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Quesions and Soluions Tes Bookle Code - C PAPE - : MATHEMATICS, PHYSICS & CHEMISTY PAT- A : MATHEMATICS sin x sin x.

() e sin x e -sin x 4 Le e sin x 4 4 4 6 4 5 e sin x + 5 No possible [.7 < e <.8] e sin x 5 No possible [Neve Negaive].

If he vecos c aˆ b ˆ and d 5aˆ 4b ˆ ae pependicula o each ohe, hen he angle beween â and ˆb is : () 6 () () (4) 4.

1 Quesions and Soluions Tes Bookle Code - C PAPE - : MATHEMATICS, PHYSICS & CHEMISTY PAT- A : MATHEMATICS sin x sin x. The equaion e e 4 has : () infinie nube of eal oos () no eal oos () exacly one eal oo (4) exacly fou eal oos. () e sin x e -sin x 4 Le e sin x e sin x + 5 No possible [.7 < e <.8] e sin x 5 No possible [Neve Negaive]. Le â and ˆb be wo uni vecos. If he vecos c aˆ b ˆ and d 5aˆ 4b ˆ ae pependicula o each ohe, hen he angle beween â and ˆb is : () 6 () () (4) 4. () cd (a b) (5a 4b) 5 6a b 8 ab a b cos cos. A spheical balloon is filled wih 45 cubic ees of heliu gas. If a leak in he balloon causes he gas o escape a he ae of 7 cubic ees pe inue, hen he ae (in ees pe inue) a which he adius of he balloon deceases 49 inues afe he leakage began is : () 9/7 () 7/9 () /9 (4) 9/ (Pg. )

2 . () dv 4 d d d 7 d 8 d () 4 Also, d d /inue AIEEE Pape and Soluion () 4. Saeen : The su of he seies + ( + + 4) + ( ) + ( ) + + ( ) is 8. Saeen : n k k (k ) n, fo any naual nube n. () Saeen is false, Saeen is ue. () Saeen is ue, Saeen is ue; Saeen is a coec explanaion fo Saeen. () Saeen is ue, Saeen is ue; Saeen is no a coec explanaion fo saeen. (4) Saeen is ue, Saeen is false. 4. () Saeen : n K (K ) K n(n ) n(n ) n Saeen is coec Saeen : ( ) + ( ) + ( ) + ( 9) 8 Saeen is coec and saeen explain saeen 5. The negaion of he saeen "If I becoe a eache, hen I will open a school", is : () I will becoe a eache and I will no open a school. () Eihe I will no becoe a eache o I will no open a school. () Neihe I will becoe a eache no I will open a school. (4) I will no becoe a eache o I will open a school. 5. () 6. If he inegal 5an x dx x a n sin x cos x k an x hen a is equal o : () () () (4) (Pg. )

3 () VIDYALANKA : AIEEE Pape and Soluion 6. (4) 5anx dx x + a ln sin x cos x + K anx Diffeeniaing on boh side 5an x a[cosx sinx] + an x sin x cos 5sinx sinx cosx a(cosx sinx) sinx cosx sin x cosx Equaing co-efficien of boh side 5 a, a a sin x cos x 7. Saeen : An equaion of a coon angen o he paabola x + y 4 is y x +. y 6 x and he ellipse 4 Saeen : If he line y x, ( ) is a coon angen o he paabola y 6 x and he ellipse x + y 4, hen saisfies () Saeen is false, Saeen is ue. () Saeen is ue, Saeen is ue, Saeen is a coec explanaion fo Saeen. () Saeen is ue, Saeen is ue, Saeen is no a coec explanaion fo Saeen. (4) Saeen is ue, Saeen is false. 7. () Pu y 4 x in x y 4 4 x x y x x 8 x 4 is a angen, disciinan of he above quadaic equaion us be zeo ( + 6) ( 4) Saeen () is a coec explanaion of saeen (). 8. Le A. u + u is equal o : () If u and u ae colun aices such ha Au () () (4) and Au, hen (Pg. )

4 8. (4) AU U a b c a a b a b c a ; b ; c AIEEE Pape and Soluion (4) AU x y z x x y x y z U U + U x ; y ; z 9. If n is a posiive inege, hen 9. () + n n is : () an iaional nube () an odd posiive inege () an even posiive inege (4) a aional nube ohe han posiive ineges n n n n n n...n C C Cn which is Iaional Nube. If ies he h e of an AP wih non zeo coon diffeence equals he 5 ies is 5 h e, hen he 5 h e of his AP is : () 5 () 5 ies is 5 h e () 5 (4) zeo (Pg. 4)

5 (5) VIDYALANKA : AIEEE Pape and Soluion. (4) Le fis e a and coon diffeence d [a + 99 d] 5 [a + 49 d] a 49 d Now, T 5 a + 49 d T 5. In a PQ, if sin P + 4 cos Q 6 and 4 sin Q + cos P, hen he angle is equal o : () 5 6 () 6 () 4 (4) 4. () P + Q + sin P + 4 cos Q 6. (i) 4 sin Q + cos P. (ii) squaing and adding (i) and (ii) sin (P + Q) 7 sin (P + Q) P + Q 6 ; 5 6 if P + Q 6 < sin P < and < cos Q < while violae saeen sin P + 4 cos Q 6. An equaion of a plane paallel o he plane x y + z 5 and a a uni disance fo he oigin is : () x y + z () x y + z + () x y + z (4) x y + z + 5. () Equaion of plane paallel o he plane x y + z 5 is x y + z + Disance fo (, ) is x y + z, o. If he line x + y k passes hough he poin which divides he line segen joining he poins (, ) and (, 4) in he aio :, hen k equals : () 9/5 () 5 () 6 (4) /5 (Pg. 5)

6 AIEEE Pape and Soluion (6). () Co odinae of p O 4, , 5 5 Saisfying he equaion x + y k k (, ) x + y k 'O' (, 4) 5 k k 6 4. Le x, x,,x n be n obsevaions, and le x be hei aiheic ean and Saeen : Vaiance of x, x,,x n is 4. be hei vaiance. Saeen : Aiheic ean of x, x,,x n is 4x. () Saeen is false, Saeen is ue. () Saeen is ue, Saeen is ue, Saeen is a coec explanaion fo Saeen. () Saeen is ue, Saeen is ue, Saeen is no a coec explanaion fo Saeen. (4) Saeen is ue, Saeen is false. 4. (4) Saeen is false because Aheic ean of x x x... xn n x. 5. The populaion p() a ie of a ceain ouse species saisfies he diffeenial equaion dp().5 p() 45. If p() 85, hen he ie a which he populaion becoes zeo is : d () n8 () n9 () n8 5. () d P().5 P() 45 d I.F P() e P() e e.5 d 45 e d 9 e c e A c c 5 P() e 9 e (4) n8 (Pg. 6)

7 (7) VIDYALANKA : AIEEE Pape and Soluion The ie of which P() is 9 e e 8 n 8 n 8 6. Le a, b be such ha he funcion f given by f(x) values a x and x. Saeen : f has local axiu a x and a x. n x bx ax, x has exee Saeen : a and b. 4 () Saeen is false, Saeen is ue. () Saeen is ue, Saeen is ue, Saeen is a coec explanaion fo Saeen. () Saeen is ue, Saeen is ue, Saeen is no a coec explanaion fo Saeen. (4) Saeen is ue, Saeen is false. 6. () f (x) x bx a bx + ax + a b + and b a, b 4 Also, f "(x) < x x x and ae poins of axia. ( )() 7. The aea bounded beween he paabolas () () y x 4 and x 9y, and he saigh line y is : () (4) 7. () A y 9y dy dy 4 5 y dy x y 4 x 9y (Pg. 7)

8 AIEEE Pape and Soluion (8) 8. Assuing he balls o be idenical excep fo diffeence in colous, he nube of ways in which one o oe balls can be seleced fo whie, 9 geen and 7 black balls is : () 88 () 69 () 6 (4) (4) No. of ways ( + ) (9 + ) (7 + ) If f : is a funcion defined by f(x) [x] cos inege funcion, hen f is : () coninuous fo evey eal x. () disconinuous only a x. () disconinuous only a non-zeo inegal values of x. (4) coninuous only a x. x, whee [x] denoes he geaes 9. () f(x) [x]cos x [x]sin ( x) which is coninuous fo all x A n I, li [x] sin ( x) [n] sin ( n) x n. If he lines x y z 4 () () 9 and x y k z () 9 inesec, hen k is equal o : (4). () If wo lines a b and a b inesec, hen a a b b a a b b K 4 ( 5) (K + ) + (4K ) K 6 + 4K + 7 K 9. Thee nubes ae chosen a ando wihou eplaceen fo {,,,, 8}. The pobabiliy ha hei iniu is, given ha hei axiu is 6, is : () /8 () /5 () /4 (4) /5. () Le x Miniu is y Maxiu is 6 x P y 5 C 5 (Pg. 8)

9 (9) VIDYALANKA : AIEEE Pape and Soluion z. If z and is eal, hen he poin epesened by he coplex nube z lies: z () eihe on he eal axis o on a cicle passing hough he oigin. () on a cicle wih cene a he oigin. () eihe on he eal axis o on a cicle no passing hough he oigin. (4) on he iaginay axis.. () Le Then z x + iy (x iy) (x iy) K, K (x y Kx + K) + i(x K)y x y Kx + K () and y(x K) () y o x x + y y o (x ) + y. Le P and Q be aices wih P Q. If P Q and P Q Q P, hen deeinan of (P + Q ) is equal o : () () () (4). () P Q (i) Q P P Q (ii) (i) + (ii) P + Q P Q + P Q P(P + Q ) Q(Q + P ) (P Q)(P + Q ) de. (P + Q ) ( P Q ) 4. If g(x) () g(x) g( ) x cos 4 d, hen g(x + ) equals : () g(x) g( ) () g(x) g( ) (4) g(x). g( ) 4. (), () g(x + ) x x x cos(4)d cos(4)d cos(4)d x g(x) + cos(4)d g(x) g( ) Bu since g( ), g(x) g( ) is also a coec opion. 5. The lengh of he diaee of he cicle which ouches he x-axis a he poin (, ) and passes hough he poin (, ) is : () / () /5 () 6/5 (4) 5/ (Pg. 9)

10 5. () If cicle ouches x axis a (, ) hen cene of he cicle will be (, ), whee is adius of he cicle ( ) + ( ) (, ) (, ) AIEEE Pape and Soluion () (, ) Diaee 6. Le X {,,, 4, 5}. The nube of diffeen odeed pais (Y, Z) ha can be foed such ha Y X, Z X and Y Z is epy, is : () 5 () 5 () 5 (4) 5 6. () Nube of diffeen odeed pais 5 ( Evey eleen has opions, eihe i can be in y bu no in z, o i can be in z bu no in y o in neihe of y o z) 7. An ellipse is dawn by aking a diaee of he cicle (x ) + y as is sei-ino axis and a diaee of he cicle x + (y ) 4 as is sei-ajo axis. If he cene of he ellipse is a he oigin and is axes ae he coodinae axis, hen he equaion of he ellipse is : () 4x + y 4 () x + 4y 8 () 4x + y 8 (4) x + 4y 6 7. (none of hese) Equaion of ellipse is 4x + y 6 x y 4 (,) (,) (,) 8. Conside he funcion, f(x) x x 5, x. Saeen : f (4) Saeen : f is coninuous in [, 5], diffeeniable in (, 5) and f() f(5). () Saeen is false, saeen is ue. () Saeen is ue, saeen is ue; saeen is a coec explanaion fo saeen. () Saeen is ue, saeen is ue; saeen is no a coec explanaion fo saeen. (4) Saeen is ue, saeen is false. 8. () By olle's heoe, Saeen is ue. Bu by olle's heoe, we can no conclude ha f (4) f (4) because f(x) is a consan funcion in [, 5]. (Pg. )

11 () VIDYALANKA : AIEEE Pape and Soluion 9. A line is dawn hough he poin (, ) o ee he coodinae axes a P and Q such ha i fos a iangle OPQ, whee O is he oigin. If he aea of he iangle OPQ is leas, hen he slope of he line PQ is : () /4 () 4 () (4) / 9. () Le he line passing hough (, ) be x y a b b a a b b Aea of iangle, A ab b b (b ) da (b )b b db (b ) b 4 and a ; Hence slope b, 4. Le ABCD be a paalleloga such ha AB q, AD p and BAD be an acue angle. If is he veco ha coincides wih he aliude dieced fo he veex B o he side AD, hen is given by () p q q- pp p () pq q p p p () pq q p p p (4) p q q pp p. () p and q p q p p p p qp pp So, p q q p q + p p p PAT- B : PHYSICS. A wooden wheel of adius is ade of wo seicicula pas (see figue). The wo pas ae held ogehe by a ing ade of a eal sip of coss secional aea S and lengh L. L is slighly less han. To fi he ing on he wheel, i is heaed so ha is epeaue ises by T and i jus seps ove he wheel. As i cools down o suounding epeaue, i pesses he seicicula pas ogehe. If he coefficien of linea expansion of he eal is, and is Young's odulus is Y, he foce ha one pa of he wheel applies on he ohe pa is : () SY T () SY T () SY T (4) SY T (Pg. )

12 . (4) L. T AIEEE Pape and Soluion () Sain T Sess Y. sain Y. T F S Y T F S Y T Foce will be exeed on boh side. Foce SY T. The figue shows an expeienal plo fo dischaging of a capacio in an C cicui. The ie consan of his cicui lies beween :. (4) () 5 sec and sec () and 5 sec () 5 sec and sec (4) sec and 5 sec In an ie consan poenial will dop o 7% of axiu volage i.e. will becae V Fo gaph i is clea, i will happen beween s o 5s.. In a unifoly chaged sphee of oal chage Q and adius, he elecic field E is ploed as a funcion of disance fo he cene. The gaph which would coespond o he above will be () () () (4). () Inside he sphee E ( adial disance fo he cene) Ouside he sphee E 4. An elecoagneic wave in vacuu has he elecic and agneic fields E and B, which ae always pependicula o each ohe. The diecion of polaizaion is given by X and ha of wave popagaion by k. Then : () X B and k B E () X E and k E B () X B and k E B (4) X E and k B E (Pg. )

13 () VIDYALANKA : AIEEE Pape and Soluion 4. () X E and K E B 5. If a siple pendulu has significan apliude (up o a faco of /e of oiginal) only in he peiod beween s o s, hen ay be called he aveage life of he pendulu. When he spheical bob of he pendulu suffes a eadaion (due o viscous dag) popoional o is velociy, wih 'b' as he consan of popoionaliy, he aveage life ie of he pendulu is (assuing daping is sall) in seconds : ().69 b () b () b (4) b 5. (4) The equaion of oion is ha of a daped haonic oscillao :... b. Soluion of his equaion is of he fo : b e sin( ' ). Thus : apliude becoes e afe a ie b 6. Hydogen ao is excied fo gound sae o anohe sae wih pincipal quanu nube equal o 4. Then he nube of specal lines in he eission speca will be : () () () 5 (4) 6 6. (4) No. of specal lines n(n ), hee n 4 7. A coil is suspended in a unifo agneic field, wih he plane of he coil paallel o he agneic lines of foce. When a cuen is passed hough he coil i sas oscillaing; i is vey difficul o sop. Bu if an aluiniu plae is placed nea o he coil, i sops. This is due o : () developen of ai cuen when he plae is placed. () inducion of elecical chage on he plae () shielding of agneic lines of foce as aluiniu is a paaagneic aeial (4) elecoagneic inducion in he aluiniu plae giving ise o elecoagneic daping 7. (4) Eddy cuen ae induced in aluinu agneic field due o which opposes he oscillaion of he coil. 8. The ass of spaceship is kg. I is o be launched fo he eah's suface ou ino fee space. The value of 'g' and '' (adius of eah) ae /s and 64 k especively. The equied enegy fo his wok will be : () 6.4 Joules () Joules () Joules (4) 6.4 Joules 8. (4) equied enegy whee V e g Ve equied enegy g g J (Pg. )

14 9. Heliu gas goes hough a cycle ABCDA (consising of wo isochoic and wo isobaic lines) as shown in figue. Efficiency of his cycle is nealy : (Assue he gas o be close o ideal gas) () 5.4% () 9.% ().5% (4).5% 9. () AIEEE Pape and Soluion (4) W Qin W Aea unde he cuve P V Q AB nc V T f n T Q BC nc P T f n T Q CD < Q DA < PV 5 (P V ) 5 P V Q in 5 P V PV PV (%) 5.4% PV 4. In Young's double sli expeien, one of he sli is wide han ohe, so ha he apliude of he ligh fo one sli is double of ha fo ohe sli. If I be he axiu inensiy, he esulan inensiy I when hey inefee a phase diffeence is given by : () I 9 (4 5cos ) () I cos () I 4cos 5 (4) I 8cos 9 4. (4) I A I KA I (say) I K(A) 4I I I + I + II cos I + 4I + () (I ) cos 5I + 4I cos I [ + 4( + cos )] I I [ + 8 cos /].() And, I I + 4I + (I ) cos I 9 I (Pg. 4)

15 (5) VIDYALANKA : AIEEE Pape and Soluion I I 9 fo equaion (), I I 9 [ + 8 cos /] 4. A liquid in a beake has epeaue () a ie and is epeaue of suoundings, hen accoding o Newon's law of cooling he coec gaph beween log e ( ) and is : () () () (4) 4. () Newon's Law of Cooling, dv K( ) d dv K d n( ) K + C I epesens equaion of saigh line in n( ) Vs plo. 4. A paicle of ass is a es a he oigin a ie. I is subjeced o a foce F() F e b in he x diecion. Is speed v() is depiced by which of he following cuves? () () () (4) 4. () dv d F e b v dv v F e F b F b b e d b b e (Pg. 5)

16 F v e b a, v a, v F b b F b AIEEE Pape and Soluion (6) 4. Two elecic bulbs aked 5 W V and W V ae conneced in seies o a 44 V supply. Which of he bulbs will fuse? () boh () W () 5 W (4) neihe 4. () P V V Which is oe han V. 5 W bulb will fuse esisance of a given wie is obained by easuing he cuen flowing in i and he volage diffeence applied acoss i. If he pecenage eos in he easueen of he cuen and he volage diffeence ae % each, hen eo in he value of esisance of he wie is : () 6% () zeo () % (4) % 44. () V I V V 4 I + 6%. I 45. A boy can how a sone up o a axiu heigh of. The axiu hoizonal disance ha he boy can how he sae sone up o will be : () () () (4) 45. (4) Accoding o boy's own capabiliy, les assue ha he axiu speed wih which he can how a ball is u, hen v u + as u gh u gh /s Now, fo axiu hoizonal ange 45 h v u? ax u g u 45 (Pg. 6)

(7) VIDYALANKA : AIEEE Pape and Soluion 46. This quesion has Saeen and Saeen. Of he fou choices given afe he Saeens, choose he one ha bes descibes he wo Saeens.

17 (7) VIDYALANKA : AIEEE Pape and Soluion 46. This quesion has Saeen and Saeen. Of he fou choices given afe he Saeens, choose he one ha bes descibes he wo Saeens. Saeen : Davisson Gee expeien esablished he wave naue of elecons. Saeen : If elecons have wave naue, hey can inefee and show diffacion. () Saeen is false, Saeen is ue. () Saeen is ue, Saeen is false () Saeen is ue, Saeen is ue, Saeen is he coec explanaion fo Saeen (4) Saeen is ue, Saeen is ue, Saeen is no he coec explanaion of Saeen 46. () 47. A hin liquid fil foed beween a U shaped wie and a ligh slide suppos a weigh of.5 N (see figue). The lengh of he slide is c and is weigh negligible. The suface ension of he liquid fil is : ().5 N (). N ().5 N (D).5 N 47. (4) Suface ension g.5 D.5 N/ 48. A chage Q is unifoly disibued ove he suface of non conducing disc of adius. The disc oaes abou an axis pependicula o is plane and passing hough is cene wih an angula velociy. As a esul of his oaion a agneic field of inducion B is obained a he cene of he disc. If we keep boh he aoun of chage placed on he disc and is angula velociy o be consan and vay he adius of he disc hen he vaiaion of he agneic inducion a he cene of he disc will be epesened by he figue : () () () (4) 48. () i di d i d di i db (di) i d db i d B B B i i d i ( ) B di d di (Pg. 7)

() GATE : AB GATE : A A B GATE : B A B Y ( A A B) ( B A B) {using A B A B and A B A B} Y (A (A B))

B Y 5. A ada has a powe of kw and is opeaing a a fequency of GHz.

The axiu disance upo which i can deec objec locaed on he suface of he eah (adius of eah 6.

18 AIEEE Pape and Soluion (8) 49. Tuh able fo syse of fou NAND gaes as shown in figue is : () () () (4) 49. () GATE : AB GATE : A A B GATE : B A B Y ( A A B) ( B A B) {using A B A B and A B A B} Y (A (A B)) ( B (A B)) (A A A B)) ( B A B B)) {since A A B B } Y ( A B) ( A B) (A B) (A B) Y (A B) (A B) So, A B Y 5. A ada has a powe of kw and is opeaing a a fequency of GHz. I is locaed on a ounain op of heigh 5. The axiu disance upo which i can deec objec locaed on he suface of he eah (adius of eah ) () 8 k () 6 k () 4 k (4) 64 k 5. () Maxiu disance d d d k h 5. Assue ha a neuon beaks ino a poon and an elecon. The enegy eleased duing his pocess is : (Mass of neuon kg Mass of poon kg Mass of elecon 9 kg) ().7 MeV () 7. MeV () 6. MeV (4) 5.4 MeV (Pg. 8)

19 (9) VIDYALANKA : AIEEE Pape and Soluion 5. () ( e + p ) ( ) e p.676 n kg kg 7 kg 7 kg E ( ) C.95 ( 8 ).55 Joules.55 ev 9.6 E.78 MeV 5. A Cano engine, whose efficiency is 4%, akes in hea fo a souce ainained a a epeaue of 5 K. I is desied o have an engine of efficiency 6%. Then, he inake epeaue fo he sae exhaus (sink) epeaue us be : () efficiency of Cano engine canno be ade lage han 5% () K () 75 K (4) 6 K 5. () Efficiency of Cano engine opeaing beween T C and T M is given by TC T M In fis case :.4 : T M 5 K T.4 C T C.6 5 K 5 Fo a desied efficiency of.6 : T C K.6.4 T M T M T M 75 K 4 5. This quesion has Saeen and Saeen. Of he fou choices given afe he Saeens, choose he one ha bes descibes he wo Saeens. I wo spings S and S of foce consans k and k, especively, ae seched by he sae foce, i is found ha oe wok is done on sping S han on sping S. Saeen : If seched by he sae aoun, wok done on S, will be oe han ha on S Saeen : k < k () Saeen is false, Saeen is ue. () Saeen is ue, Saeen is false () Saeen is ue, Saeen is ue, Saeen is he coec explanaion of Saeen (4) Saeen is ue, Saeen is ue, Saeen is no he coec explanaion of Saeen. 5. () Since he applied foce is sae and exension is also occuing o saeen ; wok done on boh going is of sae. Hence saeen canno be ue. 54. Two cas of asses and ae oving in cicles of adii and, especively. Thei speeds ae such ha hey ake coplee cicles in he sae ie. The aio of hei cenipeal acceleaion is : () : () : () : (4) : (Pg. 9)

20 54. () v v.. v a v a v v AIEEE Pape and Soluion () 55. A cylindical ube, open a boh ends, has a fundaenal fequency f, in ai. The ube is dipped veically in wae so ha half of i is wae. The fundaenal fequency of he ai colun is now: () f () f () f 4 (4) f 55. () Fundaenal fequency eains consan sae. 56. An objec.4 in fon of a lens fos a shap iage on a fil c behind he lens. A glass plae c hick, of efacive index.5 is ineposed beween lens and fil wih is plane faces paallel o fil. A wha disance (fo lens) should objec be shifed o be in shap focus on fil? () 7. ().4 (). (4) [4] In case wihou glass plae : u.4 v +.. (.4) f f Inoducing he glass plae ; The shif in posiion of iage due o plae c Thus he iage would be foed a 5 c fo lens had he plae been absen. 5 v v v v c 5.6. (Pg. )

21 () VIDYALANKA : AIEEE Pape and Soluion 57. A diaoic olecule is ade of wo asses and which ae sepaaed by a disance. If we calculae is oaional enegy by applying Boh's ule of angula oenu quanizaion, is enegy will be given by : (n is an inege) () n h () nh () n h (4) n h 57. (4) I I oaional Enegy L I k ; c 58. A specoee gives he following eading when used o easue he angle of a pis. Main scale eading : 58.5 degee Venie scale eading : 9 divisions Given ha division on ain scale coesponds o.5 degee. Toal divisions on he venie scale is and ach wih 9 divisions of he ain scale. The angle of he pis fo he above daa : () degee () degee () degee (4) 59 degee 58. () Leas coun.5 o o.5 Coec Angle o o This quesion has Saeen and Saeen. Of he fou choices given afe he Saeens, choose he one ha bes descibes he wo Saeens. An insulaing solid sphee of adius has a unifoly posiive chage densiy. As a esul of his unifo chage disibuion hee is a finie value of elecic poenial a he cene of he sphee, a he suface of he sphee and also a a poin ou side he sphee. The elecic poenial a infiniy is zeo. Saeen : When a chage 'q' is aken fo he cene o he suface of he sphee, is poenial qp enegy changes by. Saeen : The elecic field a a disance ( < ) fo he cene of he sphee is () Saeen is ue, Saeen is ue; Saeen is no he coec explanaion of Saeen. () Saeen is ue Saeen is false. () Saeen is false Saeen is ue (4) Saeen is ue, Saeen is ue, Saeen is coec explanaion of Saeen (Pg. )

22 59. () Using gauss' law : p 4 E 4 p E Saeen is coec. Saeen is diensionally incoec. AIEEE Pape and Soluion () 6. Poon, Deueon and alpha paicle of he sae kineic enegy ae oving in cicula ajecoies in a consan agneic field. The adii of poon, deueon and alpha paicle ae especively p, d and. Which one of he following elaions is coec? () p d () p < d () > d > p (4) d > p 6. () V qb v V P P K K K qb q q < D ; D q ; 4 q PAT- C : CHEMISTY 6. Which aong he following will be naed as diboidobis ( ehylene diaine) choiu (III) boide? () [C(en) ]B () [C(en) B ]B () [C(en)B 4 ] (4) [C(en)B ]B 6. () Bis (ehylene diaine) eans wo ehylene diaine ligands; diboido eans B Ligands. Only opion fis his descipion. 6. Which ehod of puificaion is epesened by he following equaion : 5 K 7 K Ti(s) I(g) Ti I4(g) Ti (s) (g) () Zone efining () Cupellaion () Poling (4) Van Akel 6. (4) The eacion sequence given in he poble is he Van Akel ehod of efining/puificaion of Ti eal. 6. Lihiu fos body cened cubic sucue. The lengh of he side of is uni cell is 5 p. Aoic adius of he lihiu will be : () 75 p () p () 4 p (4) 5 p (Pg. )

23 () VIDYALANKA : AIEEE Pape and Soluion 6. (4) Fo B.C.C. 4 a a p 64. The olecule having salles bond angle is : () NCl () AsCl () SbCl (4) PCl 64. () The salles bond angle is in SbCl 65. Which of he following copounds can be deeced by Molisch s es? () Nio copounds () Sugas () Aines (4) Piay alcohols 65. () Sugas ae deeined by Molisch s es 66. The incoec expession aong he following is : Gsyse Vf () T () In isoheal pocess, w evesible nt ln Soal Vi H T S G () lnk (4) K e T 66. () G sys T S Toal is ue In isoheal pocess, W ev nt n v v is coec T n K G T S H which is given incoec k e G /T is a coec foula 67. The densiy of a soluion pepaed by dissolving g of uea (ol. ass 6 u) in g of wae is.5 g/l. The olaiy of his soluion is : ().5 M ().78 M (). M (4).5 M 67. (4) Molaiy M n V soluion soluion W W d M V M W s s soluion s Soluion s soluion M 68. The species which can bes seve as an iniiao fo he caionic polyeizaion is : () LiAlH 4 () HNO () AlCl (4) BuLi 68. () Caionic polyeizaion equies acid caalys. (Pg. )

24 AIEEE Pape and Soluion (4) 69. Which of he following on heal decoposiion yields a basic as well as an acidic oxide? () NaNO () KClO () CaCO (4) NH 4 NO 69. () CaCO on decoposiion gives CaO which is basic and CO which is acidic. 7. The sandad educion poenials fo Zn + / Zn, Ni + / Ni, and Fe + / Fe ae.76,. and.44 V especively. The eacion X + Y + X + + Y will be sponaneous when : () X Ni, Y Fe () X Ni, Y Zn () X Fe, Y Zn (4) X Zn, Y Ni 7. (4) ) Ni + Fe + Ni + + Fe E cell Ecahode E anode E E Fe /Fe Ni /Ni.44 (.) < ; so non sponaneous ) Ni + Zn + Ni + + Zn E cell E E Zn /Zn Ni /Ni.76 (.).7 +. < ; so non sponaneous Theefoe (4) is sponaneous. Which in Zn + Ni + Ni + Zn + 7 Accoding o Feundlich adsopion isohe, which of he following is coec? x () p x () p x / n () p (4) All he above ae coec fo diffeen anges of pessue. 7. (4) x p n A n ; x n ; x p a n ; x p n. p (Pg. 4)

25 (5) VIDYALANKA : AIEEE Pape and Soluion 7. The equilibiu consan (K c ) fo he eacion N(g) O(g) NO (g) a epeaue T is 4 4. The value of K c fo he eacion, NO(g) N(g) O(g) a he sae epeaue is : (). ().5 () 4 4 (4) (4) N (g) + O (g) NO KC KC NO N O K C NO : K C N + O : K C : K C 7. The copessibiliy faco fo a eal gas a high pessue is : () + T / pb () () + pb / T (4) pb / T 7. () K C K C an P (V nb) V PV nt + Pnb Z + Pb T nt a high pessue, an V 74. Which one of he following saeens is coec? () All aino acids excep lysine ae opically acive. () All aino acids ae opically acive. () All aino acids excep glycine ae opically acive (4) All aino acids excep gluaic acid ae opically acive. 74. () NH CH COOH (glycine) which does no conain chial cabon. 75. Aspiin is known as : () Aceyl salicylic acid () Phenyl salicylae () Aceyl salicylae (4) Mehyl salicylic acid 75. () OCOCH COOH ; aceyl salicylic acid (Aspiin) (Pg. 5)

26 AIEEE Pape and Soluion (6) 76. Oho Niophenol is less soluble in wae han p and Niophenols because : () o Niophenol is oe volaile in sea han hose of and p isoes () o Niophenol shows Inaolecula H bonding () o Niophenol shows Ineolecula H bonding (4) Meling poin of o Niopehnol is lowe han hose of and p isoes. 76. () O H N O O Inaolcula hydogen bonding 77. How any chial copounds ae possible on onochloinaion of ehyl buane? () 8 () () 4 (4) () Cl / hv Cl + * d Cl + d * Cl + Cl 78. Vey pue hydogen (99.9 %) can be ade by which of he following pocesses? () eacion of ehane wih sea () Mixing naual hydocabons of high olecula weigh () Elecolysis of wae (4) eacion of sal like hydides wih wae 78. () Vey pue (99.9 %) hydogen is ade by elecolysis of wae. 79. The elecons idenified by quanu nubes n and : (a) n 4, l (b) n 4, l (c) n, l (d) n, l can be placed in ode of inceasing enegy as : () (c) < (d) < (b) < (a) () (d) < (b) < (c) < (a) () (b) < (d) < (a) < (c) (4) (a) < (c) < (b) < (d) 79. () Enegy of an elecon in an obial depends on (n + ) su. Lowe he (n + ) value lowe is he enegy and if (n + ) value is sae, lowe n eans lowe enegy. Applying hese ules we ge E d < E b < E c < E a. Thus opion is coec. 8. Fo a fis ode eacion, (A) poducs, he concenaion of A changes fo. M o.5 M in 4 inues. The ae of eacion when he concenaion of A is. M, is : ().7 5 M / in ().47 4 M / in ().47 5 M / in (4).7 4 M / in (Pg. 6)

27 (7) VIDYALANKA : AIEEE Pape and Soluion 8. (). a k log a x dx d.. log 4.5. log 4 4. log 4 k(a) whee A (A x) M / in Ion exhibis + and + oxidaion saes. Which of he following saeens abou ion is incoec? () Feous oxide is oe basic in naue han he feic oxide. () Feous copounds ae elaively oe ionic han he coesponding feic copounds. () Feous copounds ae less volaile han he coesponding feic copounds. (4) Feous copounds ae oe easily hydolysed han he coesponding feic copounds. 8. (4) Fe + is a hade acid as copaed o Fe +. Thus i would pefe OH as a ligand copaed o wae. Thus, Fe + copounds ae oe easily hydolyzed. Opion (4) is coec. 8. The ph of a. ola soluion of he acid HQ is. The value of he ionizaion consan, Ka of his acid is : () () () 5 (4) 7 8. () HQ H Q K a C (C ) [H ] C C ph [H + ] K a [ ] Which banched chain isoe of he hydocabon wih olecula ass 7u gives only one isoe of ono subsiued alkyl halide? () Teiay buyl chloide () Neopenane () Isohexane (4) Neohexane 8. () 4n + 7 n 5 C 5 H CH CH Cl /h H C C CH H C C CH Cl CH CH (Pg. 7)

28 AIEEE Pape and Soluion (8) 84. K f fo wae is.86 K kg ol. If you auoobile adiao holds. kg of wae, how any gas of ehylene glycol (C H 6 O ) us you add o ge he feezing poin of he soluion loweed o.8 C? () 7 g () 9 g () 9 g (4) 7 g 84. () T f k f Ws k f M W s Soluion T M W k s f s Soluion f 9.9 M.W. (C H 6 O ) Wha is DDT aong he following : () Geenhouse gas () A feilize () Biodegadable polluan (4) Non biodegadable polluan 85. (4) Facual 86. The inceasing ode of he ionic adii of he given isoeleconic species is : () Cl, Ca +, K +, S () S, Cl, Ca +, K + () Ca +, K +, Cl, S (4) K +, S, Ca +, Cl 86. () Fo isoeleconic species lowe he aoic nube, he highe ionic adius. Thus inceasing ode of size is Ca + < K + < Cl < S. Opion is coec. 87. Hexyne gives ans Hexene on eaen wih : () P / H () Li / NH () Pd / BaSO 4 (4) Li AlH () H Li/ NH H C C C CH CH CH CH C C CH CH CH H (ans.) 88. Iodofo can be pepaed fo all excep : () Ehyl ehyl keone () Isopopyl alcohol () Mehyl buanone (4) Isobuyl alcohol 88. (4) CH CH CH OH ; Isobuyl alcohol does no give iodofo es CH 89. In which of he following pais he wo species ae no isosucual? () CO and NO () PCl 4 and SiCl 4 () PF 5 and BF 5 (4) AlF 6 and SF 6 (Pg. 8)

29 (9) VIDYALANKA : AIEEE Pape and Soluion 89. () The sucue of polyaoic olecule/ion is deeined by he nube of valence elecon pais aound he cenal ao. In PF 5 valence elecon pais ae 5 while in BF 5 he nube is 6. Hence, hey ae no isosucual. Opion is coec. 9. In he given ansfoaion, which of he following is he os appopiae eagen? () NH NH,OH () Zn Hg / HCl () Na, Liq. NH (4) NaBH 4 9. () CH CH COCH CH CH CH CH HN NH HO HO (Pg. 9)

Prerna Tower, Road No 2, Contractors Area, Bistupur, Jamshedpur , Tel (0657) , PART A PHYSICS

Prerna Tower, Road No 2, Contractors Area, Bistupur, Jamshedpur , Tel (0657) , PART A PHYSICS Pena Towe, oad No, Conacos Aea, isupu, Jamshedpu 83, Tel (657)89, www.penaclasses.com AIEEE PAT A PHYSICS Physics. Two elecic bulbs maked 5 W V and W V ae conneced in seies o a 44 V supply. () W () 5 W