from a tree. Which of the following explains why the apple speeds up as it falls? (A) The momentum of the earth-apple system is conserved (B) There is a downward gravitational force acting on the apple (C) Gravity does positive work on the apple as it falls. (D) The apple loses potential energy as it falls. 7. The diagram shows the vertical plane containing the path of a particle which is projected from a point O on an inclined plane :- u O 11 (A) If the range on the plane is maximum then 42 (B) If T is the time of flight, the particle is at its greatest height above the plane after an interval 1T 2 (C) The maximum range is u2 [sec2 tan sec ] g (D) The kinetic energy of the particle is maximum as it leaves O. 8. A mass m moves with a given speed and collides (not necessarily head-on) elastically with another mass m that is initially at rest, as shown in Fig. Which of the figures shows an impossible outcome for the two velocities? (The velocities are drawn to scale) mm (A) (B) (C) (D) Space for Rough Work E-6/32 1001CT103516006
Leader Course/Phase-III, IV & V/25-09-2016/Paper-2 SECTION–I(ii) : (Maximum Marks : 16) This section contains TWO paragraphs. PHYSICS Based on each paragraph, there will be TWO 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. Zero Marks : 0 If none of the bubbles is darkened. Negative Marks : –2 In all other cases. Paragraph for Questions 9 and 10 As shown, a block (Object-A) of mass mA moves on a frictionless plane at initial speed v0, and lands onto a cart (Object-B in the figure, mass mB, length L, initially at rest) smoothly. Ignore the size of the block. The friction coefficient between A and B is and the cart is on a frictionless plane. The block collides elastically on the fixed wall at the end of the cart and eventually falls off the cart. A B v0 9. Which of the following statements is/are CORRECT? (A) the minimum value of v0 such that the block can indeed fall off the cart is 2 1 mA gL mB (B) the minimum value of v0 such that the block can indeed fall off the cart is 2 gL (C) final kinetic energy of system is non-zero (D) final kinetic energy of system in center of mass frame may be zero. 10. Suppose the initial speed is larger than the minimum value in above question, (A) the kinetic energy loss of the system (block + cart) is 2mAgL (B) the kinetic energy loss of the system (block + cart) is mAgL (C) linear momentum of system of block and cart is conserved (D) linear momentum of system of block and cart is not conserved Space for Rough Work 1001CT103516006 E-7/32
PHYSICS Target : JEE (Main + Advanced) 2017/25-09-2016/Paper-2 Paragraph for Questions 11 and 12 A particle of mass m moves in one dimension such that its potential energy is given as : U(x) = –ax2 + bx4 where a and b are positive constants and x is the position. 11. Which of the following is/are correct? (A) The angular frequency of small oscillations about the minima of the potential energy is equal to (2a/m)1/2 (B) The angular frequency of small oscillations about the minima of the potential energy is equal to 2(a/m)1/2 a2 (C) The minimum value of potential energy is 4b a2 (D) The minimum value of potential energy is 2b 12. Which of the following graph(s) is/are correct ? Force Force Potential energy Potential energy (A) (B) x (C) x (D) x x 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-8/32 1001CT103516006
Leader Course/Phase-III, IV & V/25-09-2016/Paper-2 SECTION–IV : (Maximum Marks : 32) This section contains EIGHT questions. PHYSICS 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 mass m travels at speed v0 perpendicularly to a stick of mass m and length l, which is initially at rest. The mass collides completely inelastically with the stick at one of its end, and sticks to it. The location of point from end A (in cm) which is at instantaneous rest just after collision is X. X/10 is (take : l = 1.2 meter) v0 A m m B 2. A uniform rod AB of weight 100 N rests on a rough peg at C and a force F acts at A as shown in figure. If BC = CM, where M is midpoint of rod, and tan = 4/3, then minimum coefficient of friction at C is X. Fill the value of 8X. B F C M A Space for Rough Work 1001CT103516006 E-9/32
Target : JEE (Main + Advanced) 2017/25-09-2016/Paper-2 PHYSICS3. A uniform disc rolls from rest from height y1 down the side of a fixed trough whose vertical dimension y is given by the equation y = kx2. The disc does not slip from A to B, but the surface of the trough is frictionless from B towards C (see figure). The disc reaches height y2 . 3y2 is (Assume radius of disc to be very small compared to y1 & y2). y1 rm y A C y1 y2 B 4. A thin ring of mass 2m and radius R is pivoted at P on a frictionless horizontal table, as shown in figure. A insect of mass m runs along the ring with speed v with respect to the ring. The insect starts from the pivot with the ring at rest. When the insect reaches the diametrically opposite point on the ring (point X), it is moving with velocity v with respect to the table. The value of v/v is. X v P insect Space for Rough Work E-10/32 1001CT103516006
Leader Course/Phase-III, IV & V/25-09-2016/Paper-2 PHYSICS 5. As shown, a large ball of mass M = m is connected on each end by a light thread of length l to small balls of mass m. Initially the three balls are along the straight line on a smooth surface. The large ball is suddenly given an initial velocity v in the direction perpendicular to the line. mv2 The tension in the thread at the moment the two small balls meet is T. The value of T is. v mM m 6. A uniform “L” shaped rigid body AOB of mass m, where AO = OB = l and AOB is a right angle, is hinged to a smooth joint at Point A of the body and can swing freely in a vertical plane. Initially, the body is released from rest with AB horizontal. The maximum kinetic energy of the 2 10 mg is. body is K.The value of K O B A Smooth joint . Space for Rough Work 1001CT103516006 E-11/32
PHYSICS Target : JEE (Main + Advanced) 2017/25-09-2016/Paper-2 7. A block of mass m is placed on a level frictionless table. The block is attached to a horizontally aligned spring fixed with its other end and is vibrating in a horizontal plane with the period T. Suddenly at the instant of time when the spring comes to the position of equilibrium and becomes unstretched the block disconnects from the spring and continues sliding across the frictionless surface away from the spring until it encounters a loop of radius R. The amplitude of vibrations of the block on the spring in order for the block to just complete the loop without falling down is A. The value of T 5gR is. A R x=0 m A 8. A river is flowing with velocity 5km/hr as shown in the figure. A boat starts from A and reaches the other bank by covering shortest possible distance. Velocity of boat in still water is 3km/hr. s The distance (in m) boat covers is s. The value of 100 is B b=300m A Space for Rough Work E-12/32 1001CT103516006
Leader Course/Phase-III, IV & V/25-09-2016/Paper-2 PART-2 : CHEMISTRY 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. Zero Marks : 0 If none of the bubbles is darkened. Negative Marks : –2 In all other cases. 1. A(g) 2B(g) + C(g), if the rate constant of reaction is 0.05 M sec–1 then which of the following is/are correct for the reaction - (A) The reaction is unimolecular (B) t = 2t (C) t3/4 = 1.5t1/2 3/4 1/2 2. Which of the following is correct (D) The reaction never goes to completion (A) Equilibrium whether in a physical or in a chemical system is always of dynamic nature. (B) If E > E then on increasing temperature equilibrium constant will increase aF aB (C) At equilibrium state of a chemical reaction Gibbs energy of system is minimum (D) At equilibrium state of a chemical reaction entropy of system is maximum 3. Identify the CORRECT statement :- (A) Peroxy linkage is present in marshall's acid (B) Pyrophosphoric acid on hydrolysis gives phosphoric acid (C) Basicity of phosphorous acid is two (D) Debye force is responsible for the formation of clathrate compound of Xe in ice Space for Rough Work 1001CT103516006 E-13/32
Target : JEE (Main + Advanced) 2017/25-09-2016/Paper-2 CHEMISTRY4. Which of the following properties are INCORRECT for mineral tremolite [Ca2Mg5(Si4O11)2(OH)2] : (A) Double chain silicate unit is present (B) Silicate unit is non-planar (C) Some tetrahedron units are sharing two corners/O-atoms (D) Some tetrahedron units are sharing three corners/O-atoms 5. Which of the following order of boiling point is INCORRECT :- (A) BF3 < B(CH3)3 (B) B(OH)3 > B(OMe)3 (C) HF < HI (D) NH3 > SbH3 6. Select options in which first compound is stronger acid than second compound : OH OH NO2 OH (B) , (A) CH3–COOH , NO2 COOH COOH O O (C) , (D) , O SO3H NO2 Space for Rough Work E-14/32 1001CT103516006
Leader Course/Phase-III, IV & V/25-09-2016/Paper-2 Cl Cl Cl CHEMISTRY 7. CH3–CH–CH–CH–Br H HY For the above compound (A) the given newmann projection can be represented Cl X Cl X & Y are respectively : (A) CH3 and CHClBr (B) CH3 & CH3 (C) –CH–CH3 & Br (D) –CH–Cl & –CH3 Cl CH3 8. (A) C HH For the above molecule (A) the following statement(s) is/are correct : (A) It has plane of symmetry (B) It has axis of symmetry (C) Above molecule is optically active (D) The molecule can show geometrical isomerism Space for Rough Work 1001CT103516006 E-15/32
CHEMISTRY Target : JEE (Main + Advanced) 2017/25-09-2016/Paper-2 SECTION–I(ii) : (Maximum Marks : 16) This section contains TWO paragraphs. Based on each paragraph, there will be TWO 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. Zero Marks : 0 If none of the bubbles is darkened. Negative Marks : –2 In all other cases. Paragraph for Questions 9 and 10 For parallel path reactions following first order kinetics at 300K. If rate contant of first and second reaction are k1 and k2 respectively and k1 = 0.693 sec–1 , k2 = 1.386 sec–1 2A K1 3B ...............(A) 3A K2 4C ...............(B) 9. Mol % of B wrt total moles of products formed at 300 K is - (A) 200 % (B) 400 % (C) 300 % (D) 500 % 11 11 11 11 10. The half life of reaction at 300K is - (A) 13 sec. (B) 6 sec. (C) 2 sec. (D) 1 sec. 6 13 8 Space for Rough Work E-16/32 1001CT103516006
Leader Course/Phase-III, IV & V/25-09-2016/Paper-2 CHEMISTRY Paragraph for Questions 11 and 12 Cl Cl H Cl C Cl Cl C (I) (II) Cl H (III) (IV) (V) H H OH CH2–OH Cl Cl C C C H OH H OH Cl Cl Cl Cl Cl Cl HO H (IX) Cl H OH CHO (X) (VI) CH2–OH (VIII) (VII) 11. Correct relationship(s) for the above compounds : (A) (III) & (IV) are distereomers (B) (I) & (II) are distereomers (C) (VII) & (VIII) are enantiomers (D) (V) & (VI) are distereomers but both are optically inactive 12. For the above compounds which of the following statements is/are correct : (A) Number of optically inactive compounds in the above are 5 (B) Compound (IX) & (X) have COS (C) Both (VII) & (VIII) are D-forms (D) (III) is more stable than (IV) 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 1001CT103516006 E-17/32
Target : JEE (Main + Advanced) 2017/25-09-2016/Paper-2 CHEMISTRY SECTION–IV : (Maximum Marks : 32) This section contains EIGHT 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. If NH0 [C6H5NH2 & HCl] = –10.6 kcal/ mol NH0 [NaOH & HCl] = –13.6 kcal/ mol then calculate |H0| of following reaction : C H NH Cl(aq.) + NaOH(aq.) C H NH OH(aq.) + NaCl(aq.) 65 3 65 3 [A] 1 2. mol/litre 0.5 0.25 12 3 time(sec) From the variation of concentration of A with time graph for the reaction A 2B Find the order of reaction ? Space for Rough Work E-18/32 1001CT103516006
Leader Course/Phase-III, IV & V/25-09-2016/Paper-2 CHEMISTRY 3. When a monoatomic ideal gas is subjected to a polytropic process the temperature of 2 mol of gas decreased by 2K on giving 4 calorie of heat to the gas. Calcualte 2(x) where x is polytropic index. 4. Identify the number of chemical species having ionic character less than LiI :- LiCl , NaCl , NaBr , KI , CsI , NaI Space for Rough Work 1001CT103516006 E-19/32
CHEMISTRY Target : JEE (Main + Advanced) 2017/25-09-2016/Paper-2 5. Find the number of chemical species which on complete hydrolysis form one of the product as dibasic oxyacid :- PCl3 , BCl3 , SOF4 , TeF6 , P4O6 6. Find the number of chemical species which does NOT exist :- H22+ , [CF6]2– , NOF3 , Ne2 , PbI4 , [SiI6]2– Space for Rough Work E-20/32 1001CT103516006
Leader Course/Phase-III, IV & V/25-09-2016/Paper-2 CHEMISTRY Br Br Br Cl Br 7. Cl Cl Cl Cl Br Cl (II) (III) (IV) Cl Cl (I) Cl Br Br Cl Br Cl Cl Br C (VIII) (V) (VI) OO (VII) Number of optically inactive compounds from above compounds is/are : CH=CH–Ph 8. Ph–CH=HC CH=CH–Ph Total number of stereoisomers for above compound is/are : Space for Rough Work 1001CT103516006 E-21/32
Target : JEE (Main + Advanced) 2017/25-09-2016/Paper-2 MATHEMATICS PART-3 : 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. Zero Marks : 0 If none of the bubbles is darkened. Negative Marks : –2 In all other cases. 1. For every real number p, the quadratic equation (p2 + 2)x2 – 2(a + p)2x + (p2 + 2p + b) = 0 has a root x1 = 1, where a,b R. Then which of the following statement(s) is(are) correct ? (A) The value of (a – b) is equal to 4 7 (B) If the other root is also unity then p is equal to 4 (C) Number of solutions of the equation sin + cos = a + b, where 2,2 is equal to 4. (D) Number of solutions of the equation t + –t b is equal to 1. = 3a 2. If 10 tan1 3 9k2 , then- k1 1 3k (A) cosec() – sec() < 0 (B) tan(3) > 0 (C) cos 2 133 (D) log 13 cot2 4 205 6 3. If ye x e x , then dy is- dx e x e x y2 4 2e x y y2 4 (A) (B) (C) (D) 2x 2x 2x 2x Space for Rough Work E-22/32 1001CT103516006
Leader Course/Phase-III, IV & V/25-09-2016/Paper-2 4. 2017 ar. cos2017r x. sin r x dx MATHEMATICS The value of 0 r0 (A) zero (B) depends upon a2r+1 (r W) (C) independent from a2r (r W) (D) independent from ar (r W) 5. Which of the following statement(s) is (are) correct ? (A) If the function g is continuous on [–1,1] such that g(–1) = 4 and g(1) = 3, then there exist a number r such that |r| < 1 and g(r) = . (B) The function ƒ x nx nx is continuous at x = e, where e is napier's constant. [Note : [x] and {x} denote greatest integer less than or equal to x and fractional part of x respectively] (C) If lim 3x2 x 1 exists and is equal to then 1 10 x2 x 2 x2 (D) If 10 sin 2x x R n,2n 1 where n I , then least integral value of is sec2 x cosec2x 2 equal to 3 45 89 6. Let P sin r sec k , then- r 1 k46 (A) sin1 P (B) cot1 log2 P tan1 2 6 (C) cot1 2 logP 2 cot1 1 (D) sin–1(sinP) = – P P2 Space for Rough Work 1001CT103516006 E-23/32
Target : JEE (Main + Advanced) 2017/25-09-2016/Paper-2 MATHEMATICS7. Consider the equation cos1 k sin1 17 x2 6x , in x then- 2 2 (A) the largest value of k for which the equation has 2 distinct solutions is 1. (B) the equation has atleast one real root if k 1, 1 2 (C) the equation has atleast one real root if k 1 ,1 2 (D) the equation has unique solution if k 1 2 8. Let ,8, are in H.P and ,8, are in A.P, (), then - (A) > (B) < (C) x 1 dx 1 x3 / 2 C (D) x 1 dx 6 1 2 tan1 x C x3 tan1 x3 (where C is constant of integration) Space for Rough Work E-24/32 1001CT103516006
Leader Course/Phase-III, IV & V/25-09-2016/Paper-2 SECTION–I(ii) : (Maximum Marks : 16) MATHEMATICS This section contains TWO paragraphs. Based on each paragraph, there will be TWO 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. Zero Marks : 0 If none of the bubbles is darkened. Negative Marks : –2 In all other cases. Paragraph for Questions 9 and 10 If x satisfied the equation px2 – qx – 2 = 0 where 1 dt (0,) and 3 t2 sin 2t , then - 0 2t cos 3 t2016 1 p t2 1 q dt 9. Which of the following option(s) is/are correct ? (A) lim p q (B) lim0 p q (C) lim 1 q2 (D) lim0 1 q 2 p p 0 0 (where [.] denotes greatest integer function) 10. The value of x can be- (A) 2 sin (B) 2 sin (C) 2 sin (D) 2 sin Space for Rough Work 1001CT103516006 E-25/32
MATHEMATICS Target : JEE (Main + Advanced) 2017/25-09-2016/Paper-2 Paragraph for Questions 11 and 12 Let P(x) be a polynomial satisfying lim xP x 1 x 2016 x6 where P(0) = 1, P(2) = 9, P(3) = 28, P(4) = 65 and P(6) = 217, then 9 11. Px x3 dx is- 3 (A) 0 (B) 12 P5 P 1 (C) (D) 8 35 x 3 dx 1 n x 6 1 n x 2 Px x3 1 Ax B x4 12. If C (where C is an integration constant), then- (A) A – 3B = 0 (B) B2 – 5A = 16 (C) A 1 (D) B = 16 48 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-26/32 1001CT103516006
Leader Course/Phase-III, IV & V/25-09-2016/Paper-2 SECTION–IV : (Maximum Marks : 32) MATHEMATICS This section contains EIGHT 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 sum of all possible distinct real values of c for which the equation x2 c2 7 x 7c2 x 3 x 2 3c 0 in x, has atleast one real solution is equal to 2. If the sum of all real values of y satisfying the equation ey x 2 x 1 where x(3,100) is S then [S] is equal to [Note : [k] denotes the greatest integer less than or equal to k] Space for Rough Work 1001CT103516006 E-27/32
MATHEMATICS Target : JEE (Main + Advanced) 2017/25-09-2016/Paper-2 3. Let <an> be an increasing arithmetic progression with a1 = 2 and 7aa2 4aa5 , then 4 10 10 ar 1 is equal to r2 3 aar r1 4. In triangle ABC, if sin2A = sin2B, (A B) and 3tanA = 4, then the value of expression 1 4 tan2 B 2 sin B A cot C cos B 1 sin2 A cos A 1 sin2 B is equal to Space for Rough Work E-28/32 1001CT103516006
Leader Course/Phase-III, IV & V/25-09-2016/Paper-2 5. / 2 8 sin2016 x 5 cos2016 x dx is a (a and b are coprime), then (a – b) is MATHEMATICS If the value of 0 sin2016 x cos2016 x b 6. Let ƒ(x) = [x]{x} + {x}[x] and ƒ ' 5 1 n2 , then value of is (where [.] and {.} represent greatest 2 integer function and fractional part of function) Space for Rough Work 1001CT103516006 E-29/32
Target : JEE (Main + Advanced) 2017/25-09-2016/Paper-2 MATHEMATICS ƒ x x3 3x ƒ1 h tan1 h 7. then value of lim is h0 sin1 h (where [.] represent greatest integer function) cot2 x cot3 x cot99 x cot x 2 99 3 8. If ... 1 cot x 1 cot99 x dx cot2 xdx cot3 x dx cot4 xdx .... cot98 x dx , then value of Space for Rough Work E-30/32 1001CT103516006
Leader Course/Phase-III, IV & V/25-09-2016/Paper-2 Space for Rough Work 1001CT103516006 E-31/32
Target : JEE (Main + Advanced) 2017/25-09-2016/Paper-2 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 Marks Marks Que. Marks Marks section — 0 +4 If none –2 of the One or more If only the bubble(s) bubbles is In all darkened I(i) correct 8 corresponding other 32 option(s) to all the correct cases option(s) is(are) darkened Paragraph +4 0 –2 If none In all Based If only the bubble(s) — of the other — bubbles is cases I(ii) (One or more 4 corresponding to all darkened 16 correct the correct option(s) 0 option(s)) is(are) darkened In all other +4 cases Single digit If only the bubble IV Integer 8 corresponding — 32 (0-9) to correct answer 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 1001CT103516006
Paper Code : 1001CT103516006 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 : 25 - 09 - 2016 Time : 3 Hours PAPER – 2 Maximum Marks : 240 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) 2017/25-09-2016/Paper-2 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 1001CT103516006
Leader Course/Phase-III, IV & V/25-09-2016/Paper-2PHYSICS HAVE CONTROL HAVE PATIENCE HAVE CONFIDENCE 100% SUCCESS ////////////////// BEWARE OF NEGATIVE MARKING -1: –I(i) : ( : 32) (A), (B), (C) (D) : +4 : 0 : –2 1. v <1 //////////////////////////////// //////////////////////////////////////////////////////// (A) (B) (C) (D) 1001CT103516006 H-3/32
PHYSICS Target : JEE (Main + Advanced) 2017/25-09-2016/Paper-2 2. (kg/m) F(t) a't' bucket F(t) chain a (A) t F(t) 3 a2t2 (B) F(t) t 3a3t4 2 8 (C) t F(t) 3 a2t2 (D) F(t) t 3a3t4 4 4 3. v L B v A (A) B L (B) A L v (C) A L (D) B L v H-4/32 1001CT103516006
Leader Course/Phase-III, IV & V/25-09-2016/Paper-2PHYSICS 4. m FLFR Pivot FR FL (A) FL= mg/2 (B) FL < FR (C) FL = FR (D) FL = FR = mg cos 5. 8m/s a 4 24 t (A) 16 m/s (B) t = 2 sec t = 4 sec 92/3 (C) t = 4 sec (D) 1001CT103516006 H-5/32
PHYSICS Target : JEE (Main + Advanced) 2017/25-09-2016/Paper-2 6. (A) (B) (C) (D) 7. O u O (A) 1 1 4 2 (B) T 12T (C) u2 [sec2 tan sec ] g (D) O 8. mm mm (A) (B) (C) (D) H-6/32 1001CT103516006
Leader Course/Phase-III, IV & V/25-09-2016/Paper-2PHYSICS –I(ii) : ( : 16) (A), (B), (C) (D) : +4 : 0 : –2 9 10 mA (-A) v0 mBL (-B) AB A B v0 9. (A) mA gL mB v021 (B) v02gL (C) (D) 10. (A) + 2mAgL (B) + mAgL (C) + (D) + 1001CT103516006 H-7/32
PHYSICS Target : JEE (Main + Advanced) 2017/25-09-2016/Paper-2 11 12 m U(x) = –ax2 + bx4 a b x 11. (A) (2a/m)1/2 (B) 2(a/m)1/2 (C) a2 4b (D) a2 2b 12. Force Force Potential energy Potential energy (A) (B) x (C) x (D) x x –II : & –III : II III H-8/32 1001CT103516006
Leader Course/Phase-III, IV & V/25-09-2016/Paper-2PHYSICS –IV : ( : 32) 09 : +4 : 0 1. m ml v0 A (cm )X X/10(l=1.2meter) v0 A m m B 2. AB 100 N C A F BC =CM M tan=4/3 C X 8X B F C M A 1001CT103516006 H-9/32
PHYSICS Target : JEE (Main + Advanced) 2017/25-09-2016/Paper-2 3. y1 y= kx2 ABBC y2 3yy12y1y2 rm y A C y1 y2 B 4. 2m R P m v X) vv/v X v P insect H-10/32 1001CT103516006
Leader Course/Phase-III, IV & V/25-09-2016/Paper-2PHYSICS 5. M=ml m vT mTv2 v mM m 6. m “L ” AO B AO = OB = l AOB A AB K 2 10 mg K O B A Smooth joint . 1001CT103516006 H-11/32
PHYSICS Target : JEE (Main + Advanced) 2017/25-09-2016/Paper-2 7. m T R AT5gR A R x=0 m A 8. 5km /hr A 3km/hrs(m)10s0 B b=300m A H-12/32 1001CT103516006
Leader Course/Phase-III, IV & V/25-09-2016/Paper-2 -2: CHEMISTRY –I(i) : ( : 32) (A), (B), (C) (D) : +4 : 0 : –2 1. A(g) 2B(g) + C(g),0.05 M sec–1 - (A) (B) t = 2t 3/4 1/2 (C) t3/4 = 1.5t1/2 (D) 2. (A) (B) EaF > E aB (C) (D) 3. :- (A) (B) (C) (D) Xe 1001CT103516006 H-13/32
CHEMISTRY Target : JEE (Main + Advanced) 2017/25-09-2016/Paper-2 4. [Ca2Mg5(Si4O11)2(OH)2] : (A) (B) (C) O- (D) O- 5. :- (A) BF3 < B(CH3)3 (B) B(OH)3 > B(OMe)3 (C) HF < HI (D) NH3 > SbH3 6. OH OH NO2 OH (B) , (A) CH3–COOH , COOH COOH NO2 OO (C) , (D) , O SO3H NO2 H-14/32 1001CT103516006
Leader Course/Phase-III, IV & V/25-09-2016/Paper-2 Cl Cl Cl CHEMISTRY 7. CH3–CH–CH–CH–Br (A) H HY X Y Cl X (A) CH3 CHClBr Cl (C) –CH–CH3 Br (B) CH3 CH3 (D) –CH–Cl –CH3 Cl CH3 8. (A) C HH (A) (A) (B) (C) (D) 1001CT103516006 H-15/32
Target : JEE (Main + Advanced) 2017/25-09-2016/Paper-2 CHEMISTRY –I(ii) : ( : 16) (A), (B), (C) (D) : +4 : 0 : –2 9 10 300K k1 k2 k1= 0.693 sec–1 , k2 = 1.386 sec–1 2A K1 3B ...............(A) 3A K2 4C ...............(B) 9. 300 K B%- (A) 200 % (B) 400 % (C) 300 % (D) 500 % 11 11 11 11 10. 300K - (A) 13 sec. (B) 6 sec. (C) 2 sec. (D) 1 sec. 6 13 8 H-16/32 1001CT103516006
Leader Course/Phase-III, IV & V/25-09-2016/Paper-2 CHEMISTRY 11 12 Cl Cl H Cl C Cl Cl C (I) (II) Cl H (III) (IV) (V) H H OH CH2–OH Cl Cl C C C H OH H OH Cl Cl Cl Cl Cl Cl HO H (IX) Cl H OH CHO (X) (VI) CH2–OH (VIII) (VII) 11. (A) (III) (IV) (B) (I) (II) (C) (VII) (VIII) (D) (V) (VI) 12. (A) 5 (B) (IX) (X) COS (C) (VII) (VIII) D- (D) (IV) (III) –II : & –III : II III 1001CT103516006 H-17/32
Target : JEE (Main + Advanced) 2017/25-09-2016/Paper-2 CHEMISTRY –IV : ( : 32) 09 : +4 : 0 1. NH0 [C H NH H Cl] = –10.6 kcal/ mol 65 2 NH0 [NaOH H Cl] = –13.6 kcal/ mol |H0| C H NH Cl(aq.) + NaOH(aq.) C H NH OH(aq.) + NaCl(aq.) 65 3 65 3 [A] 1 2. mol/litre 0.5 0.25 12 3 time(sec) A A 2B ? H-18/32 1001CT103516006
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