ALL INDIA TEST SERIES

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1 In JEE Advanced 016, FIITJEE Students bag 36 in Top 100 AIR, 75 in Top 00 AIR, 183 in Top 500 AIR Students from Long Term Classroom/ Integrated School Program & 443 Students from All Programs have qualified in JEE Advanced, 016 FIITJEE JEE (Advanced), 017 ALL INDIA TEST SERIES CONCEPT RECAPITULATION TEST II Paper Time Allotted: 3 Hours Maximum Marks: 40 Pleas e r ead th e instructions carefully. You are allotted 5 m inutes specifically for this purpose. You are not allowed to leav e th e Exam ination Hal l 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 has 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 (01 to 08) contains 8 multiple choice questions which have one or more correct answer. Each question carries +4 marks for correct answer and marks for wrong answer. Section-A (09 to 1) contains paragraphs with each having questions with one or more than one correct answer. Each question carries +4 marks for correct answer and marks for wrong answer. (ii). Section-C (01 08) contains 8 Numerical based questions with answers as numerical value from 0 to 9 and each question carries +4 marks for correct answer. There is no negative marking. Name of the Candidate Enrolment No.

2 Useful Data PHYSICS Acceleration due to gravity g = 10 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 = 10 3 kg/m 3 Atmospheric pressure P a = 10 5 N/m Gas constant R = J K 1 mol 1 CHEMISTRY Gas Constant R = J K 1 mol 1 = Lit atm K 1 mol 1 = Cal K 1 mol 1 Avogadro's Number N a = Planck s constant h = Js = ergs 1 Faraday = 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=0, Cr=4, Mn=5, Fe=6, Co=7, Ni=8, Cu = 9, Zn=30, As=33, Br=35, Ag=47, Sn=50, 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=40, Cr=5, Mn=55, Fe=56, Co=59, Ni=58.7, Cu=63.5, Zn=65.4, As=75, Br=80, Ag=108, Sn=118.7, I=17, Xe=131, Ba=137, Pb=07, U=38.

3 3 Physics PART I SECTION A (One or More than One Options Correct Type) This section contains 8 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE THAN ONE is/are correct. 1. A small solid ball of density is held inside at point A a cubical container of side L, filled with an ideal liquid of density 4 as shown in the figure. Now, if the container starts moving with constant acceleration a horizontally and the ball is released from point A simultaneously, then P L/ A L/ Q a (A) For ball to hit the top of container at end Q, a = 3g (B) For ball to hit the top of container at end Q, a = g R L S (C) Ball hits the top of container at end Q after a time t = L 3g (D) Ball hits the top of container at end Q after a time t = L 3g. A non-conducting ring of mass m and radius R has a charge Q uniformly distributed over its circumference. The ring is placed on a rough horizontal surface such that plane of the ring is parallel to the surface. A vertical magnetic field B = B 0 t tesla is switched on. After s from switching on the magnetic field the ring is just about to rotate about vertical axis through its centre: B0RQ (A) Friction coefficient between the ring and the surface is mg. B0RQ (B) Friction coefficient between the ring and the surface is mg. (C) If magnetic field is switched off after 4s, then the angle rotated by the ring before B0Q coming to stop after switching off magnetic field is m. (D) If magnetic field is switched off after 4s, then the angle rotated by the ring before B0Q coming to stop after switching off magnetic field is m.

4 4 3. Choose from following the correct statement(s) (A) The no. of significant figures in m is 3. (B) When.51 is rounded off to one decimal place the answer is.3 (C) When.51 is rounded off to one decimal place the answer is. (D) The least count of weighing machine is 100 Kg. The measured value wing this machine is written as 000 Kg. The no. of significant figure in this is one. 4. A particle of mass m and charge q is projected in a region where an electric field is existing and given by E E0ˆ i, with a velocity v0ˆ j from the origin at time t = 0, then choose the correct statement (assuming m v0 qe0mx0 ). (A) radius of curvature of the particle when its x-coordinate becomes x 0 is x 0. (B) radius of curvature of the particle when its x-coordinate becomes x 0 is 4 x 0. (C) speed of the particle when its x-coordinate becomes x 0 is v 0. (D) speed of the particle when its x-coordinate becomes x 0 is v An object of length 1m is placed on a principle axis of biconvex lens of radius 5 cm. Distance between the lens and object is 0 cm. Space between the lens and object is filled with medium of two different refractive index and 1 as shown in the figure. Refractive index is 1 on the left of the object and on the right side of the lens. Boundary of both medium is mid-way between the object and lens as shown in figure. 1 cm = =1 = cm (A) The image will be formed at distance of 7.5 cm from the optical centre. (B) The image will be formed at distance of 10 cm from the optical centre. (C) The size of the image is 0.5 cm. (D) The size of the image is 0.4 cm. 10cm

5 5 6. In the given circuit, the AC source has = 100 rad/s. Considering the inductor and capacitor to be ideal, then (A) the peak value of current through the circuit, I is 0.3 A (B) the peak value of current through the circuit, I is 0.3 A (C) the peak value of voltage across 100 resistor = 100 V (D) the peak value of voltage across 50 resistor = 10 V 100F 0.5H V ~ 7. In the series L C R circuit, the voltage across resistance, capacitance and inductance are 30V each at frequency f = f 0. (A) It the inductor is short-circuited, the voltage across the capacitor will be 30 V. (B) If the capacitor is short-circuited, the voltage drop across the inductor will be 30 V. (C) If the frequency is changed to f 0, the ratio of reactance of the inductor to that of the capacitor is 4 : 1. (D) If the frequency is changed to f 0, the ratio of the reactance of the inductor to that of the capacitor is 1 : A heavy mass M resting on the ground is connected to a lighter mass m through a light inextensible string passing over an ideal pulley. The string connected to mass M is loose. Let lighter mass m be allowed to fall freely through a height h such that the string becomes taut. If t is the time between the string become taut to just before the heavier mass again makes contact with the ground and E is change in kinetic energy to become taut at first time. m h m h (A) t = M m g Mm (C) E = gh M m (B) t = M m g (D) E = Mgh M m

6 6 Paragraph type This section contains TWO paragraphs. Based on each paragraph, there will be TWO questions. Each question has FOUR options (A), (B), (C) and (D). ONE OR MORE THAN ONE of these four option(s) is(are) correct. Paragraph for Questions 09 & 10 A radioactive nucleus X decays to nucleus Y which further decays to a stable nucleus Z as given below: X x = 0.1 sec -1 X Y Y 1 sec 30 1 Z (stable) Initially the sample contains nucleus of X only and its population is N 0 = Further, the population of Y as a function of time is given by N0 x yt xt Ny t e e x y 9. If N X, N Y and N Z represent population of X, Y and Z respectively at any instant of time t then: dny N dn Y y NY (A) (B) 0.1Nx dt 30 dt 30 dny NY dny NY (C) (D) 0.1NY dt 30 dt The time at which population of Y is maximum is: (A) In 3 (B) In 5 (C) 15 In 3 (D) 5 In 3

7 7 Paragraph for Questions 11 & 1 A long insulating cylinder of radius R and length l carries a uniformly distributed surface charge Q. A massless string is coiled around the cylinder from which a block of mass m hangs. The mass is free to move downwards and cylinder can rotate about its axis. Assuming moment of inertia of cylinder is zero, if system is released from rest at t = 0 (a is acceleration of block) m 11. Induced electric field at the surface of cylinder is 0 (A) Qa (B) Qa 0 l 4l 0 (C) Qa 30Qa (D) 4l 4l 1. Tension in the string is 0 (A) Q a l 0 (C) Q a 4l (B) (D) Q a 0 4l Q a 0 l SECTION C (One Integer Value Correct Type) This section contains 8 questions. Each question, when worked out will result in one integer from 0 to 9 (both inclusive). 1. A convex lens of focal length 1.5 m is placed in a system of coordinate axis such that its optical centre is at origin and principal axis coinciding with the x-axis. An object and a plane mirror are arranged on the principal axis as shown in figure. Find the value of d (in m) so that y- coordinate of final image (after refraction and reflection) is 0.3m. (Take tan = 0.3) (,0.1) 0.1m m (0,0) d

8 8. A solid cylinder with r = 0.1 m and mass M = kg is placed such that it is in contact with the vertical and a horizontal surface as shown in figure. The coefficient of static friction is = (1/3) for both the surfaces. Find the distance d (in cm) from the centre of the cylinder at which a force F = 40 N should be applied vertically so that the cylinder just starts rotating in anticlockwise direction. 3. Inner surface of a cylindrical shell of length l and of material of thermal conductivity k is kept at constant temperature T 1 and outer surface of the cylinder is kept at constant temperature T such that T T as shown in figure. Heat flows from inner surface to outer 1 surface radially outward. Inner and outer radii of the shell are R and R respectively. Due to lack of space this cylinder has to be R R T 1 T l replaced by a smaller cylinder of length l, inner and outer radii R 4 and R respectively and thermal conductivity of material nk. If rate of radial outward heat flow remains same for same temperatures of inner and outer surface i.e. T 1 and T, then find the value of n. 4. A ball of mass 1 kg and radius 10 cm is given an angular velocity 100 rad/s and is then dropped from a height H = 500 m from a point A above the ground. The coefficient of restitution for the collision between the ball and the floor is 0.5 and coefficient of friction between the ball and the floor is 1/3. There is a smooth wall at a distance of 50 m from point O (which is vertically below A). The collision between the ball and wall is perfectly elastic. If the height at which the ball hits the wall is 50 find the value x. x H = 500 m A O 0 50 m B

9 5. What will be angular frequency (rad/sec) for small oscillation of block of mass m in this arrangement shown. Neglect the mass of the rod. k 10 SI unit m 3 k m k l/ k l/ 6.

9 9 5. What will be angular frequency (rad/sec) for small oscillation of block of mass m in this arrangement shown. Neglect the mass of the rod. k 10 SI unit m 3 k m k l/ k l/ 6. A long straight wire carries a charge of C/m (figure). A coaxial cylindrical equipotential surface, radius 1.0 m, has a potential of 100 V. The radius of the 1000 V equipotential cylinder is e n. Find the value of n. 7. A wire is wrapped over a hemi-spherical cone of radius R. If N = number of turns and I = current per turn and the o induction at O is Ni, the value of n is nr 8. The given figure shows a YDSE apparatus are incident on slits S 1 and S ( S1S mm ) 3 at an angle 30 o with the horizontal. The medium on left side of the slits in waterw 4 / 3. To obtain the central maxima at point P, a glass slab g 3 / is introduced in front of slits S 1. If the thickness of the glass slab required for this purpose is t then find the value of 9t S 1 S D P

10 10 Chemistry PART II SECTION A (One or More than One Options Correct Type) This section contains 8 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE THAN ONE is/are correct. 1. Which of the following statement(s) is/are correct regarding the structure of XeF 4? (A) The hybridization of Xe is sp 3 d (B) The lone pairs occupy the axial positions of a tetrahedron (C) Two types of bond angles are observed in the molecule (D) The bond pair dipole moments cancel the lone pair dipole moments HI. CH OC H Pr oduct s 3 5 Which of the following product(s) is/are formed in the above reaction? (A) CH 3 OH (B) CH 3 I (C) C H 5 OH (D) C H 5 I 3. Which of the following reaction(s) take(s) place during rusting of the surface of iron? Fe s Fe aq e (A) (B) O g 4H 4 e HO l (C) 3 (D) Fe O s xh Ol Fe O.xH O 4Fe aq O g 4H O l Fe O s 8H 3 3

11 11 4. O O Choose correct statement about the above compound? (A) It reacts with CH 3 MgBr followed by hydrolysis to form a tertiary diol. (B) It exhibits tautomerism. (C) Oxidation of it with acidified permanganate solution followed by heating forms cyclohexan-1, 4-dione (D) When reacts with Clemmensen s reagent it forms 5. Borax structure contains (A) two BO 4 groups and two BO 3 groups (C) four BO 3 groups only (B) four BO 4 groups only (D) three BO 4 and one BO 3 groups 6. For the decomposition of NH 3 (g) in a sealed tube NH3 g N g 3H g (A) K p does not change with pressure (B) concentration of H (g) is less than that of nitrogen (C) concentration of ammonia does not change with pressure (D) K p changes significantly with pressure 7. Which are buffer mixtures? (A) H 3 BO 3 and borax (B) NaOH and NaNO 3 (C) CH 3 COONa and CH 3 COOH (D) NH 4 OH and NH 4 Cl

12 1 8. CaCO 3 (s) CaO(s) + CO (g) K p = atm at 300 K 0 gram CaCO 3 (solid) is heated in a closed container of volume 1 litre at 300 K. Which is/are the correct option(s)? (A) On addition of small amount of CaCO 3, pressure of CO will increase (B) On increasing temperature, the decomposition of CaCO 3 becomes faster (C) Amount of CaO should decrease on addition of CaCO 3. (D) Equilibrium constant depends on temperature. Paragraph type This section contains TWO paragraphs. Based on each paragraph, there will be TWO questions. Each question has FOUR options (A), (B), (C) and (D). ONE OR MORE THAN ONE of these four option(s) is(are) correct. Paragraph for Question Nos. 9 to 10 The rate of chemical reactions are strongly affected by temperature. The rate of certain reactions increases by or 3 times by 10 o C rise in temperature. The relation between rate constant and temperature is given by Arrhenius equation. E a /RT k Ae The constant A is called Arrhenius constant or pre- exponential factor. Taking logarithm of the equation, we have E logk log A a.303rt The rate constant of a reaction is given as: K logk sec 14 T Answer the following questions on the basis of the above write up. 9. The pre-exponential factor or frequency factor(a) of the reaction under consideration is: (A) sec -1 (B) sec -1 (C) 14 sec -1 (D) ln14 sec -1

13 At what temperature, the rate constant of the reaction is equal to the pre-exponential factor? (A) T = 0 K (B) T K 14 (C) T = K 14 (D) T K Paragraph for Questions 11 & 1 An aromatic tertiary alcohol upon acid catalysed dehydration gives a product (I). Reductive ozonolysis of (I) forms compounds (J) and (K). Compound (J) upon reaction with NaOH gives benzyl alcohol and compound (L), whereas (K) on heating with NaOH gives only (M) Answer the following questions on the basis of the above write up. 11. The tertiary alcohol in the above question is formed by the reaction of O (A) Ph H PhCH MgBr O (B) (C) (D) Ph Ph Ph O O CH 3 PhMgBr CH 3 PhCH MgBr H PhMgBr 1. The structure of the compound (I) is: (A) CH3CH C Ph (B) PhCH C CH3 Ph Ph (C) PhCH = CH CH 3 (D) PhCH C CH3 CH Ph

14 14 SECTION C (One Integer Value Correct Type) This section contains 8 questions. Each question, when worked out will result in one integer from 0 to 9 (both inclusive). 1. How many sigma bond(s) is/are formed by silicon in silica (SiO )?. The ph of the mixture of 50 ml of 0.05 M NH 4 OH + 50 ml of 0.05 M CH 3 COOH p CH COOH 4.74, p NH OH 4.74 Ka 3 Kb 4 3. In a particular reaction the time required to complete half of the reaction (i.e. t 1/ ) was found to increase 16 times when the inital concentration of the reactant was reduced to one-fourth. What is the order of the reaction? 4 What is the coordination number of beryllium in solid BeCl? 5. In a solution containing 0.0 M CH 3 COOH and 0.01MC 6 H 5 COOH. If K a CH3COOHand Ka C6H5COOH are and respectively, then the ph of solution is 6. Ammonia gas at 76 cm Hg pressure was connected to a manometer. After sparking in the flask, NH3 is partially dissociated as follows. NH 3(g) N (g) 3H (g) The level in the mercury column of the manometer was found to show the difference of 4cm. The partial pressure of H (g) at equilibrium is 6y(in cm Hg). Find the value of y 7. HF SiO A H O HF B How many total number of atom(s) or species is/are present in one molecule of (B)? 8. The molecular formula of an aliphatic monocarboxylic acid is C 6 H 1 O. How many Ka secondary carbon atom(s) is/are present in its isomer which has maximum value of p?

15 15 Mathematics PART III SECTION A Multiple Correct Choice Type This section contains 8 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 1. Let S = {1,, 3, 4,..,n} and f n be the number of those subsets of S which do not contain consecutive elements of S, then nn 1n (A) fn (B) f n f n1 6 (C) f n f n 1 f n (D) f 4 8 f " x 0 (A) f 0 f f c,0 c (B) f 0 f f 1. Let f x be twice differentiable function such that (C) f 0 f f 1 3. Let 3 in (D) f 0 f f 1 8 f x x x tan x, where 0 x, then 9 6 (A) f " x 0 (C) f ' x 0 f "' x 0 (B) (D) f x 0 0,. Then

16 16 4. A function y f x satisfies the following conditions (i) f 1 1 (ii) The tangent at any point of the graph of f x cuts off on the y axis an intercept equal to the square of the abscissa of the point of tangency Which of the following are correct? (A) The graph of y f x passes through the origin (B) y f x denotes a conic where coordinates of focus are (C) The area enclosed by f x, and the line y 3 0 is 3 (D) y f x has no maxima , 4 5. In which of the following situations, it is possible to have a triangle ABC? (All symbols used have usual meaning in a triangle.) (A) (a + c b) (a c + b) = 4bc (B) b sin C + c sin B = ab A C A C (C) a = 3, b = 5, c = 7 and C (D) cos cos 3 6. Given that x 1,x 3 are roots of the equation equation ax 4x 1 0 and x,x 4 are roots of the bx 6x 1 0. If x 1,x,x 3,x 4 are in harmonic progression, then (A) 3a b 1 (B) a b 73 (C) a 3b (D) 1 1 a b 7. Let an , then n times (A) a 91 is not prime (B) a 951 is not prime (C) a 480 is not prime (D) a 91 is not prime

17 17 8. Which of the following statement(s) is (are) correct? (A) x 0, 1, then f (x) must be bounded in [0, 1] If f x is differentiable (B) There exist a bijective function f : 0, 1 0, 1 which is not continuous be defined as f x x cos x 4, then f c (C) Let f : 1, R c 1,. (D) If 1 then f ' 4 x f x 3 x e, is equal to 1 for some Paragraph type This section contains TWO paragraphs. Based on each paragraph, there will be TWO questions. Each question has FOUR options (A), (B), (C) and (D). ONE OR MORE THAN ONE of these four option(s) is(are) correct. Paragraph for Questions 09 to 10 A sequence of ellipse E 1,E,...E n is constructed as follows. Ellipse ellipse En 1 at the extremities of the major axis of n 1 the minor axis of En 1. (e n is eccentricity of ellipse En) 9. If e n is independent of n, then the eccentricity of ellipse En is: (A) (B) (C) 3 E n is drawn so as to touch E and to have its foci at the extremities of (D) 3 1 x y 10. If equation of ellipse E 1 is 1, then the equation of ellipse E 3 is: 9 16 x y x y (A) 1 (B) x y x y (C) 1 (D)

18 18 Paragraph for Questions 11 to 1 In a triangle if the sum of two sides is x and their product is y x y x zx z y, where z is the third side of the triangle. 11. Greatest angle of the triangle is o (A) 105 (B) 10 o (C) 135 (D) 150 o o such that 1. Area of the triangle is: (A) y 3 4 (C) z 3 4 (B) x 3 4 (D) none of these SECTION C (One Integer Value Correct Type) This section contains 8 questions. Each question, when worked out will result in one integer from 0 to 9 (both inclusive). 1. An urn contain 3 red balls and n white balls. Mr. A draws two balls together from the urn. The probability that they have the same colour is 1/. Mr. B draws one ball from the urn, notes its colour and replaces it. He then draws a second ball from the urn and finds that both balls have the same colour is 5. The possible value of n is 8. Consider the system of equations ax y b, bx y a,ax by ab where a,b 0,1,,3, 4. Find the number of ordered pairs (a, b) for which system is consistent. 3. If planes ˆ ˆ ˆ ˆ ˆ ˆ r (i j k) 1, r (i aj k) and r (aˆi a ˆj k) ˆ 3 then find the number of real values of a. intersect in a line,

19 19 4. The 0 th term of an arithmetic sequence is log10 0 and the 3 nd term is log10 3. If exactly one term of the arithmetic sequence is a rational number which in lowest form is p ; p,q N then (p + q) = q 5. Let tx1 f x be a differentiable function in 1, f t f x 1 t f x 1 x 1 f t lim 1. Then value of Lim 6. If f : 0,1 and ln f x x1 f 0 1 such that n x R is a continuous function satisfying f x dx f x dx 3 1 reciprocal of f 4 is 7. Any chord of conic p q equals 0 0, then the x y xy 1 passing through origin is bisected at point (p, q), then 8. Let z and be complex numbers such that z i and z 1. If area of triangle formed by z, and origin is equal to A, then find the value of 16A.

PART A. 4cm 1 =1.4 1 =1.5. 5cm

PART A. 4cm 1 =1.4 1 =1.5. 5cm PART A Straight Objective Type This section contains 30 multiple choice questions. Each question has 4 choices (1), (), (3) and (4) for its answer, out of which ONLY ONE is correct. 1. The apparent depth