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IIT-JEE/AIEEE/PET- 2012 SAMPLE-PAPER All India Test Series

KOTA STUDY CIRCLE PAGE # 1

1. A non-conducting sphere of radius 10 cm is givenc6 charge. The intensity of electric field at a

distance of 5 cm from the centre will be

(a) Zero (b) 51027 V/m

(c) 51027 V/m (d) 51072 V/m

2. Charges 2q, q, and -q lie at the vertices of atriangle. The value of E and V at the centroid of thetriangle will be

(a) E 0 and V 0 (b) E = 0 and V = 0

(c) E 0 and V = 0 (d) E = 0 and V 0

3. Two uniformly charged similar balls A and B repel

each other with a force of 5102 N. A third similaruncharged ball C is touched to A and then placed at

the mid-point of A and B. The resultant force on Cwill be

(a) Zero

(b) 5102 from C towards A

(c) 5102 N from C towards B

(d) 5103 N from C towards A

4. Three dielectric materials are filled in a parallelplate condenser as shown in the figure. A potentialdifference is applied between the plates of the

condenser. If the area ofeach plate is S anddistance between parallelplates is d then thecapacity between thepoint X and Y will be

(a)

32

3210

KK

KK

2

KS

d(b)

d

S0

(c)d

KKSK 3210 (d)d

KSK 320

5. A parallel plate condenser is connected to a batteryof e.m.f 4 volt. If a plate of dielectric constant 8 isinserted into it, then the potential difference on thecondenser will be

(a)2

1V (b) 4 V

(c) 2 V (d) 32 V

PHYSICS

1. 10lseh f=T;k ds vpkyd xksys dks c6 vkosk fn;k

tkrk gSA dsU ls5lseh nwjh ij fo|qr {ks= dk ekugksxk

(a) 'kwU; (b) 51027 oksYV@eh

(c) 51027 oksYV@eh (d) 51072 oksYV@eh

2. ,d leckgq f=Hkqt ds R;sd dksuksa ij2q, q,rFkk-qvkosk fLFkr gSaA f=Hkqt ds dsU ij Eo V ds ekuek% gksaxs

(a) E 0rFkkV 0 (b) E = 0rFkkV = 0

(c) E 0rFkkV = 0 (d) E = 0rFkkV 0

3. leku :i ls vkosfkr /kkrq dh nks le:ih xksfy;k A

rFkkB ijLij 5102 U;wVu cy ls frdf"kZr djrhgSaA ,d vU; vukosfkr leku xksyhC dks Als LikZ

djkdjArFkkB ds e/; fcUnq ij j[k nh tkrh gSA Cij uSV cy dk eku gksxk

(a) 'kwU;

(b) 5102 U;wVuClsA dh rjQ

(c) 5102 U;wVuClsB dhrjQ

(d) 5103 U;wVuCls A dh rjQ

4.

,d lekUrj IysV la/kkfjr esa rhu ijkoS|qr fp=kuqlkjHkjs gq, gSaA lekUrj IysVksads e/; foHkokUrj vkjksfirfd;k x;k gSA ;fn IysVdk {ks=Qy S rFkklekUrj IysVksa ds e/; nwjhd gks rks XoY fcUnq dse/; /kkfjrk dk eku gksxk

(a)

32

3210

KK

KK

2

KS

d(b)

d

S0

(c)d

KKSK 3210 (d)d

KSK 320

5. ,d lekUrj ifdk la/kkfj= dks fLFkj 4 oksYV fo-ok-cy dh cSVjh ls tksM+k x;k gSA ;fn la/kkfj= esa

8r ijkoS|qrkad dh ifdk Mky nh tkos rks

la/kkfj= ij foHkkokUrj gksxk

(a)2

1V (b) 4 V

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(c) 2 V (d) 32 V

6. In the following figure the sum of charges on all thecondensers will be

(a) .0047 C (b) .0037 C(c) .0045 C (d) .0073 C

7. The ammeter reading in the adjoining circuit will be

(a) Zero (b) 1.5 A

(c) 1 A (d) 2A

8. The equivalent resistancebetween A and B in thefollowing circuit is

(a) 1 (b) 2

(c) 3 (d) 4

9. A copper wire of length 1m and radius 1mm isconnected in series with another wire of iron oflength 2m and radius 3mm. A steady current ispassed through this combination. The ratio ofcurrent densities in copper and iron wires will be

(a) 18 : 1 (b) 9 : 1

(c) 6 : 1 (d) 2 : 3

10. In the following circuit the resistance of wire AB is10 and its length is 1m. Rest of the quantities aregiven in the diagram. The potential gradient on thewire will be

(a) 0.0 8 V/m (b) 0.008 V/m

(c) 0.8 V/m (d) None of the above

11. An electric tea kettle has two heating coils. Whenone of the coils is switched on, the kettle begins toboil in six minutes. When the other coil is switchedon, the boiling begins in 8 minutes. When both thecoils are switched on in series, then boiling willbegin in

(a) 10 min (b) 14 min

(c) 18 min (d) 20 min

12. A current of 16A flows through molten NaCl for 10minutes. The amount of metallic sodium thatappears at the negative would be

(a) 11.5 gm (b) 2.3 gm

(c) 1.15 gm (d) 0.23 gm

6. layXu fp= esa lHkh la/kkfj=ksa ij vkosk dh ek=kvksa dks;ksx gksxk

(a) .0047 C (b) .0037 C

(c) .0045 C (d) .0073 C

7. fuEu ifjiFk esa vehVj dk ikB~;kad gksxk

(a) 'kwU; (b) 1.5 ,(c) 1 , (d) 2 ,

8. layXu ifjiFk esaAoBds e/; rqY; frjks/kgksxk

(a) 1 (b) 2

(c) 3 (d) 4

9. 1 ehVj yEcs vkSj 1 feeh f=T;k okys rkcs ds rkj dks2 ehVj yEcs vkSj 3 feeh f=T;k okys yksgs ds rkj lsJs.khe esa tksM+dj muesa fo|qr /kkjk okfgr dh xbZ

gSA rkcs vkSj yksgs ds rkjksa esa /kkjk /kuRo dk vuqikrgksxk

(a) 18 : 1 (b) 9 : 1

(c) 6 : 1 (d) 2 : 3

10. uhps fn;s x, fp= esa rkjAB dk frjks/k10 vkse gSrFkk yEckbZ ,d ehVj gSA 'ks"k jkfk;k fp= esa vafdr gSarks foHkoekih ds rkjAB dh foHko o.krk gksxh

(a) 0.0 8 V/m (b) 0.008 V/m

(c) 0.8 V/m (d)mi;qZDr esa dksbZ ugha

11. ,d pk; dh fo|qr dsryh esa nks rkiu dq.Mfy;kW gSaAtc ,d dq.Myh dks pkywfd;k gS rks dsryh esa ikuhN% feuV esa mcyus&yxrk gSA tc nwljh dq.Myh dkspkywfd;k tkrk gS rks ikuh 8 feuV esa mcyus yxrkgS tc nksuksa dq.Myh;ksa dks ,d lkFk Js.kh e esa pkywfd;k tkrk gS rks] ikuh mcyus yxsxk

(a) 10 feuV esa (b) 14 feuV esa

(c) 18 feuV esa (d) 20 feuV esa

12. fi?kys gq, NaCl esa ls 10 feuV ds fy, 16 A /kkjkokfgr dh tkrh gSA _.k bysdVksM ij mRiUu/kkfRod lksfM;e dh ek=k gksxh(a) 11.5 gm (b) 2.3 gm

(c) 1.15 gm (d) 0.23 gm

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13. The emf in a thermoelectric circuit with one junctionat 0 and the other at tC is given by E = at + bt2.The neutral temperature is

(a)a

b2(b)

b

a

(c)b

a (d)

b

a

2

14. What will be the magnitude ofmagnetic induction at the centre ofa square loop of side a, if a currenti is flowing in the loop

(a)

i022 (b)a

i

022

(c)a

i

0 (d)i

a

022

15. A proton, a deutron and an -particle are acceleratedthrough same potential difference and then theyenter a normal uniform magnetic field. the ratio oftheir kinetic energies will be

(a) 2:1:3 (b) 1:1:2

(c) 1:1:1 (d) 1:2:4

16. The total magnetic induction at point O due tocurved portion and straight portion in the followingfigure, will be

(a)

tan

2

0

r

i

(b)r

i

20

(c) Zero

(d)

tan0

r

i

17. There are two points A and B on the extended axisof a 2 cm bar magnet. Their distances from thecentre of the magnet are x and 2x respectively. Theratio of magnetic fields at points A and B will be

(a) 8:1 approximately (b) 4:1 (approximately)(c) 4:1 (d) 8:1

18. The total magnetic flux in a material, whichproduces a pole of strength mP when a magneticmaterial of cross-sectional area A is placed in amagnetic field of strength H, will be

(a) po mAH (b) AHo

(c) pom (d) Ampo AH

13.rki&;qXe dh ,d lfU/k0C ij rFkk nwljh lfU/ktCij j[kus ij mlesa rki fo-ok-c- fn;k tkrk gSE = at +bt2A mnklhu rki gksxk

(a)a

b2(b)

b

a

(c)b

a (d)

b

a

2

14. a Hkqtk okyh oxkZdkj dq.Myh dsdsU ij pqEcdh; {ks= dk eku D;kgksxk ;fn mlesa okfgr /kkjki gks

(a)

i022 (b)a

i

022

(c)a

i

0 (d)i

a

022

15. ,d ksVkWu] ,d M~;wVkWu rFkk ,d -d.k lekufoHkokUrj ls Rofjr gksdj ,d leku pqEcdh; {ks= dsyEcor~ osk djrs gSaA budh xfrt tkZvksa dkvuqikr% ek% gksxk(a) 2:1:3 (b) 1:1:2

(c) 1:1:1 (d) 1:2:4

16. fp=kuqlkj pkyd rkj ds o Hkkx rFkk lh/ks Hkkx dsdkj.kO ij pqEcdh; {ks= dk eku gksxk

(a)

tan

2

0

r

i

(b)r

i

20

(c) Zero

(d)

tan0

r

i

17. 2 lseh yEcs NM+ pqEcd dh c

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19. A coil of radius 1 cm and 100 turns is placed at thecentre of a long splenoid of radius 5 cm and 8turns/cm. The value of coefficient of mutualinduction will be

(a) 51015.3 H (b) 5106 H

(c) 5109 H (d) Zero

20. The electric current in a circuit is increaseduniformly from 1A to 10A during a time interval of

2second. Another coil of resistance 50 and mutualinductance 1H is placed near it. The induced currentin the second coil will be

(a) 18 A (b) 9 A

(c) 0.9 A (d) 0.09 A

21. A coil, in which number of turns and the mean area103 and 500 cm2 respectively, is lying at right anglesto a magnetic field of 0.4 Gauss. If the coil is turned

through 180 in101 second then the average

induced e.m.f. will be

(a) 0.04 V (b) 4 V

(c) 0.4 V (d) 40 V

22. In the circuit shown in the figure,neglecting source resistance, thevoltmeter and ammeter readingswill respectively be

(a) 150 V, 8A (b) 0 V, 8 A

(c) 0 V, 3 A (d) 150 V, 3 A

23. A 280 ohm electric bulb is connected to 200 V electricline. The peak value of current in the bulb will be

(a) About one ampere (b) Zero

(c) About one ampere (d) About four ampere

24. If two bulbs marked 100W, 250 V and 50 W, 250 Vare connected in series with a 250 V source, then

(a) Both bulbs will get fused

(b) 100 W bulb will get fused

(c) 50 W bulb will get fused(d)None of two will get fused

25. A stream of electron of velocity 7103 m/s isdeflected 2mm in passing 10 cm through an electricfield of 1800V/m perpendicular to their path. Thevalue of e/m for electrons will be

(a) 111078.1 coul/kg (b) 11102 coul/kg

(c) 111022.2 coul/kg (d) 111061.3 coul/kg

19. 100 ?ksjksa rFkk 1 lseh- f=T;k dh ,d dq.Myh dks ,dyEch ifjukfydk ftldh f=T;k 5 lseh- rFkk 8?ksjs@lseh gSa] ds chpksa&chp j[kk tkrk gSA vU;ksU; izsj.kxq.kkad dk eku gksxk

(a) 51015.3 H (b) 5106 H

(c) 5109 H (d) 'kqU;

20. fdlh fo|qr ifjiFk esa /kkjk dks 1 ,- ls 10 ,- rd 2ls- ds vUrjky esa leku nj ls c

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26. An -particle is fired towards a nucleus with amomentum p and the distance of closest approach isr. if its momentums is increased to 4p, the distanceof closest approach will be

(a) 4r (b)4

r

(c) 16 r (d) 16

r

27. On using light of wavelength 6000, the stoppingpotential for a photo cell is 2.4 volt. If light ofwavelength 4000 is used, then stopping potentialwill be

(a) 2.9 volt (b) 1.9 volt

(c) 3.43 volt (d) 9.4 volt

28. The curve between photoelectric current (i) and

frequency (v) is

(a) (b)

(c) (d)

29. The De Broglie wavelength associated with electronin nth Bohr orbit is

(a)n

r2A (b) n2 A

(c)n

1A (d) nA

30. The ratio of wavelengths of deutron and protonaccelerated through the same potential differencewill be

(a)2

1(b)

1

2

(c)2

1(d)

1

2

26. ,d-d.k dks ,d ukfHkd dh vksjplaosx l s {ksfirfd;k x;k gS rFkk fudVre igqp nwjhr gSA ;fn bldklaosx 4prd c

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1. What is the ratio of time periodic in first and second

orbit of hydrogen atom? (If periodic time T =V

r2)

(a) 1 : 8 (b) 1 : 4

(c) 1 : 2 (d) 2 : 1

2. What is the conclusion of Rutherfords particle

scattering experiment

(a) Mass and energy are related to each other

(b) Neutrons are present in nucleus

(c) Power produced from collision with matter canbe determined

(d) Electrons possess space around the nucleus

3. Electronic configuration of nitrogen is11122 222,2,1 zyx pppss and not ,2222,1

01222zyx pppss

this is determined by

(a) Aufbau rule

(b) Panli exclusion princple

(c) Hunds rule

(d) Uncertainty principle

4. If the radius of first orbit of H is r, then the radius of

first Bohrs orbit of 2Li will be

(a) 3r (b) 27r

(c)27

r(d)

3

r

5. Which of the following formula is wrong

(a) Time periodv

rT

2

(b)242

33

4 Zme

hnT

(c) Momentum =nh

Zm22

(d) Frequency =33

2224

hn

Zme

6. Element of atomic number 19 is very reactive. Theelement of which of the following atomic numberwill also be more reactive

(a) 18 (b) 26

(c) 38 (d) 37

CHEMISTRY

1. gkbMkstu ijek.kq d izFke o f}rh; d{kk esa bysDVkWuds vkorZ dky dk vuqikr D;k gksxkA (;fn vkorZ

dkyT =V

r2gks)

(a) 1 : 8 (b) 1 : 4

(c) 1 : 2 (d) 2 : 1

2. jnjQksMZ ds d.k izdh.kZu iz;ksx ls fu"d"k.kZfudyrk gS fd

(a) nzO;eku vkSj tkZ ijLij lEcfU/kr gS

(b) U;wVkWu ukfHkd esa mifLFkr gksrs gS

(c) nzO; ds lkFk VDdj ls mRiUu 'kfDr dks fu/kkZfjrdj ldrs gS

(d) bysDVkWu ukfHkd ds pkjksa vksj LFkku xzg.k djrs gS

3. ukbVkstu dks bysDVksfud foU;kl11122 222,2,1 zyx pppss gS ,2222,1

01222zyx pppss ugha

gSA ,slk fdlds }kjk fu/kkZfjr gS

(a) vkWQckm fu;e

(b) ikmyh viotZu fu;e

(c) gq.M dk fu;e

(d) vfufprrk fl}kUr

4. ;fnH izFke cksj d{k dh f=T;krgks rks 2Li ds izFkecksj d{k dh f=T;k gksxh

(a) 3r (b) 27r

(c)

27

r(d)

3

r

5. fuEufyf[kr esa ls xyr lw= gS

(a) vkorZdkyv

rT

2

(b)242

33

4 Zme

hnT

(c)laosx=nh

Zm22

(d) vko`fr=33

2224

hn

Zme

6. ijek.kq ekad 19 okyk rRo vR;Ur f;kkhy gSAfuEufyf[kr esa ls dkSuls ijek.kq ekad dk rRo Hkhvf/kd f;kkhy gksxk(a) 18 (b) 26

(c) 38 (d) 37

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7. Electronic configuration of argon is [Ne] .33 62 ps

Last electron of element of atomic number 42 willenter in

(a) d4 (b) d3

(c) s4 (d) p4

8. Electronic configuration of last and penultimate shellof an element X is 262 )1()1()1( nsdnpnsn x

If 4n and ,5x then atomic number of the

element is

(a) 25 (b) 27

(c) 28 (d) 51

9. If there are 2 electrons in outermost shell, 8 in thepenultimate shell and 20 in pre-penultimate shell,then element is called

(a) An inner transition element(b) A transition element

(c) A normal element

(d) An inert element

10. Which of the following statements is false regardingchlorine

(a) It is a member of 17th group

(b) Its electron affinity is highest

(c) It accepts one electron and there are three lonepairs on it

(d) Quantum numbers of its last electron are,3mn 1m

11. The bond present in OHCuSO 24 5, will be

(a) Ionic bond and hydrogen bond

(b) Covalent bond

(c) Coordinate bond

(d) All of the above

12. If 1600.....)()( molKJegAsA

12 260......)()(2

1 molKJgBegB

12 550......)()(

2

1)( molKJsABgBsA

then lattice energy of AB (s) will be

(a) 160

(b) 890

(c) 420

(d) + 360

7. vkxZu dks bysDVkWfud foU;kl [Ne] 62 33 ps gSA

crkb;s ijek.kq ekad42okys rRo dk vfUre bysDVkWufdlesa izosk djsxk

(a) d4 (b) d3

(c) s4 (d) p4

8. ,d rRo X ds vfUre o mikUR; dksk dk foU;klfuEufyf[kr gS262 )1()1()1( nsdnpnsn x

;fn 4n , 5x gks rks rRo dk ijek.kq ekad gksxk

(a) 25 (b) 27

(c) 28 (d) 51

9. ;fn ,d rRo ds ckre dksk esa2,mikUR; dksk esa 8vkSj iwoZ mikUR; dksk esa 20 bysDVkWu gksa rks ;g rRodgykrs gSa

(a) vkUrfjd lae.k rRo(b)lae.k rRo

(c)lkekU; rRo

(d) vf; rRo

10. Dyksjhu ds lUnHkZ esa vlR; dFku gS

(a) ;g17osaoxZ dk lnL; gS

(b) bldh bysDVkWu ca/kqrk mPpre gS

(c) ;g ,d bysDVkWu xzg.k dj ysrk gS rFkk bl ijrhu ,dkdh ;qXe gksrs gSaA

(d) blds vfUre bysDVkWu dh DokaVe la[;k ,3mn 1m gS

11. OHCuSO 24 5, esa ca/k fo|eku gksxk

(a) vk;fud ca/k ,oa gkbMkstu ca/k

(b)lgla;kstd ca/k

(c)milgla;kstd ca/k

(d)mijksDr lHkh

12. ;fn 1600.....)()( molKJegAsA

12 260......)()(

21 molKJgBegB

12 550......)()(

2

1)( molKJsABgBsA

gks rksAB (s) dh tkyd tkZ gksxh

(a) 160

(b) 890

(c) 420

(d) + 360

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13. Percentage of ionic character is determined in themolecule AB by the following formula

100)035.016.0( 2

where .BA XX Which of the following bonds

will have maximum ionic character

(a) H F (b) H Cl

(c) H Br (d) H I

14. Reason of oNitrophenol being more volatile thanpNitrophenol is

(a) Resonance

(b) Intramolecular hydrogen bondign

(c) Conjugation

(d) Isomerism

15. Which of the following species ha boron in 3sp

hybridization state(a) 4BF (b) 3BH

(c) 62HB (d) 3BCl

16. If the value of equilibrium constant K of 2HI

,22 HH then equilibrium constant of 22 IH 2HI

will be

(a) 1.0 (b) 4.0

(c) 3.0 (d) 2.0

17. 2.5 moles of hydriodic acid are taken in a 10litrevessel. If 0.1 mole/litre HI is present at equilibrium,

then the concentration of 2H at equilibrium will be

(a) 0.075 (b) 0.15

(c) 0.25 (d) 0.175

18. In the reaction C(s) + )(2 gO ),(2 gCO if

number of moles of C, 2O and 2CO are 1, 2 and 5,

respectively, then what will be the mole fraction of

2CO in gaseous state

(a) 0.14 (b) 0.2(c) 0.08 (d) 0.3

19. The equilibrium )(3)( 22 gHgN )(2 3 gNH is

established on mixing equal moles of 2N and ,2H

then which of the following will be true

(a) ][][ 22 NH (b) ][][ 22 NH

(c) ][][ 22 NH (d) None of these

13. v.kq AB esa izfrkr vk;fud y{k.k fuEufyf[kr lw=ls Kkr djrs gS

100)035.016.0( 2

tgk BA XX gSA fuEufyf[kr ca/kkas esa ls fdleas

vf/kdre vk;fud y{k.k gksaxs

(a) H F (b) H Cl

(c) H Br (d) H I

14. oukbVksQhukWy] pukbVksQhukWy ls vf/kd ok"i'khygksus dks dkj.k gS

(a) vuqukn

(b) var% v.kqd gkbMkstu ca/k

(c)la;qXeu

(d)leko;ork

15. B dk ,d ;kSfxd ftlesa cksjkWu 3sp ladfjr voLFkk esa

gks] dkSu lk gS(a) 4BF (b) 3BH

(c) 62HB (d) 3BCl

16. 2HI 22 IH dk lkE; fLFkjkadKdk eku0.25

gks rks 22 IH 2HI dk lkE; fLFkjkad gksxk

(a) 1.0 (b) 4.0

(c) 3.0 (d) 2.0

17. 10yhVj ds ik= esa2.5 eksy gkbMksvk;ksfMd vEy dksfy;k x;kA ;fn lkE; ij HI = 0.1 eksy/yhVjmifLFkr gks rks lkE; ij 2H dh lkUnzrk gksxh

(a) 0.075 (b) 0.15

(c) 0.25 (d) 0.175

18. C(s) + )(2 gO )(2 gCO vfHkf;k ea lkE; ijC,

2O rFkk 2CO ds eksy ek% 1, 2 ,oa 5 gksa rks 2CO dk

vkafkd nkc gksxk

(a) 0.14 (b) 0.2(c) 0.08 (d) 0.3

19. )(3)( 22 gHgN )(2 3 gNH dh lkE;koLFkk

2N o 2H ds leku eksy feykus ij LFkkfir gks tkrh

gS rks dkSulk dFku lR; gS

(a) ][][ 22 NH (b) ][][ 22 NH

(c) ][][ 22 NH (d)lHkh xyr gS

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20. How is the total pressure defined, on adding an inertgas in the equilibrium reaction, 5PCl 3PCl +

,2Cl if the pressures of ,5PCl ,3PCl 2Cl and inert

gas (x) are ,spcl

P23

, ClPCl PP and ,xP respectively,

andpK = ?

1 2

2

x

Px

(a) 325 PClClPCl PPP

(b) xPClClPCl PPPP 325

(c) xPClPClPCl PPPP 235

(d)35 PClPCl

PP

21. Solubilities of PbSO4 in some solutions are as follows

(a) In water 1s (b) In 0.1 242 sSONa

(c) In 0.01 M 342 sSONa (d) In 0.001 M 42 sPbCl

Then order of 321 ,, sss and 4s will be(a) 4321 ssss (b) 2341 ssss

(c) 2341 ssss (d) All are same

22. Hydrolysis constant of potassium acetate is10104.5 if ionic product of water is ,108.1 14

then dissociation constant of the acid will be

(a) 4103 (b) 4103.0

(c) 5106 (d) 2103.5

23. A maximum of how many moles of 243 )(POBa

will be obtained on mixing 0.5 moles of 2BaCl with

0.2 moles of 43POH

(a) 0.20 (b) 0.70

(c) 0.50 (d) 0.10

24. If solubility product of AgCl, AgBr and Agl are 1.7

1310 103.3,10 and 27105.8 , respectively,

then the order of their solubility will be

(a) AgIAgBrAgCl (b) AgIAgBrAgCl (c) AgIAgBrAgCl (d) AgIAgBrAgCl

25. Correct formula for degree of hydrolysis ofammonium acetate is

(a)C

Kh (b)ba

w

KK

K

(c)CK

K

a

w

(d) CKb

20. 5PCl 3PCl + 2Cl vfHkf;k ds lkE; esa vf;k

xSl feykus ij dqy nkc dks fdlls ifjHkkf"kr djsaxs];fn ,5PCl ,3PCl 2Cl o vf; xSl(x) dk nkc ek

,spcl

P23

, ClPCl PP rFkk xP gS rFkk pK = 2

2

1 x

Px

gS

(a)325 PClClPCl

PPP

(b) xPClClPCl PPPP 325

(c) xPClPClPCl PPPP 235

(d)35 PClPCl

PP

21. PbSO4dh fuEu foy;uksa esa foys;rk fuEu gS

(a) ty esa 1s (b) 0.1 42SONa esa 2s

(c) 0.01 M 42SONa esaa 3s (d) 0.001M 2PbCleas 4s

rks 321 ,, sss , 4s dk e gksxk

(a) 4321 ssss (b) 2341 ssss (c) 2341 ssss (d)lHkh esa cjkcj

22. iksVSfk;e ,slhVsV dk vEy vi?kVu fLFkjkad10104.5 gS ;fn ty dk vk;fud xq.kuQy14108.1 gks rks vEy dk fo;kstu fLFkjkad gksxk

(a) 4103 (b) 4103.0

(c) 5106 (d) 2103.5

23.2

BaClds0.5 v.kq dks 43

POHds 0.2 v.kq ds lkFkfeykus ij ds 243 )(POBa vf/kdre fdrus v.kq izkIr

gksaxs

(a) 0.20 (b) 0.70

(c) 0.50 (d) 0.10

24. ;fn AgCl, AgBroAgl ds foys;rk xq.kuQy ek%

1.7 1310 103.3,10 o 27105.8 gksa rks budhfoys;rk dk e gksxk

(a) AgIAgBrAgCl (b) AgIAgBrAgCl

(c) AgIAgBrAgCl (d) AgIAgBrAgCl

25. vkeksfu;k ,slhVsV ds ty vi?kVu dh ek=k dk lghlw= gS

(a)C

Kh (b)ba

w

KK

K

(c)CK

K

a

w

(d) CKb

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26. Some bases are written below in increasing order oftheir base strengths. What will be the decreasingorder of the acid strengths of their respectiveconjugate acid

COOCHCHCOOCHA 233

(a) COOHCHCHHACOOHCH 233

(b) COOHCHCHCOOHCHHA 233 (c) COHCHHACOHCHCH 323

(d) HACOOHCHCOOHCHCH 323

27. The following equilibrium is established when HClis dissolved in acetic acid

COOHCHHCl 3 23COOHCHCl

Which of the following sets will be conjugate acid-base pairs

(a) ),( 3COOHCHHCl and )( 23 ClCOOHCH

(b) ),( 23COOHCHHCl and ),( 3

ClCOOHCH

(c) ),( 23 HClCOOHCH and )( 3COOHCHCl

(d) ),( ClHCl and ),( 323 COOHCHCOOHCH

28. Half-life of 23890Th is10103.1 year. In how much

time, its 3101 kg will become 4105 kg afterdisintegration

(a) 5103.1 year (b) 4103.1 year

(c) 10106.2 year (d) 10103.1 year

29. If amount of a radioactive element is increased twotimes, then what should be the change indisintegration per unit time

(a) Decreases half (b) Remains unchanged

(c) Becomes two times (d) Increases 2 times

30. What should be the ratio of root mean squarevelocity of molecular hydrogen and molecular

oxygen, respectively(a) 4 : 1 (b) 1 : 4

(c) 1 : 2 (d) 1 : 8

26. dqN la;qXeh {kkjd {kkjhd xq.kksa ds c

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1. )()(

1lim

12Nn

axaxn

equals

(a) (b)

(c) 0 (d) Does no exist

2.3

)1log(cossin1

0

lim

x

xxx

x

equals

(a) 1/2

(b) 1/2

(c) 0

(d) None of these

3.

dx

x

x

dx

d

x2

cos1

0lim is equal to

(a)2

1(b)

2

1

(c) 0 (d) 1

4. If 4)(',1)(,2)(',3)( agagafaf then

ax

xfagafxg

ax

)()()()(lim equals

(a) 5 (b) 10

(c) 10 (d) 5

5.

)1(

1....

4.3

1

3.2

1lim

nnnequals

(a) 1 (b) 0

(c)2

1(d) 2

6.

2/1

2

)1(cosh2

0lim

x

x

x

x

equals

(a)12

1(b)

12

1

(c) 12/1e (d) 12/1e

7. 0lim

x

n

e

x

x, (n is an integer) for

(a) No value of n

(b) All values of n

(c) Only negative value of n

(d) Only positive values of n

Mathematics

1. )()(

1lim

12Nn

axaxn

cjkcj gS

(a) (b)

(c) 0 (d) fo|eku ugha gS

2.

3

)1log(cossin1

0

limx

xxx

x

cjkcj gS

(a) 1/2

(b) 1/2

(c) 0

(d) buesa ls dksbZ ugha

3.

dx

x

x

dx

d

x2

cos1

0lim cjkcj gSa

(a)2

1(b)

2

1

(c) 0 (d) 1

4. ;fn 4)(',1)(,2)(',3)( agagafaf , rc

ax

xfagafxg

ax

)()()()(lim cjkcj gSa

(a) 5 (b) 10

(c) 10 (d) 5

5.

)1(

1....

4.3

1

3.2

1lim

nnncjkcj gSa

(a) 1 (b) 0

(c)2

1(d) 2

6.

2/1

2

)1(cosh2

0lim

x

x

x

x

cjkcj gSa

(a)12

1(b)

12

1

(c) 12/1e (d) 12/1e

7. 0lim

x

n

e

x

x, (tgk n ,d iw.kkZd gS)

(a) n ds fdlh Hkh eku ds fy;s ugha

(b) n ds lHkh ekuksa ds fy,

(c) n ds dsoy _.kkRed ekuksa ds fy,

(d) n ds dsoy /kukRed ekuksa ds fy,

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8.3

24

||1

)/1sin(lim

x

xxx

x

equals

(a) 0 (b) 1

(c) 1 (d)

9. Iff(x) =

0,

0,sin1

xk

xxax

is continuous x = 0, then k

is equal to

(a) 0 (b) 1

(c) a (d) None of these

10. Function f(x) = | sin x | +|cos x| + | x | isdiscontinuous at

(a) x = 0 (b) x = 2/

(c) x = (d) No where

11. If f(x) = x1

1and g(x) = f[f{f(x)}], then g(x) is

discontinuous at

(a) x = 3 (b) x = 2

(c) x = 0 (d) x = 4

12. Consider the following statements:

I.A function f is continuous at a point 0x Dom (f)

if )()(lim 00

xfxfxx

II. f is continuous in [a, b] if f is continuous in (a, b)and f(a) = f(b)

III. A constant function is continuous in an intervalOut of these correct statements are

(a) I and II (b) II and III

(c) I and III (d) All the above

13. If function f(x) =

1

2

xthen in the interval ],0[

(a) tan [f(x)] is discontinuous but 1/f (x) is continuous

(b) tan [f(x)] is continuous but)(

1

xfis discontinuous

(c) tan [f(x)] and )(1

xf

is continuous(d) tan [f(x)] and 1/f (x) both are discontinuous

14. dxxxx 3secsin equals

(a) cxx ]tan[sec2

1 2 (b) cxxx ]tansec[2

1 2

(c) cxxx ]tansec[2

1 2 (d) cxx ]tan[sec2

1 2

8.3

24

||1

)/1sin(lim

x

xxx

x

cjkcj gSa

(a) 0 (b) 1

(c) 1 (d)

9.

;fnf(x) =

0,

0,sin 1

xk

x

x

ax

x = 0 ij larr gS] rc k

cjkcj gksxk(a) 0 (b) 1

(c) a (d) buesa ls dksbZ ugha

10. Qyuf(x) = | sin x | +| cos x | + | x | vlarr gS(a) x = 0 (b) x = 2/

(c) x = (d) dgha ugha

11. ;fnf(x) = x1

1rFkkg(x) = f[f{f(x)}],rFkkg(x)

vlarr gS(a) x = 3 (b) x = 2

(c) x = 0 (d) x = 4

12. fuEu dFkukas ij /;ku nhft,s:

I.Qyuf,d fcUnq 0x izkUr )(f ij larr gS ;fn

).()(lim 00

xfxfxx

II. f, [a, b] esa larr gS ;fnf,(a, b) esa larr rFkkf(a) =f(b)

III. ,d vpj Qyu fdlh vUrjky esa larr gSMijksDr dFkuksa esa ls dkSulk dFku lgh gS(a) IrFkkII (b) IIrFkkIII(c) IrFkkIII (d) ;g lHkh

13. ;fn Qyuf(x) =

1

2

xgks rks vUrjky ],0[ esa

(a) tan [f(x)] vlarr gS ijUrq 1/f (x)larr gS

(b) tan [f(x)]larr gS ijUrq)(

1

xfvlarr gS

(c) tan [f(x)]rFkk )(1

xf

larr gS(d) tan [f(x)]rFkk1/f (x) nksukas vlarr gS

14. dxxxx3secsin cjkcj gSa

(a) cxx ]tan[sec2

1 2 (b) cxxx ]tansec[2

1 2

(c) cxxx ]tansec[2

1 2 (d) cxx ]tan[sec2

1 2

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15.

dxx

xx

2

2

1

1

(a) cxx ]1[sin2

1 421

(b) cxx ]1[sin2

1 221

(c) cxx 421

1sin

(d) cxx 221 1sin

16. dx

xbxa

xx22 sincos

cossin is equal to

(a) cxbxa )sincoslog( 22

(b) cxbxaba )sincoslog()(2

1 22

(c) cxbxaab

)sincoslog()(2

1 22

(d) None of these

17.

dxx

x

coscos

2cos2cos

(a) cxx ]cos[sin2

(b) cx ]sin[sin2

(c) cxx ]cossin[2

(d) cx ]sin[sin2

18. if ,)sin(2)sin(cos cxdxxx then isequal to

(a)3

(b)

3

(c)4

(d)

4

19.

xex

11

2

11 dx is equals to

(a) ce xx

1

(b) ce xx

1

(c) ce xx

12

(d) ce xx

22 1

20. xxx

dxequals

(a) cxxx log (b) cx 1

(c) cx 14 (d) cxxx 2

15.

dxx

xx

2

2

1

1

(a) cxx ]1[sin2

1 421

(b) cxx ]1[sin2

1 221

(c) cxx 421

1sin (d) cxx 221 1sin

16. dx

xbxa

xx22 sincos

cossin cjkcj gSa

(a) cxbxa )sincoslog( 22

(b) cxbxaba )sincoslog()(2

1 22

(c) cxbxaab

)sincoslog()(2

1 22


17.

dxx

x

coscos

2cos2cos

(a) cxx ]cos[sin2

(b) cx ]sin[sin2

(c) cxx ]cossin[2

(d) cx ]sin[sin2

18. ;fn

,)sin(2)sin(cos cxdxxx rc

cjkcj gS

(a)3

(b)

3

(c)4

(d)

4

19.

xex

11

2

11 dx cjkcj gSa

(a) cex

x

1

(b) cex

x

1

(c) ce xx

12

(d) ce xx

22 1

20. xxx

dxcjkcj gSa

(a) cxxx log (b) cx 1

(c) cx 14 (d) cxxx 2

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21.

dxxx

xx22

88

cossin21

cossinis equal to

(a) cx 2sin (b) cx 2sin2

1

(c) cx 2sin2

1(d) cx 2sin

22. If x = f (t) cos t + f (t) sin t, y = f (t) sin t + (f)

cos t, then

2/122

dt

dy

dt

dxdt is equal to

(a) ctftf )(")(' (b) ctftf )(")("

(c) ctftf )(")( (d) ctftf )(")("

23. If ,2sin xdxelx then for what value of k,

)2cos22(sin xxekl x constant

(a) 1 (b) 3

(c) 5 (d) 7

24.

2

2

11log

1

2

xx

e xdx equals

(a) Ce x

2

11log

(b) Cx

x

2

1tan

2

1 21

(c) Cx

x

2

1tan

2

1 21 (d) Cx

x

2

1tan

21

25.

x

xx3

3

cos1

coscosdx is equal to

(a) Cx )(cossin3

2 2/31

(b) Cx )(cossin2

3 2/31

(c) Cx )(coscos32 2/31

(d) None of these

26. If |,1|||)( xxxf then 2

0

)( dxxf equals

(a) 3 (b) 2

(c) 0 (d) 1

21.

dxxx

xx22

88

cossin21

cossincjkcj gSa

(a) cx 2sin (b) cx 2sin2

1

(c) cx 2sin2

1(d) cx 2sin

22. If x = f (t) cos t + f (t) sin t, y = f (t) sin t + (f)

cos t,rks

2/122

dt

dy

dt

dxdt cjkcj gSa

(a) ctftf )(")(' (b) ctftf )(")("

(c) ctftf )(")( (d) ctftf )(")("

23. ;fn ,2sin xdxelx rks k ds fdl eku ds fy,]

)2cos22(sin xxekl x vpj] gSa

(a) 1 (b) 3

(c) 5 (d) 7

24.

2

2

11log

1

2

xx

e xdx cjkcj gSa

(a) Ce x

2

11log

(b) Cx

x

2

1tan

2

1 21

(c) Cx

x

2

1tan

2

1 21 (d) Cx

x

2

1tan

21

25.

x

xx3

3

cos1

coscosdx cjkcj gSa

(a) Cx )(cossin3

2 2/31

(b) Cx )(cossin2

3 2/31

(c) Cx )(coscos32 2/31


26. ;fn |,1|||)( xxxf rks 2

0

)( dxxf cjkcj gSa

(a) 3 (b) 2

(c) 0 (d) 1

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27. 1

0

0)(2

dxxex

, then

(a) 21 (b) 0

(c) 10 (d) 0

28. If

2

log

,e

e x

dxl and

2

12 dx

x

el

x

, then

(a) 21 ll (b) 21 ll

(c) 21 ll (d) None of these

29.

0

4 2sinh xe x dx equals

(a)12

1(b)

6

1

(c)3

1(d) 4/1

30. If )()( xfxbaf then b

a

x f(x)dx is equal to

(a)

b

a

dxxfba

)(2

(b)

b

a

dxxbfba

)(2

(c)

b

a

dxxfab

)(2

(d) None of these

27. 1

0

0)(2

dxxex

rks

(a) 21 (b) 0

(c) 10 (d) 0

28. ;fn

2

log

,e

e x

dxl rks

2

1

2 dx

x

el

x

rc

(a) 21 ll (b) 21 ll

(c) 21 ll (d) buesa ls dksbZ gSa

29.

0

4 2sinh xe x dx cjkcj gSa

(a)12

1(b)

6

1

(c)

3

1(d) 4/1

30. ;fn )()( xfxbaf rks b

a

x f(x)dx cjkcj gS

(a)

b

a

dxxfba

)(2

(b)

b

a

dxxbfba

)(2

(c)

b

a

dxxfab

)(2

(d) blesa dksbZ ugha

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