AIPMT 2014 TEST PAPER WITH SOLUTIONS (HELD ON SUNDAY 04 th MAY, 2014)

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Noah Norman
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1 . If foce (F), elocity (V) and time (T) ae taken as fundamental units, then the dimensions of mass ae:- () [F V T ] () [F V T ] () [F V T ] (4) [F V T] [mass] Foce Foce cceleation Velocity / time [F V T]. pojectile is fied fom the suface of the eath with a elocity of 5 ms and angle with the hoizontal. nothe pojectile fied fom anothe planet with a elocity of ms at the same angle follows a tajectoy which is identical with the tajectoy of the pojectile fied fom the eath. The alue of the acceleation due to gaity on the planet is (in ms ) gien g 9.8 m/s ().5 () 5.9 () 6. (4).8 ns. () s ange u sin g so g u Theefoe g planet (9.8 m / s ).5 m/s 5. paticle is moing such that its position coodinate (x, y) ae (m, m) at time t (6m, 7m) at time t s and (m, 4m) at time t 5s. eage elocity ecto ( V a ) fom t to t 5 s is :- () i ˆ 4 ˆ j 5 () 7 ˆ i ˆ j () ˆ i ˆj (4) ˆ i ˆ j a t IMT 4 TT WITH OLUTIO (HLD O UDY 4 th MY, 4) 5 ( )i ˆ (4 ) ˆj 5 (i ˆ ˆ j) 5 COD- 4. system consists of thee masses m, m and m connected by a sting passing oe a pulley. The mass m hangs feely and m and m ae on a ough hoizontal table (the coefficient of fiction ). The pulley is fictionless and of negligible mass. The downwad acceleation of mass m is : (ssume m m m m) () () m g( g) 9 g( ) cceleation m m mg (m m )g m m m () g (4) g( ) et foce in the diection of motion Total mass of system g ( ) 5. The foce 'F' acting on a paticle of mass 'm' is indicated by the foce-time gaph shown below. The change in momentum of the paticle oe the time inteal fom zeo to 8 s is :- F () 6 t (s) () 4 s () s () s (4) 6 s Change in momentum, p Fdt 4 6 ea of F-t gaph s

2 IMT-4 6. balloon with mass 'm' is descending down with an acceleation 'a' (whee a < g). How much mass should be emoed fom it so that it stats moing up with an acceleation 'a'? () ma g a () ma g a 8. The oscillation of a body on a smooth hoizontal suface is epesented by the equation, X cos(t) whee X displacement at time t fequency of oscillation Which one of the following gaphs shows coectly the aiation 'a' with 't'? () ma g a (4) ma g a ns. () Let upthust of ai be F a then fo downwad motion mg F a ma fo upwad motion F a (m m) (m m)a Theefoe m ma g a 7. body of mass (4m) is lying in x-y plane at est. It suddenly explodes into thee pieces. Two pieces, each of mass (m) moe pependicula to each othe with equal speeds (). The total kinetic enegy geneated due to explosion is :- ns. () () m () m () m (4) 4 m m m m By conseation of linea momentum m m a () O a T () O T t a () O T t a (4) O T t Displacement, x cos(t) dx Velocity, sin( t) dt d cceleation, a cos( t) dt 9. solid cylinde of mass 5 kg and adius.5 m is fee to otate about the hoizontal axis. massless sting is wound ound the cylinde with one end attached to it and othe hanging feely. Tension in the sting equied to poduce an angula acceleation of eolutions s is :- () 5 () 5 () 78.5 (4) 57 Hee eolutions/s 4 ad/s t Total K geneated m m (m) m + m m I M s I T (5) (.5) 5 4 Kg-m so T I 5 4 I 4 (.5) 5 57

3 . The atio of the acceleations fo a soldi sphee (mass 'm' and adius '') olling down an incline of angle '' without slipping and slipping down the incline without olling is :- () 5 : 7 () : () : 5 (4) 7 : 5 ns. () Fo olling motion without slipping on inclined plane a gsin K and fo slipping motion on inclined plane a gsin a 5 equied atio a K 7 5. black hole is an object whose gaitational field is so stong that een light cannot escape fom it. To what appoximate adius would eath (mass kg) hae to be compessed to be a black hole? () 9 m () 6 m () m (4) m scape elocity GM c speed of light 4 GM m c ( ) m. Dependence of intensity of gaitational field () of eath with distance () fom cente of eath is coectly epesented by :- () O () O COD-. Coppe of fixed olume 'V; is dawn into wie of length 'l'. When this wie is subjected to a constant foce 'F', the extension poduced in the wie is 'l'. Which of the following gaphs is a staight line? ns. () () l esus l () l esus l F Y F Y But V so V Theefoe F VY () l esus l (4) l esus l 4. cetain numbe of spheeical dops of a liquid of adius '' coalesce to fom a single dop of adius '' and olume 'V'. If 'T' is the suface tension of the liquid, then : () enegy 4VT is eleased () enegy VT is absobed () enegy VT is eleased (4) negy is neithe eleased no absobed s suface aea deceases so enegy is eleased. eleased enegy 4 T[n / ] whee n / 4 T () O (4) O VT ns. ()

4 IMT-4 5. team at C is passed into g of wate at C. When wate acquies a tempeatue of 8 C, the mass of wate pesent will be : [Take specific heat of wate cal g C and latent heat of steam 54 cal g ] () 4 g ().5 g () 4.5 g (4).5 g Heat lost Heat gained ml + ms w m W s W m 54 + m ( 8) (8 ) m.5 g Total mass of wate ( +.5)g.5g 6. Cetain quantity of wate cools fom 7 C to 6 C in the fist 5 minutes and to 54 C in the next 5 minutes. The tempeatue of the suoundings is:- () 45 C () C () 4 C (4) C ns. () By ewton's law of colling k t k 5 k[65 ]... (i) and k k[57 ]... (ii) By diiding (i) by (ii) we hae monoatomic gas at a pessue, haing a olume V expands isothemally to a olume V and then adibatically to a olume 6V. The final pessue of Fo isothemal pocess V V V (V) Fo adiabatic pocess () (6) 5 / 8 64 V V 8. themodynamic system undegoes cyclic pocess BCD as shown in fig. The wok done by the system in the cycle is :- C B D V V V () V () V V () (4) Zeo Wok done by the system in the cycle ea unde V cue & V-axis ( )(V V ) + V V V V 9. The mean fee path of molecules of a gas, (adius '') is inesely popotional to :- ns. () () () () (4) the gas is : (take 5 ) () 64 () () 64 (4) 6 Mean fee path m d n whee d diamete of molecule m 4

5 . If n, n and n ae the fundamental fequencies of thee segments into which a sting is diided, then the oiginal fundamental fequency n of the sting is gien by :- () n n n n () n n n n () n n n n () n n + n + n ns. () Total length of sting + + But fequency so n n n n length. The numbe of possible natual oscillation of ai column in a pipe closed at one end of length 85 cm whose fequencies lie below 5 Hz ae : (elocity of sound 4 ms ) () 4 () 5 () 7 (4) 6 Fequency CO, f n (n + ) 4 fo n, f Hz n, f Hz n, f 5 Hz n, f 7 Hz n 4, f 4 9 Hz n 5, f 5 Hz Which ae less than 5 Hz.. speeding motocyclist sees tafic jam ahead of him. He slows down to 6 km/hou. He finds that taffic has eased and a ca moing ahead of him at 8 km/hou is honking at a fequency of 9 Hz. If the speeds of sound is 4 m/s, the fequency of the honk as head by him will be :- () Hz () 7 Hz () 4 Hz (4) 464 Hz ppaent fequency n' n Hz. 4 5 COD-. Two thin dielectic slabs of dielectic constants K and K (K < K ) ae inseted between plates of a paallel plate capacito, as shown in the figue. The aiation of electic field '' between the plates with distance 'd' as measued fom plate is coectly shown by :- () () () (4) + K K d d d d lectic field, K s K < K so > 4. conducting sphee of adius is gien a chage. The electic potential and the electic field at the cente of the sphee espectiely ae :- () Zeo and 4 () 4 and Zeo () 4 and 4 (4) Both ae zeo ns. () t cente, & V 4 5

6 IMT-4 5. In a egion, the potential is epesented by V(x, y, z) 6x 8xy 8y + 6yz, whee V is in olts and x, y, z ae in metes. The electic foce expeienced by a chage of coulomb situated at point (,, ) is :- () 6 5 () () 4 (4) 4 5 V ˆ i V ˆ j V k ˆ x y z [(6 8y) î + ( 8x 8 + 6z) ĵ + (6y) ˆk ] t (,, ), i ˆ j ˆ 6kˆ ( ) Two cities ae 5 km apat. lectic powe is sent fom one city to anothe city though coppe wies. The fall of potential pe km is 8 olt and the aeage esistance pe km is.5. the powe loss in the wies is :- () 9. W () 9. kw () 9. J (4). kw ns. () esistance (.5/km) (5 km) 75 Total oltage dop (8 V/km) (5 km) V owe loss ( V) () 75 9 W 9. kw 7. The esistance in the two ams of the mete bidge ae 5 and, espectiely. When the esistance is shunted with an equal esistance, the new balance point is at.6. The esistance is :- 5 W 8. potentiomete cicuit has been set up fo finding the intenal esistance of a gien cell. The main battey used acoss the potentiomete wie, has an emf of. V and a negligible intenal esistance. The potentiomete wie itself is 4m long, When the esistace, connected acoss the gien cell, has alues of. (i) infinity (ii) 9.5 The balancing lengths', on the potentiomete wie ae found to be m and.85 m, espectiely. The alue of intenal esistance of the cell is ().5 ().95 ().5 (4).75 Intenal esistance, V V.85 (9.5) Following figues show the aangement of ba magnets in diffeent configuations. ach magnet has magnetic dipole moment m. Which configuation has highest net magnetic diple moment? (a) (c) (b) 6 () (a) () (b) () (c) (4) (d) (d) et magnetic moment Mcos G B () () 5 () (4) 5 ns. () and 5.6 /.6 which is maximumfo option (). In an ammete.% of main cuent passes though the galanomete. If esistance of galanomete is G, the esistance of ammete will be :- () 499 G () G () G 5 5 (4) 499 G

7 COD- I 998I I G. thin semicicula conducting ing () of adius is falling with its plane etical in a hoizontal magnetic field B, as shown in figue. The potential diffeence deeloped acoss the ing when its speed is, is :- B I 998I G G 499 Total esistance of mmete G F G 499 G G G 5 G 499. Two identical long conducting wies OB and COD ae placed at ight angle to each othe, with one aboe othe such that O is thei common point fo the two. The wies cay I and I cuents espectiely. oint is lying at distance d fom O along a diection pependicula to the plane containing the wies. The magnetic field at the point will be :- () I d I () (I I ) d () (I I ) d (4) (I I ) d et magnetic field, B B B I I d d d I I / () Zeo () B / and is at highe potnetial () B and is at highe potnetial (4) B and is at highe potential Induced emf B() B. tansfome haing efficiency of 9% is woking on V and kw powe supply. If the cuent in the seconday coil is 6, the oltage acoss the seconday coil and the cuent in the pimay coil espectiely ae :- () V, 5 () 45 V, 5 () 45V,.5 (4) 6V, 5 ns. () V I V I.9 V (6) V 45V s V I so I 5 4. Light with an enegy flux of 5 4 Wm falls on a pefectly eflecting suface at nomal incidence. If the suface aea is 5 cm, the aeage foce exeted on the suface is :- ().5 6 ().5 6 (). 6 (4). 6 ns. () eage foce F a p I t c

8 IMT-4 5. beam of light of 6 nm fom a distant souce falls on a single slit mm wide and the esulting diffaction patten is obseed on a sceen m away. The distance between fist dak finges on eithe side of the cental bight finge is :- (). cm (). mm ().4 cm (4).4 mm Width of cental bight finge 8. The angle of a pism is. One of its efacting sufaces is sileed. Light ays falling at an angle of incidence on the fist suface etuns back though the same path afte suffeing eflection at the sileed suface. The efactie index, of the pism is :- () sin () cos () cos (4) tan 8 6 D 6 m.4 m.4 mm 6. In the Young's double-slit expeiment, the intensity of light at a point on the sceen whee the path diffeence is is K, ( being the wae length of light used). The intensity at a poijnt whee the path diffeence is /4, will be :- () K () K/4 () K/ (4) Zeo Fo path diffeence, phase diffeence ad Fo path diffeence 4, phase diffeence ad s K 4I so intensity at gien point whee path diffeence is 4 K' 4I cos 4 I K 7. If the focal length of objectie lens is inceased then magnefying powe of :- () micoscope will incease but that of telescope decease. () micoscope and telescope both will incease. () micoscope and telescope both will decease (4) micoscope will decease but that of telescope incease. Magnifying powe of Micoscope f Magnifying powe of Telescope fe LD f f e ƒ ƒ ns. () 9 By nell's law () sin () sin cos 9. When the enegy of the incident adiation is incedased by %, the kinetic enegy of the photoelectons emitted fom a metal suface inceased fom.5 ev to.8 ev. The wok function of the metal is :- ().65 ev (). ev (). ev (4).5 ev ns. () By using h + K max We hae h (i) and.h (ii) Theefoe. ev 4. If the kinetic enegy of the paticle is inceased to 6 times its peious alue, the pecentage change in the de-boglie waelength of the paticle is :- () 5 () 75 () 6 (4) 5 ns. () l h mk K K 6K 4 K 4 75% 4

9 4. Hydogne atom is gound state is excited by a monochomatic adiation of 975 Å. umbe of spectal lines in the esulting spectum emitted will be () () () 6 (4) 4. The Binding enegy pe nucleon of 7 Li and 4 He nuclei ae 5.6 MeV and 7.6 MeV, espectiely. COD- 44. The gien gaph epesents V - I chaacteistic fo a semiconducto deice. I V B In the nuclea eaction 7 Li + H 4 He +, the alue of enegy eleased is :- () 9.6 MeV ().4 MeV () 8.4 MeV (4) 7. MeV B of He MeV 7 B of Li MeV 7 Li + H He 4 + He MeV 4. adio isotope 'X' with a half life.4 9 yeas decays to 'Y' which is stable. sample of the ock fom a cae was found to contain 'X' and 'Y' in the atio : 7. The age of the ock is : ().96 9 yeas ().9 9 yeas () 4. 9 yeas (4) yeas s x x 7 8 y x y so t T /.4 9 ys ys. Which of the following statement is coect? () It is V - I chaacteistic fo sola cell whee, point epesents open cicuit oltage and point B shot cicuit cuent. () It is a fo a sola cell and point and B epesent open cicuit oltage and cuent, espectiely. () It is fo a photodiode and points and B epesent open cicuit oltage and cuent, espectiely. (4) It is fo a LD and points and B epesent open cicuit oltage and shot cicuit cuent, espectiely. ns. () 45. The baie potential of a p-n junction depends on: (a) type of semi conducto mateial (g) amount of doping (c) tempeatue Which one of the following is coect? () (a) and (b) only () (b) only () (b) and (c )only (4) (a), (b) and (c) 9

Unit 6 Practice Test. Which vector diagram correctly shows the change in velocity Δv of the mass during this time? (1) (1) A. Energy KE.

Unit 6 Practice Test. Which vector diagram correctly shows the change in velocity Δv of the mass during this time? (1) (1) A. Energy KE. Unit 6 actice Test 1. Which one of the following gaphs best epesents the aiation of the kinetic enegy, KE, and of the gaitational potential enegy, GE, of an obiting satellite with its distance fom the