(India) Private Limited - Vibrant Academy...SAMPLE PAPER (GOOGOL COURSE) Time : 3 Hours Maximum Marks : 216 Please read the instructions carefully. You are allotted 5 minutes specifically

SAMPLE PAPER (GOOGOL COURSE)Time : 3 Hours Maximum Marks : 216Please read the instructions carefully. You are allotted 5 minutes specifically for this purpose.

INSTRUCTIONSA. General :

1. This booklet is your Question Paper containing 72 questions.

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VIBRANT ACADEMY(India) Private Limited

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USEFUL DATAAtomic weights: Al = 27, Mg = 24, Cu = 63.5, Mn = 55, Cl = 35.5, O = 16, H = 1, P = 31, Ag = 108, N = 14, Li = 7,I = 127, Cr = 52, K=39, S = 32, Na = 23, C = 12, Br = 80, Fe = 56, Ca = 40, Zn = 65.5, Ti = 48, Ba = 137, U = 238,Co= 59, B =11, F = 19, He = 4, Ne = 20, Ar = 40 , Mo = 96, g = 10 m/s2

Vibrant Academy (I) Pvt. Ltd. "A-14(A)" Road No.1, IPIA, Kota (Raj.) Ph. 06377791915 (www.vibrantacademy.com) [2]

PART I : MATHEMATICSSingle Correct Choice Type

This section contains 24 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for itsanswer, out of which ONLY ONE is correct.

1. The lines k–4–z

13–y

12–x

and 1

5–z2

4–yk

1–x are coplanar if k is

js[kk,sak–4–z

13–y

12–x

rFkk 1

5–z2

4–yk

1–x leryh; gksxh ;fn K cjkcj gks

(A) 1 or –1 (B) 0 or –3 (C) 3 or – 3 (D) 0 or (–1)

2. In [0, 1] lagrange's mean-value theorem is not applicable to

vUrjky [0, 1] esa fdl ij ysxzkat izes; ugha yxrk gS

(A) f(x) =

2/1x,x–21

2/1x,x2/12

(B) f(x) =

0x;1

0x;x

xsin

(C) f(x) = x|x| (D) f(x) = |x|

3. Let c,b,a be unit vectors and , , are angles between the vector a,candc,b;,b,a respectively. If

cba is also a unit vector then cos + cos + cos is equal to

ekuk c,b,a bdkbZ lfn'k gks rFkk , , Øe'k% c,b;,b,a rFkk a,c ds e/; dks.k gSA ;fn cba bdkbZ lfn'k

gks rks cos + cos + cos dk eku gksxk(A) –1 (B) 3 (C) –3 (D) 1

4. If the circles x2 + y2 – 2x = 0 and x2 + y2 + 2y = 4 have only one common tangent then can be

;fn oÙkks x2 + y2 – 2x = 0 rFkk x2 + y2 + 2y = 4 ,d mHk;fu"B Li'khZ j[krs gks rks dk eku gks ldrk gS(A) 1 (B) –1 (C) 0 (D) 2

5. If 1

xsin

2 xsin–1dt)t(ft then

31f is equal to

;fn 1

xsin

2 xsin–1dt)t(ft rks

31f dk eku gksxk

(A) 1/3 (B) –3 (C) 3 (D) 3

6. The set of values of 'a' for which the graph of the function f(x) = a(x2 + 1) + x is always above the x-axis is

'a' ds ekuks dk leqPp; ftlds fy, Qyu f(x) = a(x2 + 1) + x dk ys[kkfp= lnSo x-v{k ds mij jgsxk(A) (1/2, ) (B) (–, –1/2) (C) (–1/2, 1/2) (D) None

7. If point (a, a2) falls inside the angle made by the lines y = x21

(x > 0) and y = 3x (x > 0) then a belongs to

;fn fcUnq (a, a2) js[kkvksa y = x21

(x > 0) rFkk y = 3x (x > 0) ds e/; dks.k es gks rks a vo;o gS fuEu dk

(A) (0, 1/2) (B) (3, ) (C) (1/2, 3) (D) (–3, –1/2)


MATHEMATICS8. The system of equations (lehdj.k fudk;)

x + 2y + 3z = 0x – y + 4z = 0

2x + y + 7z = 0 has (j[krk gS)

(A) only one solution (,d gy) (B) only two solutions (nks gy)

(C) no solution (dksbZ gy ugha) (D) infinitely many solutions (vuUr gy)

9. If z be a complex number satisfying z4 + z3 + 2z2 + z + 1 = 0 then |z| is equal to

;fn z ,d lfEeJ la[;k gS tks z4 + z3 + 2z2 + z + 1 = 0 dks larq"Vdjrh gS rks |z| dk eku gksxk(A) 1/2 (B) 3/4 (C) 1 (D) None of these

10. If cos2x + 2cosx = 1 then sin2x (2 – cos2x) is equal to

(A) 1 (B) –1 (C) 5– (D) 5

11. If solution set of [x + 5] + [x + 6] 7 be A and that of x3–x

1rr

x271

1033

be B, then

(where [] is greatest integer function)

;fn vlfedk [x + 5] + [x + 6] 7 dk gy leqPp; A gks rFkk x3–x

1rr

x271

1033

dk B gks rks

( [] egÙke iw.kkZad Qyu gS)(A) A B (B) B A (C) A = B (D) None of these

12. Equation of the circle for which straight lines x2 + 3y + xy + 3x = 0 are normals and its size is just sufficientto contain the circle x2 + y2 + 2x – 6y + 9 = 0

og or ftlds vfHkyEc j[kk,sa x2 + 3y + xy + 3x = 0 gks rFkk og oÙk x2 + y2 + 2x – 6y + 9 = 0 dks Bhd i;kZIr :i

ls vUrfuZfgr djrk gks] gksxk(A) (x + 3)2 + (y – 3)2 = 1 (B) (x – 3)2 + (y + 3)2 = 1(C) (x + 3)2 + (y – 3)2 = 9 (D) (x – 3)2 + (y + 3)2 = 9

13. The domain of definition of the function y = 2x)x–1(log

1

10 is :

Qyu y = 2x)x–1(log

1

10 dk izkar gksxk :

(A) (–3, –2) excluding – 2.5 (B) [0, 1) excluding 0.5(C) [–2, 1) excluding 0 (D) None of these

14. If G(x) = 2x 1

G(x) – G(1)– 25 – x then limx – 1

;fn G(x) = 2x–25– rks

1–x

)1(G–)x(Glim1x

(A) 241

(B) 51

(C) 24– (D) None of these


MATHEMATICS

15. If f(x) = 221'f,B

2xsinA

and ,A2dx)x(f1

0

then constants A and B are :

;fn f(x) = 221'f,B

2xsinA

rFkk ,A2dx)x(f1

0

rks vpj A rFkk B dk eku gksxk

(A) 2

and2

(B)

3and2(C) 0 and

4–(D) 0and4

16. The points (–a, –b), (0, 0), (a, b) and (a2, ab) are :

fcUnq (–a, –b), (0, 0), (a, b) rFkk (a2, ab) gS :

(A) collinear (lajs[kh;) (B) vertices of a rectangle (vk;r ds 'kh"kZ)

(C) vertices of a parallelogram (lekUrj prqHkZqt ds 'kh"kZ) (D) vertices of a triangle (f=Hkqt ds 'kh"kZ)

17. Two circles x2 + y2 = 6 and x2 + y2 – 6x + 8 = 0 are given. Then the equation of the circle through their pointsof intersection and the point (1, 1) is :

nks oÙk x2 + y2 = 6 rFkk x2 + y2 – 6x + 8 = 0 gSA ml o`Ùk dk lehdj.k tks o`Ùkks ds izfrPNsnu fcUnqvks rFkk fcUnq

(1, 1) ls xqtjs] gksxk(A) x2 + y2 – 6x + 4 = 0 (B) x2 + y2 – 3x + 1 = 0(C) x2 + y2 – 4x + 2 = 0 (D) x2 + y2 – 3y + 1 = 0

18. Consider a circle with its centre lying on the focus of the parabola y2 = 2px such that it touches the directrixof the parabola. Then a point of intersection of the circle and parabola is :

,d o`Ùk ftldk dsUnz ijoy; y2 = 2px dh ukfHk ij gS rFkk ;g ijoy; dh fu;rk dks Li'kZ djrk gSA oÙk ,oa

ijoy; dk izfrPNsnu fcUnq gksxkA

(A)

p,–2porp,

2p

(B)

2p,–

2p

or

2p,

2p

(C)

p,2p– or

p,2p

(D)

2p,–

2p– or

2p,

2p

19. Given A = sin2+ cos4 then for all values of

;fn A = sin2+ cos4 rks ds lHkh ekuks ds fy, fuEu esa ls lR; gksxk

(A) 1 A 2 (B) 1A43

(C) 613A1 (D) 6

13A43

20. If tan = 34– then sin is :

;fn tan = 34– rks sin gksxk :

(A) 54notbut

54–

54– ijUrq 5

4ugh (B) 5

4or54–

54– rFkk 5

4

(C) 54–notbut

54

54

ijUrq – 54

ugh (D) None of these buesa ls dksbZ ugh


21. The scalar product of ))CBA()CB((.A

equal to :

vfn'k xq.kuQy ))CBA()CB((.A

cjkcj gksxkA

(A) 0 (B) ]ACB[]CBA[

(C) ]CBA[

(D) ]CBA[–

22. If z = ,2i–

23

2i

23

55

then :

;fn z = ,2i–

23

2i

23

55

rks

(A) Re(z) = 0 (B) Im(z) = 0(C) Re(z) > 0, Im(z) > 0 (D) Re(z) > 0, Im(z) < 0

23. The area of the triangle formed by the positive x-axis and the normal and the tangent to the

x2 + y2 = 4 at 3,1 is

oÙk x2 + y2 = 4 ds fcUnq 3,1 ij Li'khZ] vfHkyEc rFkk x v{k ds }kjk cuk;s x,s f=Hkqt dk {ks=Qy gksxk

(A) 3 (B) 32 (C) 33 (D) 34

24. The unit vector perpendicular to the plane determined by P(1, –1,2), Q(2, 0, –1), R(0,2,1) is

fcUnq P(1, –1,2), Q(2, 0, –1), R(0,2,1) dks j[kus okys lery ds yEcor bdkbZ lfn'k gksxk

(A) kji261

(B) k–ji3111

(C) k–ji31

(D) kj2–i61


PART II : PHYSICSSingle Correct Choice Type


25. When a mass m is connected individually to two springs S1 and S2, the oscillation frequencies are v1 and v2.If the same mass is attached to the two springs as shown in figure, the oscillation frequency would be

tc ,d nzO;eku m, nks fLizxksa S1 rFkk S2 ls vyx&vyx tksM+k tkrk gS] rks nksyu vkofÙk;k¡ v1 rFkk v2 gSaA ;fn ogh

nzO;eku nksuksa fLizxksa ls fp=kuqlkj tksM+k tk;s] rks nksyu vkofÙk gksxh

(A) v1 + v2 (B) 22

21 vv

(C) 1–

21 v1

v1

(D) 2

221 v–v

26. Along a streamline

,d /kkjk js[kk ds vuqfn'k(A) the velocity of a fluid particle remains constant.

fdlh nzo d.k dk osx fu;r gSA(B) the velocity of all fluid particles crossing a given position is constant.

fdlh fcUnq ls xqtjus okys lHkh nzo&d.kksa dk osx fu;r gSA(C) the velocity of all fluid particles at a given instant is same.

fdlh le;] leLr nzo d.kksa dk osx leku gSA(D) the speed of a fluid particle remains constant.

fdlh nzo d.k dh pky fu;r gSA

27. A rigid bar of mass M is supported symmetrically by three wires each of length . Those at each end are ofcopper and the middle one is of iron and the rod is horizontal. The ratio of diameters of copper wires to thatof iron wire, if each is to have the same tension, is equal to

nzO;eku M dh ,d n<+ NM+] rhu rkjksa ¼izR;sd dh yEckbZ ½ ls lefer :i ls Vaxh gqbZ gSA nksuksa fljksa ij ds rkj

rkacs ds rFkk chp okyk yksgs dk gSA ;fn izR;sd rkj esa leku ruko gks] rks rkacs ds rkjksa ds O;kl dk yksgs ds rkjksa

ds O;kl ls vuqikr gksxk] ;fn NM+ /kjkry ds lekUurj gSa

(A) Ycopper / Yiron (B) copper

iron

YY

(C) 2copper

2iron

YY

(D) copper

iron

YY

28. A particle of mass m is moving in yz-plane with a uniform velocity v with its trajectory running parallel to +vey-axis and intersecting z-axis at z = a (Figure). The change in its angular momentum about the origin as it

bounces elastically from a wall at y = constant is ( xe is a unit vector along x-axis)

m nzO;eku dk ,d d.k y-z ry esa fu;r osx v ls xfr dj jgk gSA bldk iFk /kukRed y-v{k ds lekarj gS rFkk

z-v{k dks z = a ij dkVrk gS ¼fp=½A tc ;g y = fu;r] ij ,d nhokj ls iw.kZ izR;kLFkr% Vdjk dj ykSVrk gS rks

ewy fcUnq ds lkis{k blds dks.kh; laosx esa gksus okyk ifjorZu gksxk ( xe x-v{k ds vuqfn'k bdkbZ lfn'k gS)

(A) xemva

(B) xemva2

(C) xeymv

(D) xeymv2


PHYSICS29. A man squatting on the ground gets straight up and stand. The force of reaction of ground on the man during

the process is

Hkwfe ij cSBk ,d O;fDr lh/ks mBdj [kM+k gks tkrk gSA bl izØe ds nkSjku Hkwfe }kjk euq"; ij yxk;k x;k izfrfØ;k

cy

(A) constant and equal to mg in magnitude. (fu;r gS rFkk ifjek.k esa mg ds rqY; gSA)

(B) constant and greater than mg in magnitude. (fu;r gS rFkk ifjek.k esa mg ls cM+k gSA)

(C) variable but always greater than mg. (ifjorZu'khy gS ijUrq lnSo mg ls cM+k gSA)

(D) at first greater than mg, and later becomes equal to mg. (igys mg ls cM+k gS] ijarq ckn esa mg ds rqY; gSA)

30. A car of mass m kg starts from rest and acquires a velocity along east )0v(i)s/mv( in two seconds.

Assuming the car moves with uniform acceleration, the force exerted on the car is

m kg nzO;eku dh ,d dkj fojkekoLFkk ls izkjaHk djds nks lsd.M esa iwoZ fn'kk esa )0v(i)s/mv( dk osx izkIr djrh

gSA dkj dh xfr esa leku Roj.k ekurs gq;s] dkj ij yxus okyk cy gS

(A) 2

mv N eastward and is exerted by the car engine.

2mv

N iwoZ fn'kk esa rFkk dkj ds batu }kjk yxk;k tkrk gSA

(B) 2

mv N eastward and is due to the friction on the tyres exerted by the road.

2mv

N iwoZ fn'kk esa rFkk dkj ds Vk;jksa ij lM+d ds ?k"kZ.k }kjk yxk;k tkrk gSA

(C) more than 2

mvN eastward exerted due to the engine and overcomes the friction of the road.

iwoZ fn'kk esa 2

mvN ls vf/kd rFkk batu }kjk yxrk gS rFkk ¼lM+d ds½ ?k"kZ.k ij Hkkjh iM+rk gSA

(D) 2

mvN exerted by the engine.

2mv

N batu }kjk yxrk gSA

31. The linear momentum p of a body varies with time t as p = + t2 where and are constants. The netforce acting on the body for one dimensional motion varies as

,d fi.M dk js[kh; laosx p, le; t ds lkFk p = + t2 ds vuqlkj ifjofrZr gksrk gSA ,d foeh; xfr ds fy;s]

fi.M ij yxus okyk ifj.kkeh cy fuEukuqlkj ifjofrZr gksrk gS(A) t2 (B) t–1 (C) t–2 (D) t

32. For the stationary wave (vizxkeh rjax)

),t96cos(15

xsin4y

what is distance between a node and next antinode? (ds fy;s] Øekxr fu"ian rFkk izLian ds e/; nwjh D;k gS\)

(A) 7.5 units (bdkbZ) (B) 15 units (bdkbZ) (C) 22.5 units (bdkbZ) (D) 30 units (bdkbZ)


PHYSICS33. Consider the following statements : (fuEu rF;ksa ij fopkj djsa %)

1. The velocity of sound is greater in fluids whose compressibility is low.

de laihM~;rk ds rjy inkFkksZa esa /ofu dh pky vfèkd gksrh gSA2. The velocity of sound is greater in solids than in gases.

/ofu dh pky Bkslksa esa nzoksa dh vis{kk vf/kd gksrk gSAWhich of the above statement is/are correct?

mi;qZDr dFkuksa esa ls dkSulk@dkSuls lgh gS@gSa\(A) 1 only (B) 2 only (C) Both 1 and 2 (D) Neither 1 nor 2

34. A particle moves in x-y plane with velocity jbxiav where a, b are constants. Initially the particle was

located at x = 0 and y = 0. What is the equation of trajectory of the particle?

,d d.k x-y ry esa osx jbxiav ls xfr djrk gS] tgk¡ a, b fu;rkad gSA izkjaHk esa d.k x = 0 rFkk y = 0 ij

FkkA blds iFk dk lehdj.k D;k gS\(A) ay = bx2 (B) by = ax2 (C) 2ay = bx2 (D) ay = bx2

35. A particle executing SHM has kinetic energy ko cos2 t (t is time). The maximum values of potential energyand total energy are respectively

ljy vkorZ xfr djrs ,d d.k dh xfrt ÅtkZ ko cos2 t ¼t le; gS½ gSA bldh egÙke fLFkfrt ÅtkZ rFkk dqy

ÅtkZ Øe'k% gS

(A) 2

ko and ko (B) ko and 2ko (C) ko and ko (D) 0 and 2ko

36. What is the magnitude of external work done (approximately) when 1 g of helium is heated through 1ºC atconstant pressure?

tc 1 g ghfy;e dks fLFkj rki ij 1ºC xeZ fd;k tkrk gS rks fdrus ¼yxHkx½ ifjek.k dk ckâ; dk;Z fd;k tkrk gS\(A) 1 J (B) 2 J (C) 4 J (D) 8 J

37. An ideal gas is taken through a cycle ABCA as shown below in P-V diagram. What is the work done duringthe cycle?

uhps n'kkZ;s x;s P-V fp= ds vuqlkj ,d vkn'kZ xSl ,d pØh; izØe ABCA esa izÑr gksrh gSA bl pØh; izØe esa

fd;k x;k dk;Z fdruk gS\

(A) 2

PV(B) PV (C) 2 PV (D) Zero

38. If a thermometer reads melting point of ice as 20ºC and boiling point of water as 180ºC, how much does thethermometer read when the actual temperature is 60ºC?

,d rkiekih fge dk nzo.kkad 20ºC rFkk ikuh dk DoFkukad 180ºC crkrk gSA tc okLrfod rkieku 60ºC gks rks

bl rkiekih dk ikB~;kad fdruk gksxk\(A) 98ºC (B) 116ºC (C) 120ºC (D) 126ºC


PHYSICS39. A particle begins its motion in a straight line with a velocity v and moves under a retardation equal to k times

the distance described. What is the distance covered before it comes to rest?

,d d.k ,d ljy js[kk esa v pky ls xfr izkjaHk djrk gS rFkk pyh x;h nwjh ds k xquk cjkcj eanu ds varxZr xfr

djrk gSA fojke esa vkus ls igys blds }kjk r; dh xbZ nwjh D;k gS\

(A) kv (B) kv

(C) kv2

(D) None of these

40. An amount of 100 g of copper with specific heat 0.1 cal g–1 ºC–1 at 200ºC is dipped into 100 cc of water at24ºC. What is the final temperature of the system?

100 g rkack ¼fof'k"V m"ek 0.1 cal g–1 ºC–1½] ftldk rki 200ºC gS] 24ºC ds 100 cc ikuh esa Mkyk tkrk gSA bl

fudk; dk vafre rkieku D;k gS\(A) 30ºC (B) 40ºC (C) 50ºC (D) 60ºC

41. If U and W represent the increase in internal energy and work done by the system respectively in athermodynamical process, then which one of the following is correct?

;fn ,d m"ek xfrd izØe esa] vkarfjd ÅtkZ esa o`f) rFkk fudk; }kjk fd;k x;k dk;Z Øe'k% U rFkk W ls fpfUgr

gks] rks fuEu esa ls dkSulk lgh gS

(A) U = W in adiabatic process (U = W :)ks"e izØe esa)

(B) U = –W in isothermal process (U = –W lerkih izØe esa)

(C) U = –W in adiabatic process (U = –W :)ks"e izØe esa)

(D) U = W in isothermal process (U = W lerkih izØe esa)

42. Two cylinders P and Q have the same length and diameter and are made of different materials having thermalconductivities in the ratio 2 : 3. These two cylinders are combined “end to end” to make a cylinder. One end ofP is kept at 100ºC and the other end of Q at 0ºC. The temperature at the interface of P and Q will be (in steady-state)

nks csyu P rFkk Q ,d gh yEckbZ rFkk O;kl ds gS rFkk ,sls fHkUu inkFkksZ ls cus gS] ftudh m"ek pkydrkvksa dk

vuqikr 2 : 3 gSA bu nksuksa csyuksa dks *fljs ls fljk* feykdj ,d csyu cuk;k tkrk gSA P dk ,d fljk 100ºC ij

rFkk Q dk nwljk fljk 0ºC ij j[ks tkrs gS rks P rFkk Q ds mHk;fu"B ry dk ¼lkE;koLFkk½ esa rki gS(A) 30ºC (B) 40ºC (C) 58ºC (D) 60ºC

43. In an H2 - gas process, PV2 = constant. The ratio of work done by gas to change in its internal energy is

H2 - xSl ds ,d izØe esa] PV2 = fu;rA xSl }kjk fd;s x;s dk;Z dk bldh vkarfjd ÅtkZ esa gq;s ifjorZu ls vuqikr

gS

(A) 32

(B) 0.4 (C) –0.4 (D) 1.5

44. Charges Q and 2Q are placed at two vertices of an equilateral triangle of side L. The electric field magnitudeat the third vertex must be

vkos'k Q rFkk 2Q, L Hkqtk ds leckgq f=Hkqt ds nks fljksa ij gSA rhljs fljs ij fo|qr {ks= gS

(A) 20L45Q

(B) 20L47Q

(C) 20L43Q

(D) None


PHYSICS45. Ne22 nucleus, after absorbing energy, decays into two -particles and an unknown nucleus. The unknown

nucleus is

Ne22 ukfHkd] ÅtkZ vo'kksf"kr djus ds i'pkr] nks -d.kksa rFkk ,d vKkr ukfHkd esa fo?kfVr gksrk gSA vKkr ukfHkd

gS

(A) Nitrogen (ukbVªkstu) (B) Carbon (dkcZu) (C) Boron (cksjksu) (D) Oxygen (vkWDlhtu)

46. Consider a 'beam expander' which consists of two converging lenses of focal lengths 40 cm and 100 cmhaving a common optical axis. A laser beam of diameter 4 mm is incident on the 40 cm focal length lens. Thediameter of the final beam will be

,d fdj.k&izlkjd* ij fopkj dhft;s ftlesa 40 lseh rFkk 100 lseh Qksdl nwjh ds nks vfHklkjh ySal ,d mHk;fu"B

izdkf'kd v{k ij gSA 4 mm O;kl dh ,d yslj fdj.k iqat 40 lseh Qksdl nwjh ds ySal ij vkifrr gSA vafre

fdj.k&iqat dk O;kl gksxk

(A) 2.5 cm (B) 0.8 cm (C) 1 cm (D) 2 cm

47. In the figure shown, battery 1 has emf = 6 V and internal resistance = 1. Battery 2 has emf = 2V andinternal resistance = 3. The wires have negligible resistance. What is the potential difference across theterminals of battery 2?

n'kkZ;s fp= esa] cSVjh 1 dk fo-ok-c- 6 V rFkk vkarfjd izfrjks/k 1gSA cSVjh 2 dk fo|qr okgd cy 2V rFkk vkarfjd

izfrjks/k 3gSA cSVjh 2 ds VfeZuyksa ds e/; foHkokUrj D;k gS\

(A) 4 V (B) 1.5 V (C) 5 V (D) 0.6 V

48. A thin metal plate of large area is moving with a constant velocity v in a region of uniform magnetic field B,directed perpendicular to the velocity. Both the velocity and magnetic field are parallel to the plane of theplate. The magnitude of surface density of induced charges on a surface of the plate is

fo'kky {ks=Qy dh ,d iryh /kkrq IysV] ,dleku pqEcdh; {ks= B esa] fu;r osx v ¼pqEcdh; {ks= B ds yEcor½ ls

xfr dj jgh gSA osx rFkk pqEcdh; {ks= IysV ds ry ds lekarj gSA IysV ds ,d i"B ij izsfjr vkos'k dk i"B ?kuRo

gS

(A) vB0 (B) 2vB0 (C) 0

vB (D) None


PART III : CHEMISTRYSingle Correct Choice Type


49. Which of the following is correct order of solubility

fuEu es ls foys;rk dk lgh Øe gS(A) CaCO3 > KHCO3 > NaHCO3 (B) NaHCO3 > KHCO3 > CaCO3

(C) KHCO3 > NaHCO3 > CaCO3 (D) CaCO3 > NaHCO3 > KHCO3

50. What is the largest wavenumber in the Pfund series of He+ ion?

He+ vk;u dh Q.M Js.kh dh vf/kdre rjax la[;k D;k gSA

(A) R25

(B) R4

(C) 25R4

(D) None of these

51. Which of the following copound is optically active?

fuEufyf[kr es ls dkSulk ;kSfxd izdkf'kd lfØ; gS\

(A) (B) (C) (D) A & B both

52. Which of the following pair has same value of magnetic moment (spin only)?

fuEu es ls fdl ;qXe ds fy, pqEcdh; vk?kw.kZ ¼pzd.k ls izkIr½ dk eku leku gS\(A) FeCl2 and CuCl2 (B) VOCl2 and CuCl2 (C) VOCl2 and FeCl2 (D) FeCl2 and MnCl2

53. For the silver-zinc button cell, net reaction is

flYoj&ftad cVu lsy ds fy, ifj.kkeh vfHkfØ;kZn(s) + Ag2O (s) ZnO (s) + 2Ag(s)

Given (fn;k gqvk gS) : (f G°) Ag2O = –20 kJ mol–1 ; (f G°)ZnO = –320 kJ mol–1

What is the Eº of button cell?

cVu lSy ds Eº dk eku D;k gSa ?(A) 3.10 V (B) 1.55 V (C) 1.1 V (D) 0.775 V

54. Which of the following oxide is Amphoteric?

fuEu es ls dkSulk vkWDlkbM mHk;/kehZ gS\(A) CO2 (B) SiO2 (C) SnO2 (D) CaO

55. 3AlCl

Product (mRikn) (P)

Major product 'P' should be

eq[; mRikn (P) dh lajpuk gksxh\

(A) (B) (C) (D)


CHEMISTRY56. Galvanization is

xSyouhdj.k gS

(A) Coating of tin on Iron (yksgs ij fVu dk ysiu) (B) Coating of lead on Iron (yksgs ij ySM dk ysiu)

(C) Coating of Zinc on Iron (yksgs ij ftad dk ysiu) (D) Coating of Silver on lead (ysM ij flYoj dk ysiu)

57. In which case van’t Hoff factor is maximum?

fuEu esa ls fdl fLFkfr es ok.VgkWQ xq.kkad dk eku vf/kdre gSA

(A) KCl, 50% ionised (vk;fudr) (B) K2SO4 40% ionised (vk;fudr)

(C) SnCl4, 20% ionised (vk;fudr) (D) FeCl3, 30% ionised (vk;fudr)

58. 3 2

3

3

OH3 major product (mRikn) (P)

Major product 'P' will be


(A) (B) (C) (D)

59. Which of the following statement is incorrect regarding refining of copper by electrolysis?

dkWij ds fo|qr vi?kVuh ifj"dj.k ds lUnHkZ es vlR; dFku gS\(A) CuSO4 15% solution and 5% H2SO4 solution are used as electrolyte.

fo|qr vi?kV; ds :i esa 15% CuSO4 foy;u ,oa 5% H2SO4 foy;u dk mi;ksx fd;k tkrk gSA(B) Impure 'Cu' is used as cathode and Pure 'Cu' is used as Anode.

v'kq++++) Cu dk dSFkksM ,oa 'kq) Cu dk ,uksM fy;k tkrk gSA(C) More electropositive impurities like Fe, Zn, Ni etc dissolved in electrolyte solution.

vf/kd fo|qr/kuh /kkrq,W tSls Fe, Zn, Ni vkfn] fo|qr vi?kV~; foy;u es foys; gks tkrh gSA(D) Less electropositive metals such as Ag, Au and Pt are collected below anode called anode mud.

de fo|qr/kuh /kkrq,¡ tSls Ag, Au ,oa Pt vkfn ,uksM ds uhps ,uksM eM^ ds :i es ,df=r gks tkrh gSA

60. The number of nearest neighbours around each particle in a face-centred cubic lattice is

Qyd dsfUnzd ?kuh; tkyd es izfr d.k fudVre iM+kslh;ks dh la[;k gSA(A) 4 (B) 6 (C) 8 (D) 12

61. A first order reaction is 25% completed in 20 minutes at 300 K. When same reaction is carried out at 320K, it is 25% complete in 5 minute. What is the activation energy of reaction (in kJ/mole)?

,d izFke dksfV dh vfHkfØ;k 300 K rki ij 20 feuV es 25% iw.kZ gksrh gSA tc ;gh vfHkfØ;k 320 K rki ij 5

feuV es 25% iw.kZ gksrh gS rks vfHkfØ;k dh lfØ;.k ÅtkZ dk eku (in kJ/mole) es D;k gksxk?[Take : R = 8 J/K mole and ln 2 = 0.7 ](A) 26.88 kJ (B) 53.76 kJ (C) 13.44 kJ (D) None of these

62. Which of the following compound gives positive Iodoform Test?

fuEufyf[kr es ls dkSulk ;kSfxd vk;ksMksQkWeZ ijh{k.k nsxk \

(A) 3-Hexanone (gsdlsukWu) (B) 2-Hexanone (gsDlsukWu)

(C) Hexanal (gsDlsusy) (D) 1-Butanol (C;wVsukWy)


CHEMISTRY63. Which of the following molecule has sp3 hybridized central atom and also planar?

fuEu es ls dkSulk v.kq sp3 ladfjr dsUnzh; ijek.kq j[krk gS ,oa leryh; Hkh gS\(A) SnCl2 (B) SO2 (C) SeCl2 (D) All of these

64. Which of the following is more stable?

fuEu es ls dkSulk vf/kd LFkk;h gS\(A) [Fe(H2O)6]3+ (B) [FeF6]3– (C) [Fe(C2O4)3]3– (D) [FeCl6]3–

65. CH3CH2CONH2

KOH

Br2 major product (mRikn (P))

structure of major product will be

eq[; mRikn (P) dh lajpuk gksxh\(A) CH3CH2NH2 (B) CH3NH2 (C) CH3 – CH2CH2NH2 (D) CH3CH3

66. The values of KC for the following reactions are given as below

fuEu vfHkfØ;kvks ds fy, lkE;fu;rkad KC ds eku fn, x,s gSAA B, KC = 1, B C, KC = 3 and

C D, KC = 5

Evaluate the value of KC for A D

rks vfHkfØ;k A D ds fy, KC dk eku Kkr djsa(A) 15 (B) 5 (C) 3 (D) 1

67. HCHO + Ph – CHO NaOH.Conc ProductsProducts formed during given reaction will be

cuus okys mRikn dh lajpuk gksxh\(A) HCOONa + PhCOONa (B) Ph – COONa + CH3OH

(C) aNHCOO

– + PhCH2OH (D) CH3OH + PhCH2OH

68. )P()3(

HBF)2(

HClNaNO)1(

4

2

Product 'P' should be


(A) (B) (C) (D)


69. Total number of hydrogen atoms in one litre of water is :

,d yhVj ty es dqy gkbMªkstu ijek.kqvks dh la[;k gSA(A) 55.55 × NA (B) 55.55 × 2 × NA (C) 55.55 (D) 55.55 × 3 × NA

70. Which of the compound react with NaHCO3 to give CO2

fuEufyf[kr es ls dkSulk ;kSfxd NaHCO3 ds lkFk CO2 xSl eqDr djsxk\

(A) (B) (C) (D)

71. A system is provided 50 J of heat and work done on the system is 10 J. The change in internal energy duringthe process is

,d fudk; dks 50 J m"ek nh tkrh gS o fudk; ij 10 J dk dk;Z fd;k tkrk gS] rks bl izØe ds nksjku vkUrfjd

ÅtkZ es ifjorZu Kkr djsA(A) 40 J (B) 60 J (C) 80 J (D) 50 J

72. Thermal decomposition of FeSO4 at high temperature gives?

FeSO4 dks mPp rki ij rkih; vi?kVu ls izkIr gksrk gS\(A) SO2 (B) Fe2(SO4)3 (C) FeO + SO3 (D) Fe2O3 + SO2 + SO3

Question paper format : The question paper consists of 3 parts (Mathematics, Physics and Chemistry).

Each part contains 24 multiple choice questions. Each question has 4 choices (A),(B), (C) and (D) for its answer, out of which only one is correct.

Marking Scheme : For each question, you will be awarded 3 marks if you darken the bubble

corresponding to the correct answer and zero mark if no bubble is darkened. In caseof bubbling of incorrect answer, minus one (–1) mark will be awarded.

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