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1 From Classroom/Integrated School Programs 7 in Top 0, 3 in Top 00, 5 in Top 300, 06 in Top 500 All India anks & 3 Students from Classroom /Integrated School Programs & 373 Students from All Programs have been Awarded a ank in JEE (Advanced), 03 FIITJEE JEE (Main), 0 ALL INDIA TEST SEIES CNCEPT ECAPITULATIN TEST - II Time Allotted: 3 Hours Maximum Marks: 3 Pleas e r ead th e instructions carefully. You are allotted 5 m inutes specifically for this purpose. You are not allowed to leave the Exam ination Hall before t he end of the test. INSTUCTINS A. General Instructions. Attempt ALL the questions. Answers have to be marked on the M sheets.. This question paper contains Three Parts. 3. Part-I is Physics, Part-II is Chemistry and Part-III is Mathematics.. Each part has only one section: Section-A. 5. ough 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 M Sheet. Ensure matching of M sheet with the Question paper before you start marking your answers on M sheet.. n the M 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. M sheet contains alphabets, numerals & special characters for marking answers. C. Marking Scheme For All Three Parts. (i) Section-A (0 to 03 and 0 to ) contains 6 multiple choice questions which have only one correct answer. Each question carries +8 marks for correct answer and mark for wrong answer. Section-A (0 to 09 and 3 to 30) contains multiple choice questions which have only one correct answer. Each question carries + marks for correct answer and mark for wrong answer. Name of the Candidate Enrolment No.

2 Useful Data PHYSICS Acceleration due to gravity g = 0 m/s Planck constant Charge of electron Mass of electron h = J-s e = C m e = kg Permittivity of free space 0 = C /N-m Density of water water = 0 3 kg/m 3 Atmospheric pressure P a = 0 5 N/m Gas constant = 8.3 J K mol CHEMISTY Gas Constant = 8.3 J K mol = 0.08 Lit atm K mol =.987 Cal K mol Avogadro's Number N a = Planck s constant h = Js = ergs Faraday = coulomb calorie =. joule amu = kg ev = J Atomic No: H=, He =, Li=3, Be=, B=5, C=6, N=7, =8, N=9, Na=, Mg=, Si=, Al=3, P=5, S=6, Cl=7, Ar=8, K =9, Ca=0, Cr=, Mn=5, Fe=6, Co=7, Ni=8, Cu = 9, Zn=30, As=33, Br=35, Ag=7, Sn=50, I=53, Xe=5, Ba=56, Pb=8, U=9. Atomic masses: H=, He=, Li=7, Be=9, B=, C=, N=, =6, F=9, Na=3, Mg=, Al = 7, Si=8, P=3, S=3, Cl=35.5, K=39, Ca=0, Cr=5, Mn=55, Fe=56, Co=59, Ni=58.7, Cu=63.5, Zn=65., As=75, Br=80, Ag=08, Sn=8.7, I=7, Xe=3, Ba=37, Pb=07, U=38.

3 3 Physics PAT I SECTIN A Single Correct Choice Type This section contains 30 multiple choice questions. Each question has four choices,, and (D) out of which NLY NE is correct.. Two similar blocks A and B are riveted rigidly with a rigid rod of length L such that block A can slide along an inclined plane as shown in the figure. If masses of the both blocks and the rod are each equal to m and kinetic friction between A and inclined plane is k = 0.5 then the magnitude of acceleration of centre of mass of the block rod system is 6 m/s m/s 5 m/s (D) m/s = sin (3/5) A B L k = 0.5. A wedge of mass M and dimensions as shown in the figure is lying completely inside a region (I) of zero pressure. The pressure inside region II is Pa. The surfaces are smooth. The wedge is imparted an initial velocity v 0 so that it just travels a distance b inside region II before finally coming to rest. The value of v 0 is h b egion - I a egion - II abh M abh 3 M 3 abh M (D) abh 3 M

4 3. A block A of mass m and a box B of same mass are lying on a horizontal surface as shown in the above figure. The coefficient of kinetic friction between the block and horizontal surface is A, while that between the box and surface is B. Given that B > A. At t = 0, the position is as shown in the figure and both are simultaneously given a velocity v 0 to the right. The time after which block will collide with the right end of the box is L g B A L g B A A B L L g B A (D) L g B A. It is observed that only 0.39% of the original radioactive sample remains undecayed after eight hours. Hence choose the incorrect statement. The half life of that substance is hr. The mean life of that substance is /ln hr The decay constant of the substance is ln hr (D) The half life of the substance is / hr 5. The figure shows a hollow circular tube fixed to a frictionless horizontal table. It is the top view of the arrangement. A ball is shot into end A of the tube to leave the other end B at high speed. The balls diameter is slightly less than the internal diameter of the tube. Which of the paths below will the ball follow on the table after it leaves the tube? B A (D) None of these

5 5 6. A mass m on the end of an ideal spring stretches the spring to a length when at rest. The mass is now set into motion so that it executes up and down vibrations while swinging back and forth as a simple pendulum. The mass moves in a figure eight pattern in a vertical plane a shown in the figure. The force constant of the spring assuming small oscillations is mg mg mg k (D) mg m m 7. When an ultrasonic waves travels from air into water, waves bends towards the normal frequency of waves changes from air to water. speed of ultrasonic wave is greater in water than that in air. (D) speed of ultrasonic wave is less in water than that in air. 8. A narrow tunnel is made through the earth of mass M and radius from the centre to the surface. The speed (in m/s) with which a particle should be projected from the centre of the earth through the tunnel so that it escapes to the space is g g 3g (D) g 9. A cubical block of volume v and density 3 is placed inside a liquid of density and attached to a spring of spring constant k as shown in the figure. Assuming ideal spring and pulley and spring is attached at A which is at / from centre. The compression in the spring at equilibrium is k C A vg k 3 vg k vg k vg (D) k

6 6 0. A conductor having uniform linear charge density is placed in circular form in 3 quadrants with different polarities as shown in the figure. Let E 0 made by E 0 tan tan 3 be the electric field at. Then the angle with the line along y-axis is tan (D) None y x. The pulley and the string are light and all the surfaces are frictionless. The system is initially held at rest and The string is just taut. The kg block on the plane is suddenly imparted a velocity of 5m/s to the left, and the system is simultaneously released. Find the displacement of the kg block (on the plane) after 3s. [Take g = 0 m/s ] 0 m 0 m 30 m (D) 0 m kg kg. A light thread is wound on a disk of mass m and other end of thread is connected to a block of mass m, which is placed on a rough ground as shown in diagram. Find the minimum value of coefficient of friction for which block remain at rest: 3 (D) 5 m r m 3. A milli ammeter of range 5 ma and resistance 0.5 is joined in a circuit as shown. Find the value of current for which meter gives full scale deflection when A & B are used as Terminal: 50 ma 5 ma 00 ma (D) A S ma B C D

7 7. In the circuit shown, the batteries E = E = V, E 3 =.5 V and the resistances = 0, = 0. The potential difference across the capacitor is 0. V 0. V 0.5 V (D). V E E E 3 C 5. A horizontal spring mass system of mass M performs simple harmonic motion of amplitude a 0 and time period T 0. When the mass M passes through mean position another stationary mass M sticks to it and both move together. If a and T be new amplitude and time period. Then a 0 a a a0 T 0 T (D) None 6. System is shown in figure. Assume the cylinder remains in contact with the two wedges. The velocity of cylinder is u m/s 30 o 30 o u m/s u m/s v m/s 3v m/s (D) 7u m/s 7. Consider the following statements for a particle moving in an elliptic orbit under the influence of a central force: () The radius vector covers equal area in equal time. () The motion takes place in a plane. (3) The angular momentum is constant of motion. Which of options given above are correct? & only & 3 only & 3 only (D) all

8 8 8. A person is standing on a weighing machine placed on the floor of an elevator. The motion of the elevator is shown in the adjacent diagram. The maximum and the minimum weights recorded are 66 kg and 57 kg. The magnitude of the upward accelerations is [Take g = 0 m/s.] Velocity (upward) m/s 0.5 m/s m/s (D) 0.5 m/s Time in seconds 9. When a charge particle of charge c and mass gm is released at origin in gravity free space having E E0ˆ j and B B0ˆ j (E 0 = 0 3 N/c and B0 = 5T). Then its speed depends only of X co-ordinate depends only on Y co-ordinate depends only on z co-ordinate (D) depends only on X, Y, Z co-ordinate 0. A neutral metallic finite block is placed at large but finite distance from a large charged sheet in the middle space in front of sheet. Then the block will be Attracted towards the sheet epelled away from the sheet Depend on nature of charge on the sheet (D) Zero force on the block. Two equal masses hang on either side of a pulley at the same height from the ground. The mass on the right is given a horizontal speed, after some time. The mass on the left will be nearer to ground. The mass on the right will be nearer to ground. Both the masses will be at equal distance from the ground. (D) Nothing can be said regarding their positions.. is the centre of mass of a body of mass M as shown in the figure. A, B, C are three different point on the body. B = 8 cm, C = 0 cm, BC = 6 cm and A = 0 cm. Which of the following can be written by using parallel axis theorem? I 0 is the moment of inertia about the axis passing through point and perpendicular to plane of object. I B = I C + M(BC) I C = I B + M(BC) I A = I 0 + M(B) (D) None of these B u Ground A C

9 9 3. A solid sphere of radius, and dielectric constant k has spherical cavity of radius /. A point charge q is placed in the cavity. Another charge q is placed outside the sphere at a distance of r from q. Then Coulombic force of interaction between them is found to be F. When the same charges are separated by same distance in vacuum then the force of interaction between them is found to be F then F = F /k F = F /k F. F = k (D) F = F. The relation between and r (internal resistance of the battery) for which the power consumed in the external part of the circuit is maximum. r = r = r (D) =.5 r r 5. An equilateral triangular loop having a resistance and length of each side is placed in a magnetic field which is varying at db dt in the loop will be 3 3 (D) = T/s. The induced current 3 3 x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x 6. The temperature of a mono-atomic gas in an uniform container of length L varies linearly from T 0 to T L as shown in the figure. If the molecular weight of the gas is M 0, then the time taken by a wave pulse in travelling from end A to end B is A T 0 L B T L L ( T T ) L 0 3M 5 3(T T ) L 0 5M L 0 L ( T T ) L 0 3M 5 (D) L M 0 (T T ) L 0

10 0 7. identical rods made of same material are arranged in the form of a cube. The temperature of P and are maintained at 90 0 C and 30 0 C respectively. Then the temperature of point V, when steady state is reached, 65C 60C 0C (D) 50C P 90 0 C S T W Q a U V 30 0 C 8. A spring block system with mass of block m and spring constant K (all the surfaces of block are perfectly reflecting and smooth) is placed on a smooth horizontal plane as shown in the diagram. A light beam of intensity I is switched on from rightwards. Find the amplitude of oscillations of the block. I I KC KC I (D) Zero KC m 9. A rod of mass M and length L is placed on a smooth horizontal table and is hit by a ball moving horizontally and perpendicular to length of rod and sticks to it. Then conservation of angular momentum can be applied About any point on the rod About a point at the centre of the rod About end point of the rod (D) None 30. Magnetic force on a spiral carrying current I 0 and placed in magnetic field B 0 parallel to the plane of spiral as shown in diagram, will be nearly (initial point, final point and centre lie on a line) I B r r Zero I B r r 0 0 (D) 0 0 I B r 0 0 r I 0 r r B 0

11 Chemistry PAT II SECTIN A Single Correct Choice Type This section contains 30 multiple choice questions. Each question has four choices,, and (D) out of which NLY NE is correct.. The pressure (P) and density () of a diatomic gas 3, 3 8 the value of P P is: 3 (D) changes from P to P. If. 0. mol of NH Cl are introduced into an empty container of 0 litre and heated to 37 o C to attain equilibrium as NHCls NH3 g HClg, K p = 0.36 atm. The quantity of solid NH Cl left is: 0.0 mole mole mole (D) mole 3. Which of the following alcohols will give same alkene on reaction with conc. H S? H H H H (I) (II) (III) (IV) I and II I, II and III II and III (D) II, III and IV

12 . The correct set of reagents for the following conversion is: 3 CH CHCH P /I, Na, conc. H S P 5, LiAlH P /I, Na, P 5 / (D) P 5 /, H, P /I, Na 5. rder of basic strength of the following compounds is: (I) (II) IV > II > I > III II > III > IV > I CH NH (III) (IV) III > II > IV > I (D) II > III > I > IV 6. When K Cr is added to CuS solution there is formation of CuCr and CuCr 7. Formation of CuCr 7 is due to: basic nature of CuS solution which converts Cr to Cr 7 acidic nature of CuS solution which converts CuS has a typical property of converting (D) none of the above is correct Cr Cr to 7. Amorphous boron is extracted from borax by following steps: X Y Z Borax H B B Boron What are (X) and (Z)? H S, Al HCl, Fe to Cr Cr 7 7 HCl, C (D) H S, Na 8. Heat of neutralisation of strong acid and strong base under atm and 5 o C is 3.7 kcal. If standard Gibbs energy change for dissociation of water to H + and H is 9. kcal, the change in standard entropy for dissociation of water in cal k - mol - is: (D) none of these

13 3 9. A metal crystallises in bcc lattice. The % of fraction of edge length not covered by atom is: 0.% 3.%.% (D).% 0 0. E 3.66 V and K sp of Al(H) 3 = The reaction potential of above couple at Al / Al ph = is: -. 3 V +.0 V +.3 V (D) -.0 V. Which of the following is correct option of reagent for the given conversion? CH CH Br / h, MgCl, Br / h, HCH Cl / h, Br / h, MgCl, MgCl, (D) 3 3 Br / h, KCN / H3 Cl / h,ch MgBr,Br / h,ch CH Br / h, NaNH, HCN, H3. Which is correct statements about P 6 and P 0? Both form oxyacids H 3 P 3 and H 3 P respectively. In P each P is joined to three and in P 0 each P is joined to four atoms. Both of these (D) None of these ml of a solution of Na C 3 neutralizes 9.35 ml of N HCl. The reaction is represented as C H C H 3 The density of this Na C 3 solution is.5 g ml -. The percentage of Na C 3 in it is: (D) 6.7

14 . In the extraction of copper, the reaction which does not take place in Bessemer converter is: CuFeS CuS FeS S Cu CuS 6Cu S CuS 3 Cu S (D) FeS 3 Fe S 5. In the following compounds of manganese what is the distribution of electrons on d-orbitals of manganese? (i) [Mn(H ) 6 ] + (ii) [Mn(CN) 6 ] - 3 t e in both 5 0 t e in both g g t e in (i) and g t e in (ii) (D) t 5 e 0 in i and t 3 e ii g g g g g g g g 6. Cl C C Cl LiAlH Conc. HS X Cl C The final product (X) is: (D) 7. H3 A B Compounds A and B can be differentiated by, -DNP Fehling solution Lucas reagent (D) NaHS 3

15 5 8. H H Major product (D) H H 9. Arrange the following reactions ion decreasing order of electrophilic addition reaction: H 3 C H 3 C H 3 C HCl HCl C CH, C CH, HCl C CH H 3 C H 3 C H 3 C NH (I) (II) (III) I > II > III II > III > I III > II > I (D) I = II = III 0. eductive ozonolysis of alkene C 0 H gave CH 3 C CH 3, CH 3 CCH and CH CH C CH in : : ratio. Which of the following is the most likely structure of alkene. (D)

16 6. Temperature of moles of an ideal gas is raised from 300 K to 350 K. What is value of H E for this process? ( = 8.3 J J mol - K - ) 0 5 J.5 (D) 660 J. K sp of CdS is and that of H S is M CdCl solution is precipitated on passing H S when ph is about 6 5 (D) 7 3. For the following equilibrium reaction N g N g given temperature. Hence, vapour density of equilibrium mixture is: (D) 0.0 H, N is 50% of total volume at. To synthesize CH CH 3 CH 3 Which of the following reactants cannot be suitable: CH CH 3, CH 3 MgBr CH 3, CH 3 CH MgBr CH, CH 3 CHMgBr (D) C H 3 CH CH 3, MgBr H C CH 3 5. The number of stereoisomers possible for the compound H 3 C CH CH CH(H)CH is 6 (D) 8

17 7 6. Aspartame, an artificial sweetener is peptide and has the following structure: CH NH C C NH CH 3 Free amino acids obtained by the hydrolysis of aspartame are H N CH H NH NH HC (D) Both and C H C NH 7. Haworth projection of -D-glucose is CH H H H H H H 3 H H H H H H Both and (D) None of these H CH H H H H 8. Which of the following is having highest bondlength? N N CN (D) CN 9. A 0.00 molal solution of Pt(NH 3 ) Cl in aqueous solution decreases the freezing point by o C. If K f =.86 K kg mol -. What is the formula of the complex: [Pt(NH 3 ) Cl ] [Pt(NH 3 ) 5 Cl]Cl 3 [Pt(NH 3 ) Cl ]Cl (D) [Pt(NH 3 ) 3 Cl 3 ]Cl.NH Holm s signal can be given by using CaC + CaCN CaC + Ca 3 P CaC + CaC 3 (D) Ca 3 P + CaCN H H H

18 Mathematics 8 PAT III SECTIN A Single Correct Choice Type This section contains 30 multiple choice questions. Each question has four choices,, and (D) out of which NLY NE is correct.. The points A(3, ) and B(, 3) lies on same or opposite side of the line ax + by + c = 0, (a, b, c + ) in which origin lies and P and P are length of perpendicular from A and B to the line such that P + 3P = 0 then the line ax + by + c = 0 touches the circle (x 8) + (y 7) = 8 7 x y x y 5 5 (D) (x 3) + (y 6) =. If a hyperbola whose foci are (, ) and (, 6) touches y axis then equation of hyperbola is x 3y 7 x 3y 8 x 3y 3x y x y 8 x 3y (D) x 3y 3x y x x 5 f x 5 x x, zeroes are of the form a b (D) 8 0 8, a, b z then a + b is equal to. The number is an example of nine digit number which contain each of the digits to 9 exactly one, it also has the property that the digit to 5 occur in their natural order, while the digit to 6 do not. Number of such numbers are (D) 560 Space for rough work

19 9 5. Let z = 8 + 6i, where z = a + ib (a, b ) is the cube root of z having least positive argument then the value of ab(a + b) is 8 0 (D) 0 6. A parabola touches two given straight lines originating from a given point. The locus of mid point of portion of any tangent. Which is intercepted between the given straight line is parabola ellipse straight line (D) hyperbola 7. z, z and z 3 are three points on a circle centred at origin. A point z is chosen on the circle such that the line joining z and z is perpendicular to the line joining z and z 3. Which of the following is true? zz + z z 3 = 0 z z + z + z z 3 = 0 z + z z 3 = 0 (D) zz z z 3 = 0 n tan nx 8. Let C n dx then sin nx lim n n n C equals 0 (D) n 9. We have identical balls available with us which we need to be distributed amongst 3 boys A, B and C such that A always gets an even number of balls. The number of possible ways of doing this is 0 6 (D) 3 0. / x The equation x a a x = a, a ; a, x has x only one solution as x = only positive solution as x = infinite solutions (D) none of these Space for rough work

20 0. A card from a pack of 5 cards is lost. From the remaining cards two cards are drawn at random and are found to be spades. What is the probability that the missing card was a spade (D) 5. The latus rectum of a conic section is the width of perpendicular line segment through the focus. The positive difference between the lengths of the latus rectum of 3y = x + x 9 and x + y 6x + 6y = is 3 (D) 5 3. Let A be a (n n) matrix with A =, B is the adjoint of the matrix A such that B = 0. What is the value of n? 3 5 (D) more than 5. Suppose that the domain of the function f(x) is set D and the range is the set, where D and x are the subsets of real numbers. Consider the functions: f(x), f(x + ), f(x), f, f x. If m is the number of functions listed above that must have the same domain as f(x) and n is the number of functions that must have the same range as f(x) then the ordered pair (m, n) is (, 5) (, 3) (3, ) (D) (3, 3) 5. Let a, a.. a n be the sides of a regular polygon inscribed in a circle of unit radius. If a a a a... a a a a a a... a a smallest possible value of n is 3 n = 3 n 6 8 (D) Space for rough work

21 6. Let us consider f(x) = x + [x] [ x] and g(x) = x lim n (cosn+ x) the graph of f(x) is a straight line passing through origin. The graph of g(x) is straight line passing through origin the graph of both f(x) and g(x) is a straight line not passing through origin the graph of f(x) is a straight line passing through origin whereas for that of g(x) is not passing through origin (D) will not be a straight line for either of the curve 7. Let f(x) = [x] + {x} :, then area of figure bounded by y = f (x), y = 0 between the ordinates x = and x = 5 is (where [.] and {.} represent the greatest integers and fractional part functions respectively) (D) sec sec What is the minimum value of tan tan for, B k, k z? 8 (D) 6 9. Consider straight line ax + by = c where abc + and a, b, c are distinct. This line meets the coordinate axes at P and Q respectively. If area of PQ, being origin does not depend upon a, b and c then a, b, c are in GP a, c b are in GP a, b, c are in AP (D) a, c, b are in AP 0. In a ABC, a, c, A are fixed. The third side may have two possible values say b and b. It is given that b = b. Then find the value of 8sin A a 3 (D). If A is an invertible idempotent matrix and B = 7A 7 + 6A 6 + 5A A then B is equal to 7 8 (D) 35 Space for rough work

22 . Find the number of triangles formed by the lines represented by x 3 x x = 0 and x y + x y + x y y 8 = 0 one two three (D) none of these 3. Let f(x) = sin 3 x + sin x for < x < and > 0. The interval in which should lie in order that f(x) has exactly one minimum and one maximum is 0 < < 3 0 < < < < (D) < < 3/. If P(x) = ax + bx + c leaves a remainder of when divided by x, a remainder of 3 when divided by (x + ) and a remainder of when divided by (x ) then P() is (D) 6 5. Let L : x + 3y + p 3 = 0 and L : x + 3y + p + 3 = 0 be two lines and p z. Let C : x + y + 6x + 0y + 30 = 0. If it is given that at least one of the lines L L is chord of C the probability that both are chords of C is (D) 5 n 6. n 3 If lim n n n n x n then the range of x is (n N) [, 5] (, 5) (, 5) (D) (, ) Space for rough work

23 3 7. The coordinate plane is constrained by the hyperbola x y = so that only the region exterior of the hyperbola is accessible what are the possible values of the ordinates of the center of a circular disc of radius where centres lies on the y axis?,,, 3 3,, 6 6, (D), 6 6, 8. If x sin x x sin x then x 0, x, x (D) x, 0 9. A plane P makes intercepts with the axes, the sum of whose square is a constant equal to K. The foot of the perpendicular from the origin P is (,, ) the value of in terms of K is K K K K (D) Let x e f x In x then the range of g x sin f x cos f x is 3/, /,, (D) (, ) Space for rough work