Paper Code : 1001CT103516013 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 : 14 - 01 - 2017 Time : 3 Hours PAPER – 1 Maximum Marks : 210 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 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) 2017/14-01-2017/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 1001CT103516013
Leader Course/Phase-III, IV & V/14-01-2017/Paper-1 HAVE CONTROL HAVE PATIENCE HAVE CONFIDENCE 100% SUCCESS BEWARE OF NEGATIVE MARKING PHYSICS PART-1 : PHYSICS SECTION–I(i) : (Maximum Marks : 30) This section contains TEN 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 In all other cases 1. A block of mass m is placed very gently on a wedge of mass M connected with initially relaxed spring as shown in the figure. Inclined face of wedge is rough and ground is smooth. What is compression of spring if system remains in equilibrium? µ0 k µ=0 m M (A) mg sin cos 1 M2 (B) mg sin 1 M2 R R (C) mg cos 1 M2 (D) Spring is not compressed R Space for Rough Work 1001CT103516013 E-3/28
Target : JEE (Main + Advanced) 2017/14-01-2017/Paper-1 PHYSICS2. A point P moves along a circle of radius r with constant speed v. Its angular velocity about any fixed point on the circle will be : v v v v (A) (B) (C) r2 (D) 2r2 r 2r 3. A sports car accelerates from zero to a certain speed in t seconds. How long does it take for it to accelerate to twice that speed starting from rest, assuming the power of the engine to be constant (independent of velocity) and neglecting any resistance to motion? (A) 2 t sec. (B) 2t sec. (C) 3t sec. (D) 4t sec. 4. Two pendulums of time periods 3 s and 7s respectively start oscillating simultaneously from two opposite extreme positions. After how much minimum time they will be in phase :- (A) 21 s (B) 21 s (C) 21 s (D) 21 s 8 4 2 10 Space for Rough Work E-4/28 1001CT103516013
Leader Course/Phase-III, IV & V/14-01-2017/Paper-1 PHYSICS 5. Two small electric dioples, one of dipole moment p 1 at point A and the other of dipole moment p 2 at point B, are as shown in the figure. The torque experienced by the dipole p 2 is :- p1 p2 x (A) Zero (C) Can't determined (B) (D) None of these 6. Power transfer by a non-ideal cell to an external resistor can be same for two different values. Out of which one value (R1) is less than internal resistance of cell and another (R2) is greater than internal resistance of cell then : (A) R1 will give less internal loss (B) R1 will give more battery life (C) R2 will give less efficiency (D) R2 will give more battery life Space for Rough Work 1001CT103516013 E-5/28
PHYSICS Target : JEE (Main + Advanced) 2017/14-01-2017/Paper-1 7. For the circuit shown in figure the ratio of energy stored in capacitor (1) to that of in capacitor (2) is :- C2 R1 R2 C1 E R1C1 R1C2 (C) R12C1 (D) R1C12 (A) R2C2 (B) R2C1 R22C2 R2C22 8. A string is under tension and stationary vibrations are produced in it. A, B, C, D are positions of consecutive nodes. Choose the INCORRECT option. (A) The distance AB 2 (B) The phase difference between a vibrating point on AB and another on BC is zero. (C) The amplitudes of vibration of different points between A and the midpoint of A and B are different. (D) When every point of AB is having maximum displacement then every point of BC is having maximum displacement in opposite direction. Space for Rough Work E-6/28 1001CT103516013
Leader Course/Phase-III, IV & V/14-01-2017/Paper-1 PHYSICS 9. Three rings each having equal radius R, are placed mutually perpendicular to each other and each having its centre at the origin of coordinate system. If current I is flowing through each ring then the magnitude of the magnetic field at the common centre is :- y x 3I (B) 30I (C) 0 (D) 3 1 0I (A) 2R 2R 2R 10. In figure shown, wire P1Q1 and P2Q2, both are moving towards right with speed 5 cm/sec. Resistance of each wire is 2 . Then current through 19 resistor is : P1 P2 4 cm 19 Q1 Q2 B = 1 Tesla (A) 0 (B) 0.1 mA (C) 0.2 mA (D) 0.3 mA Space for Rough Work 1001CT103516013 E-7/28
Target : JEE (Main + Advanced) 2017/14-01-2017/Paper-1 PHYSICS SECTION–I(ii) : (Maximum Marks : 20) This section contains FIVE 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 : –1 In all other cases. 11. A particle is moving in x-y plane with constant speed in anticlockwise direction such that sum of distances from the two fixed point A (–a, 0) and B (a, 0) is always constant = 3a. At any instant it has equal distance from A and B at that instant : (A) vy 0 (B) vx 0 (C) ax 0 (D) ay 0 12. Two particles A & B of masses m and 2m respectively are connected through a spring in its natural length. They are projected directly away from each other along spring with the same speed. Mark the correct statement(s) : (A) At the moment of maximum distance between them, the particles are moving with same speed in same direction (B) At the moment of maximum distance between them, the particles are moving with same speed in opposite direction (C) Minimum individual speed of the particles A & B are both zero (D) Minimum individual speed of the particles A & B are both non-zero Space for Rough Work E-8/28 1001CT103516013
Leader Course/Phase-III, IV & V/14-01-2017/Paper-1 PHYSICS 13. Two parallel resistanceless rails are connected by an inductor of inductance L at one end as shown in the figure. A magnetic field B exists in the space which is perpendicular to the plane of the rails. Now a conductor of length and mass m is placed transverse on the rails and given an impulse J towards the rightward direction. Then choose the CORRECT option(s). B J (A) Velocity of the conductor is half of the initial velocity after a displacement of the conductor 3J 2 L d = 4B22m (B) Current flowing through the inductor at the instant when velocity of the conductor is half 3J 2 of the initial velocity is i = 4Lm (C) Velocity of the conductor is half of the initial velocity after a displacement of the conductor 3J 2 L d = B22m (D) Current flowing through the inductor at the instant when velocity of the conductor is half 3J 2 of the initial velocity is i = mL Space for Rough Work 1001CT103516013 E-9/28
PHYSICS Target : JEE (Main + Advanced) 2017/14-01-2017/Paper-1 14. Initially key was placed on (1) till the capacitor got fully charged. Key is placed on (2) at t = 0. The time when the energy in both capacitor and inductor will be same- (1) (2) L E C (A) LC (B) LC (C) 5 LC (D) 5 LC 4 2 4 2 15. The switch is closed at t = 0 in the adjoining circuit. Which of the following is/are CORRECT? RL R R X YZ sE (A) The potential difference across YZ at t = 0 is 2E/3 (B) The potential difference across XY at t = is E/2 (C) The potential difference across YZ at t = 0 is E/2 (D) The potential difference across XY at t = is 2E/3 Space for Rough Work SECTION –II : Matrix-Match Type & SECTION –III : Integer Value Correct Type No question will be asked in section II and III E-10/28 1001CT103516013
Leader Course/Phase-III, IV & V/14-01-2017/Paper-1 SECTION–IV : (Maximum Marks : 20) This section contains FIVE 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 If none of the bubbles is darkened. Negative Marks : –1 In all other cases. 1. What minimum force (in N) should be applied to the end of the lever of a double pulley system to hold a load P = 10 kg ? The length of the lever is = 1m, the radius of the larger pulley of the system r1 = 20 cm, the radius of the smaller pulley r2 = 10 cm (figure). (Axle of the double pulley is fixed.) lever r2 r1 P 2. A free particle of mass 'm' is confined to a region of length L. The de-Broglie wave associated with the particle is sinusoidal in nature as given in figure. The kinetic energy of the particle n2h2 is 8mL2 then find the value of n. y x L/3 2L/3 L Space for Rough Work 1001CT103516013 E-11/28
PHYSICS Target : JEE (Main + Advanced) 2017/14-01-2017/Paper-1 3. A radioactive sample contains two radio nucleoids A and B having decay constant hr–1 and 2 hr–1. Initially 25% of total decay comes from A. How long (in hr) will it take before 75% of total decay comes from A. [Take = n 3] 4. The time period of Jupiter is (125)1/2 years. The distance of Jupiter from Sun in terms of astronomical unit is given by AU. Find the value of . (Astronomical unit is defined as the average distance of Earth from the Sun). 5. Activity of radioactive material sample A and B at t = 0 is in ratio n2 : 1 and at t = n2T days, ratio of their activities is : 1, the half life of A is T days and half life of B is nT days. The value of '' for n = 2. Space for Rough Work E-12/28 1001CT103516013
Leader Course/Phase-III, IV & V/14-01-2017/Paper-1 PART-2 : CHEMISTRY CHEMISTRY SECTION–I(i) : (Maximum Marks : 30) This section contains TEN 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 In all other cases 1. A sample of 100 ml of a solution of a weak monoprotic acid of unknown concentration is titrated with 0.500 M NaOH to give the titration curve shown 14 12 10 8 6 4 2 0 5 10 15 20 25 All of the statements are correct except - (A) Phenolphthalein would be a suitable indicator for this titration (B) A buffer solution is formed when 15 ml of NaOH is added (C) The pKa of the acid is 4 (D) The initial concentration of the acid is 0.1M 2. It takes 126.5 minutes using a current of 5.15 A to deposit all of the nickel from 225 ml of a solution containing Ni2+. What was the original concentration of Ni2+ in the solution- (A) 3.6 M (B) 1.8 M (C) 0.9 M (D) 1.5 × 10–2 M 3. For which reaction (s) is the H value close to the E value ? I CH4(g) + 2O2(g) CO(g) + 2H2O(l). II C2H4(g) + 3O2(g) 2CO(g) + 2H2O(g) (A) I only (B) II only (C) Both I & II (D) Neither I & II Space for Rough Work 1001CT103516013 E-13/28
Target : JEE (Main + Advanced) 2017/14-01-2017/Paper-1 CHEMISTRY4. Which of the following statement is CORRECT for the conversion given below :- I –x III – y Mn(CN)6 Zn Mn(CN)6 –4 air M n (CN )6 (I) (II) (A) (I) is paramagnetic and (II) is diamagnetic (B) High Spin complex (I) is formed by reduction with Zn (C) 0 : (I) > (II) (D) (II) acts as oxidizing agent 5. Which of the following will not give any coloured compound on heating ? (A) Zn(NO3)2 (B) Hg(NO3)2 (C) (NH4)2Cr2O7 (D) NH4NO2 6. Which of the following option is INCORRECT ? (A) (AlH3)n contain 3c–2e banana bond and it is nonplanar (B) Bond order : CO < CO+ (C) Solubility order in water BeF2 > MgF2 > CaF2 (D) Stability order : Br3 > Cl3 7. Which of the following complex show geometrical isomerism and structural isomerism but does not show optical isomerism :- (A) [Pd(NH2 –CH(CH3)–CO2–)2]0 (B) [Pd2Cl4(PPh3)2] (C) [Pt(bn)2]2+ (D) [Zn(gly)2]0 Space for Rough Work E-14/28 1001CT103516013
Leader Course/Phase-III, IV & V/14-01-2017/Paper-1 8. The conversion CHEMISTRY O OH H3C— C —CH2CH2CO2CH3 H3C— CH —CH2CH2CH2OH can be effected using : (A) LiAlH4 and then H+ (B) B2H6(THF) ; H2O / H+ (C) Na + EtOH (excess) (D) All 9. The final major product (Q) is : dil. NaOH (P) NaBH4 (Q) HO CH3OH O OH OH O (A) (B) (C) (D) OH 10. For the given reaction H2SO4 (P) (i) m-CPBA (Q) Red P + HI (R) OH (ii) H3O+ Incorrect statement is : (A) Number of monohalogenated product for (R) is 6 (B) (P) show positive bromine water test (C) (Q) gives methane with CH3MgBr (D) (Q) does not show the reaction with Na Space for Rough Work 1001CT103516013 E-15/28
Target : JEE (Main + Advanced) 2017/14-01-2017/Paper-1 CHEMISTRY SECTION–I(ii) : (Maximum Marks : 20) This section contains FIVE 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 : –1 In all other cases. 11. What occurs when an aqueous solution of Na2SO4 containing several drops of phenolphthalein is electrolyzed between Pt electrodes (A) The colourless solution turns pink at the cathode (B) The pink solution becomes colourless at the cathode (C) The colourless solution remains colourless at the anode (D) The colourless solution remains colourless at cathode 12. Which of the following statement(s) is/are correct about the triple point of water- (A) The triple point for a substance varies with the pressure (B) The three phases (solid, liquid, gas) have the same density (C) The three phases ( solid, liquid, gas) are in equilibrium (D) The three phases (solid, liquid and gas) are distinguishable in appearance. 13. Which of the following change(s) takes place during smelting in the blast furnace for extraction of Fe ? (A) CaCO3 — CaO + CO2 (B) Fe2O3 + 3CO — 2Fe + 3CO2 (C) Mn + CO — C + MnO (D) 2P2O5 + 10C — P4 + 10CO Space for Rough Work E-16/28 1001CT103516013
Leader Course/Phase-III, IV & V/14-01-2017/Paper-1 CHEMISTRY 14. Which of the given sequences are correctly matched with their final major product : O CH2–NH2 (A) HCl + NaNO2 OH (B) O H3O+ (P) [Ag(NH3)2]+ – CH3COO– OH SeO2 (L) CrO3 (M) N2H4 O N H2O2 (C) H3C H H3C H (D) Na in Liq. NH3 15. Which of the following give pair of diastereomers on reaction with CH3MgBr followed by H2O : O (B) O O (A) O (C) (D) 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 1001CT103516013 E-17/28
Target : JEE (Main + Advanced) 2017/14-01-2017/Paper-1 CHEMISTRY SECTION–IV : (Maximum Marks : 20) 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 If none of the bubbles is darkened. Negative Marks : –1 In all other cases. 1. K2Cr2O7 is the powerful oxidising agent in acidic medium. In the same medium if oxidising power of Cr2O72– decreases by 'x' volts, when pH of the solution increases from 0 to 5 at 298 K , then the value of '10x' will be. [Take : 2.303RT 0.06 ] F Fill your answer as sum of digits (excluding decimal places) till you get the single digit answer. 2. Among the following total number of complexes which are low spin complex :- K2[PtCl6] , [CrO4]2– , [Co(H2O)6]3+ , Na2[Zn(CN)4] , [IrF6]3– , [Cr(en)3]Cl3 , [Fe(NH3)6]2+ 3. Find the total number of alloy which contain Cu :- Solder , Brass , Bronze , German silver , Gun metal Space for Rough Work E-18/28 1001CT103516013
Leader Course/Phase-III, IV & V/14-01-2017/Paper-1 4. How many of following reactions are correctly match with their major product : CHEMISTRY (i) H2 O Pd-BaSO4 (ii) ZnHg / HCl CH2OH COOH OH O (iii) (t-BuO)3Al / O OH O Ph Br (iv) HIO4 Ph (v) HBr OH O OH Cl OEt O (i) O3 (vi) (ii) Zn / EtO OH (vii) (iii) NaBH4 (viii) COOH CH3 PCl3 OH (ix) CH3–CH2Cl Aq. NaOH CH3–CH2OH Space for Rough Work 1001CT103516013 E-19/28
Target : JEE (Main + Advanced) 2017/14-01-2017/Paper-1 CHEMISTRY5. How many of the given show positive Iodoform test : O O O (i) CH3–C–OH (ii) O (iii) (iv) CH3–C–H OH O OH (viii) O (v) OH (vii) O OCH3 O OH (vi) (ix) OH (x) O Space for Rough Work E-20/28 1001CT103516013
Leader Course/Phase-III, IV & V/14-01-2017/Paper-1 PART-3 : MATHEMATICS MATHEMATICS SECTION–I(i) : (Maximum Marks : 30) This section contains TEN 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 In all other cases 1. Area bounded by x y 1 y x 2 & y < 0 is equal to - 3 9 3 9 (A) 8 (B) 8 (C) 4 (D) 4 2. lim sgn cot1 x cot1 x2 (where sgn(x) is signum function), then - x0 (A) LHL = RHL = 1 (B) LHL = RHL = –1 (C) LHL = 1, RHL = –1 (D) LHL = –1, RHL = 1 x 2 dx 2x2 cos2 x 3. 0 1 sin , 2 If x then dx is - 0 (1 sin x)2 (A) (B) + 2 – 2 (C) (D) + 4 + 2 xyz x 2 y 1 z 2 4. Equation of the line of shortest distance between the lines and 2 3 1 3 5 2 is - (B) 3x – 62 = 3y – 93 = 3z + 31 (A) 3(x – 21) = (3y – 92) = (3z – 32) (x 21) y 92 z 32 62 31 3 3 3 3 (C) (D) x y 31 z 33 3 Space for Rough Work 1001CT103516013 E-21/28
Target : JEE (Main + Advanced) 2017/14-01-2017/Paper-1 MATHEMATICS5. Let a, b, c R0 and distinct such that aiˆ bˆj ckˆ and (b c)ˆi (c a)ˆj (a b)kˆ are parallel then | | is - || (A) 3 1 (C) 2 1 (B) (D) 2 3 6. Let z1, z2, z3 are roots of the equation z3 + z2(i – 1) + z(2 – i) – 2 = 0, then Re(z1) + Re(z2) + Re(z3) is - (A) –1 (B) 0 (C) 1 (D) 2 7. Number of points of intersection of |z – (1 + i)| = 1 and z z 4 is - (A) 0 (B) 1 (C) 2 (D) 3 8. Let the equation x4 – x3 – x2 – x – = 0, where N and >>>then number of integral roots of the equation is - (A) 0 (B) 2 (C) 4 (D) 3 9. Let P(x1, y1) & Q(x2, y2) are points lying on hyperbola x2 y2 1 . If tangents drawn at the a2 b2 points P & Q are perpendicular, then x1x2 is - y1y2 a2 a2 a4 a4 (A) b2 (B) b2 (C) b4 (D) b4 10. Let x, y are non zero and non collinear vectors such that (a2 b c)x (a2 b c)y (a2 b c)(x y ) 0 , then (a + b + c) is (where a,b,c R) (A) –2 (B) –1 (C) 0 (D) 4 Space for Rough Work E-22/28 1001CT103516013
Leader Course/Phase-III, IV & V/14-01-2017/Paper-1 SECTION–I(ii) : (Maximum Marks : 20) MATHEMATICS This section contains FIVE 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 : –1 In all other cases. 11. Let a,b,c are three non coplanar vectors such that a 2b 3c, a 3b 4c and a c and . If then b 21a 41b 54c x1 x2 x3 , (A) x3 > x2 > x1 (B) x1, x2, x3 are in A.P. (C) H.C.F. of x1 & x3 is 2 (D) x1, x2, x3 are in H.P. 12. Consider a variable plane x + my + nz = k (k > 0) and , m, n are direction cosines of normal of the plane. Let the given plane intersects co-ordinate axis at A, B, C, then area of ABC may be - 3 3k2 3 3k2 (C) 3 3k2 (D) 12 3k2 (A) (B) 2 4 13. For the parabola y2 – 4y + 8 = 4x which of the following is(are) false - (A) Distance between focus and vertex is 2 unit. (B) Equation of directrix is x = 2. (C) Circle (x – 1)2 + (y – 2)2 = 4 cuts the given parabola at 4 points. (D) Number of common tangents between the parabola and y2 – 4y + 4x = 0 is one. Space for Rough Work 1001CT103516013 E-23/28
MATHEMATICS Target : JEE (Main + Advanced) 2017/14-01-2017/Paper-1 14. Let tangents PA & PB are drawn from variable point P on the parabola y2 = 4x to the circle x2 + y2 + 10x – 4y + 25 = 0, then locus of circumcentre of PAB (A) is a parabola (B) is satisfied by point 5 , 1 2 (C) never cuts y-axis (D) intersect x-axis. 15. Let ƒ(x)ƒ'(x)ƒ''(x) > 0 x R, then which of the following is(are) graph of ƒ(x) ƒ(x) ƒ(x) (A) (B) x x ƒ(x) ƒ(x) (C) x (D) 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-24/28 1001CT103516013
Leader Course/Phase-III, IV & V/14-01-2017/Paper-1 SECTION–IV : (Maximum Marks : 20) MATHEMATICS This section contains FIVE questions. The answer to each question is a SINGLE DIGIT INTEGER ranging from 0 to 9, both inclusive. For each question, darken the bubble corresponding to the correct integer in the ORS. For each question, marks will be awarded in one of the following categories : Full Marks : +4 If only the bubble corresponding to the correct answer is darkened. Zero Marks : 0 If none of the bubbles is darkened. Negative Marks : –1 In all other cases. 1. Let (x, y, z) is three dimensional point which satisfies xyz4 = 16 where (x, y, z > 0) its minimum distance from origin is , then 2 is 2. Let S = (x,y); y(3x 1) 0 and S' = {(x, y) A × B; –1 < A < 1 and –1 < B < 1}. Then area x(3x 2) of S S' is 3. If ax2 + 2hxy + by2 + 2gx + 2ƒy + c = 0 and ax2 + 2hxy + by2 – 2gx – 2ƒy + c = 0 each represent pair of straight lines and area of parallelogram enclosed by them is |c| , then || is h2 ab Space for Rough Work 1001CT103516013 E-25/28
MATHEMATICS Target : JEE (Main + Advanced) 2017/14-01-2017/Paper-1 4. If the parabola y = ax2 + bx + c has vertex at (4, 2) and a [1,3] such that difference between extreme values of abc is , then is 1728 5. Let chord of contact is drawn from every point lying on circle x2 + y2 = 100 to the ellipse x2 y2 1 49 such that all the lines touches an standard ellipse whose eccentricity is e, then 81e2 is 13 Space for Rough Work E-26/28 1001CT103516013
Leader Course/Phase-III, IV & V/14-01-2017/Paper-1 1001CT103516013 E-27/28
Target : JEE (Main + Advanced) 2017/14-01-2017/Paper-1 QUESTION PAPER FORMAT AND MARKING SCHEME : 16. The question paper has three parts : Physics, Chemistry and Mathematics. 17. Each part has two sections as detailed in the following table. Que. No. Category-wise Marks for Each Question Maximum Section Type of Full Partial Zero Negative Marks of the Que. Marks Marks Marks Marks section +3 0 In all I(i) Single If only the bubble other cases correct option 10 corresponding to — — 30 the correct option is darkened +4 0 –1 If none In all One or more If only the bubble(s) of the other bubbles is cases I(ii) correct 5 corresponding — darkened 20 option(s) to all the correct option(s) is(are) darkened +4 0 –1 In all Single digit If only the bubble If none other cases IV Integer 5 corresponding — of the 20 (0-9) to correct answer bubbles is is darkened 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 1001CT103516013
Paper Code : 1001CT103516013 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 : 14 - 01 - 2017 Time : 3 Hours PAPER – 1 Maximum Marks : 210 1. 2. (ORS) 3. 4. 5. 2820 6. 7. 8. 9. : 10. 11. 12. : 13. 14. 15. g = 10 m/s2
Target : JEE (Main + Advanced) 2017/14-01-2017/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 H-2/28 1001CT103516013
Leader Course/Phase-III, IV & V/14-01-2017/Paper-1PHYSICS HAVE CONTROL HAVE PATIENCE HAVE CONFIDENCE 100% SUCCESS BEWARE OF NEGATIVE MARKING -1: –I(i) : ( : 30) (A), (B), (C) (D) : +3 : 0 1. m M (relaxed) µ0 k µ=0 m M (A) mg sin cos 1 M2 (B) mg sin 1 M2 R R (C) mg cos 1 M2 (D) R 1001CT103516013 H-3/28
PHYSICS Target : JEE (Main + Advanced) 2017/14-01-2017/Paper-1 2. Pv r v v v v (A) r (B) 2r (C) r2 (D) 2r2 3. t (A) 2 t sec. (B) 2t sec. (C) 3t sec. (D) 4t sec. 4. 3s7s (A) 21 s (B) 21 s (C) 21 s (D) 21 s 8 4 2 10 H-4/28 1001CT103516013
Leader Course/Phase-III, IV & V/14-01-2017/Paper-1PHYSICS 5. p1Ap 2B p2 p1 p2 x (A) (C) (B) (D) 6. (R1) (R2) (A) R1 (B) R1 (C) R2 (D) R2 1001CT103516013 H-5/28
PHYSICS Target : JEE (Main + Advanced) 2017/14-01-2017/Paper-1 7. (1)(2) C2 R1 R2 C1 E (A) R1C1 (B) R1C2 (C) R12C1 (D) R1C12 R2C2 R2C1 R22C2 R2C22 8. A,B,C, D (A) AB 2 (B) AB BC (C) A A B (D) AB BC H-6/28 1001CT103516013
Leader Course/Phase-III, IV & V/14-01-2017/Paper-1PHYSICS 9. R I y x 3I (B) 30I (C) 0 (D) 3 1 0I (A) 2R 2R 2R 10. P1Q1 P2Q2 5cm/sec2 19 P1 P2 4 cm 19 Q1 Q2 B = 1 Tesla (A) 0 (B) 0.1 mA (C) 0.2 mA (D) 0.3 mA 1001CT103516013 H-7/28
Target : JEE (Main + Advanced) 2017/14-01-2017/Paper-1 PHYSICS –I(ii) : ( : 20) (A), (B), (C) (D) : +4 : 0 : –1 11. x-y A(–a,0) B(a,0) 3aAB (A) vy 0 (B) vx 0 (C) ax 0 (D) ay 0 12. AB m2m (A) (B) (C) A B (D) A B H-8/28 1001CT103516013
Leader Course/Phase-III, IV & V/14-01-2017/Paper-1PHYSICS 13. L B m J B J (A) d= 3J 2 L 4B22m (B) i=3J2 4Lm (C) d= 3J 2 L B22m (D) i=3J2 mL 1001CT103516013 H-9/28
PHYSICS Target : JEE (Main + Advanced) 2017/14-01-2017/Paper-1 14. (1)t=0(2) (1) (2) L E C (A) LC (B) LC (C) 5 LC (D) 5 LC 4 2 4 2 15. t=0 RL R R X YZ sE (A) t = 0 YZ 2E/3 (B) t = XY E/2 (C) t = 0 YZ E/2 (D) t = XY 2E/3 –II : & –III : II III H-10/28 1001CT103516013
Leader Course/Phase-III, IV & V/14-01-2017/Paper-1PHYSICS –IV : ( : 20) 09 : +4 : 0 : –1 1. (N ) P = 10kg =1m,r1=20cm r2 = 10 cm () lever r2 r1 P 2. 'm' L 8nm2hL 22 n y x L/3 2L/3 L 1001CT103516013 H-11/28
PHYSICS Target : JEE (Main + Advanced) 2017/14-01-2017/Paper-1 3. A B hr–1 2 hr–1 25%,A 75%A [= n 3] 4. (125)1/2 AU () 5. ABt = 0 n2 : 1 t=n2T : 1 AT B nTn=2 '' H-12/28 1001CT103516013
Leader Course/Phase-III, IV & V/14-01-2017/Paper-1 -2: CHEMISTRY –I(i) : ( : 30) (A), (B), (C) (D) : +3 : 0 1. 100ml 0.500 M NaOH 14 12 10 8 6 4 2 0 5 10 15 20 25 - (A) (B) 15 ml NaOH (C) pKa 4 (D) 0.1M 2. 5.15 A Ni2+225 ml 126.5 Ni2+ - (A) 3.6 M (B) 1.8 M (C) 0.9 M (D) 1.5 × 10–2 M 1001CT103516013 H-13/28
Target : JEE (Main + Advanced) 2017/14-01-2017/Paper-1 CHEMISTRY3. H E ? I CH4(g) + 2O2(g) CO(g) + 2H2O(l). II C2H4(g) + 3O2(g) 2CO(g) + 2H2O(g) (A) I (B) II (C) I II (D) III 4. :- I –x III – y Mn(CN)6 Zn Mn(CN)6 –4 air M n (CN )6 (I) (II) (A) (I) (II) (B) Zn (I) (C) 0 : (I) > (II) (D) (II) 5. ? (A) Zn(NO3)2 (B) Hg(NO3)2 (C) (NH4)2Cr2O7 (D) NH4NO2 6. ? (A) (AlH3)n 3c–2e banana bond) (B) : CO < CO+ (C) BeF2 > MgF2 > CaF2 (D) :Br3 > Cl3 7. :- (A) [Pd(NH2 –CH(CH3)–CO2–)2]0 (B) [Pd2Cl4(PPh3)2] (C) [Pt(bn)2]2+ (D) [Zn(gly)2]0 H-14/28 1001CT103516013
Leader Course/Phase-III, IV & V/14-01-2017/Paper-1 CHEMISTRY 8. O OH H3C— C —CH2CH2CO2CH3 H3C— CH —CH2CH2CH2OH (A) LiAlH4 H+ (B) B2H6(THF) ; H2O / H+ (C) Na + EtOH (D) 9. (Q) dil. NaOH (P) NaBH4 (Q) O HO CH3OH O OH OH (A) (B) (C) (D) OH 10. H2SO4 (P) (i) m-CPBA (Q) Red P + HI (R) OH (ii) H3O+ (A) (R) 6 (B) (P) (C) (Q) , CH3MgBr (D) (Q) , Na 1001CT103516013 H-15/28
Target : JEE (Main + Advanced) 2017/14-01-2017/Paper-1 CHEMISTRY –I(ii) : ( : 20) (A), (B), (C) (D) : +4 : 0 : –1 11. Na2SO4 Pt (A) (B) (C) (D) 12. - (A) (B) . (C) . (D) 13. Fe ? (A) CaCO3 — CaO + CO2 (B) Fe2O3 + 3CO — 2Fe + 3CO2 (C) Mn + CO — C + MnO (D) 2P2O5 + 10C — P4 + 10CO H-16/28 1001CT103516013
Leader Course/Phase-III, IV & V/14-01-2017/Paper-1 14. CHEMISTRY O CH2–NH2 (A) HCl + NaNO2 OH (B) O H3O+ (P) [Ag(NH3)2]+ – CH3COO– OH SeO2 (L) CrO3 (M) N2H4 O N H2O2 (C) H3C H H3C H (D) Na in Liq. NH3 15. C H3MgBr H2O OO O (A) (B) (C) (D) O –II : & –III : II III 1001CT103516013 H-17/28
Target : JEE (Main + Advanced) 2017/14-01-2017/Paper-1 CHEMISTRY –IV : ( : 20) 09 : +4 : 0 : –1 1. K2Cr2O7 298K pH 0 5 Cr2O72– 'x' '10x'[: 2.303RT 0.06 ] F ( ) 2. :- K2[PtCl6] , [CrO4]2– , [Co(H2O)6]3+ , Na2[Zn(CN)4] , [IrF6]3– , [Cr(en)3]Cl3 , [Fe(NH3)6]2+ 3. alloyCu:- Solder , (Brass) , (B ronze) , , (G un metal) H-18/28 1001CT103516013
Leader Course/Phase-III, IV & V/14-01-2017/Paper-1 CHEMISTRY 4. (i) H2 O Pd-BaSO4 (ii) ZnHg / HCl CH2OH COOH OH O (iii) (t-BuO)3Al / O OH O Ph Br (iv) HIO4 Ph (v) HBr OH O OH Cl OEt O OH (i) O3 (vi) (ii) Zn / EtO (iii) NaBH4 COOH CH3 PCl3 (vii) (viii) OH (ix) CH3–CH2Cl Aq. NaOH CH3–CH2OH 1001CT103516013 H-19/28
CHEMISTRY Target : JEE (Main + Advanced) 2017/14-01-2017/Paper-1 5. O O O O (i) CH3–C–OH (ii) (iii) (iv) CH3–C–H O OH OH OH (viii) O (v) (vi) (vii) O OCH3 O OH OH (ix) (x) O H-20/28 1001CT103516013
Leader Course/Phase-III, IV & V/14-01-2017/Paper-1 -3: MATHEMATICS –I(i) : ( : 30) (A), (B), (C) (D) : +3 : 0 1. x y 1 y x 2 y< 0 - 3 9 3 9 (A) 8 (B) 8 (C) 4 (D) 4 2. lim sgn cot1 x cot1 x2 (sgn(x) ), - x0 (A) LHL = RHL = 1 (B) LHL = RHL = –1 (C) LHL = 1, RHL = –1 (D) LHL = –1, RHL = 1 x 2 2x2 cos2 x sin 2 3. 1 x dx 0(1 sin x )2 dx - 0 (A) (B) + 2 – 2 (C) (D) + 4 + 2 4. 2x y z x3 2 y 1 z 2 - 3 1 5 2 (A) 3(x – 21) = (3y – 92) = (3z – 32) (B) 3x – 62 = 3y – 93 = 3z + 31 (x 21) y 92 z 32 62 31 3 3 3 3 (C) (D) x y 31 z 33 3 1001CT103516013 H-21/28
MATHEMATICS Target : JEE (Main + Advanced) 2017/14-01-2017/Paper-1 5. a, b, c R0 aiˆb ˆj ckˆ (b c)iˆ (c a)ˆj (a b)kˆ || - || (A) 3 1 (C) 2 1 (B) (D) 2 3 6. z1, z2, z3 z3 + z2(i – 1) + z(2 – i) – 2 = 0 Re(z1)+ Re(z2) + Re(z3) - (A) –1 (B) 0 (C) 1 (D) 2 7. |z – (1 + i)| = 1 z z 4 - (A) 0 (B) 1 (C) 2 (D) 3 8. x4 – x3 – x2 – x – = 0, N >>> - (A) 0 (B) 2 (C) 4 (D) 3 9. P(x1, y1) Q (x2, y2), x2 y2 1 PQ a2 b2 x1x2- y1y2 a2 a2 a4 a4 (A) b2 (B) b2 (C) b4 (D) b4 10. x, y (a2 b c)x (a2 b c)y (a2 b c)(x y ) 0 (a+ b + c) (a,b,c R) (A) –2 (B) –1 (C) 0 (D) 4 H-22/28 1001CT103516013
Search
