TEST No. 5 PAPER - I. for. JEE (Main) 2014

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1 Roll No.: Test Date: 19/01/014 Centre Code: Test Booklet Code A TEST No. 5 PAPER - I for INDIA AAKASH TEST SERIES ALL JEE (Main) 014 INSTRUCTIONS FOR CANDIDATE 1. Read each question carefully.. It is matory to use Black Ball point PEN to darken the appropriate circle in the answer sheet. 3. Mark should be dark should completely fill the circle. 4. Rough work must not be done on the answer sheet. 5. Do not use white-fluid or any other rubbing material on answer sheet. 6. Student cannot use log tables calculators or any other material in the examination hall. 7. Before attempting the question paper, student should ensure that the test paper contains all pages no page is missing. 8. Before hing over the answer sheet to the invigilator, cidate should check that Roll No., Centre Code Date of Birth have been filled marked correctly. 9. Immediately after the prescribed examination time is over, the answer sheet to be returned to the invigilator. 10. There are three parts in the question paper A, B C consisting of Physics, Chemistry Mathematics having 30 questions in each part of equal weightage. Each question is allotted 4 (four) marks for each correct response. 11. The Test booklet consists of 90 questions. The maximum marks are One fourth (¼) marks will be deducted for indicating incorrect response of each question. No deduction from the total score will be made if no response is indicated for any question in the answer sheet. 13. Pattern of the questions are as under: Section I : Straight Objective Type Questions Section II : Assertion Reason Type Questions

2 Test No. 5 Paper I TOPICS OF THE TEST Physics Electric Charges Field, Electrostatics Potential Capacitance, Current Electricity Chemistry General Principles & Processes of Isolation of Elements, The d & f - Block Elements, Coordination Compounds, Qualitative Analysis Mathematics Sets, Relations & Functions (XI & XII), Limits & Derivatives, Continuity Differentiability

3 Test - 5 (Paper-I) All India Aakash Test Series for JEE (Main) 014 Time : 3 Hrs. MM : 360 TEST - 5 (Paper-1) PART - A (PHYSICS) SECTION - I Straight Objective Type Questions This section contains 5 multiple choice questions numbered 1 to 5. Each question has 4 choices, (),, out of which ONLY ONE is correct. Choose the correct answer : 1. Figure shows two concentric shells. Whose radii are a b. If outer shell has charge +q, charge on inner shell would be 3. The dimensional formula for rate of change of electrical flux per unit current is [ML 3 T 4 A ] () [ML T 4 A ] [ML 3 T A ] [ML 3 T A 1 ] 4. Which is the correct representation of the charges on the surface of a conductor at the bend when current is flowing? a b () O Zero () q qb a a q b. Maximum rate of heat dissipation in the resistance R is V R 1 V 4 V Electric field which is directed along y-axis. Varies along x-axis as shown in figure. Potential difference between x = 1 m to x = 3 m is E(N/C) x (m) W () 1 W 4.5 W 0.5 W 50 V () 0 V 375 V V 1/1

4 All India Aakash Test Series for JEE (Main) A resistance wire is connected across the voltmeter, which is in series of an ammeter a battery. Choose the correct statement. Ammeter reading decreases voltmeter reading increases () Ammeter reading increases voltmeter reading decreases Readings of both meters will increase Readings of both meters will decrease 7. A small dipole is directed along Y-axis is centered at point P(a, 0). There is point charge fixed at origin. Work done in moving dipole from large distance to point P is W 1 from P to Q( a, 0) keeping same orientation is W. Choose the correct statement. W 1 > W () W > W 1 W 1 = W W 1 > 0, W < 0 8. Two parallel plates A B are having 1 C 4 C charges. Their arrangement forms capacitance of F. It is connected with resistance of 1 at t = 0. Choose correct statement. A R B Test - 5 (Paper-I) 9. A proton is either released at rest or launched with certain velocity in a uniform electric field. Which of the following graph could not represent possible variation of kinetic energy with time? KE KE t t () KE KE 10. Eight small spheres of mercury, each with a diameter of 1 mm a charge of 5 nc unite to form a large sphere. Potential energy stored in the large sphere is 7 mj () 7. mj 0.7 mj 0.07 mj 11. A point charge of 1 nc is placed at 50 cm from the centre of a thin conducting shell of 0 cm radius having 1nC charge. Net potential at point P (AP = 10 cm) would be. t t Charge on the plate A is 4e t/ C, where t is time in S A P B () Charge on the plate B is 4e t/ C, where t is time in S Charge on the plate A is 8 + 4e t/ C, where t is time in S Charge on the plate B is 8 + 4e t/ C, where t is time in S 7 V () 45 V 49.5 V.5 V /1

5 Test - 5 (Paper-I) All India Aakash Test Series for JEE (Main) Three particle charges of same magnitude different nature are placed at some distance along a line evaluate correct variation of potential along line joining of separation. +q +q q 14. Each plate of a parallel plate air capacitor has an area S. How much work has to be performed to slowly increase the distance between the plates form x 1 to x, if potential difference across plates V is kept constant? v () SV 0 0 SV 1 1 x1 x 1 1 x x1 () v v v 13. A long cylinder with uniformly charged surface cross sectional area a moves with constant velocity v along its axis. An electric field strength at the surface of cylinder is equal to E. The current due to mechanical transfer of charge would be Eav () 0 Eav Eav Zero 1 1 0SV x 1 x Zero 15. Two rectangular frames ( m 30 cm) ( m 40 cm) are joined along the common length. Their planes are perpendicular to each other. A long charged wire of linear charge density 4 0 C/m is placed at 5 cm from common length of planes. Net electric flux through both the frames 4 Nm /C () 8 Nm /C 0.4 Nm /C 0.8 Nm /C 16. A system consists of a uniformly charged sphere of radius R surrounding medium filled by a charge with the volume charge density, where is a r positive constant r is the distance from the centre of the sphere. Find charge on the sphere for which electric field intensity outside sphere is 1 independent of r R 0 C ().0 C 5.0 C 4.0 C 3/1

6 All India Aakash Test Series for JEE (Main) An uniformly charged long thin wire is kept along x-axis as shown in figure. Linear charge density is. Electric field at P : (x, y, z) would be (where x 0, y 0, z 0) y x x yjˆ zkˆ 0 y z () xiˆyjˆzk ˆ x y z 0 yjˆ zkˆ 0 y z kq r 1 kq () r Test - 5 (Paper-I) Cannot be determined Zero 19. In the measurement of resistance by a meter-bridge percentage error is minimum when the null point is Close to 0 cm () Close to 50 cm Close to 75 cm Close to 100 cm 0. A semicircular frame of radius R is having charge q q in the respective quadrants. Frame is free to rotate about C in uniform electric field E. The work done to rotate the frame in the given sense to bring diameter AB parallel to electric field. q E B R C xiˆyjˆzk ˆ x y z 0 q A 18. A point charge q is placed inside cavity of a spherical conductor as shown in figure. Electric field at a point lying outside the conductor due to charge on surface of cavity would be () R qe R qe C q r r 1 P 4R qe 4 R qe 4/1

7 Test - 5 (Paper-I) All India Aakash Test Series for JEE (Main) A rod of mass m length l uniformly distributed with charge density is placed horizontally on the support O P in electric field Ex ˆ 0 ( j). For what value of E 0 rod is about to topple? 4. Two thin conductors of same length same area are connected in series as shown in figure. An electric current i flows through them. The total charge accumulated at junction would be ( are their resistivity) y i 3 i mg l 3mg l O P mg () l 3mg l. Time constant of circuit would be 1 V R 3 = R 1 = 3 x i 0 () i 0 3 i 0 Zero 5. A slide wire of linearly varying radius from a to a of the cross-sections uniform resistivity with 1 V source is applied in the experimental circuit. Unknown emf E of the source is balanced at mid-point of the wire. The value of E. E 1 V J G C = 5 F R = 6 0 s () 10 s 5 s 1 s E xyz,, xi yj 3k exists C in space. Charge density at (1, 0, 1) would be N 3. An electric filed ˆ ˆ ˆ 0 () V () 8 V 10 V 4 V SECTION - II Assertion Reason Type Questions Directions : Questions number 6 to 30 are Assertion- Reason type questions. Each of these questions contains two statements. (Assertion) Statement- (Reason). Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select the correct choice. 5/1

8 All India Aakash Test Series for JEE (Main) 014 Test - 5 (Paper-I) 6. : A parallel plate capacitor at constant potential is being filled by a long dielectric slab, moves with constant speed after some time. Statement- : After some time moving dielectric slab will interact with fringing field on both sides. is True, Statement- is True; Statement- is a correct explanation for () is True, Statement- is True; Statement- is NOT a correct explanation for is True, Statement- is False is False, Statement- is True 7. : A conducting sphere cannot be charged beyond a definite potential. Statement- : Dielectric strength of the medium surrounding conductor it does not allow infinite charge. is True, Statement- is True; Statement- is a correct explanation for () is True, Statement- is True; Statement- is NOT a correct explanation for is True, Statement- is False is False, Statement- is True 8. : Electrostatic field lines never form closed loop. Statement- : Electrostatic field is conservative field. is True, Statement- is True; Statement- is a correct explanation for () is True, Statement- is True; Statement- is NOT a correct explanation for is True, Statement- is False is False, Statement- is True 9. : A uniform resistance wire of thermal coefficient of resistivity is divided in three equal length joined parallel to each other. Equivalent thermal coefficient of resistivity ( e ) is. R Statement- : e, where R is the resistance R of the segments connected in parallel is its coefficient of thermal resistivity. is True, Statement- is True; Statement- is a correct explanation for () is True, Statement- is True; Statement- is NOT a correct explanation for is True, Statement- is False is False, Statement- is True 30. : Coulomb's law obeys Gauss theorem. Statement- : Coulomb's law obeys inverse square law. is True, Statement- is True; Statement- is a correct explanation for () is True, Statement- is True; Statement- is NOT a correct explanation for is True, Statement- is False is False, Statement- is True 6/1

9 Test - 5 (Paper-I) All India Aakash Test Series for JEE (Main) 014 SECTION - I Straight Objective Type Questions This section contains 5 multiple choice questions numbered 31 to 55. Each question has 4 choices, (),, out of which ONLY ONE is correct. 31. An inorganic carbonate salt is strongly heated. The residue is yellow while hot white when cold. The salt contains Pb + () Zn + Hg + NH On being heated, a salt gives a gas which turns lime water milky an acidified dichromate solution green. The salt may be a Carbonate () Sulphide Nitrate Sulphite 33. Which of the following pairs of cations turns borax beads blue in a oxidising flame? Fe + Co + () Co + Cu + Cu + Mn + Cu + Cr Which of the following pairs of cations can be separated by adding NH 4 Cl NH 4 OH to the mixture? Fe +3, Al +3 () Cr +3, Ni + Al +3, Cr +3 Fe +3, Cr Which of the following pairs of cations cannot be separated by adding NH 4 Cl, NH 4 OH then (NH 4 ) CO 3 to the mixture? Ca +, Sr + () Sr +, Mg + Ca +, Mg + Ba +, Mg Which of the following cations will form an insoluble red-brown compound with [Fe(CN) 6 ] 4? Hg + () Pb + Cu + Cd + PART - B (CHEMISTRY) 37. Following ligs can show linkage isomerism CNS () NO CN All of these 38. Which of the following compounds show optical isomerism? i. cis [Co(en) Cl ] + ii. trans [Co(en) Cl ] + iii. cis-[co(en) ] iv. [Co(en) 3 ] + Select the correct answer using the codes given below (i) & (ii) () (ii) & (iii) (iii) & (iv) (i), (iii) & (iv) 39. EAN of Ni in [Ni(CN) 4 ] is 34 () The co-ordination number of Pt in the complexion [Pt(en) Cl ] + is 3 () Spin only magnetic moment of the Hg[Co(SCN) 4 ] is 3 BM () 15 BM 4 BM 8 BM 4. Which is not the square planar complex? [Cu(NH 3 ) 4 ] + () [PtCl 4 ] [NiCl 4 ] [AuCl 4 ] 43. The number of unpaired electrons expected for the complexion [Cr(NH 3 ) 6 ] 3+ is () /1

10 All India Aakash Test Series for JEE (Main) 014 Test - 5 (Paper-I) 44. Of the following complex ions one exhibits optical isomerism. That one is cis [Co(en) Cl ] + () [Co(NH 3 ) 4 Cl ] + [Co(NH 3 ) Cl 4 ] trans [Co(en) Cl ] The correct order of ionic radii is Lu +3 < Eu +3 < La +3 < Y +3 () La +3 < Eu +3 < Lu +3 < Y +3 Y +3 < La +3 < Eu +3 < Lu +3 Y +3 < Lu +3 < Eu +3 < La The basic character of the transition oxides TiO > FeO > VO > CrO () TiO > VO > CrO > FeO VO > CrO > TiO > FeO CrO > VO > FeO > TiO 47. Which shows maximum magnetic moment among the bivalent ions of the first transition series? Fe + () Co + Ni + Mn In Na [Fe(CN) 5 NO] Oxidation state of Fe is + () Oxidation state of NO is +1 Both & () are correct Oxidation state of NO is zero 49. Which of the following compound is amphoteric? Cr(OH) () Fe(OH) Cr(OH) 3 Fe(OH) 3 phx phy Cr O CrO Cr O ph values x y can be 4 5 () In the alumino thermite process Al acts as An oxidising agent () A flux Solder A reducing agent 5. Extraction of Al from bauxite ore, reduction is carried out by Carbon () Magnesium Electrolysis Hydrogen 53. In the extraction of copper from copper pyrites, iron is removed as FeSO 4 () FeSiO 3 Fe 3 O 4 Fe O The iron obtained from the blast furnace is called Pig iron () Cast iron Wrought iron Steel 55. Blister copper is Pure copper () Ore of copper Alloy of copper Impure copper SECTION - II Assertion Reason Type Questions Directions : Questions number 56 to 60 are Assertion- Reason type questions. Each of these questions contains two statements. (Assertion) Statement- (Reason). Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select the correct choice. 56. : In froth flotation process sodium ethyl xanthate is used as collector. Statement- : Sulphide ores are water soluble. is True, Statement- is True; Statement- is a correct explanation for () is True, Statement- is True; Statement- is NOT a correct explanation for is True, Statement- is False is False, Statement- is True 8/1

11 Test - 5 (Paper-I) All India Aakash Test Series for JEE (Main) : Cryolite is used in electrolytic extraction of Al from alumina. Statement- : It dissolves alumina. is True, Statement- is True; Statement- is a correct explanation for () is True, Statement- is True; Statement- is NOT a correct explanation for is True, Statement- is False is False, Statement- is True 58. : In acidic medium, Zn + is not precipitated by S ions. Statement- : Common ion effect reduces the concentration of S ions to the minimum level. is True, Statement- is True; Statement- is a correct explanation for () is True, Statement- is True; Statement- is NOT a correct explanation for is True, Statement- is False is False, Statement- is True SECTION - I Straight Objective Type Questions This section contains 5 multiple choice questions numbered 61 to 85. Each question has 4 choices, (),, out of which ONLY ONE is correct. 61. Set A has 10 elements. The number of subsets of A having or 3 elements is 165 () PART - C (MATHEMATICS) 59. : K 3 [Fe(CN) 6 ] is more stable than K 4 [Fe(CN) 6 ]. Statement- : In K 4 [Fe(CN) 6 ], effective atomic number of Fe is 36. is True, Statement- is True; Statement- is a correct explanation for () is True, Statement- is True; Statement- is NOT a correct explanation for is True, Statement- is False is False, Statement- is True 60. : Ce +4 is used as an oxidising agent in volumetric analysis. Statement- : Ce +4 has the tendency to attain +3 oxidation state. is True, Statement- is True; Statement- is a correct explanation for () is True, Statement- is True; Statement- is NOT a correct explanation for is True, Statement- is False is False, Statement- is True 6. Let n(s) represents the number of elements in set 'S' n(a) = 4, n(b) = 6, n(c) = 3. If n((a B) C) is maximum, then A B () B A A B B C C A B 63. Let n(x) represents the number of elements in set X. If n(a B C) = 6, then the maximum value of n(a B B A) is 1 () /1

12 All India Aakash Test Series for JEE (Main) 014 Test - 5 (Paper-I) 64. A relation 'S' is defined on the set of real numbers such that S = {(x, y): x(x y) + y 0} then 'S' is Reflexive only () Symmetric only Not transitive Equivalence 65. Let f : R R, f(x) = x 3 + x + kx + 6 is one-one for all x R, then the least integral value of k is 4 () If { } [ ] represents fractional function greatest integer function respectively, then the domain of f( x) (log{ x} [ x]) is 3 [1, ] 3 (1, 3) () 3 (1, ) 3 (1, 4) 67. xx x3 x 3 The range of f( x) xx x4 x 4 is (, ) A. The sum of all elements of set A is () Let f : R R defined as f(x) = x 3 + x + 1, 1 x. The graph of y = g(x) is the reflection of graph of y = f(x) through the line y = x. If the domain of g(x) is [a, b], then a + b is equal to 3 () The graph of y = f(x) is symmetric about the curves represented by x 6x + 8 = 0, then the period of f(x) is 1 () Consider that f(x), g(x) h(x) are functions defined from R to R such that f(x) = g(h(x)) f(x) is even function. Now consider the following statements S 1, S, S 3, S 4. S 1 : g(x) may even function S : g(x) is odd function h(x) is even S 3 : g(x) is even function h(x) may be odd function S 4 : g(x + y) = g(x) + g(y), h( + ) = h() + h() The incorrect statement is S 4 () S 3 S S ( x 1) x x 1 lim x x x x 1 is equal to 1 () If { } represents fractional function, then the value of lim x tan x xcot x x0 is 0 () 1 Not in existence cos 4x sin 4x lim x0 x Is 9/4 () Is 9/4 Does not exist as LHL does not exist Does not exist as LHL RHL 74. If [ ] represent greatest integer function, then sum of values of 'x' at which f(x) = min{x [x], x [ x]} is not differentiable in (0, 1) is 5 7 () 3 10/1

13 Test - 5 (Paper-I) All India Aakash Test Series for JEE (Main) The value of lim (cot x)[ tan x] x, where [ ] represents greatest integer function, is 1 () 3 Not in existence 76. If { } [ ] represents fractional function greatest integer function respectively, then the number of points where f(x) = [{x + x }] + {[ x 4x + 3 ]} is not continuous is 0 () The number of point(s), where is not f( x) x 5 ( x 6x 5) x x 1 continuous is 4 () The number of elements in sets A, B C are, 3 4 respectively. Then Number of functions from A to B is 6 () Number of surjective functions from B to C is 36 Number of surjective functions from C to B is 36 Number of one-one function from A to B is 8. A relation R is defined on the set of real numbers. If { } [ ] represents fractional greatest integer function respectively arb such that R = {(a, b) : {a + } > [a + ] > {b + 3}}, then R is reflexive () Number of ordered pairs in R is R is symmetric relation R is null relation 78. d y If y = 8sinx cosx cosx cos4x 10 dx = ky, then the value of (k ) is 1 () Let f(x) be a function defined on the set of real numbers. If are any two real numbers such that ( 5 ) (f() f()) 5, then f(x) is One one function () f(x) is always odd function f(x) is always even function The fundamental period of f(x) is 80. The sum of values of x satisfying the equation [log x] log x = 0, where [ ] represents greatest integer function, is 5 () The range of f( x) x, where x > 0, x x x is equal to [a, b) then a is equal to 1 () Let f : R R defined by f(x) = x + sin x. If g(x) is the inverse of f(x), then the value of g(0) is equal to 1 () Consider that of f is ( f x) 3f 5x1 x, then the value 1 () /1

All India Aakash Test Series for JEE (Main) 014 SECTION - II Assertion Reason Type Questions Directions : Questions number 86 to 90 are Assertion- Reason type questions.

14 All India Aakash Test Series for JEE (Main) 014 SECTION - II Assertion Reason Type Questions Directions : Questions number 86 to 90 are Assertion- Reason type questions. Each of these questions contains two statements. (Assertion) Statement- (Reason). Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select the correct choice. Test - 5 (Paper-I) 88. : If [ ] represents greatest integer function, then lim ([x 3] [3 x] 6) 4. x4 4 x 1 cos x Statement- : lim x0 sin x = 0. is True, Statement- is True; Statement- is a correct explanation for 86. : Set A has two elements, then number () is True, Statement- is True; of reflexive relations from A to A is 4. Statement- is NOT a correct explanation for Statement- : If [ ] represents greatest integer is True, Statement- is False log [ x] sin x is False, Statement- is True function, then lim 0. x [ x] x 89. : f(x) = x 4, then f = 1. is True, Statement- is True; Statement- is a correct explanation for Statement- : f(x) = x 4, is not continuous at x = 4. is True, Statement- is True; () is True, Statement- is True; Statement- is a correct explanation for Statement- is NOT a correct explanation for () is True, Statement- is True; Statement- is NOT a correct explanation for is True, Statement- is False is False, Statement- is True is True, Statement- is False 87. is False, Statement- is True sin cos x cos cos x : lim 4 x0. x x : lim sin x 4 3. x x x sin x Statement- : lim tan x e. Statement- : If 3 1 4x x x 0 f x x0 4 k x 0 is is True, Statement- is True; continuous at x = 0, then k = 1. Statement- is a correct explanation for is True, Statement- is True; Statement- is a correct explanation for () is True, Statement- is True; Statement- is NOT a correct explanation for () is True, Statement- is True; Statement- is NOT a correct explanation for is True, Statement- is False is True, Statement- is False is False, Statement- is True is False, Statement- is True 1/1

15 Test Booklet Code A Test No. 4 Paper I for ALL INDIA AAKASH TEST SERIES JEE (Main) 014

16 Test - 4 (Paper-I) (Answers & Hints) All India Aakash Test Series for JEE (Main)-014 TEST - 4 (Paper-I) ANSWERS PHYSICS CHEMISTRY MATHEMATICS 1. (). 3. () 4. (Deleted) () () 17. () () () 4. (Deleted) 5. () () 33. () () () () () () () () () () () () () 1/1

TEST - 5 (Paper-I) ANSWERS

TEST - 5 (Paper-I) ANSWERS PHYSICS CHEMISTRY MATHEMATICS. () 3. () 6. (). (3) 3. () 6. () 3. () 33. () 63. (3). () 3. () 6. () 5. () 35. () 65. (3) 6. () 36. (3) 66. () 7. (3) 37. () 67. () 8. (3) 38.