Paper Code : 0000CT103116002 CLASSROOM CONTACT PROGRAMME (Academic Session : 2016 - 2017) ENGLISH JEE (Main + Advanced) : LEADER & ENTHUSIAST COURSE DO NOT BREAK THE SEALS WITHOUT BEING INSTRUCTED TO DO SO BY THE INVIGILATOR TARGET : JEE (ADVANCED) 2017 Test Type : ALL INDIA OPEN TEST Test Pattern : JEE-Advanced TEST DATE : 12 - 02 - 2017 Time : 3 Hours PAPER – 1 Maximum Marks : 186 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 28 pages and that all the 18 questions in each subject and along with the options are legible. If not, contact the invigilator for replacement of the booklet. 6. You are allowed to take away the Question Paper at the end of the examination. OPTICAL RESPONSE SHEET : 7. The ORS will be collected by the invigilator at the end of the examination. 8. Do not tamper with or mutilate the ORS. Do not use the ORS for rough work. 9. Write your name, form number and sign with pen in the space provided for this purpose on the ORS. Do not write any of these details anywhere else on the ORS. Darken the appropriate bubble under each digit of your form number. DARKENING THE BUBBLES ON THE ORS : 10. Use a BLACK BALL POINT PEN to darken the bubbles on the ORS. 11. Darken the bubble COMPLETELY. 12. The correct way of darkening a bubble is as : 13. The ORS is machine-gradable. Ensure that the bubbles are darkened in the correct way. 14. Darken the bubbles ONLY IF you are sure of the answer. There is NO WAY to erase or \"un-darken\" a darkened bubble. 15. Take g = 10 m/s2 unless otherwise stated. Please see the last page of this booklet for rest of the instructions
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Advanced)/12-02-2017/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-2/28 0000CT103116002
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Advanced)/12-02-2017/PAPER-1 HAVE CONTROL HAVE PATIENCE HAVE CONFIDENCE 100% SUCCESS MATHEMATICS BEWARE OF NEGATIVE MARKING PART-1 : MATHEMATICS SECTION–I(i) : (Maximum Marks : 15) This section contains FIVE 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 option is darkened. Zero Marks : 0 If none of the bubbles is darkened. Negative Marks : –1 In all other cases 1. If the product of power of point (1,1) and (–1,–1) with respect to circle x2 + y2 + 2px + 2qy + 4 = 0 is negative and the circle neither touches nor intersects co-ordinate axes, then the area of region formed by the set of ordered pair (p,q) on pq-plane is- (A) 1 (B) 2 (C) 3 (D) 4 2. The sum of the distances of the point P lying inside the triangle formed by lines y = 0; 4x – 3y = 0 and 3x + 4y – 9 = 0 is 3. Then the locus of P is- (D) x – 2y – 6 = 0 (A) 7x + 6y – 24 = 0 (B) x – 2y + 24 = 0 (C) 7x – 4y + 6 = 0 3. Let M(n) be the largest integer m such that m m 1 (where n nCr and n N), then n 1 n r the value of lim Mn is- n n (A) 3 5 (B) 3 5 (C) 5 1 (D) 5 1 2 2 2 2 Space for Rough Work 0000CT103116002 E-3/28
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Advanced)/12-02-2017/PAPER-1 MATHEMATICS4. 5 1 1 Let a0 and ak a2 2 for k > 1, then the value of k0 ak is- k 1 2 1 2 3 4 (A) 5 (B) 5 (C) 7 (D) 7 5. If the reflection of the parabola y2 = 4(x – 1) in the line x + y = 2 is the curve Ax + By = x2, then the value of (A + B) is- (A) 0 (B) 1 (C) 2 (D) 3 Space for Rough Work E-4/28 0000CT103116002
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Advanced)/12-02-2017/PAPER-1 SECTION–I(ii) : (Maximum Marks : 32) MATHEMATICS 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 : –2 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 –2 marks, as a wrong option is also darkened 6. A circular disc with 3 sectors marked as alphabet O,A,B has circumference 1. The alphabet coming infront of marker is noted down after each spin (as shown in diagram). Assume boundary of AO sectors do not come infront of marker. It is spun 6 times around its B centre and resulting alphabet which comes infront of marker are arker noted down in order. If the probability that the word BAOBAA to be formed is maximised, then (where x,y,z respectively denotes the probability of occurrence of alphabet O,A,B) - (A) x 1 (B) y 1 (C) y 1 (D) z 1 2 2 3 6 7. If x, y, 0, and cos xsin y 1 tan z , then z can lie in- 2 sin y (A) 0, (B) , (C) , 3 (D) 3 , 2 2 2 2 2 Space for Rough Work 0000CT103116002 E-5/28
MATHEMATICS ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Advanced)/12-02-2017/PAPER-1 8. Which of the following limits is/are equal to unity ? (A) lim tan x sinx sin x tanx x0 (B) lim 1 ex 1 cos x x0 sin x 1 (C) lim 1|x| |x| (where [.] denotes greatest integer function) x0 n1 k2 k 1 lim n n (D) , n N k2 k 1 dy y 9. If a curve passing through P(4,2) and satisfies the differential equation dx x y2 is a conic then which of the following is correct ? (A) focus of conic lies on line y = 2 (B) equation of directrix of conic is 4x – 17 = 0 (C) eccentricity of conic is 1 (D) eccentricity of conic is 3 10. A plane contains the line L1 : y z 1,x 0 and is parallel to the line L2 : x z 1,y 0 , b c a c then- (A) equation of plane is x y z 1 0 b c a (B) equation of plane is x y z 1 0 a b c (C) if shortest distance between line L1 and line L2 is 1 , then 111 is 64 4 a2 b2 c2 (D) if shortest distance between line L1 and line L2 is 1 , then 111 is 192 4 a2 b2 c2 Space for Rough Work E-6/28 0000CT103116002
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Advanced)/12-02-2017/PAPER-1 MATHEMATICS 11. If the two parabolas y2 = 4x and y2 = (x – k) have a common normal other than x-axis, then value of K can be - (A) 1 (B) 2 (C) 3 (D) 4 12. Let M be the set of all possible 2 × 2 matrices A of integer entries such that AAT = I where I 1 0 , then- (where det A denotes determinant value of matrix A) 1 0 (A) Number of matrices in set M is 8 (B) Number of matrices in set M is 4 (C) Number of matrices in set M such that det.(A – I) 0 is 3 (D) Number of matrices in set M such that det.(A – I) 0 is 2 13. Let z1 = 16 + 6i, z2 = 10 + 6i (where i 1 ). If z is any complex number such that z z1 amp z z2 is , then which of the following is/are always correct ? 4 (A) Locus of z is minor arc of a circle (B) Locus of z is major arc of a circle (C) z 13 9i 3 2 (D) z 13 3i 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 0000CT103116002 E-7/28
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Advanced)/12-02-2017/PAPER-1 MATHEMATICS SECTION–IV : (Maximum Marks : 15) 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 : +3 If only the bubble corresponding to the correct answer is darkened. Zero Marks : 0 In all other cases. ƒ x tan1 x 2 2 4 tan1 x 3 ........... 2 1. Let tan1 x upto infinite terms. If the equation ƒ2(x) + (sin–1x)2 = k posses a solution, then the number of integral values of k is 2. If ƒ : R R satisfies the functional equation ƒ x ƒ 1 1 tan 1 x, x R 0 and x 1 let N ƒ x dx , then least integer greater than or equal to N is 0 Space for Rough Work E-8/28 0000CT103116002
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Advanced)/12-02-2017/PAPER-1 3. Let y = ƒ(x) be a thrice differentiable function defined on R such that ƒ(x) = 0 has at least 5 distinct MATHEMATICS zeros, then minimum number of zeros of the equation ƒ(x) + 6ƒ'(x) + 12ƒ\"(x) + 8ƒ\"'(x) = 0 is 1 x1007 1 x 1007 dx N 22015 1 0 x1007 Let 4. , then the number of divisors of N of the form 1 x2016 1007 dx 0 4n + 2, (n N) is Space for Rough Work 0000CT103116002 E-9/28
MATHEMATICS ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Advanced)/12-02-2017/PAPER-1 5. A certain kind of bacteria either die, split into two or split into three bacteria. All splits are 11 exact copies. The chances of dying is , the chances of splitting into two is and splitting 42 1 into three is . If the probability that it survives for infinite length of time is 4 m 13 (m,n N), then the value of (m+n) is n Space for Rough Work E-10/28 0000CT103116002
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Advanced)/12-02-2017/PAPER-1 PART-2 : PHYSICS PHYSICS SECTION–I(i) : (Maximum Marks : 15) This section contains FIVE 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 option is darkened. Zero Marks : 0 If none of the bubbles is darkened. Negative Marks : –1 In all other cases 1. The radius of a spherical enclosure containing a monatomic gas increases linearly with temperature such that r = r0 + kT. If the walls of the spherical enclosure is adiabatic. Choose 1 dp the correct graph of variation of p dT with radius (r) :- 1 dp 1 dp 1 dp 1 dp p dT p dT p dT p dT (A) (B) (C) (D) rr r r 2. In the figure shown find the total magnification after two successive reflections first on M1 and then on M2. (Assume paraxial rays only) f=30cm f=20cm //////////////////////////////////////////////////// ///////////////////////////////////////////////// M2 M1 10cm 30cm (A) +6 (B) –6 (C) +3 (D) –3 Space for Rough Work 0000CT103116002 E-11/28
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Advanced)/12-02-2017/PAPER-1 3. Two thermally insulated equal globes, one filled with one mole of a light ideal gas, and the PHYSICS other with one mole of a heavy ideal gas at the same temperature and pressure, are placed one above the other with the light gas uppermost. When communication is open between the globes, the gases are completely mixed in a short time. Assuming the gases to be monatomic, find change of temperature when the light gas is helium (density = 0.18 × 10–3 g cm–3) and the heavy gas is xenon (density = 6 × 10–3 g cm–3), at standard temperature and pressure, for a distance h between the centres of the globes = 100cm. MXe = 131 gm, MHe = 4 gm. (A) –0.01°C (B) –0.025°C (C) +0.01°C (D) +0.025°C 4. A spring is placed between the jaws of screw gauge such that the spring is not at all compressed. The main scale reads 2 divisions and circular scale reads 28 divisions. Now we turn the circular scale by 18° such that the spring is compressed. The circular scale has 200 divisions and the least count of the main scale is 1mm. What is the force exerted by the spring on the jaws if the spring constant is 100 N/m. (A) 4 mN (B) 3 mN (C) 5 mN (D) 7 mN 5. Two thin lenses with lens powers D1 and D2 are located at distance L = 25 cm from each other, and their main optical axes coincide. This system creates a direct real image of the object, located at the main optical axis closer to lens of power D1 with the magnification +1. If the positions of the two lenses are exchanged, the system again produces a direct real image, with the magnification +4. What are the possible types of lens? (i) 1 is converging and 2 is diverging (ii) 1 is diverging and 2 is converging (iii)both are converging (iv) both are diverging (A) all four are possible (B) iii only (C) i, ii and iii (D) iii and iv Space for Rough Work E-12/28 0000CT103116002
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Advanced)/12-02-2017/PAPER-1 SECTION–I(ii) : (Maximum Marks : 32) This section contains EIGHT questions. PHYSICS 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 : –2 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 –2 marks, as a wrong option is also darkened 6. In the figure shown a conducting rod of mass m, length '' and resistance 'R' can smoothly move along parallel rails in horizontal plane. Initially the rod is at rest. A uniform magnetic field B perpendicular to the plane of motion exists in the region. Now switch S is closed at t = 0, then : SC B m,,R (A) The charge on the capacitor in steady state is mc/(m + cB22) (B) The charge on the capacitor in steady state is 2mc/(m + cB22) (C) Velocity of conducting rod in steady state is 2Bc/(m + cB22) (D) Velocity of conducting rod in steady state is Bc/(m + cB22) Space for Rough Work 0000CT103116002 E-13/28
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Advanced)/12-02-2017/PAPER-1 7. A teacher asks 4 students to find the speed of sound using resonance column apparatus. The PHYSICS set of apparatus used by each of student was different. The frequency of tuning fork used was known precisely. He wants the error in speed of sound to be within 1%. Which of the student(s) did the experiment correctly. Their results are tabulated below. Student Frequency 1st resonance 2nd resonance (A) 476 Hz 17.0 cm 50.0 cm (B) 340 Hz 25.2 cm 76.0 cm (C) 544 Hz 15.6 cm 46.0 cm (D) 510 Hz 16.0 cm 48.2 cm 8. Consider the situation shown in the figure. The switch S is open for a long time and then closed and again steady state reached then : C X 2C 2C S C Y V 2CV CV (A) Charge flowing from X to Y is (B) Charge flowing from Y to X is 3 3 CV 2 2CV2 (C) Work done by battery is (D) Work done by battery is 3 3 Space for Rough Work E-14/28 0000CT103116002
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Advanced)/12-02-2017/PAPER-1 PHYSICS 9. A thin copper tube of outer radius 0.5 cm carries a liquid flowing at T = 100°C. The copper tube loses heat according to Newton's law with constant of proportionality 3 × 10–3 cal/cm2 sec°C. The temperature of surrounding is 20°C. Now we coat a layer with thermal conductivity 2.8 × 10–3 cal/cm°C sec. The layer is 0.5 cm thick. Assume that outer surface of layer loses heat with same constant of proportionality : (Take : n2 = 0.7) 8 (A) The rate of heat loss becomes 7 times 7 (B) The rate of heat loss becomes 8 times (C) The temperature T of outer surface of layer is approximately 65.7°C (D) The temperature T of outer surface of layer is approximately 42.2°C 10. A small sphere is charged uniformly and placed at point A(x, y)m, so that at point B (8, 7) m electric field strength is 54iˆ 72ˆj N/C and potential is +900 volt. The di-electric strength E of air is 3 × 106 v/m. Choose the CORRECT option(s) : (A) Co-ordinate of point A are (2, –1)m (B) Charge of the sphere is 2µC (C) Minimum possible radius of sphere is 30cm so that air does not break down. (D) None of the above Space for Rough Work 0000CT103116002 E-15/28
PHYSICS ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Advanced)/12-02-2017/PAPER-1 11. In the circuit shown both cells are ideal and of fixed emf, the resistor of resistance R1 has fixed resistance and the resistance of resistor R2 can be varied (but the value of R2 is not zero). Then : R1 E1 R2 E2 (A) The electric power delivered to resistor of resistance R1 is independent of R2 (B) Electric power delivered by E1 is independent of R2 (C) Electric power delivered by E1 is dependent on R2 (D) Electric power delivered to R1 is dependent on R2. 12. An insect of mass m, moves on a rough inclined surface from point A. As the surface is very sticky, the coefficient of friction between the insect and the incline is µ = 1. Assume that it can move in any direction; up the incline or down the incline then (g = 10 m/s2). Choose the correct option :- A µ=1 =37° (A) The maximum possible acceleration of the insect is 14 m/sec2 (B) The maximum possible acceleration of the insect is 2 m/sec2 (C) The insect can move with a constant velocity (D) No friction force will act on insect when it moves with constant velocity. Space for Rough Work E-16/28 0000CT103116002
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Advanced)/12-02-2017/PAPER-1 PHYSICS 13. Find the moment of inertia (in kg-m2) of a semicircular plane of radius 1 m and mass 1 kg as shown. Given sin = 3/32. B X’ A X (A) IXX' = 0.5 kg m2 (B) IXX' = 0.25 kg m2 (C) IAB = 1 kg m2 (D) IAB 15 32 kgm2 Space for Rough Work 12 SECTION –II : Matrix-Match Type & SECTION –III : Integer Value Correct Type No question will be asked in section II and III 0000CT103116002 E-17/28
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Advanced)/12-02-2017/PAPER-1 SECTION–IV : (Maximum Marks : 15) 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 : +3 If only the bubble corresponding to the correct answer is darkened. Zero Marks : 0 In all other cases. 1. Suppose a hypothetical magnetic field exists in space Bˆ B0uˆ r above the earth surface where uˆ r is a unit vector directed radially outward from origin. Origin is on surface of earth. A light charged particle has to perform uniform circular motion in the combined uniform (vertical) gravitational field of earth and magnetic field with speed v and radius r. Height of the plane nv2 of motion from earth surface will be h . Find n. g 2. ABCD is a square frame of conductor of electrical resistivity . The frame lies in a vertical plane. PQ is an imaginary boundary separating space into two parts. Left of PQ, a uniform gravitational field g exists (figure) whereas no gravitational field is present right of PQ. The electrical potential difference between A and B will be k mgh . e is charge on an electron and 4e m is mass of electron. Find k. P D A gh B C Q Space for Rough Work E-18/28 0000CT103116002
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Advanced)/12-02-2017/PAPER-1 PHYSICS 3. A shell of radius 1m is coated with a thin layer of – active material. It's initial charge is zero and initial number of active atoms is 4 1012 . If half life of decay is 1 hr and all the electron 3 are emitted with an energy of 1.44 keV, find the time (in hr.) after which charge on the sphere becomes constant. Neglect the time taken by electron to return back. 4. In the circuit shown, find the current in Amp through the battery at t = 0.1 ln 2 sec, if switch is closed at t = 0. S R=3 L=0.5H =180/11V R=3 R=3 R=3 Space for Rough Work 0000CT103116002 E-19/28
PHYSICS ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Advanced)/12-02-2017/PAPER-1 5. A ball is projected with initial velocity 40 2 m/s at an angle of 60° with horizontal as shown in figure. When its velocity is making an angle of 45° with downward vertical, it collides a vertically hanging ball of same mass and sticks to it as shown in figure. Find the maximum value of length (in m) of the string, so that the combined mass completes the vertical circle in subsequent motion. 402m/s 60° 45° Space for Rough Work E-20/28 0000CT103116002
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Advanced)/12-02-2017/PAPER-1 PART-3 : CHEMISTRY CHEMISTRY SECTION–I(i) : (Maximum Marks : 15) This section contains FIVE 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 option is darkened. Zero Marks : 0 If none of the bubbles is darkened. Negative Marks : –1 In all other cases 1. CH4 + O2 CO + H2 ; H = – 36 kJ per mol of methane CH4 + H2O CO + H2 ; H = 216 kJ per mol of methane Find the ratio in which O2 and H2O are passed in an adiabatic container at constant pressure, containing large amount of CH4 , such that temperature remains unchanged. (A) 1 : 1 (B) 6 : 1 (C) 3 : 1 (D) 2 : 1 2. Find standard reduction potential of CuBr electrode at 298K using following information Pt|H2(g)(1bar)| HBr (10–4M) |CuBr | Cu ; Ecell = 0.6 volt ; Ksp [CuBr] = 10–12M2 [Given : 2.303R 298 0.06 ] F (A) 0.84 volt (B) 0.6 volt (C) 0.12 volt (D) 0.36 volt 3. When N2 can be absorbed by calcium carbide at the temperature around 1100°C then compound 'Q' is formed :- (A) Q is CaNCN and it is called nitrolim (B) Q is good fertiliser (C) Both (A) and (B) (D) None of these 4. NO gas is absorbed by :- (A) FeSO4 (B) Fe2(SO4)3 (C) Both (A) and (B) (D) None of these 5. The best reaction sequence to convert 2-methyl-1-bromopropane into 4-methyl-2-bromopentane is : (A) (i) Mg in ether (ii) acetaldehyde (iii) NH4Cl ; (iv) SOBr2 (B) (i) NaCCH in ether (ii) H O+ + HgSO (iii) HBr, heat 3 4 (C) (i) Alcoholic KOH (ii) CH3COOOH (iii) H2 / Pt (iv) HBr, heat (D) (i) NaCCH in ether (ii) H, Lindlar catalyst (iii) HCl , peroxide 2 Space for Rough Work 0000CT103116002 E-21/28
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Advanced)/12-02-2017/PAPER-1 CHEMISTRY SECTION–I(ii) : (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 : –2 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 –2 marks, as a wrong option is also darkened 6. The label on a bottle containing a dilute aqueous solution of an acid became damaged, only its concentration was readable. A pH meter was nearby and a quick measurement showed that the [H+] is equal to the value on the lebel. The acid could be - (A) A strong monoprotic acid (B) H2SO4(aq.) [strong for both dissociation] (C) A weak monoprotic acid (D) A strong monoprotic base 7. Select the INCORRECT statements (A) Diameter of colloidal particles is between 1 nm to 100 nm (B) Enzyme form colloidal solution in H2O (C) For the coagulation of negative sol, coagulation power is in the order PO43– > SO42– > Cl– (D) As the number of 'C' atom per molecules increases, CMC values normally increases Space for Rough Work E-22/28 0000CT103116002
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Advanced)/12-02-2017/PAPER-1 8. HNO2 + Urea X+Y+Z CHEMISTRY (neutral oxide) Brown K2[HgI4]/OH– P H2O Mg lime water W Milky solution ppt. CuO X Which of the following compound have two bond in it's structure : (A) X (B) Y (C) W (D) P 9. Which of the following compound(s) has/have linear geometry :- (A) [Ag(NH3)2]+ (B) [Ag(CN)2] (C) [Au(CN)2]– (D) ICl2 10. Metal oxide + syngas Metal + H2O M + 4CO 50°–60° 'X' 200°–230°C (Impure) Metal (pure) carbonyl complex Which of the following statements are CORRECT about given reaction :- (A) Metal M is Ni (B) Process is known as Mond's process in which pure metal is obtained (C) Hybridisation of metal in 'X' is sp3 (D) Maximum five atoms are present in one plane in 'X' Space for Rough Work 0000CT103116002 E-23/28
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Advanced)/12-02-2017/PAPER-1 CHEMISTRY11. For the following sequence, choose the correct option(s) ? COOH S Br2 R NH3 N3H P (i) HNO2 Q NaOH H2SO4 (ii) H2O , Boil (X) (A) (Q) will give positive Br2, H2O test (B) (R) on reaction with NaNO2, HCl produces (X) (C) Major product (P) & (S) are identical (D) Reaction sequence involves schmidt & Hoffmann bromamide degradation reaction 12. The compound(s) that will NOT react(s) with hot concentrated aqueous alkali at atmospheric pressure is/are : Cl CHO CH2CHO Cl NO2 (B) (C) (D) (A) OCH3 CH3 OCH3 NO2 13. Following are the structure of D-Glucose and D-Galactose. CHO CHO H OH H OH HO H HO H H OH HO H H OH H OH CH2OH CH2OH Which of the following statements are correct about these compounds ? (A) They are diastereomers (B) Both are component of lactose (C) They are C–4 epimer (D) Both are optically active 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-24/28 0000CT103116002
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Advanced)/12-02-2017/PAPER-1 SECTION–IV : (Maximum Marks : 15) 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 : +3 If only the bubble corresponding to the correct answer is darkened. Zero Marks : 0 In all other cases. 1. An excited H-like species when bombarded by photons of wavelength 54 nm gets excited to another excited state. In returning back to ground state it emits, a total six different types of photons. Out of six different photons three have wave length less than 54 nm. Determine atomic no. of H-like species. (Shortest wavelength of Lyman series of H-atom is 90 nm.) 2. An atom of U238 disintegrates by a series of -decays and -decays until it becomes Pb206 which is stable. How many of the following ten nuclides may formed from the series of distintegration starting at U238. U235, U234, Ac228, Ra224, Rn224, Rn220, Po215, Po212, Pb212, Pb211 3. Consider following compounds :- M(AA)3 n , M(AB)3 n , M(AB)2 b2 n , Ma3bcdn , Ma4b2 n Find the number of complex compound which have two geometrical isomer Space for Rough Work 0000CT103116002 E-25/28
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Advanced)/12-02-2017/PAPER-1 CHEMISTRY4. Among the following, the number of molecules which are optically active & possess C2 axis of symmetry are : Cl Cl Me Me HH Me Me Et Et CHCl3 2,5-dimethylthiophene Cl Cl Me Me H H 5. Total number of moles of CO2 evolved in following reaction per mole of compound 'M' is KMnO4 'M' Space for Rough Work E-26/28 0000CT103116002
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Advanced)/12-02-2017/PAPER-1 Space for Rough Work 0000CT103116002 E-27/28
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Advanced)/12-02-2017/PAPER-1 QUESTION PAPER FORMAT AND MARKING SCHEME : 16. The question paper has three parts : Mathematics, Physics and Chemistry. 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 –1 In all I(i) Single If only the bubble If none other cases correct option 5 corresponding to — of the 15 the correct option bubbles is is darkened darkened +4 +1 0 –2 In all One or more If only the bubble(s) For darkening a bubble If none other cases I(ii) correct 8 corresponding corresponding toeach of the 32 option(s) to all the correct correct option, provided bubbles is option(s) is(are) NO incorrect option darkened darkened darkened +3 0 Single digit If only the bubble In all IV Integer 5 corresponding — other — 15 (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-28/28 Your Target is to secure Good Rank in JEE 2017 0000CT103116002
Paper Code : 0000CT103116002 CLASSROOM CONTACT PROGRAMME (Academic Session : 2016 - 2017) HINDI JEE (Main + Advanced) : LEADER & ENTHUSIAST COURSE TARGET : JEE (ADVANCED) 2017 Test Type : ALL INDIA OPEN TEST Test Pattern : JEE-Advanced TEST DATE : 12 - 02 - 2017 Time : 3 Hours PAPER – 1 Maximum Marks : 186 1. 2. (ORS) 3. 4. 5. 2818 6. 7. 8. 9. : 10. 11. 12. : 13. 14. 15. g = 10 m/s2
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Advanced)/12-02-2017/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-2/28 0000CT103116002
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Advanced)/12-02-2017/PAPER-1 MATHEMATICS HAVE CONTROL HAVE PATIENCE HAVE CONFIDENCE 100% SUCCESS BEWARE OF NEGATIVE MARKING -1: –I(i) : ( : 15) (A), (B), (C) (D) : +3 : 0 : –1 1. (1,1)(–1,–1) x2+y2+ 2px + 2qy + 4 = 0 pq-(p,q) - (A) 1 (B) 2 (C) 3 (D) 4 2. y=0; 4x – 3y = 0 3x + 4y – 9 = 0 P 3P- (A) 7x + 6y – 24 = 0 (B) x – 2y + 24 = 0 (C) 7x – 4y + 6 = 0 (D) x – 2y – 6 = 0 3. M (n), m nm1 m 1 (nr n Cr n N) n lim M n - n n (A) 3 5 (B) 3 5 (C) 5 1 (D) 5 1 2 2 2 2 0000CT103116002 H-3/28
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Advanced)/12-02-2017/PAPER-1 MATHEMATICS4. a0 5 k> 1 ak a2 2 1 1 - k 1 k0 ak 2 1 2 3 4 (A) 5 (B) 5 (C) 7 (D) 7 5. x+ y = 2 y2 = 4(x – 1) Ax + By = x2 (A+ B) - (A) 0 (B) 1 (C) 2 (D) 3 H-4/28 0000CT103116002
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Advanced)/12-02-2017/PAPER-1 –I(ii) : ( : 32) MATHEMATICS (A), (B), (C) (D) : +4 : +1 : 0 : –2 (A),(C) (D ) +4 (A)(D ) +2(A ) (B) –2 6. O,A,B 1 AO B 6 BAOBAA arker () (x,y,z O,A,B )- (A) x 1 (B) y 1 (C) y 1 (D) z 1 2 2 3 6 7. x, y, 0, cos xsin y 1 tan z z- 2 sin y (A) 0, (B) , (C) , 3 (D) 3 , 2 2 2 2 2 0000CT103116002 H-5/28
MATHEMATICS ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Advanced)/12-02-2017/PAPER-1 8. (A) lim tan x sinx sin x tanx x0 (B) lim 1 ex 1 cos x x0 sin x 1 (C) lim 1|x||x| ([.] ) x0 n1 k2 lim k1 kn n 2 , n N (D) k 1 9. P(4,2) dy y y2 dx x (A) y= 2 (B)4x– 17 = 0 (C) 1 (D) 3 10. L1:by z 1,x 0 L2:axzc 1,y 0 - c (A) x y z 1 0 a bc (B) ax y z 1 0 b c (C) L1 L2 14a12 1 1 = 64 b2 c2 (D) L1 L2 14a12 1 1 = 192 b2 c2 H-6/28 0000CT103116002
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Advanced)/12-02-2017/PAPER-1 11. y2 = 4x y2 = (x – k) x-K MATHEMATICS - (A) 1 (B) 2 (C) 3 (D) 4 12. M, 2×2 AAAT=II 1 0 - 0 1 (det A, A) (A) M 8 (B) M 4 (C) M det.(A–I) 0 3 (D) M det.(A–I) 0 2 13. z1 = 16 + 6i, z2 = 10 + 6i (i 1 ) z ampzz z1 = z2 4 ? (A) z (B)z (C) z 13 9i 3 2 (D) z 13 3i 3 2 –II : & –III : II III 0000CT103116002 H-7/28
MATHEMATICS ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Advanced)/12-02-2017/PAPER-1 –IV : ( : 15) 09 : +3 : 0 ƒx tan1 x 2 tan1 x 2 4 2 1. tan1 x 3 ...... ƒ2(x) + (sin–1x)2 = k k 2. ƒ : R R, ƒ x ƒ 1 1 tan 1 x, x R 0 1 x Nƒx dx 0 N H-8/28 0000CT103116002
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Advanced)/12-02-2017/PAPER-1MATHEMATICS 3. y= ƒ(x)R ƒ(x)=05 ƒ(x) + 6ƒ'(x) + 12ƒ\"(x) + 8ƒ\"'(x) = 0 1 4n+ 2, (n N) N x1007 1 x 1007 dx N 22015 1 0 4. x1007 1 x2016 1007 dx 0 0000CT103116002 H-9/28
MATHEMATICS ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Advanced)/12-02-2017/PAPER-1 5. 14, 1 14 m1 3 2 n (m,n N) (m+ n) H-10/28 0000CT103116002
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Advanced)/12-02-2017/PAPER-1 PHYSICS -2: –I(i) : ( : 15) (A), (B), (C) (D) : +3 : 0 : –1 1. r=r0+kT 1pddTp (r) :- 1 dp 1 dp 1 dp 1 dp p dT p dT p dT p dT (A) (B) (C) (D) rr r r 2. M1 M2 ( ):- f=30cm f=20cm //////////////////////////////////////////////////// ///////////////////////////////////////////////// M2 M1 10cm 30cm (A) +6 (B) –6 (C) +3 (D) –3 0000CT103116002 H-11/28
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Advanced)/12-02-2017/PAPER-1 3. PHYSICS (=0.18×10–3 gcm–3) (=6×10–3 gcm–3) h=100cm.MXe=131 gm, MHe = 4 gm (A) –0.01°C (B) –0.025°C (C) +0.01°C (D) +0.025°C 4. 2 2818° 200 1mm 100N/m (A) 4 mN (B) 3 mN (C) 5 mN (D) 7 mN 5. D1 D2 L=25cm D1 +1 +4? (i) 1 2 (ii) 1 2 (iii) (iv) (A) (B) iii (C) i, ii iii (D) iii iv H-12/28 0000CT103116002
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Advanced)/12-02-2017/PAPER-1PHYSICS –I(ii) : ( : 32) (A), (B), (C) (D) : +4 : +1 : 0 : –2 (A),(C) (D ) +4 (A)(D ) + 2 (A) (B ) –2 6. m,'' 'R' B St= 0 : SC B m,,R (A) mc/(m+cB22) (B) 2mc/(m+cB22) (C) 2Bc/(m+cB 22) (D) Bc/(m+cB22) 0000CT103116002 H-13/28
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Advanced)/12-02-2017/PAPER-1 7. 4 PHYSICS 1% 1st 2nd (A) 476 Hz 17.0 cm 50.0 cm (B) 340 Hz 25.2 cm 76.0 cm (C) 544 Hz 15.6 cm 46.0 cm (D) 510 Hz 16.0 cm 48.2 cm 8. S C X 2C 2C S C Y V (A) X Y 2C3V (B) Y X C3V (C) CV2 (D) 2CV2 3 3 H-14/28 0000CT103116002
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Advanced)/12-02-2017/PAPER-1PHYSICS 9. 0.5cm T=100°C 3×10–3 cal/cm2sec°C 20°C 2.8× 10–3 cal/cm°C sec 0.5cm (n2=0.7) (A) 8 7 (B) 7 8 (C) T65.7°C (D) T42.2°C 10. A(x,y)mB(8, 7) m E 54iˆ 72ˆj N/C +900 3×106v/m (A) A (2, –1)m (B) 2µC (C) 30cm (D) 0000CT103116002 H-15/28
PHYSICS ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Advanced)/12-02-2017/PAPER-1 11. R1R2 (R2 ):- R1 E1 R2 E2 (A) R1 R2 (B) E1 R2 (C) E1 R2 (D) R1 R2 12. mA µ=1 (g= 10 m/s2) A µ=1 =37° (A) 14m/sec2 (B) 2m/sec2 (C) (D) H-16/28 0000CT103116002
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Advanced)/12-02-2017/PAPER-1PHYSICS 13. 1m 1kg (kg-m 2) sin = 3/32 B X’ A X (A) IXX' = 0.5 kg m2 (B) IXX' = 0.25 kg m2 (C) IAB = 1 kg m2 (D) IAB 15 32 kgm2 12 –II : & –III : II III 0000CT103116002 H-17/28
PHYSICS ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Advanced)/12-02-2017/PAPER-1 –IV : ( : 15) 09 : +3 : 0 1. Bˆ B0uˆr uˆr vr h nv2 n g 2. AB CD PQ PQ g PQ AB k4megh emk P D A gh B C Q H-18/28 0000CT103116002
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Advanced)/12-02-2017/PAPER-1PHYSICS 3. 1m – 41012 1.44keV 3 () 4. t=0.1ln2 sec t =0 S R=3 L=0.5H =180/11V R=3 R=3 R=3 0000CT103116002 H-19/28
PHYSICS ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Advanced)/12-02-2017/PAPER-1 5. 402m/s 60° 45° (m) 402m/s 60° 45° H-20/28 0000CT103116002
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Advanced)/12-02-2017/PAPER-1 -3: CHEMISTRY –I(i) : ( : 15) (A), (B), (C) (D) : +3 : 0 : –1 1. CH4 + O2 CO + H2 ; H = – 36 kJ CH4 + H2O CO + H2 ; H = 216 kJ O2H2O CH4 (A) 1 : 1 (B) 6 : 1 (C) 3 : 1 (D) 2 : 1 2. 298 K CuBr Pt|H2(g)(1bar)| HBr (10–4M) |CuBr | Cu ; Ecell = 0.6 volt ; Ksp [CuBr] = 10–12M2 [:2.303R 298 0.06 ] F (A) 0.84 volt (B) 0.6 volt (C) 0.12 volt (D) 0.36 volt 3. 1100°C N2 'Q':- (A) Q, CaNCN (B)Q (C) (A) (B) (D) 4. NO :- (A) FeSO4 (B) Fe2(SO4)3 (C) (A) (B) (D) 5. 2--1-4--2- (A) (i) Mg(ii) (iii)NH4Cl ; (iv) SOBr2 (B) (i) NaC CH (ii) H3O+ + HgSO4 (iii) HBr, (C) (i) KOH(ii) CH COOOH (iii) H / Pt (iv) HBr, 32 (D) (i) NaCCH (ii) H , (iii)HCl , 2 0000CT103116002 H-21/28
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Advanced)/12-02-2017/PAPER-1 CHEMISTRY –I(ii) : ( : 32) (A), (B), (C) (D) : +4 : +1 : 0 : –2 (A),(C) (D ) +4 (A)(D ) + 2 (A) (B ) –2 6. pH pH [H+] (A) (B) H2SO4(aq.) [] (C) (D) 7. (A) 1nm100 nm (B) H 2O (C) PO43–>SO42– > Cl– (D) 'C'CMC H-22/28 0000CT103116002
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