JEE MAIN 2017 QUESTION PAPER & SOLUTION CHEMISTRY

Transcription

1 JEE MAIN 07 QUESTIN PAPER & SLUTIN CHEMISTRY JEE MAIN 07 CDE (C). The freezing point of benzene decreases by 0.5 o C when 0. g of acetic acid is added to 0 g of benzene. If acetic acid associated to form a dimer in benzene, percentage association of acetic acid in benzene will be : ( K f for benzene = 5. K kg mol ) () 9.6% () 6.6% () 80.% () 7.6% Sol. () 0. / i 0 / i %. n treatment of 00 ml of 0. M solution of CoCl.6H with excess AgN ; precipitated. The complex is : () [Co(H) 5Cl]Cl.H () [Co(H) Cl ]Cl.H () [Co(H) Cl ].H () [Co(H) 6]Cl Sol. ().0 n ppt 0 60 n compound ne mole compound gives two mores ppt. Co H Cl Cl 5 H. 0 ions are. Which of the following compounds will form significant amount of meta product during mononitration reaction? NHCCH H CCH NH () Sol. () NH () NH () NH () HN,HS N heat -I Meta directing group (7%) N CENTERS : MUMBAI /DELHI /AKLA /LUCKNW /NASHIK /PUNE /NAGPUR /BKAR /DUBAI #

2 JEE MAIN 07 CDE (C). The product obtained when chlorine gas reactions with cold and dilute aqueous NaH are : () Cl and Cl () Cl and Cl () Cl and Cl Sol. () NaH(Cold and Dilute) Cl NaCl NaCl () Cl and Cl 5. Both lithium and magnesium display serval similar properties due to the diagonal relationship; however, the one which is incorrect, si : () nitrates of both Li and Mg yield N and on heating () both form basic carbonates () both form soluble bicarbonates () both form nitrides Sol. () or () 'Mg 'forms:- MgC.Mg H.H which is basic carbonate Lithium doesn t form basic carbonate. 6. A water sample has ppm level concentration of following anions F 0; S 00; N 50 The anion / anions that makes / makes the water sample unsuitable for drinking is / are : () nly S () only N () both S and N () only F Sol. () Maximum permissible value for drinking: ppm for F ppm ppm for S ppm,, N 5000ppm 50 ppm As given ppm for F is 0 ppm That is why answer is () 7. The formation of which of the following polymers involves hydrolysis reaction? () Terylene () Nylon 6 () Bakelite () Nylon 6, 6 Sol. () Nylon 6 Formation involves hydrolysis Caprolactum n NH 5K, C H Caprolactum Nylon - 6 Ans is () NH CH n CENTERS : MUMBAI /DELHI /AKLA /LUCKNW /NASHIK /PUNE /NAGPUR /BKAR /DUBAI #

3 JEE MAIN 07 CDE (C) 8. The Tyndall effect is observed only when following conditions are satisfied: (a) The diameter of the dispersed particles is much smaller than the wavelength of the light used. (b) The diameter of the dispersed particles is not much smaller than the wavelength of the light used. (c) The refractive indices of the dispersed phase and dispersion medium are almost similar in magnitude. (d) The refractive indices of the dispersed phase and dispersion medium differ greatly in magnitude () (b) and (c) () (a) and (d) () (b) and (d) () (a) and (c) Sol. () Condition for Tyndall effect are : () The diameter of the dispersed particle is not much smaller than the wavelength of light used () The refractive indices of the disperse phase and dispersion medium differ greatly in magnitude 9. pk a of a weak acid (HA) and pk b of a weak base (BH) are. and., respectively. The ph of their salt (AB) solution is : ().0 () 7. () 6.9 () 7.0 Sol. () ph The major product obtained in the following reaction is : DIBAL H CH H CH CH () CH H () CH CH CH () CH Sol. () DIBAL H reduces esters to aldehydes. CH DIBAL H H () CH CH CH CENTERS : MUMBAI /DELHI /AKLA /LUCKNW /NASHIK /PUNE /NAGPUR /BKAR /DUBAI #

4 JEE MAIN 07 CDE (C). Which of the following compounds will behave as a reducing sugar in an aqueous KH solution? HH C CH CH HH C CH H H H () H HH C H H CH H () HH C H H CCH CH H CH () Sol. () H () H H H CH H CH H CH KH CH H CH H H hemiacetal group is present Tollen's test positive Ag. The correct sequence of regents for the following conversion will be : H CH () CH H CH CH Ag NH H, CH MgBr, H CH H () Ag NH H, H CH H, CH MgBr () CHNgBr, H CH H, Ag NH H () CH MgBr, Ag NH H, H CH H Sol. () CENTERS : MUMBAI /DELHI /AKLA /LUCKNW /NASHIK /PUNE /NAGPUR /BKAR /DUBAI #

5 JEE MAIN 07 CDE (C) AqCH H C H H CH C - H CHH H H CH MgBr CH C CH H C CH. Which of the following species is not paramagnetic? () B () N () C () Sol. () For C Px, s, s, s, p, s All electrons are paired. z Py. Which of the following, upon treatment with tert-buna followed by addition of bromine water, fails to decolourize the colour of bromine? CH () Br () Br C 6 H 5 CH () Br () Br CENTERS : MUMBAI /DELHI /AKLA /LUCKNW /NASHIK /PUNE /NAGPUR /BKAR /DUBAI # 5

6 C H CH Sol. () Br CH H C K CH Br / Water CH CH CH JEE MAIN 07 CDE (C) No deccolourlization 5. Which of the following reactions is an example of a redox reaction? () XeF6 H XeF HF () XeF F XeF6 () XeF F XeF6 () XeF6 H XeF HF Sol. () oxidation 6 0 XeF F XeF 6 Reduction 6. U is equal to: () Isothermal work () Isochoric work () Isobaric work () Adiabatic work Sol. () By st law of thermodynamics U q For adiabatic q 0 Hence U 7. Which of the following molecules is least resonance stabilized? CH CH () () () () Sol. () All other compounds are aromatic except N CENTERS : MUMBAI /DELHI /AKLA /LUCKNW /NASHIK /PUNE /NAGPUR /BKAR /DUBAI # 6

7 JEE MAIN 07 CDE (C) 8. The increasing order of the reactivity of the following halides for the SNreaction is: CHCHCHCH C (I) p HC C6H CH Cl (III) CHCHCHCl (II) () II III I () III II I () II I III () I III II Sol. () CH CH CH CH CH CH CH Cl C (I) CH Cl (II) CH (III) Carbocation would be most stable in (III) then (I) & (II). Rate of SN reactivity is II I III 9. gram of a carbonate MC on treatment with excess HCl produces mole of C. The molar mass of MC in g mol - is ().86 () 86 () 8. () 8.6 Sol. () M C HCl MCl H C n NC n C x x x.5 Molar mass of NC.5 60 CENTERS : MUMBAI /DELHI /AKLA /LUCKNW /NASHIK /PUNE /NAGPUR /BKAR /DUBAI # 7

8 JEE MAIN 07 CDE (C) 0. Sodium salt of an organic acid X produces effervescence with conc. HS. X reacts with the acidified aqueous CaCl solution to give a white precipitate which decolourises acidic solution of KMn X is: () NaC () C6H5CNa () HCNa () CHCNa Sol. () Na C C C, C Ca CaC conc.h white C Mn H C Mn H. The most abundant elements by mass in the body of a healthy human adult are: xygen 6.% ; Carbon.9%, Hydrogen 0.0% ; and Nitrogen.6%. The weight which a 75 kg person would gain if all H atoms are replaced by H atoms is: () 0 kg () 5 kg () 7.5 kg () 7.5 kg Sol. () Weight of person 75Kg 0 Hydrogen Kg Atoms if H New mass of H mass of atom No. of atoms gm Weight gain due to H gm 7.5Kg. The major product obtained in the following reaction is: Br H C 6 H t BuK 5 C 6 H 5 Sol. () t () C6H5CH BuCHC6H5 () t () C6H5CH CHC6H5 () t Br H C 6 H 5 C 6 H 5 BrK C H CH Bu CH C H C H CH Bu CH C H H C 6 H 5 C 6 H 5 carbon carbon H H H C 6 H 5 C 6 H 5 CENTERS : MUMBAI /DELHI /AKLA /LUCKNW /NASHIK /PUNE /NAGPUR /BKAR /DUBAI # 8

9 JEE MAIN 07 CDE (C) This is a typical example of E elimination Ansis. Given C g C g ; graphite 0 H r 9.kJ mol H g g Hl ; kj mol r H C g H l CH g g ; H 0 r 890.kJ mol Based on the above thermochemical equations, the value of C H g CH g will be: () graphite.0kj mol () 7.8kJ mol ().0kJ mol () 7.8kJ mol Sol. () C g C g () graphite H g g H. () C g H CH g g.. () graphite graphite C g H H C H g CH g. () gives () C g H g g C g H CH g r 7.8KJ mol. In the following reactions, Zn is respectively acting as a / an: Zn Na Na Zn (a) H 0 r at 98 K for the reaction (b) Zn C ZnC () acid and base () base and acid () base and base () acid and acid Sol. () Zn Na Na ZN ZN C ZnC Acidic Basic Basic Acidic 5. The radius of the second Bohr orbit for hydrogen atom is: (Planck s const. h Js mass of electron 9 e C; permittivity of vacuum ) () kg m A 0.A () 0.65A () 0.76A () kg; charge of electron A CENTERS : MUMBAI /DELHI /AKLA /LUCKNW /NASHIK /PUNE /NAGPUR /BKAR /DUBAI # 9

10 JEE MAIN 07 CDE (C) Sol. () o r 0.59 A o. A 6. Two reactions Rand R have identical pre exponential factors. Activation energy of Rexceeds that of R by 0 kj mol -. If k and kare rate constants for reactions R and R respectively at 00 K, then ln k k is equal to: R 8. J mol K () () 8 () () 6 Sol. () R R e e R R ln 7. A metal crystallises in a face centred cubic structure. If the edge length of its unit cell is a, the closest approach between two atoms in metallic crystal will be: a () () a () a () a Sol. () a a The closest distance between two atoms in metallic crystal is a Ans. is () a 8. The group having isoelectronic species is: (),F, Na, Mg (),F, Na,Mg Sol. () 0 electrons are present in each species () (), F, Na,Mg,F, Na,Mg 9. Given 0 0 E.6 V,E 0.7 V E Cl Cl Cr Cr.V, E. 0 0 Cr7 Cr Mn Mn.5V Among the following, the strongest reducing agent is: () Cl () Cr () Mn () CENTERS : MUMBAI /DELHI /AKLA /LUCKNW /NASHIK /PUNE /NAGPUR /BKAR /DUBAI # 0 Cr

11 JEE MAIN 07 CDE (C) Sol. () o E 0.7 Cr/Cr xidation potential is maximum hence stronger reducing agent. 0. -Methyl-pent--ene on reaction with HBr in presence of peroxide forms an addition product. The number of possible stereoisomers for the product is: () Four () Six () Zero () Two Sol. () Br H HBr H C CH RooR H C * * CH CH Antimarkovinikov's CH In products two chiral carbon are generated & molecule is unsymmetric Total isomers are Ans is () CENTERS : MUMBAI /DELHI /AKLA /LUCKNW /NASHIK /PUNE /NAGPUR /BKAR /DUBAI #

12 JEE MAIN 07 CDE (C). The integral dx is equals cos x MATHEMATICS () () () () Sol. () I I I Add I dx cos x dx cos x x dx cos x dx cos x I cosec xdx I. Let I n n tan x dx, n the ordered pair.if a, b is equal to (), (),0 5 5 Sol. () I tan x dx n n 6 I I6 tan x tan x dx tan x,sec x dx t dt 5 t c 5 tan x C 5 a, b 0 5 tan x sec x dx 5 5 I I6 a tan c bx C, where C is a constant of integration, then (), 5 (),0 5 CENTERS : MUMBAI /DELHI /AKLA /LUCKNW /NASHIK /PUNE /NAGPUR /BKAR /DUBAI #

13 . The area JEE MAIN 07 CDE (C) in sq.units of the region x, y : x 0, x y, x y and y x is: () 7 () 5 Sol. () x 0, x y, x y & y x 0,, y x /, y x () 59 () x y,0 x x A x dx x dx 0 / x x x x x x A bod contains 5 green and 0 yellow balls. If 0 balls are randomly drawn, one-by-one, with replacement, then the variance of the number of green balls drawn is: () () 6 5 Sol. () PG 5 P y 5 Variance n pq Variance () 5 () 6 CENTERS : MUMBAI /DELHI /AKLA /LUCKNW /NASHIK /PUNE /NAGPUR /BKAR /DUBAI #

14 JEE MAIN 07 CDE (C) 5. If sin x y cos x 0 and () dy dx () Sol. () dy sin x y cos x 0 dx dy cos x dx y sin x n y n sin x C Now, y0 C n n y n sin x n y sin x y 0, then y () is equal to () Now, y 6. Let be a complex number such that z where z. If k Then k is equal to: () () () z Sol. () n solving i k z 7. Let a iˆ ˆj kˆ and b ˆi ˆj. Let c be a vector such that c a between c and a b be 0. Then a.c is equal to () 5 () () Sol. () ˆi ˆj kˆ a i ˆ ˆj kˆ, b ˆi ˆj, a b i ˆ j ˆ kˆ Now, c a c c.a 0, Now, 0 a b c, () z a b c and the angle () CENTERS : MUMBAI /DELHI /AKLA /LUCKNW /NASHIK /PUNE /NAGPUR /BKAR /DUBAI #

15 JEE MAIN 07 CDE (C) a b c sin, c sin c 6 c c.a 0 c.a 8. The radius of a circle, having minimum area, which touches the curve y x is: () () () () Sol. () Let radius r Centre 0, r y x 0 r r r r r 9. If for x 0,, the derivative of 6x x tan is 9x x () 9x Sol. () () 9x 6x x tan x x tan 9x x x Put x x tan 6x x tan Then tan tan tan 9x tan tan y tan x x Differentiating dy 9 x dx 9x 9 gx 9x tan x x x.g x,then 9 () 9x g x equals: y x and the lines x x () 9x CENTERS : MUMBAI /DELHI /AKLA /LUCKNW /NASHIK /PUNE /NAGPUR /BKAR /DUBAI # 5

16 JEE MAIN 07 CDE (C) 0. If two different numbers are taken from the set 0,,,,...,0 ; then the probability that their sum as well as absolute difference are both multiple of, is: () () Sol. () Case I Both number are of form Case II Both number are of form Probability 6 55 K C k C () 6 55 () 55. cot x cos x lim x x equals: () () 8 Sol. () cos x cos x sin x t x x sin x cos x t sin x 8 x sin x cos x t 8 x x x 8 6 () () 6. The value of C 0 C C 0 C 0 0 C C C C... C 0 0 C0 () 0 9 () Sol. () C C... C 0 C C C... C () () is: 0 CENTERS : MUMBAI /DELHI /AKLA /LUCKNW /NASHIK /PUNE /NAGPUR /BKAR /DUBAI # 6

17 . For three events A,B and C, P (Exactly one of A or B occurs) =P (Exactly one of B or C occurs) JEE MAIN 07 CDE (C) =P (Exactly one of C or A occurs) Then the probability that at least one of the events occurs, is: () 7 () () Sol. () P A P B P A B () P B P C P B C () PA PC PA C () PA B C 6 Adding () +()+ () PA P B PC PA B PB C PA C 8 7 PA B C and P (All the three events occur simultaneously) 6. () 7 6. Let a vertical tower AB have its end A on the level ground. Let C be the mid-point of AB and P be a point on the ground such that AP AB. If BPC, then tan is equal to: () 9 () 9 () 6 7 () Sol. () B x x C x A x P C x / tan x tan tan tan tan tan 8 tan 9 CENTERS : MUMBAI /DELHI /AKLA /LUCKNW /NASHIK /PUNE /NAGPUR /BKAR /DUBAI # 7

18 JEE MAIN 07 CDE (C) 5. The eccentricity of an ellipse whose centre is at the origin is. If one of its directrices is x, then the equation of the normal to its at, is: () x y 7 () x y () y x () x y Sol. () e a a e b a e a cos, bsin, Normal: ax sec bycos ec a b x y 6. If, for a positive integer n, the quadratic equation, x x x x... x n x n 0n Has two conservative integral solutions, then n is equal to: () 0 () () () 9 Sol. () n n nx n x 0n n x nx 0 0 n n n n n 7. The following statement p q ~ ~ P q q is: () equivalent to p ~ q () a fallacy () a tautology () equivalent to ~ p q Sol. () p Q p q ~ p q ~ p T T T F T T T F F F T F F T T T T T F F T T F T ~ p q q CENTERS : MUMBAI /DELHI /AKLA /LUCKNW /NASHIK /PUNE /NAGPUR /BKAR /DUBAI # 8

19 JEE MAIN 07 CDE (C) p q ~ p q q T T T T 8. The normal to the curve yx x x 6 at the point where the curve intersects the y-axis passes through the point: (), (), Sol. () Put x 0, y In y' x x yx yx y ' Hence normal is x y 9. For any three positive real numbers a,b and c, 9 5a b 5 c ac 5b a c (), Then: () a,b and c are in A.P. () a,b and c are in G.P. () b,c and a are in G.P. () b,c and a are in A.P. Sol. () 5a 9b 5c 5ab 5bc 75ac 0 5a b b 5c 5c 5a 0 5a b 5c only k k k a, b,c If the image of the point P,, (), in the plane, x y z 0 measured parallel to the line, x y z is Q, then PQ is equal to : 5 () () 6 5 () 5 () Sol. () x y z 5 Q,,5 Image 5 6 Mid point by PQ,, Lie on x y z P,, Q,6, PQ 6 00 CENTERS : MUMBAI /DELHI /AKLA /LUCKNW /NASHIK /PUNE /NAGPUR /BKAR /DUBAI # 9

20 5. If 5 tan x cos x cos x 9, then the value of cos x is : () () 9 Sol. () cos x t 5 tan x 5cos x cos x 9 5 t 5t t 9 t 5 5t 5t t 7 t 9t t 5 0 9t 5t t 5 0 t t 5 t t, cos x cos x cos x cos x cos x Let,,, a b c R. If f x y f x f y xy, x, y 7 () 9 f x ax bx c R, then f n () 5 JEE MAIN 07 CDE (C) is such that a b c and CENTERS : MUMBAI /DELHI /AKLA /LUCKNW /NASHIK /PUNE /NAGPUR /BKAR /DUBAI # 0 0 is equal to : () 90 () 55 () 0 () 65 Sol. () f ' x y f ' x y n Put x 0, f ' y f ' 0 y [Clearly f ' y y k y f y ky c f 0 0 c 0 y f y ky f k 5 k f 0 0 ]

21 JEE MAIN 07 CDE (C) x 5 f x x 0 n f n 0 5. The distance of the point (,, 7) from the plane passing through the point,,, having normal perpendicular to both the lines x y z and () () () Sol. () Equation of plane x y z 0 Distance from,, 7 is 0 8 x y z 7, is : 0 () 8 5. If S is the set of distinct values of b for which is following system of linear equations x y z x ay z ax by z 0 has no solution, then S is : () a finite set containing two or more elements () a singleton () an empty set () an infinite set Sol. () a 0 a b By solving a and b R Then the planes are x y z x y z x by z 0 If b, infinite solution If b, no solution CENTERS : MUMBAI /DELHI /AKLA /LUCKNW /NASHIK /PUNE /NAGPUR /BKAR /DUBAI #

22 55. If A then adj A A 5 8 () () 6 5 Sol. () 6 9 A 7 6 A A 8 5 AdjA A is equal to : 56. A hyperbola passes through the point, hyperbola at P also passes through the point : 7 6 () () 8 7 P and has foci at (), (), (), (), Sol. () x y a b a b a b a b b b b b b and a x y So equation is Hence point is, JEE MAIN 07 CDE (C), 0. Then the tangent to this 57. Let k be an integer such that the triangle with vertices k, k, 5, k and k, units. Then the orthocenter of this triangle is at the point: (), (), (), Sol. () Area 5k k 0 8 K, 6 5,, So vertices are rthocenter is, (), has area 8 sq. CENTERS : MUMBAI /DELHI /AKLA /LUCKNW /NASHIK /PUNE /NAGPUR /BKAR /DUBAI #

23 JEE MAIN 07 CDE (C) 58. Twenty meters of wire is available for fencing off a flower-bed in the form of a circular sector. Then the maximum area (in sq. m) of the flower-bed, is : () 5 () 0 ().5 () 0 Sol. () Length of arc 0 r r 0 r r Clearly A 0r r r A 5 r 5 So max value is 5 when r x The function f : R, defined as f x x, is : () surjective but not injective () neither injective nor surjective () invertible () injective but not surjective Sol. () f.r, x Consider f x x x tan / To find range let f x is same as sin range /,/ For injection f ' x Hence not injective x x clearly non-monotonic 60. A man X has 7 friends, of them are ladies and are men. His wire Y also has 7 friends, of them are ladies and are men. Assume X and Y have no common friends. Then the total number of ways in which X and Y together can throw a party inviting ladies and men, so that friends of each of X and Y are in this party, is : () 69 () 8 () 85 () 68 Sol. () HUSBAND WIFE C M F MF FM C. C 8 C. C M F F m F M r 0 r 85 r C CENTERS : MUMBAI /DELHI /AKLA /LUCKNW /NASHIK /PUNE /NAGPUR /BKAR /DUBAI #

24 JEE MAIN 07 CDE (C) PHYSICS 6. An observers is moving with half the speed of light towards a stationary microwave source emitting waves at frequency 0 GHz. What is the frequency of the microwave measured by the observer? 8 (speed of light 0 ms ) (). GHz () 7. GHz () 5. GHz () 0. GHz Sol. () f0 fs, where v0 c c v0 ( moving towards source) 0 f 0 GH z 7.GHz 6. The following observations were taken for determining surface tension T of water by capillary method: diameter of capillary, D.5 0 m rise of water, h.5 0 m Using g = 9.80 m/s rhg and the simplified relation T 0 N m, the possible error in surface tension is closest to: ().5 % (). % () 0% () 0.5% Sol. () % errors % 6. Some energy levels of a molecule are shown in the figure. The ratio of the wavelengths r, is given by: () r () r () Sol. () hc E E hc or r () r CENTERS : MUMBAI /DELHI /AKLA /LUCKNW /NASHIK /PUNE /NAGPUR /BKAR /DUBAI #

25 JEE MAIN 07 CDE (C) 6. A body of mass m = 0 kg is moving in a medium and experiences a frictional force initial speed is 0 0ms. If, after 0 s, its energy is m 0, the value of k will be: 8 () 0 kgs () 0 kg m () 0 kg m s () 0 kg m Sol. () dv k v dt m 5 k 0 dt 0 v 0 0 k k 0 kg / m 00 F k. Its 65. C P and C V are specific heats at constant pressure and constant volume respectively. It is observed that C p Cv a for hydrogen gas C p Cv b for nitrogen gas The correct relation between a and b is: () a = b () a = b () a = 8 b () a b Sol. () For Hydrogen J K C C a gm p P v J K C C b gm p v v J k C c b 8gm a b 8 r a b b a 66. The moment of inertia of a uniform cylinder of length l and radius R about its perpendicular bisector is I. What is the ratio l R such that the moment of inertia is minimum? () () () Sol. () mr ml I m l r, as r l m () CENTERS : MUMBAI /DELHI /AKLA /LUCKNW /NASHIK /PUNE /NAGPUR /BKAR /DUBAI # 5

26 JEE MAIN 07 CDE (C) m m l l For minimum I, di 0 dl m l 0 l l r 67. A radioactive nucleus A with a half life T, decays into a nucleus B. At t = 0, there is no nucleus B. At some time t, the ratio of the number of B to that of A is 0.. Then, t is given by: log. T T log () t T () t T log. () t () t log log. log. Sol. () N N e 0 N0 N e. t ln. t t 0 ln. t T ln hn 68. Which of the following statements is false? () In a balanced wheatstone bridge if the cell and the galvanometer are exchanged, the null point is disturbed () A rheostat can be used as a potential divider () Krichhoff s second law represents energy conservation. () Wheatstone bridge is the most sensitive when all the four resistances are of the same order of magnitude Sol. () Theoretical 69. A capacitance of F is required in an electrical circuit across a potential difference of.0 kv. A large number of F capacitance are available which can withstand a potential difference of not more than 00 V The minimum number of capacitors required to achieve this is () 6 () () () Sol. () Let there be P branches in parallel and every branch consists of S capacitors in series. F Ceq f, P F S P = S (i) a capacitor cannot withstand more than 00 V, So S CENTERS : MUMBAI /DELHI /AKLA /LUCKNW /NASHIK /PUNE /NAGPUR /BKAR /DUBAI # 6

27 JEE MAIN 07 CDE (C) 0 S S (ii) No of capacitors = P S 70. In the given circuit diagram when the current reaches steady state in the circuit, the charge on the capacitor of capacitance C will be: () Sol. () r CE () r r r CE r () r r CE r r () CE At steady state ir ir r r i r, 0 V V i r C r r r r r Cr Q CVC r r 7. In the above circuit the current in each resistance is () 0.5 A () 0.5 A () 0 A () A Sol. () CENTERS : MUMBAI /DELHI /AKLA /LUCKNW /NASHIK /PUNE /NAGPUR /BKAR /DUBAI # 7

28 JEE MAIN 07 CDE (C) 7. In amplitude modulation, sinusoidal carrier frequency used in denoted by c and the signal frequency is denoted by. The bandwidth. Which of m of the signal is such that m c the following frequencies is not contained in the modulated wave? () c () m c () c m () m Sol. () Refer Theory 7. In a common emitter amplifier circuit using an n p n transistor, the phase difference between the input and the output voltage will be () 90 0 () 5 0 () 80 0 () 5 0 Sol. () Refer Theory 7. A copper ball of mass 00 gm is at a temperature T. It is dropped in a copper calorimeter of mass 00gm, filled with 70 gm of water at room temperature. Subsequently, the temperature of the system is found to be 75 0 C. T is given by: (Given: room temperature = 0 0 C, specific heat of copper = 0. cal/gm 0 C) () C () 50 0 C () 85 0 C () C Sol. () Heat released by Cu ball = Heat absorbed by water + Calorimeter M S T m S T m S T Cu Cu w w cal w 000.T T C 75. In a Young s double slit experiment, slits are separated by 0.5 mm, and the screen is placed 50 cm away. A beam of light consisting of two wavelengths, 650 nm and 50 nm, is used to obtain interference fringes on the screen. The least distance from the common central maximum to the point where the bright fringes due to both the wavelengths coincide is: () 7.8 mm () 9.75 mm () 5.6 mm ().56 mm Sol. () nd n D d d n n 5 y n D.5650 d mm m CENTERS : MUMBAI /DELHI /AKLA /LUCKNW /NASHIK /PUNE /NAGPUR /BKAR /DUBAI # 8

29 JEE MAIN 07 CDE (C) 76. An electric dipole has a fixed dipole moment P, which makes an angle with respect to x axis. When subjected to an electric field E Ei, it experiences a torque T k. When subjected to another electric field E E j it experiences a torque T T. The angle is () 5 0 () 60 0 () 90 0 () 0 0 Sol. () P E E & E don t have k component and & only have k component so P will be i j plane. Let P P x i P y j k P i P j Ei x y PyE () k P i P j E j x y 0 60 Px E 77. A slender uniform rod of mass M and length l is pivoted at one end so that it can rotate in a vertical plane (see figure). There is negligible friction at the pivot. The free end is held vertically above the pivot and then released. The angular acceleration of the rod when it makes an angle with the vertical is () g sin l Sol. () I () g cos l () g cos l () g sin l g sin 78. An external pressure P is applied on a cube at 0 0 C so that it is equally compressed from all sides. K is the bulk modulus of the material of the cube and is its coefficient of linear expansion. Suppose we want to bring the cube to its original size by heating. The temperature should be raised by: () P K Sol. () P PV B or V V B V () PK () PK () CENTERS : MUMBAI /DELHI /AKLA /LUCKNW /NASHIK /PUNE /NAGPUR /BKAR /DUBAI # 9 P K

30 JEE MAIN 07 CDE (C) Also, V V. T V. T pv V.T B P r T B 79. A diverging lens with magnitude of focal length 5 cm is placed at a distance of 5 cm from a converging lens of magnitude of focal length 0 cm. A beam of parallel light falls on the diverging lens. The final image formed is: () virtual and at a distance of 0 cm from convergent lens () real and at a distance of 0 cm from the divergent lens () real and at a distance of 6 cm from the convergent lens () real and at a distance of 0 cm from convergent lens Sol. () For L : f v u 0 v 0 v 0cm 80. An electron beam is accelerated by a potential difference V to hit a metallic target to produce X rays. It produces target to produce X rays. It produces continuous as well as characteristic X rays. If min is the smallest possible wavelength of X ray in the spectrum, the variation of log min with log Y is correctly represented in () () () () Sol. () hc c ev hc cv constant e ln ln V ln c ln c ln V cosntant CENTERS : MUMBAI /DELHI /AKLA /LUCKNW /NASHIK /PUNE /NAGPUR /BKAR /DUBAI # 0

31 JEE MAIN 07 CDE (C) 8. The temperature of an open room of volume 0 m increases from 7 0 C to 7 0 C due to sunshine. The 5 atmospheric pressure in the room remains 0 Pa. 5 5 ().8 0 ().5 0 ().5 0 ().6 0 Sol. () pv n f n0 R Tf T0 5 0 pa 0m 8.J mol x mol J In a coil of resistance 00, a current is induced by changing the magnetic flux through it as shown in the figure. The magnitude of change in flux through the coil is : 0 Current (amp.) Time 0.5 sec () 5 Wb () 50 Wb () 75 Wb () 00 Wb Sol. () d R 8. When a current of 5 ma is passed through a galvanometer having a coil of resistance 5, it shows full scale deflection. The value of the resistance to be put in series with the galvanometer to convert it into a voltmeter of range 0 0 V is : ().050 ().550 () Sol. () V ig R G 0 G 50 R = R () A time dependent force F = 6t acts on a particle of mass kg. if the particle starts from set, the work done by the force during the first sec. will be : () J () 9 J () 8 J ().5 J Sol. () F 6t dv m 6t dt CENTERS : MUMBAI /DELHI /AKLA /LUCKNW /NASHIK /PUNE /NAGPUR /BKAR /DUBAI #

32 JEE MAIN 07 CDE (C) v dv 6tdt 0 0 v t Work done k m vf mvi 0.5J t A magnetic needle of magnetic moment Am and moment of inertial kg m is performing simple harmonic oscillations in a magnetic field of 0.0 T. Time taken for 0 complete oscillations is : () 8.89 s () 6.89 s () 8.76 s () 6.65 s Sol. () 6 I MB The variation of acceleration due to gravity g with distance d from centre of the earth is best represented by (R = Earth s radius) : g g () R d () R d g g () Sol. () Theoretical R d () d 87. A body is thrown vertically upwards. Which one of the following graphs correctly represent the velocity vs time? t t () () CENTERS : MUMBAI /DELHI /AKLA /LUCKNW /NASHIK /PUNE /NAGPUR /BKAR /DUBAI #

33 JEE MAIN 07 CDE (C) t () Sol. () u Initial velocity is +ve dv g dt V dv g dt 0 U t V U gt V U gt (straight line with negative slope) () t 88. A particle A of mass m and initial velocity collides with a particle B of mass m which is at rest. The collision is head on, and elastic. The ratio of the de-broglie wavelength collision is : A () A () A () A () B B B B Sol. () m mv mv v v v v () v 0 v v () n solving v v, v v h mv h m v A to B after the 89. A particle is executing simple harmonic motion with a time period T. At time t = 0, it is at its position of equilibrium. The kinetic energy-time graph of the particle will look like: () KE KE 0 T t () KE KE 0 T T t () Sol. () 0 T T T t () 0 T T T t CENTERS : MUMBAI /DELHI /AKLA /LUCKNW /NASHIK /PUNE /NAGPUR /BKAR /DUBAI #

34 JEE MAIN 07 CDE (C) 90. A man grows into a giant such that his linear dimensions increase by a factor of 9. Assuming that this density remains same, the stress in the leg will change by a factor of : () 9 Sol. () Stress v g A q vg q A q Mg A () 8 () 8 () 9 CENTERS : MUMBAI /DELHI /AKLA /LUCKNW /NASHIK /PUNE /NAGPUR /BKAR /DUBAI #