PAPER - 1 : PHYSICS, CHEMISTRY & MATHEMATICS

Transcription

1 .JEE-MAIN. Test Booklet Code PAPER - : PHYSICS, CHEMISTRY & MATHEMATICS Do not open this Test Booklet until you are asked to do so. Read carefully the Instructions on the Back Cover of this Test Booklet. Important Instructions :. Immediately fill in the particulars on this page of the Test Booklet with Blue/Black Ball Point Pen. Use of pencil is strictly prohibited.. The Answer Sheet is kept inside this Test Booklet. When you are directed to open the Test Booklet, take out the Answer Sheet and fill in the particulars carefully.. The test is of hours duration. 4. The Test Booklet consists of 9 questions. The maimum marks are There are three parts in the question paper A, B, C consisting of, Physics, Chemistry and Mathematics having questions in each part of equal weightage. Each question is allotted 4 (four) marks for each correct response. 6. Candidates will be awarded marks as stated above in instruction No. 5 for correct response of each question. /4 (one fourth) 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 an item in the answer sheet. 7. There is only one correct response for each question. Filling up more than one response in any question will be treated as wrong response and marks for wrong response will be deducted accordingly as per instruction 6 above. 8. Use Blue/Black Ball Point Pen only for writting particulars/ marking responses on Side and Side of the Answer Sheet. Use of pencil is strictly prohibited. 9. No candidates is allowed to carry any tetual material, printed or written, bits of papers, pager, mobile phone, any electronic device, etc., ecept the Admit Card inside the eamination hall/room.. Rough work is to be done on the space provided for this purpose in the Test Booklet only. This space is given at the bottom of each page and in pages (Pages ) at the end of the booklet.. On completion of the test, the candidate must hand over the Answer Sheet to the Invigilator on duty in the Room / Hall. However, the candidates are allowed to take away this Test Booklet with them.. The CODE for this Booklet is P. Make sure that the CODE printed on Side of the Answer Sheet is the same as that on this booklet. In case of discrepancy, the candidate should immediately report the matter to the invigilator for replacement of both the Test Booklet and the Answer Sheet.. Do not fold or make any stray marks on the Answer Sheet. Name of the Candidate (in Capital letters) : Roll Number : in figures : in words Eamination Centre Number : Name of Eamination Centre (in Capital letters) : Candidate s Signature : Invigilator s Signature : (Pg. )

2 JEE-MAIN : Paper and Solution () READ THE FOLLOWING INSTRUCTIONS CAREFULLY :. The candidates should fill in the required particulars on the Test Booklet and Answer Sheet (Side-) with Blue/Black Ball Point Pen.. For writing/marking particulars on Side- of the Answer Sheet, use Blue/Black Ball Point Pen only.. The candidates should not write their Roll Numbers anywhere else (ecept in the specified space) on the Test Booklet/Answer Sheet. 4. Out of the four options given for each question, only one option is the correct answer. 5. For each incorrect response, one-fourth (¼) of the total marks allotted to the question would be deducted from the total score. No deduction from the total score, however, will be made if no response is indicated for an item in the Answer Sheet. 6. Handle the Test Booklet and Answer Sheet with care, as under no circumstances (ecept for discrepancy in Test Booklet Code and Answer Sheet Code), will another set be provided. 7. The candidates are not allowed to do any rough work or writing work on the Answer Sheet. All calculations/writing work are to be done in the space provided for this purpose in the Test Booklet itself, marked Space for Rough Work. This space is given at the bottom of each page and in pages (Pages ) at the end of the booklet. 8. On completion of the test, the candidates must hand over the Answer Sheet to the Invigilator on duty in the Room/Hall. However, the candidates are allowed to take away this Test Booklet with them. 9. Each candidate must show on demand his/her Admit Card to the Invigilator.. No candidate, without special permission of the Superintendent or Invigilator, should leave his/her seat.. The candidates should not leave the Eamination Hall without handing over their Answer Sheet to the Invigilator on duty and sign the Attendance Sheet again. Cases where a candidate has not signed the Attendance Sheet a second time will be deemed not to have handed over the Answer Sheet and dealt with as an unfair means case. The candidates are also required to put their left hand THUMB impression in the space provided in the Attendance Sheet.. Use of Electronic/Manual Calculator and any Electronic Item like mobile phone, pager etc. is prohibited.. The candidates are governed by all Rules and Regulations of the JAB/Board with regard to their conduct in the Eamination Hall. All cases of unfair means will be dealt with as per Rules and Regulations of the JAB/Board. 4. No part of the Test Booklet and Answer Sheet shall be detached under any circumstances. 5. Candidates are not allowed to carry any tetual material, printed or written, bits of papers, pager, mobile phone, electronic device or any other material ecept the Admit Card inside the eamination hall/room. (Pg. )

3 () VIDYALANKAR : JEE-MAIN : Paper and Solution PART- A : PHYSICS.Questions and Solutions.. A uniform cylinder of length L and mass M having cross - sectional area A is suspended, with its length vertical, from a fied point by a massless spring, such that it is half submerged in a liquid of density σ at equilibrium position. The etension of the spring when it is in equilibrium is : () Mg Mg LAσ Mg LAσ Mg LAσ () () (4) + k k M k M k M (Here, k is spring constant). () LA K + σ g mg Mg LA α k M. A metallic rod of length l is tied to a string of length l and made to rotate with angular speed ω on a horizontal table with one end of the string fied. If there is a vertical magnetic field B in the region, the e.m.f. induced across the ends of the rod is : () Bωl () Bωl () 4Bωl (4) 5Bωl. (4) V ( ) V l v B dl ωbd 5Bωl l ω l l V ga. This question has statement I and Statement II. Of the four choice given after the statements, choose the one that best describes the two statements. Statement I : A Point particle of mass m moving with speed v collides with stationary point particle of mass M. If the maimum energy loss possible is given as m f mv thenf M+ m. Statement II : Maimum energy loss occurs when the particles get stuck together as a result of the collision. () Statement - I is true, Statement - II is true, statement - II is a correct eplanation of Statement - I () Statement - I is true, Statement - II is true, statement - II is not a correct eplanation of Statement I () Statement - I is true, Statement - II is false (4) Statement I is false, Statement II is true (Pg. )

4 JEE-MAIN : Paper and Solution (4). (4) Maimum energy loss when inelastic collision takes place mv (m + M) v m v v m+ M ki mv m v m k f (m+ M)v' (m+ M) mv (m + M) M+ m m M Loss of energy ki kf mv mv M+ m M+ m 4. Let [ε ] denote the dimensional formula of the permittivity of vacuum. If M mass, L length, T Time and A electric current, then : () [ε ] [M L T A] () [ε ] [M L T 4 A ] () [ε ] [M L T A ] (4) [ε ] [M L T A] 4. () C [ ε ] A T N m MLT L 4 [ ε ] M L T A 5. A Projectile is given an initial velocity of (i ˆ + j)m/s, ˆ where î is along the ground and ĵ is along the vertical. If g m/s, the equation of its trajectory is : () y 5 () y 5 () 4y 5 (4) 4y 5 5. () u + 5 θ tan g Equation : y tan θ u cos θ y 5 5 y 5 6. The amplitude of a damped oscillator decreases to.9 times its original magnitude in 5s. In another s it will decrease to α times its original magnitude, where α equals : ().7 ().8 ().79 (4).6 6. () A A o e kt.9a o A o e kt kt l n (.9) 5 k l n (.9) 5 k l n (.9) A A o e 5k A n(.9) o e l (.9) A o.79 A o (Pg. 4)

5 (5) VIDYALANKAR : JEE-MAIN : Paper and Solution 7. Two capacitors C and C are charged to V and V respectively. It is found that by connecting them together the potential on each one can be made zero. Then : () 5C C () C 5C () C + 5C (4) 9C 4C 7. () Potential on connecting them together i.e. Q i.e. C V C V [capacitance is positive but they are connected with opposite polarity] C C C 5C 8. A sonometer wire of length.5 m is made of steel. The tension in it produce an elastic strain of %. What is the fundamental frequency of steel if density and elasticity of steel are 7.7 kg / m and. N/m respectively? () 88.5 Hz () 78. Hz ().5 Hz (4) 77 Hz 8. () Stress Y. 9 T V 9 T T L stress. M M μ density L L V V l Hz 9. A circular loop of radius. cm lies parallel to a much bigger circular loop of radius cm. The centre of the small loop is on the ais of the bigger loop. The distance between their centres is 5 cm. If a current of. A flows through the smaller loop, then the flu linked with bigger loop is: () 9. weber () 6 weber (). weber (4) weber 9. () First we find the mutual inductance of the assembly. Let current I flow through the larger loop. μir The strength of induction at the smaller loop R + d Flu through smaller loop Mutual inductance Flu linked through coil μ ( + ) μπir r ( + ) R d Rr R d / μπrr ( + d ) d R / / i ( ) / r I R 7 6 4π π 4 9 ( ) ( ) / 9. Weber 5.65 (Pg. 5)

6 JEE-MAIN : Paper and Solution (6). Diameter of a plano - conve lens is 6 cm and thickness at the centre is mm. If speed of light in material of lens is 8 m/s, the focal length of the lens is : () 5 cm () cm () cm (4) cm. () r + r r 6r 9 r r cm mm 6r 99 r + r 5.5 m ( μ ) f R R R plane R conve 5 cm 8 μ 8 f 5 f cm. What is the minimum energy required to launch a satellite of mass m from the surface of a planet of mass M and radius R in a circular orbit at an altitude of R? () 5GmM () GmM () GmM (4) GmM 6R R R R. () The kinetic energy at altitude R GMm 6R The gravitational potential energy at altitude R GMm R GMm Total energy kε+ PE 6R Potential energy at the surface is GMm R GMm GMm 5GMm Req. kinetic energy R 6R 6R. A diode detector is used to detect an amplitude modulated wave of 6% modulation by using a condenser of capacity 5 pico farad in parallel with a load resistance kilo ohm. Find the maimum modulated frequency which could be detected by it. ().6 MHz ().6 khz () 5. MHz (4) 5. khz. (). A beam of unpolarised light of intensity I is passed through a polaroid A and then through another polaroid B which is oriented so that its principal plane makes an angle of 45 relative to that of A. The intensity of the emergent light is : () I () I / () I /4 (4) I /8. () Intensity of light is halved upon passage through first polaroid. (Pg. 6)

7 (7) VIDYALANKAR : JEE-MAIN : Paper and Solution I Using Malus Law : I cos θ θ 45 (The angle between the polarization aes of the polaroids) I I I 4 4. The supply voltage to a room is V. The resistance of the lead wires is 6Ω. A 6 W bulb is already switched on. What is the decrease of voltage across the bulb, when a 4 W heater is switched on in parallel to the bulb? () zero Volt ().9 Volt (). Volt (4).4 Volt 4. (no option matches) R b ( ) 6 4 Ω, R H 4 4 V V Ω R b 4 V R H 6 Ω v R b 4 V 6 V V (R b R H) V 48 (R b R H) V Loss in potential V V V. (no option matches) 5. The above p-v diagram represents the thermodynamic cycle of an engine, operating with an ideal monoatomic gas. The amount of heat, etracted from the source in a single cycle is : () pv () p v () pv (4) 4pv (Pg. 7)

8 5. () Heat etracted from the source C C V PV PV p + PV PV R R PV + 5P V PV ( ) ( ) JEE-MAIN : Paper and Solution (8) 6. A hoop of radius r and mass m rotating with an angular velocity ω is placed on a rough horizontal surface. The initial velocity of the centre of the hoop is zero. What will be the velocity of the centre of the hoop when it ceases to slip? 6. () rω () 4 rω () COAM about the contact point Iω Iω + mvr m r ω mr ω + mvr mvr rω v rω () (4) rω 7. An ideal gas enclosed in a vertical cylindrical container supports a freely moving piston of mass M. The piston and the cylinder have equal cross sectional area A. When the piston is in equilibrium, the volume of the gas is V and its pressure is P. The piston is slightly displaced from the equilibrium position and released. Assuming that the system is completely isolated from its surrounding, the piston eecutes a simple harmonic motion with frequency : AP γ VMP A γp MV () () () (4) π V M π A γ π MV π A P 7. () As adiabatic process PV γ Constant dp p + dv γ v Pγ dp dv V P γ (A) ( is small displacement) V P γa F (dp) A V P γa a mv ω f ω P γa mv ω P γa π π mv ω v γ (Pg. 8)

9 (9) VIDYALANKAR : JEE-MAIN : Paper and Solution 8. If a piece of metal is heated to temperature θ and then allowed to cool in a room which is at temperature θ, the graph between the temperature T of the metal and time t will be closed to : () () () (4) 8. () Since, by Newton s law of cooling, the rate of change of temperature is proportional to the difference in temperature between the object and surrounding, as the temperature of the piece of metal approaches θ, the rate of change of temperature will approach zero. 9. This question has statement I and Statement II. Of the four choices given after the Statements, choose the one that best describes the two statements. Statement I : Higher the range, greater is the resistance of ammeter. Statement II : To increase the range of ammeter, additional shunt needs to be used across it. () Statement - I is true, Statements - II is true, Statement - II is the correct eplanation of Statements - I () Statement - I is true, Statement - II is true, Statement - II is not the correct eplanation of Statement - I. () Statement - I is true, Statement - II is false. (4) Statement - I is false, Statement - II is true. 9. (4) r i i; i Maimum allowed current through ammeter coil. R + r r resistance of the shunt. To increase the range i r has to be reduced so effective resistance of ammeter decreases.. In an LCR circuit as shown below both switches are open initially. Now switch S is closed, S kept open. (q is charge on the capacitor and τ RC is Capacitive time constant). Which of the following statement is correct? () Work done by the battery is half of the energy dissipated in the resistor () At t τ, q CV / () At t τ, q CV ( e ) (4) At t τ, q CV ( e ). () Case Its normal RC circuit W bat CV U CV H Wbat U CV ( W ba ) (H) So () is wrong. t/ q CV( e α ) At t α, R V C (Pg. 9)

10 at t α, q cv ( e ) is correct q CV( e ) is wrong. JEE-MAIN : Paper and Solution () At t α q CV( e / ) (4) is wrong.. Two coherent point sources S and S are separated by a small distance 'd' as shown. The fringes obtained on the screen will be : () points () straight lines () semi circles (4) concentric circles. (4) So, on a circle, path difference will be same locus of points having same path difference will be a circle, so fringes will make concentric circles.. The magnetic field in a travelling electromagnetic wave has a peak value of nt. The peak value of electric field strength is : () V () 6V () 9V (4) V m m m m. () Eo c B E o cb o o S S ( 9 T) 8 6 V/m.. The anode voltage of a photocell is kept fied. The wavelength λ of the light falling on the cathode is gradually changed. The plate current I of the photocell varies as follows : () () () (4). (4) As λ will increase k ma will decrease so current should decrease and finally fall to zero when λ is achieved. (Pg. )

11 () VIDYALANKAR : JEE-MAIN : Paper and Solution 4. The I V characteristic of an LED is : () () () (4) 4. () 5. Assume that a drop of liquid evaporates by decrease in its surface energy. So that its temperature remains unchanged. What should be the minimum radius of the drop for this to be possible? The surface tension is T, density of liquid is ρ and L is its latent heat of vaporization. () 5. (4) ρl T () T ρl Surface energy of the drop ( π ) Let (δm) mass evaporate. 4 R T () T ρl (4) T ρl (δm)l 8πR. δrt 4 m R ρ π δm 4 R π ρ δr ρ4π R L 8π R.T R T Lρ 6. In a hydrogen like atom electron makes transition from an energy level with quantum number n to another with quantum number (n ). If n >>, the frequency of radiation emitted is proportional to : () n 6. (4) R (n ) n λ () C λ RC n (n ) (n )n n () / n (4) n (Pg. )

12 n ν RC (n ) n RC n 4 n RC ν n ν n JEE-MAIN : Paper and Solution () 7. The graph between angle of deviation (δ) and angle of incidence (i) for a triangular prism is represented by : () () () (4) 7. () Factual 8. Two charges, each equal to q, are kept at a and a on the ais. A particle of mass m and charge q q is placed at the origin. If charge q is given a small displacement (y << a) along the y ais, the net force acting on the particle is proportional to : () y () y () y (4) y 8. () F F q θ q q q qq F net cos θ 4πε y + a qq y qq y / 4πε y + a 4πε a F y ( ) as (y << a) 9. Two short bar magnets of length cm each have magnetic moments. Am and. Am respectively. They are placed on a horizontal table parallel to each other with their N poles pointing towards the South. They have a common magnetic equator and are separated by a distance of. cm. The value of the resultant horizontal magnetic induction at the mid - point O of the line joining their centre is close to (Horizontal component of earth s magnetic induction is.6 5 Wb / m ) ().6 5 Wb/m ().56 4 Wb/m ().5 4 Wb/m (4) Wb/m 9. (4) (Pg. )

13 () VIDYALANKAR : JEE-MAIN : Paper and Solution μ μ S S B / 4π L + y y N N 7. B / (.) + (.5) B B H ( ) (.) 7 5. Wb / m (South to North) 5 Wb/m (south to North) 5.6 Wb / m (South to North) 5 B net ( ) Wb / m W N S E. A charge Q is uniformly distributed over a long rod AB of length L as shown in the figure. The electric potential at the point O lying at a distance L from the end A is : () Q 8πε L () Q 4πε L () Q 4πε Lln (4) Qln 4πε L. (4) O A B L L V KdQ L Q K d L KQ d L L KQ n L L l KQ n l Qln 4πε L ( ) L PART- B : CHEMISTRY. Which of the following comple species is not epected to ehibit optical isomerism? () [Co(en) ] + () [Co(en) Cl ] + () [Co(NH ) Cl ] (4) [Co(en)(NH ) Cl ] +. () [Co(NH ) Cl ] will not ehibit optical isomerism due to presence of plane of symmetry.. Which one of the following molecules is epected to ehibit diamagnetic behaviour? () C () N () O (4) S. () O is epected to diamagnetic in nature but actually it is paramagnetic. (Pg. )

14 JEE-MAIN : Paper and Solution (4). A solution of ( ) chloro phenylethane in toluene racemises slowly in the presence of a small amount of SbCl 5,due to the formation of : () carbanion () carbene () carbocation (4) free radical. () Racemises slowly due to formation of intermediate carbocation. 4. Given : E.74 V ; E V Cr /Cr CrO 7 /Cr MnO 4 /Mn E +. V ; E.6 V Cl/Cl Based on the data given above, strongest oidising agent will be : () Cl () Cr + () Mn + (4) MnO4 4. (4) MnO is strongest oidizing agent A piston filled with.4 mol of an ideal gas epands reversibly from 5. ml to 75 ml at a constant temperature of 7. C. As it does so, it absorbs 8 J of heat. The values of q and w for the process will be : (R 8.4 J / mol K) (ln 7.5.) () q +8 J, w 8 J () q 8 J, w 8 J () q 8 J, w +8 J (4) q +8 J, w +8 J 5. () q + 8 J (as it absorb heat) v w Rew. nrt log v 75. (.4) 8.4 () log 5 8 J 6. The molarity of a solution obtained by miing 75 ml of.5(m)hcl with 5 ml of (M)HCl will be : ().875 M (). M ().75 M (4).975 M 6. () (Molarity) Mi.875M 7. Arrange the following compounds in order of decreasing acidity : () II > IV > I > III () I > II > III > IV () III > I > II > IV (4) IV > III > I > II 7. () Acidic nature order (III) > (I) > (II) > (IV) (Pg. 4)

15 (5) VIDYALANKAR : JEE-MAIN : Paper and Solution 8. For a gaseous state, if most probable speed is denoted by C *, average speed by C and mean square speed by C, then for a large number of molecules the ratios of these speeds are : () C * : C : C.5 :.8 : () C * : C : C.8 :.5 : () C * : C : C :.8 :.5 (4) C * : C : C :.5 :.8 8. () * RT 8RT RT C:C:C M πm M : 8.4 :.8 :.5 9. The rate of a reaction doubles when its temperature changes from K to K. Activation of such a reaction will be : (R 8.4 JK and log.) () 5.6 kj mol () 48.6 kj mol () 58.5 kj mol (4) 6.5 kj mol 9. () Ea T T..R TT Ea E a 5.6 kj mol 4. A compound with molecular mass 8 is acylated with CH COCl to get a compound with molecular mass 9. The number of amino groups present per molecule of the former compound is : () () 5 () 4 (4) 6 4. () No. of amino group Which of the following arrangements does not represent the correct order of the property stated against it? () V + < Cr + < Mn + < Fe + : paramagnetic behaviour () Ni + < Co + < Fe + < Mn + : ionic size () Co + < Fe + < Cr + < Sc + : stability in aqueous solution (4) Sc < Ti < Cr < Mn : number of oidation states 4. () Number of unpaired e in Fe + is less than Mn The order of stability of the following carbocations : is : () III > II > I () II > III > I () I > II > III (4) III > I > II 4. (4) On the basis of number of resonating structure (III) > (I) > (II) (Pg. 5)

16 JEE-MAIN : Paper and Solution (6) 4. Consider the following reaction : + + z MnO4 + yco4 + zh Μ n + yco + HO The values of, y and z in the reaction are, respectively : () 5, and 6 (), 5 and 8 (), 5 and 6 (4) 5, and 8 4. () + + MnO + 5C O + 6H Mn + CO + 8H O Which of the following is the wrong statement? () ONCl and ONO are not isoelectronic () O molecule is bent () Ozone is violet black in solid state (4) Ozone is diamagnetic gas. 44. () ONCl and ONCl are isoelectronic in nature. 45. A gaseous hydrocarbon gives upon combustion.7 g. of water and.8 g of CO. The empirical formula of the hydrocarbon is : () C H 4 () C H 4 () C 6 H 5 (4) C 7 H (4) y y CH y + + O CO + HO 4 y.8.7 : : i.e. 7 y y In which of the following pairs of molecules / ions, both the species are not likely to eist? + () H,He () H,He 46. () H + and H does not eist. () H +,He (4) + H,He 47. Which of the following eists as covalent crystals in the solid state? () Iodine () Silicon () Sulphur (4) Phosphorus 47. () Silicon eists as covalent crystals in the solid state. 48. Synthesis of each molecule of glucose in photosynthesis involves : () 8 molecules of ATP () molecules of ATP () 8 molecules of ATP (4) 6 molecules of ATP 48. (4) C 6 H O 6 + 6ADP + 6H PO 4 + 6O 6CO + 6ATP + 4H O 49. The coagulating power of electrolytes having ions Na +, Al + and Ba + for arsenic sulphide sol increases in the order : () Al + < Ba + < Na + () Na + < Ba + < Al + () Ba + < Na + < Al + (4) Al + < Na + < Ba () Factual (Pg. 6)

17 (7) VIDYALANKAR : JEE-MAIN : Paper and Solution 5. Which of the following represents the correct order of increasing first ionization enthalpy for Ca, Ba, S, Se and Ar? () Ca < S < Ba < Se < Ar () S < Se < Ca < Ba < Ar () Ba < Ca < Se < S < Ar (4) Ca < Ba < S < se < Ar 5. () Factual 5. Energy of an electron is given by E.78 8 Z J. Wavelength of light required to n ecite an electron in an hydrogen atom from level n to n will be : (h Js and c. 8 ms ) ().4 7 m ().86 7 m () m (4) m 5. () RH Z λ n n Z n n λ.4 7 m 5. Compound (A), C 8 H 9 Br, gives a white precipitate when warmed with alcoholic AgNO. Oidation of (A) gives an acid (B), C 8 H 6 O 4. (B) easily forms anhydride on heating. Identify the compound (A). () () () (4) 5. (4) (A) CH CH Br [O] (B) COOH COOH 5. Four successive members of the first row transition elements are listed below with atomic numbers. Which one of them is epected to have the highest E M + /M + value? () Cr(Z 4) () Mn(Z 5) () Fe(Z 6) (4) Co(Z 7) 5. (4) Factual (C) O C C O O (Pg. 7)

18 JEE-MAIN : Paper and Solution (8) 54. How many litres of water must be added to litre of an aqueous solution of HCl with a ph of to create an aqueous solution with ph of? (). L ().9 L (). L (4) 9. L 54. (4). ( + v). + v.. + v v 9L 55. The first ionisation potential of Na is 5. ev. The value of electron gain enthalpy of Na + will be : ().55 ev () 5. ev (). ev (4) +.55 ev 55. () E.A. Ionisation potential EA of Na + 5. ev 56. An organic compound A upon reacting with NH gives B. On heating, B gives C. C in presence of KOH reacts with Br to give CH CH NH. A is : () CH COOH () CH CH CH COOH () CH CH COOH (4) CH CH COOH CH 56. (4) O O CH CH C OH CH CH C NH NH Δ CH CH NH Br /KOH 57. Stability of the species Li, Li and Li + increases in the order of : () Li < Li + < Li () Li < Li + < Li () Li < Li < Li + (4) Li < Li < Li () B.O. of Li +.5 B.O. of Li.5 + Hence stability order Li < Li < Li 58. An unknown alcohol is treated with the Lucas reagent to determine whether the alcohol is primary, secondary or tertiary. Which alcohol reacts fastest and by what mechanism : () secondary alcohol by S N () tertiary alcohol by S N () secondary alcohol by S N (4) tertiary alcohol by S N 58. () Fastest reaction with Lucas reagent given by R OH and it follow SN mech. 59. The gas leaked from a storage tank of the Union Carbide plant in Bhopal gas tragedy was : () Methylisocyanate () Methylamine () Ammonia (4) Phosgene 59. () Factual (Pg. 8)

19 (9) VIDYALANKAR : JEE-MAIN : Paper and Solution 6. Eperimentally it was found that a metal oide has formula M.98 O. Metal M, is present as M + and M + in its oide. Fraction of the metal which eists as M + would be : () 7. % () 4.8 % () 6.5 % (4) 5.8 % 6. () + (.98 ) % of M %.98 PART- C : MATHEMATICS 6. Distance between two parallel planes + y +z 8 and 4 + y + 4z + 5 is : () () 5 () 7 (4) 9 6. () Planes are + y + z 8 & + y +z + 5 Distance is 5 ( 8) At present, a firm is manufacturing items. It is estimated that the rate of change of production P w.r.t. additional number of workers is given by dp. If the firm d employs 5 more workers, then the new level of production of items is : () 5 () () 5 (4) () dp d / P + C P / 8 + C () Given if, P C So, () becomes P 8 / + If 5 (is 5 move workers) P 5 8 (5 ) / Let A and B be two sets containing elements and 4 elements respectively. The number of subsets of A B having or more elements is : () 56 () () 9 (4) 6. () A {, y} B {a, b, c, d} A B having 4 8 elements Total subsets of A B is 8 56 Total no. of subsets of A B having or more elements (Pg. 9)

20 C null single ton subset having set set elements JEE-MAIN : Paper and Solution () 64. If the lines y z 4 and y 4 z 5 are coplanar, then k can have : k k () any value () eactly one value () eactly two values (4) eactly three values 64. () Lines are co planer S. D k k k k ( + k) + ( + k ) ( k) k + k k (k + ) k or k Eactly two values. 65. If the vectors AB i + 4k and AC 5i j+ 4k are the sides of a triangle ABC, then the length of the median through A is : () 8 () 7 () (4) () (i ˆ+ k) ˆ + (5i ˆ ˆj + 4k) ˆ Median through A is 4i ˆ ˆj + 4kˆ So, Length The real number k for which the equation, + + k has two distinct real roots in [, ] () lies between and () lies between and () lies between and (4) does not eist 66. (4) f() + + k f' 6 + ( ) f' ( ) Not Possible. As condition for two distinct real root is f(α) f(β) f' ) (where α, β are roots of ( ) 67. The sum of first terms of the sequence.7,.77,.777,, is : 7 () ( 79 7 ) () ( 99 ) () ( ) (4) ( 99 + ) 8 9 (Pg. )

21 () VIDYALANKAR : JEE-MAIN : Paper and Solution 67. () [ ] 9 7 [(.) + (.) + (.) (...)] [79 + ] A ray of light along + y gets reflected upon reaching ais, the equation of the reflected ray is : () y + () y () y (4) y 68. () Slope of + y is m (let) So, tan θ θ θ θ 5 (, ) So, slope of reflected ray is tan So, equation of reflected ray is y ( ) y 69. The number of values of k, for which the system of equations : (k + ) + 8y 4k k + (k + )y k has no solution, is : () infinite () () (4) 69. () k+ 8 Δ k + 4k + 8k k k+ k 4k + (k ) ( k ) Δ 4k 8 k k + 4k + k 4k + 8 4k k + 8 4(k k + ) 4(k ) (k ) (Pg. )

22 JEE-MAIN : Paper and Solution () Δ k + 4k k k k + k 4k k + k (k ) As given no solution Δ & Δ But Δ k 7. If the equations + + and a + b + c, a, b, c R, have a common root, then a : b : c is () : : () : : () : : (4) : : 7. () + + D 4 < Both roots comple Both roots are common of + + & a + b + c a b c 7. The circle passing through (, ) and touching the ais of at (, ) also passes through the point : () ( 5, ) () (, 5) () (5, ) (4) (, 5) 7. () Let centre C(, k) As touches X ais r k So, circle is ( ) + (y k) k Given it passes (, 7) 4 + (k + ) k 4 + k + 4k + 4 k 4k 8 k Circle is ( ) + (y + ) 4 Obviously (5, ) satisfy 7. If, y, z are in A.P. and tan, tan y and tan z are also in A.P., then : () y z () y 6z () 6 y z (4) 6 4y z 7. () y + z () As tan, tan y, tan z in AP tan y tan + z y y + z y z + z z + z by () z (, ) (, ) (Pg. )

23 () VIDYALANKAR : JEE-MAIN : Paper and Solution ( + z) y z + z or z y y z, y, z in GP. As, y, z AP & GP y z 7. Consider : Statement I : ( p q) ( p q) Statement II : ( p q) ( q p) is a fallacy. is a tautology. () Statement I is true; Statement II is true; Statement II is a correct eplanation for Statement I. () Statement I is true; Statement II is true; Statement II is not a correct eplanation for Statement I. () Statement I is true; Statement II is false. (4) Statement I is false; Statement II is true. 7. () p q ~p ~q P ^ ~q ~p ^ q T T F F F F F T F F T T F F F T T F F T F F F T T F F F It is Fallacy p q ~p ~q P q ~q ~ p (p q) (~q ~p) T T F F T T T T F F T T T T F T T F F F T F F T T T T T It is tautology 74. If f( ) d ( ) 5 ψ, then f( ) () ( ) ( ) d C ψ ψ + () ψ( ) ψ ( ) d + C () ψ( ) ψ ( ) d + C (4) ψ ( ) ψ ( ) d + C 74. () f()d dis equal to : ψ(), then 5 f( )d I f() d Let t d dt dt I tf(t) (Pg. )

24 I I I I [t f (t) dt f (t) dt] d ψ( ) (t) f(t) dt c + dt ψ( ) ψ ( ) d + c ( ) ( ) d c ψ ψ + JEE-MAIN : Paper and Solution (4) 75. lim () ( cos )( + cos ) tan4 () (4) ( cos )( + cos ) lim tan4 (sin )( + cos ) lim tan sin (+ cos) lim 4 is equal to : ( + ) 4 () (4) 76. Statement I : The value of the integral Statement II : b a b ( ) ( + ) a π f d f a b d d π is equal to. tan 6 π 6 + () Statement I is true; Statement II is true; Statement II is a correct eplanation for Statement I. () Statement I is true; Statement II is true; Statement II is a not a correct eplanation for Statement I. () Statement I is true; Statement II is false. (4) Statement I is false; Statement II is true. 76. (4) I π/ d (i) tan π /6 + π/ d I (ii) π /6+ cot Adding (i) and (ii) I π/ I 6 π d π π I π /6 6 I π (Pg. 4)

25 (5) VIDYALANKAR : JEE-MAIN : Paper and Solution y 77. The equation of the circle passing through the foci of the ellipse +, and having centre 6 9 at (, ) is : () + y 6y 7 () + y 6y + 7 () + y 6y 5 (4) + y 6y () Co-ordinate of Foci are (ae, ) ; ( ae, ) 9 e 6 y (, ) e 7 4 ( 4, ) (4, ) (, ) Co-ordinate of Foci are ( 7,);( 7,) R ( ) + (y ) 4 + y 6y y 6y A multiple choice eamination has 5 questions. Each question has three alternative answers of which eactly one is correct. The probability that a student will get 4 or more correct answers just by guessing is : 7 () 5 () 5 () () Total No. of ways of attempting the question 5 (, ) ( 7,) ( 7,) (4) 5 4 ' 5 5C 4 + 5C The coordinate of the incentre of the triangle that has the coordinates of mid points of its sides as (, ) (, ) and (, ) is : () + () () + (4) 79. () a, b),( (,) ( a, b + ) (,) (a +, + b) (Pg. 5)

26 On solving a and b, JEE-MAIN : Paper and Solution (6) I I I ( ) I 8. The term independent of in epansion of + is : () 4 () () (4) 8. () + / / / + / / ( + ) (+ ) / / [ ] T r + C r ( / ) r ( / ) r T r + C r C r T r + 5r r 4 T 5 C 4 r r ( ) r 5r ( ) r 6,, 8 8. The area (in square units) bounded by the curves y, y +, ais, and lying in the first quadrant is : 8. () () 9 () 6 () 8 (4) 7 4 y and y d d y (9, ) y / 9 / 9 square units 9 (, ) y + (Pg. 6)

27 (7) VIDYALANKAR : JEE-MAIN : Paper and Solution 8. Let T n be the number of all possible triangles formed by joining vertices of a n sided regular polygon. If T n+ T n then the value of n is : () 7 () 5 () (4) 8 8. () n+ n C C On solving n 5 8. If z is a comple number of unit modulus and argument θ, then + z arg + z equals : () θ () π θ () θ (4) π θ 8. () Let z ω Now z + +ω + z +ω ω ω ω + z arg arg ω θ + z (put z cos θ + i sin θ) 84. ABCD is a trapezium such that AB and CD are parallel and BC CD. If ADB θ, BC p and CD q, then AB is equal to : ( p + q ) sinθ p + q cosθ p + q ( ) () () () pcosθ+ qsinθ pcosθ+ qsinθ p cosθ+ q sinθ (4) p + q sinθ pcosθ+ qsinθ ( ) 84. () BD p + q ABD BDC α DAB π (θ + α) D θ α q C p tan α p q Δ ABD AB sin θ BD sin ( π ( θ+α) ) BD sin θ AB sin ( ) BD sin ( θ+α) θ θ+α) θ θ+α BD sin BDsin ( BD sin BDsin θcos α+βdcosθsin α (p + q )sin θ qsinθ+ pcosθ α 85. If P is the adjoint of matri A and A 4, then α is equal to : 4 4 () 4 () () 5 (4) 85. () α A α 6 6 α. A π (θ + α) α B (Pg. 7)

28 86. The intercepts on ais made by tangents to the curve, the line y, are equal to () ± () ± () ± (4) ± () y t dt Case I : If t > t y dy d and y (y ) ( ) y +. Hence intercept. Case II : t < Similarly, intercept. JEE-MAIN : Paper and Solution (8) y t dt, R, which are parallel to 87. Given : A circle, + y 5 and a parabola, y 4 5. Statement I : An equation of a common tangent to these curves is y Statement II : If the line, y m + ( m ) is their common tangent, then m m 4 satisfies m m +. () Statement I is true; Statement II is true; Statement II is a correct eplanation for Statement I. () Statement I is true; Statement II is true; Statement II is not a correct eplanation for Statement I. () Statement I is true; Statement II is false. (4) Statement I is false; Statement II is true. 87. () Obviously y + 5 is common tangent. Statement I is true. 5 Statement : Let y m+ is common tangent circle & parabola. m + y 5 As tangent 5 m + m 5 + m m 4 + m m m ± So, Statement II is true. Hence (). (Pg. 8)

29 (9) VIDYALANKAR : JEE-MAIN : Paper and Solution dy 88. If y sec( tan ),then at is equal to : d () () () (4) 88. () y sec (tan ) dy d sec (tan ) tan (tan ) + dy d + tan A cot A 89. The epression + cota tana can be written as : () sina cosa + () seca coseca + () tana + cota (4) seca + coseca 89. () Ep. tan A + tan A tan A tan A tan A tan A tan A tan A + tan A + tan A tan A + cot A + sec A cosec A + 9. All the students of a class performed poorly in Mathematics. The teacher decided to give grace marks of to each of the students. Which of the following statistical measures will not change even after the grace marks were given? () mean () median () mode (4) variance 9. (4) (Pg. 9)