HALF COURSE TEST VIII. Time Allotted: 3 Hours Maximum Marks: 234

Transcription

1 In JEE Advanced 16, FIITJEE Students bag 36 in Top 1 AIR, 75 in Top AIR, 183 in Top 5 AIR Students from Long Term Classroom/ Integrated School Program & 443 Students from All Programs have qualified in JEE Advanced, 16 FIITJEE ALL INDIA INTEGRATED TEST SERIES HALF COURSE TEST VIII Paper 1 Time Allotted: 3 Hours Maximum Marks: 34 Pleas e r ead th e instructions carefully. You are allotted 5 minutes specifically for this purpose. You are not allowed to leav e th e Exam ination Hall before the end of the test. INSTRUCTIONS A. General Instructions 1. Attempt ALL the questions. Answers have to be marked on the OMR sheets.. This question paper contains Three Parts. 3. Part-I is Physics, Part-II is Chemistry and Part-III is Mathematics. 4. Each part is further divided into two sections: Section-A & Section-C 5. Rough spaces are provided for rough work inside the question paper. No additional sheets will be provided for rough work. 6. Blank Papers, clip boards, log tables, slide rule, calculator, cellular phones, pagers and electronic devices, in any form, are not allowed. B. Filling of OMR Sheet 1. Ensure matching of OMR sheet with the Question paper before you start marking your answers on OMR sheet.. On the OMR sheet, darken the appropriate bubble with black pen for each character of your Enrolment No. and write your Name, Test Centre and other details at the designated places. 3. OMR sheet contains alphabets, numerals & special characters for marking answers. C. Marking Scheme For All Three Parts. (i) Section-A (1 8) contains 8 multiple choice questions which have only one correct answer. Each question carries +3 marks for correct answer and 1 mark for wrong answer. Section-A (9 1) contains 4 multiple choice questions which have more than one correct answer. Each question carries +4 marks for correct answer. There is no negative marking. Section-A (13 to 18) contains 3 paragraphs with each having questions. Each question carries +3 marks for correct answer and 1 mark for wrong answer. (ii) Section-C (1 5) contains 5 Numerical based questions with answers as numerical value and each question carries +4 marks for correct answer. There is no negative marking. Name of the Candidate Enrolment No. JEE (Advanced)-17

2 Useful Data PHYSICS Acceleration due to gravity g = 1 m/s Planck constant Charge of electron Mass of electron h = J-s e = C me = kg Permittivity of free space = C /N-m Density of water water = 1 3 kg/m 3 Atmospheric pressure Pa = 1 5 N/m Gas constant R = J K 1 mol 1 CHEMISTRY Gas Constant R = J K 1 mol 1 =.81 Lit atm K 1 mol 1 = Cal K 1 mol 1 Avogadro's Number Na = Planck s constant h = Js = ergs 1 Faraday = 965 coulomb 1 calorie = 4. joule 1 amu = kg 1 ev = J Atomic No: H=1, He =, Li=3, Be=4, B=5, C=6, N=7, O=8, N=9, Na=11, Mg=1, Si=14, Al=13, P=15, S=16, Cl=17, Ar=18, K =19, Ca=, Cr=4, Mn=5, Fe=6, Co=7, Ni=8, Cu = 9, Zn=3, As=33, Br=35, Ag=47, Sn=5, I=53, Xe=54, Ba=56, Pb=8, U=9. Atomic masses: H=1, He=4, Li=7, Be=9, B=11, C=1, N=14, O=16, F=19, Na=3, Mg=4, Al = 7, Si=8, P=31, S=3, Cl=35.5, K=39, Ca=4, Cr=5, Mn=55, Fe=56, Co=59, Ni=58.7, Cu=63.5, Zn=65.4, As=75, Br=8, Ag=18, Sn=118.7, I=17, Xe=131, Ba=137, Pb=7, U=38.

3 3 Physics PART I SECTION A Straight Objective Type This section contains 8 multiple choice questions numbered 1 to 8. Each question has 4 choices (A), (B), (C) and (D), out of which only ONE is correct 1. A particle is thrown from a stationary platform with velocity v at an angle of 6 with the horizontal. The range obtained is R. If the platform was moving horizontally in the direction of target with velocity v, and particle was thrown with same speed v (w.r.t. platform) at same angle, then the range would have been (A) 3R/ (B) 5R/ (C) R (D) 3R. The kinetic energy K of a particle of mass 1 kg moving along a circle of radius R depends upon the distance travelled s, as K = as. The force acting on the particle is- (A) s a R s (B) as 1 R s (C) as (D) as 1 R 3. Two cars start from the same point, but travel in opposite directions on a circular path of radius R, each at speed v. While each car travels a distance less than (/) R, (one quarter circle) the centre of mass of the two cars (A) remains at the initial point (B) travels along a diameter of the circle at speed < v (C) travels along a diameter of the circle at speed = v (D) travels along a diameter of the circle at speed > v 4. Potential energy of a particle executing SHM varies sinusoidally. If the frequency of oscillation of the particle is f then frequency of oscillation of potential energy is (A) f (B) f/ (C) 4f (D) f 1/ 1/

4 4 5. Find distance travelled by a body executing SHM of amplitude a about origin along x-axis in 1 a seconds if at t = the body is at x and is moving towards the right extreme position. (Time period = 3 sec) (A) 13a (B) 14a (C) 13.5a (D) 14.5a 6. Three rods made of the same material and having the same crosssectional area have been joined as shown in the figure. Each rod is of the same length. The left and right ends are kept at Cand 9 C respectively. The temperature of the junction of the three rods will be (A) 45 (B) 6 C (C) 3 C (D) C C 9 C 9 C 7. A gas is undergoing an adiabatic process. At a certain state, the value of volume and temperature (V,T ) and the magnitude of the slope of V-T curve is. The value of CV is T (A) 1 R V (B) T (C) 1 R V (D) RV T RT V 8. You wish to lift a heavy block through a height h by attaching a string of negligible mass to it and pulling so that it moves at a constant velocity. You have the choice of lifting it either by pulling the string (i) vertically upward or (ii) along a frictionless inclined plane (see diagram).which one of the following statements is true? (i) h (ii) (A) The magnitude of the tension force in the string is smaller in case (i) than in case (ii). (B) The work done on the block by the tension force is the same in both cases. (C) The work done on the block by the tension force is smaller in case (ii) than in case (i). (D) The work done on the block by the gravitational force is smaller in case (ii) than in case (i). h

5 5 Multiple Correct Choice Type This section contains 4 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for its answer, out of which only ONE OR MORE THAN ONE is/are correct 9. In the figure shown, the rod is uniform and has a mass m, length L. The horizontal thread is connected to the rod at a point at a distance L/3 along the rod from lower end and angle between rod and wall is 6. (A) In equilibrium, tension in the thread is 3mg/. (B) In equilibrium, tension in the thread is 33mg/. (C) The minimum value of friction coefficient between the lower end of rod and the vertical wall for the rod be in equilibrium is /33. (D) The maximum value of friction coefficient between the lower end of rod and the vertical wall for the rod be in equilibrium is / A gas is enclosed in a cylinder of volume V fitted with piston of crosssectional area A and mass m. Atmospheric pressure is P. Adiabatic exponent of gas is. The piston is slightly depressed and released. mv (A) Time period of oscillation of piston if the process is isothermal is A P (B) Time period of oscillation of piston if the process is adiabatic is (C) Time period of oscillation of piston if the process is isothermal is mv A P mv (D) Time period of oscillation of piston if the process is adiabatic is A P mv AP P

6 6 11. Two identical beads connected by an inextensible massless string can slide along the two arms AB and BC of rigid smooth wire frame in a vertical plane. The system is released from rest as shown in figure. When they have moved by a distance.1m, (A) the speed of the bead moving along the arm BC is 1/5 m/s. (B) the speed of the bead moving along the arm BC is 8/5 m/s. (C) the speed of the bead moving along the arm AB is 1/5 m/s. (D) the speed of the bead moving along the arm AB is 8/5 m/s. A.4m B.3m C 1. Two rods of equal cross-sections, one of copper and the other of steel are joined end to end, to form a composite rod of length m. At C, length of copper rod is.5m. When the temperature is raised to 1 C, length increases to.m. If the same composite rod of length m at C is fixed between rigid walls & thus not allowed to expand, it is found that the length of the component rods also do not change with increase in temperature. Young s Modulus for copper = Pa, Coefficient of linear expansion of copper = C (A) No stress is induced in the rods in the nd case (when fixed between rigid walls) (B) Young s Modulus of steel = Pa (C) Coefficient of linear expansion of steel / C (D) All above statements are false

7 7 Comprehension Type This section contains 3 groups of questions. Each group has multiple choice question based on a paragraph. Each question has 4 choices (A), (B), (C) and (D) for its answer, out of which only ONE is correct Paragraph for Question Nos. 13 to 14 A cube of ice is floating in a liquid in a cylindrical beaker. The ice melts completely. The level of the liquid in the beaker after the ice melts is compared to the level of liquid in the beaker when the ice was floating. 13. If the liquid in beaker is mercury (A) Level will fall (C) Level will remain same (B) Level will rise (D) data insufficient 14. If liquid in beaker has density less than water but more than ice (A) Level will fall (B) level will rise (C) Level will remain same (D) data insufficient Paragraph for Question Nos. 15 to 16 An open rectangular tank with dimensions 5m 4m 3m contains water upto height of m as shown in fig. It is accelerated horizontally along the longer side. (g = 1m/s, Density of water = 1 kg/m 3 ) AB is the rear wall. CD is the front wall 3m A water a C m B 5m 15. Find the maximum acceleration that can be given to the tank without spilling water (A) m/s (B) 4m/s (C) 5m/s (D) none of above D 16. If this acceleration is increased by %, as compared to the value in the previous question, what is percentage of water spilled over (A) 5% (B) % (C) 1% (D) none of above

8 8 Paragraph for Question Nos. 17 to 18 When a particle is projected at some angle with the horizontal, the path of the particle is parabolic in nature. In the process the horizontal velocity remains constant but the magnitude of vertical velocity changes. At any instant during flight the acceleration of particle remains g in vertically downward direction. During flight at any point the path of particle can be considered as a part of circle and radius of that circle is called the radius of curvature of the path of particle. Consider that a particle is projected with velocity u = 1 m/s at an angle = 6º with the horizontal then: Answer the following questions 17. The radius of curvature of path of particle at the instant when the velocity vector of the particle becomes perpendicular to initial velocity vector is 1 (A) m (B) m (C) 4 m 3 3 (D) 8 m The magnitude of acceleration of particle at that instant is (A) 1 m/s (B) 5 3 m/s (C) 5 m/s (D) 1 3 m/s

9 9 SECTION C (One Integer Value Correct Type) This section contains 5 questions. Each question, when worked out will result in one integer from to 9 (both inclusive). 1. A rigid body can be hinged about any point on the x axis. When it is hinged such that the hinge is at x, the moment of inertia is given by I = x 1x + 7. The x coordinate of centre of mass is equal to. An ice cube of mass.1kg at C is placed in an isolated container which is at 7 C. The specific heat S of the container varies with temperature T according to the empirical relation S = A + BT, where A = 1.5 cal/kg-k and B = cal Kg K. If the final temperature of the container is 7 C, the mass of the container is (in Kg) 3. Four identical springs of spring constant k each are fixed to a particle of mass m kept at origin as shown. The system is kept on a horizontal plane. Time period of small oscillations of the particle along x = y is Find n. m. nk Y m X F (in Newton) 4. A block of mass 5 kg resting on a horizontal surface is acted upon by a force F which varies as shown in the figure. If the coefficient of friction between the block and surface is., find N the time (in second) when the block will come to rest. (g = 1 m/s ). O 1 t (in sec) 5. A solid homogeneous cylinder of height h and base radius r is kept vertically on a conveyer belt moving horizontally with an increasing velocity v = a + bt. If the cylinder is not allowed to slip, the gr time when the cylinder is about to topple is n where n is equal to 8bh

10 1 Chemistry PART II SECTION A Straight Objective Type This section contains 8 multiple choice questions numbered 1 to 8. Each question has 4 choices (A), (B), (C) and (D), out of which only ONE is correct 1. Some liquid is taken in an evacuated vessel and the vessel is sealed. Which of the following graph will correctly represent the achievement of equilibrium of liquid with its vapour at constant temperature? (re = rate of evaporation and rc = rate of condensation) (A) (B) Rate r e Rate r e r c r c (C) Time (D) Time Rate r c Rate r c r e r e Time Time. If saturated vapours are compressed slowly and isothermally to half of the initial volume, the pressure exerted by vapours will (A) become four times (B) become double (C) remain unchanged (D) become half 3. The conformation of the following compound is Et Me CMe 3 (A) CMe 3 Me Et (B) Me 3 C Me Et (C) CMe 3 Me Et (D) Et CMe 3 Me

11 11 4. Inorganic benzene reacts with HCl to form a compound B3N3H9Cl3. The protonation occurs at: (A) B-atom (B) N-atom (C) first at B then rearranges to N-atom (D) first at N then rearranges to B-atom. 5. In the system, LaCl3(s) + HO(g) + heat LaClO(s) + HCl(g), equilibrium is established. More water vapour is added to disturb the equilibrium. If the pressure of water vapour at new equilibrium is double of that at initial equilibrium, the factor by which pressure of HCl is changed is: (A) times (B) times (C) 1 times (D) 4 times. 6. Addition of Br to cis butene would give a product, which is (A) meso (B) achiral (C) racemic (D) optically active 7. What could be the product for the following reaction? O Cl (i) Anhy. AlCl3 (ii) HO Product? (A) (B) O O (C) O (D) O Cl OH 8. Addition of NaCO3 to a solution of an oxide in water produces CO. This experiment indicates that: (A) the oxide is basic (B) the oxide is emphoteric (C) the oxide is that of a metal (D) the oxide is that of non-mental

12 1 Multiple Correct Choice Type This section contains 4 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for its answer, out of which only ONE OR MORE THAN ONE is/are correct 9. Among the following, select the correct information(s) (A) the opposite lobes in any d-orbital have the same sign of wave function. (B) 1s orbital is the only orbital for which the sign of wave function doesn t have radial as well as angular dependency. (C) the number of radial nodes is always greater than that of angular nodes. (D) all the orbitals belonging from an orbit have the same number of total nodes. 1. The correct statements about sodium and its compounds would include that: (A) sodium forms an ionic hydride NaH (B) sodium nitrate decomposes to the nitrite on heating (C) sodium is a hard metal (D) sodium carbonate decomposes readily on heating. 11. At critical temperature: (A) dliquid = dvapour (B) dliquid > dvapour (C) boundary between liquid and vapour phase disappears (D) a transition state exists between liquid and vapour state. 1. Which of the following molecules have zero dipole moment? (A) F H (B) F H C C C C C C C (C) H F F (D) H F F F H H F F F

13 13 Comprehension Type This section contains 3 groups of questions. Each group has multiple choice question based on a paragraph. Each question has 4 choices (A), (B), (C) and (D) for its answer, out of which only ONE is correct Paragraph for Question Nos. 13 to 14 To find the Ksp of AgBrO3, a student prepared 1L of a just saturated solution by adding AgBrO3 in water at 7 C. He found that a copper wire left in the solution overnight became covered with silver and Cu + ions were also formed in the solution. The wire was cleaned, dried and found to weight 6.35mg less than its original weight. Given: Cu s Ag aq Cu aq Ag s Gº KJ (R = 8. J/K mol; Cu = 63.5 g mol 1 ) 13. The number of moles of Cu reacted was (A) (B) 1. (C).1 (D) The Ksp for AgBrO3 is: (A) (B) (C) (D) Paragraph for Question Nos. 15 to 16 Strictly speaking, then dehydration is not an E1 reaction of the protonated alcohol. In a true E1 elimination, the rate of reaction depends upon heterolysis step. Here that is not the case for carbocations are formed reversibly from the protonated alcohol. Where the structure of alkyl group permits, rearrangement takes place. 15. conc. HSO4 OH Product (A) is: (A) CH 3 A (B) CH 3 CH 3 (C) CH 3 H 3 C CH 3 (D) none

14 CH OH conc. HSO4 HOH C Product (B) is: (A) CH 3 (B) B (C) CH (D) none C H Paragraph for Question Nos. 17 to 18 Formation of bride bond is best explained by molecular orbital theory. According to which a bride bond is formed by filling electrons into M.O. which spread over three nuclei hence such bonds are specified as three centred bond. 17. In which of the following dimer empty atomic orbital of central atom of monomer doesn t involve in hybridisation: (A) GaH6 (B) AlBr6 (C) BeH4 (D) ClO Which of the following compound is having maximum number of atoms in same plane? (A) AlMe6 (B) BH6 (C) BeH4 (D) C3H4.

15 15 SECTION C (One Integer Value Correct Type) This section contains 5 questions. Each question, when worked out will result in one integer from to 9 (both inclusive). 1. The difference between total number of lone pairs and total number of -bonds in [B3O3(OH)6] 3 molecular ion is?. Total number of stereoisomer of compound given below is: H 3 C CH CH CH CH CH C H 5 Cl 3. Electron falls from 7 th energy level and lower energy levels to produce bands in the Paschen series. The total number of bands obtained will be: 4. Degree of unsaturation in is: 5. At identical temperature and pressure the rate of diffusion of hydrogen gas is 3 3 times that of a hydrocarbon having molecular formula CnHn. The value of n is:

16 16 Mathematics PART III SECTION A Straight Objective Type This section contains 8 multiple choice questions numbered 1 to 8. Each question has 4 choices (A), (B), (C) and (D), out of which only ONE is correct 1. If (sinx + cosx) = (secx + cosecx), then the number of possible values of (tanx + cotx) is (A) 1 (B) (C) (D) 4. A monic quadratic equation (means a quadratic equation whose coefficient of x is 1(unity)) p(x) is such that p(x) = and p(p(p(x))) = have a common root, then (A) p() p(1) > (B) p() p(1) < (C) p() p(1) = (D) p() = and p(1) = A B C 3. If in a triangle ABC, x = 1 tan tan 3tan, then x is (A) 1 (B) 1 (C) 1 (D) 1 1 n 4. Let f(n) = k C n k1 k, then the value of f(5) is equal to (A) 1 (B) 15 (C) 175 (D) 5 5. Number of integral values of x for which sin 4x x x tan (A) (B) 5 (C) 6 (D) 8 is independent of x is 6. A student is allowed to select atmost n books from a collection of n 1 books, If the total number of ways in which he can select at least one book is 55, then n is (A) 3 (B) 4 (C) 5 (D) 8

17 17 7. Let f(x) = x 4 + x 3 + x + x + 1 then remainder on dividing f(x 5 ) by f(x) is (A) 1 (B) 3 (C) 4 (D) 5 8. If the product of the perpendiculars drawn from the point (1, 1) on the lines is 1, then h a b ab h a b ab (A) (B) (C) ha b ab (D) Multiple Correct Choice Type h a b ab ax hxy by This section contains 4 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for its answer, out of which only ONE OR MORE THAN ONE is/are correct 9. For x, y, z,, let cosx = tany, cosy = tanz and cosz = tanx. Which of the following is (are) true (A) siny > 1 (C) sinz < 1 (B) sinx = 5 1 (D) sinx = siny = sinz 1. If coefficient of x 3 and x 4 in (1 + ax + bx )(1 x) 18 are zero, then (A) a = 16 (B) b = 7 3 (C) a = 15 (D) b = x 34x 71 For x R, the expression cannot lie between x x 7 (A) (5, 7) (B) (1, 9) (C) (1, 4) (D) (8, 9) 1. Number of ways in which 15 identical coins can be put into 6 different bags (A) is co-eff of (B) is coefficient of 15 6 x in x 1 x x... 6 if no bag remains empty 15 x in 1 x 6 (C) is same as number of the integral solutions of a + b + c + d + e + f = 15 (D) is same as number of non negative integral solutions of 6 i1 x 15 i

18 18 Comprehension Type This section contains 3 groups of questions. Each group has multiple choice question based on a paragraph. Each question has 4 choices (A), (B), (C) and (D) for its answer, out of which only ONE is correct Paragraph for Question Nos. 13 to 14 Read the following write up carefully and answer the following questions: For < x <, let Pmn(x) = mlogcosx(sinx) + nlogcosx(cotx) where m, n {1,, 3,, 9} For example P9(x) = logcosx(sinx) + 9logcosx(cotx). 13. Which one of the following is always correct? (A) Pmn(x) m m n (C) Pmn(x) n m n (B) Pmn(x) n m n (D) Pmn(x) m m n 14. The mean proportional of numbers P49 and P (A) 4 (B) 6 (C) 9 (D) 1 is equal to Paragraph for Question Nos. 15 to 16 Read the following write up carefully and answer the following questions: 3x 9 Consider a function f(x) = which has greatest value equal to 3 x The minimum value of f(x) is equal to (A) tan 3 (C) cos 3 (B) sin 6 (D) cot 16. If the equation f(x) = b has two distinct real roots then the number of integral values of b is equal to (A) (B) 1 (C) (D) 3

19 19 Paragraph for Question Nos. 17 to 18 Read the following write up carefully and answer the following questions: The sum of the first 1 terms of a geometric progression is. The sum of the first 44 terms of the same series is The sum of the first 636 terms (A) 58 (B) 54 (C) 54 (D) Sum of infinite terms of the same series (A) (B) 54 (C) 6 (D) not exists SECTION C (One Integer Value Correct Type) This section contains 5 questions. Each question, when worked out will result in one integer from to 9 (both inclusive). 1. In a triangle ABC, the median to the side BC is of length into angles 3 and 45. The length of the side BC is and it divides the angle A. If one of the diameters of the circle x + y x 6y + 6 = is a chord to the circle with centre (, 1), then the radius of the circle is 3. The digit at the unit place of the sum 1!! 3!... 11! is 4. All chords of the curve 3x y x + 4y =, which subtend a right angle at the origin pass through a fixed point. The square of its distance from the origin is 5. The value of the ratio is