start 2016 sample test paper clsss 11 maths

CLASS: XI STREAM: SCIENCE-MATHS

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SCIMATHTP-XI-1

5th Edition

S Ta R Ttudent lent eward estSTaRTNATIONAL TALENT-O-METER

PART - I (PHYSICS) Hkkx- I HkkSfrd foKku

Straight Objective Type This section contains (1-20) multiple choice questions. Each question has choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

lh/ks oLrqfu"B izdkj bl [k.M esa (1-20) cgq&fodYih iz'u gSaA izR;sd iz'u ds 4 fodYi (A), (B), (C) rFkk (D) gSa] ftuesa ls flQZ ,d lgh gSA

1. An elastic ball P strikes a moving elevator with a velocity V perpendicular to elevator surface. If the elevator has a constant upward velocity V, then the maximum height attained by the ball after the first collision and before the second collision measured from the position of first collision is : (g is vertically downwards)

(A) 23V

2g (B)

22Vg

(C) 29V

2g (D)

2V2g

Elevator V

V P

fyV V osx ls xfr'khy ,d izR;kLFk xsan P] xfr'khy fyV dh lrg ls yEcor~ Vdjkrh gSA ;fn fyV ij dh vksj

fu;r osx V ls xfr'khy gks rks izFke VDdj dh fLFkfr ds lkis{k] izFke VDdj ds i'pkr~ rFkk f}rh; VDdj ds igys xsan }kjk izkIr vf/kdre pkbZ gksxh & (g /okZ/kj uhps dh rjQ gSA)

(A) 23V

2g (B)

22Vg

(C) 29V

2g (D)

2V2g

2. Angular speed of rotation of plate P is = g2R

. The coefficient of friction between the block of mass m and

the plate is = 0.75. The axes of rotation of the plate is vertical and the block is rotating in horizontal plane in a circle of radius R, then the friction force between the block and plate such that block is at rest relative to plate is : (g = 10 m/s2)

(A) mg2

(B) 3mg4

(C) mg4

(D) None of these

R

m P

IysV P ds ?kw.kZu dh dks.kh; pky = g2R

gSA m nzO;eku ds CykWd rFkk IysV ds e/; ?k"kZ.k xq.kkad = 0.75 gSA

IysV dh ?kw.kZu v{k /okZ/kj gS rFkk CykWd {kSfrt ry esa R f=kT;k ds o`k esa ?kw.kZu dj jgk gS rks CykWd rFkk IysV ds e/; ?k"kZ.k cy D;k gksxkA ;fn CykWd IysV ds lkis{k fLFkj gks : (g = 10 m/s2)

(A) mg2

(B) 3mg4

(C) mg4

(D) buesa ls dksbZ ugha



SCIMATHTP-XI-2

5th Edition


3. A particle moves in a straight line obeying the Vt graph as shown in figure. The average velocity of the particle from t = 0 to t = T is :

(A) Zero (B) 0V2

(C) 02V3

(D) 03V4

V0

V

T t0

ljy js[kk ij xfr'khy d.k fp=k esa iznf'kZr osx xzkQ dk ikyu djrk gSA t = 0 ls t = T le;kUrjky ds e/; d.k dk vkSlr osx gksxk :

(A) 'kwU; (B) 0V2

(C) 02V3

(D) 03V4

4. Two blocks of masses 2 Kg and 3 Kg are placed on a plank. An external force of 10N is acting on 2 Kg block and the whole system including the plank is moving vertically up with a constant acceleration a0 = 2 m/s2. The normal reaction force between the 3 Kg block and Plank is : (g = 10 m/s2)

(A) 34 N (B) 64 N (C) 52 N (D) 70 N

2 Kg

3 Kg

Plank (r [ r k)

10 N

a0

2 Kg rFkk 3 Kg nzO;eku ds nks CykWd ,d r[rs ij j[ks gq, gSA 2 Kg nzO;eku ds CykWd ij ,d ckg~; cy 10N

vkjksfir gS rFkk lEiw.kZ fudk; r[rs ds lkFk /okZ/kj ij dh vksj fu;r Roj.k a0 = 2 m/s2 ls xfr'khy gSA 3 Kg nzO;eku ds CykWd rFkk r[rs ds e/; vfHkyEc izfrf;k cy gksxk : (g = 10 m/s2)

(A) 34 N (B) 64 N (C) 52 N (D) 70 N

5. A particle of mass m moves with a velocity V which varies with time as V = 0tV 1T

, where T and V0

are positive constants, then the instantaneous power delivered to the particle at time t = T2

is :

(A) 202mV

3T (B)

203mV

2T (C)

20mV

2T (D) None of these

m nzO;eku dk d.k V osx ls xfr'khy gS bldk osx le; ds lkFk V = 0tV 1T

ds vuqlkj ifjofrZr gksrk gS, tgk

T rFkk V0 /kukRed fu;rkad gS, rks le; t = T2 ij d.k dks nh xbZ rkR{kf.kd 'kfDr gksxh :

(A) 202mV

3T (B)

203mV

2T (C)

20mV

2T (D) buesa ls dksbZ ugha



SCIMATHTP-XI-3

5th Edition


6. A disc (of radius r cm) of uniform thickness and uniform density has a square hole with sides of

length = r2

cm. One corner of the hole is located at the center of the disc ''O'' and centre of the hole

lies on y-axis as shown. Then the y-coordinate of position of center of mass of disc with hole (in cm) is

,dleku eksVkbZ rFkk ,dleku ?kuRo dh (r cm f=kT;k dh) ,d pdrh esa HkqTkk = r2

cm ds oxZ ds vkdkj dk

,d fNnz gSA fNnz dk ,d dksuk pdrh ds dsUnz ''O'' ij fLFkr gS rFkk fNnz dk dsUnz y-v{k ij fLFkr gS tSlk fd fn[kk;k x;k gSA rks fNnz;q pdrh ds nzO;eku&dsUnz dh fLFkfr dk y-funsZ'kkad (cm esa) gksxk &

(A) r2 ( )

(B) r4 ( )

(C) r4 ( )

(D) 3 r4 ( )

7. The moment of inertia of a door of mass m, length 2 and width about its longer side is

(A) 211m

24 (B)

25 m24 (C)

2m3 (D) none of these

m nzO;eku dk ,d njoktk ftldh yEckbZ 2 o pkSM+kbZ gS] mldh yEch Hkqtk ds lkis{k njokts dk tM+Ro vk?kw.kZ gksxk

(A) 211m

24 (B)

25 m24 (C)

2m3 (D) buesa ls dksbZ ugha

8. The components of a force acting on a particle are varying according to the graphs shown. When the particle moves from (0, 5, 12) to (4, 20, 0) then the work done by this force is :

(A) 192 J (B) 400/3 J (C) 0 (D) None of these

,d d.k ij dk;Zjr cy ds ?kVd iznf'kZr xzkQ ds vuqlkj ifjofrZr gksrs gSaA tc d.k (0, 5, 12) ls (4, 20, 0) rd pyrk gS rc bl cy }kjk fd;k x;k dk;Z gS :

Fx(U; wVu esa)

(ehVj esa)

Fy (U; wVu esa)

y (ehVj esa)

Fz (U; wVu esa)

z (ehVj esa)

(A) 192 J (B) 400/3 J (C) 0 (D) buesa ls dksbZ ugha



SCIMATHTP-XI-4

5th Edition


9. Two particles tied to different strings are whirled in a horizontal circle as shown in figure. The ratio of

lengths 12

LL

of the strings so that they complete their circular path with equal time period is :

(A) 32

(B) 23

(C) 1 (D) None of these

fHkUu&fHkUu jLlh ls cU/ks nks d.kksa dks fp=kkuqlkj {kSfrt o`kkdkj iFk esa ?kqek;k tkrk gSA jfLl;ksa dh yEckbZ dk

vuqikr 12

LL

D;k gS ftlls os viuk o`kh; iFk leku le; vUrjky esa iwjk djrs gS &

(A) 32

(B) 23

(C) 1 (D) bueas ls dksbZ ughA 10. A ring shaped tube contains two ideal gases with equal masses and atomic mass numbers M1 = 32 and

M2 = 28. The gases are separated by one fixed partition P and another movable conducting partition S which can move freely without friction inside the tube. The angle as shown in the figure in equilibrium is:

,d oy; vkd`fr dh uyh esa leku nzO;eku okyh nks vkn'kZ xSlsa Hkjh gSa] ftuds ijek.kq Hkkj e'k% M1 = 32 rFkk M2 = 28 gSA xSlksa dks ,d fLFkj foHkktd P rFkk vU; pyk;eku pkyd foHkktd S }kjk foHkkftr fd;k x;k gSA foHkktd S uyh esa fcuk ?k"kZ.k xfr ds fy, LorU=k gSA lkE;koLFkk esa fp=k esa n'kkZ;s vuqlkj dks.k gS &

M 1 M 2

P

S

(A) 78 (B) 8

7 (C) 15

16 (D) 16

15

11. A uniform rod of mass m and length is attached to smooth hinge at end A and to a string at end B as shown in figure. It is at rest initially. The angular acceleration of the rod just after the string is cut is: ,d m nzO;eku rFkk yEckbZ dh ,d leku NM+ ,d fljs A ij fpdus dhyd ?kwe ldrh gS ls rFkk nwljs fljs B ij

jLlh ls fp=kkuqlkj tqM+h gSA izkjEHk esa ;g fLFkjkoLFkk esa gSA jLlh dks dkVus ds Bhd i'pkr NM+ dk dks.kh; Roj.k gksxk %&

(A) 3g2

(B) 3g4

(C) 5g4

(D) 5g2



SCIMATHTP-XI-5

5th Edition


12. A lift is moving upwards with a constant speed of 5 m/s. The speed of one of the pulleys is 5 m/s as shown. Then the speed of second pulley is :

(A) 5m/s (B) zero (C) 7.5 m/s (D) 10 m/s

,d fyV 5 m/s dh fu;r pky ls ij dh vksj xfreku gSA fp=k esa n'kkZ;s x, vuqlkj ,d vkn'kZ f?kjuh dk osx

5 m/s gS rks nwljh f?kjuh dh pky gksxh % (A) 5m/s (B) 'kwU; (C) 7.5 m/s (D) 10 m/s 13. A sphere of radius R is in contact with a wedge. The point of contact is R/5 from the ground as shown in

the figure. Wedge is moving with velocity 20 m/s, then the velocity of the sphere at this instant will be : R f=kT;k dk ,d xksyk] xqVds ls lEidZ esa gSA fp=k esa fn[kk;s vuqlkj Li'kZ fcUnq tehu ls R/5 nwjh ij gSA ;fn

xqVdk 20 m/s ls xfr djrk gS] rks bl le; xksys dk osx gksxkA

(A) 20 m/s (B) 15 m/s (C) 5 m/s (D) 10 m/s 14. A small block of mass m is taken slowly up a fixed hemisphere from P to Q and then slowly down along

its surface from Q to S by force F, which at each point of the surface, is tangential to the surface. If the coefficient of friction is , then the work performed by the force F in taking the block from P to S along the hemispherical surface of radius R is :

m nzO;eku dk ,d CykWd /khjs&/khjs ,d tMor v/kZ xksys ij fcUnq P ls Q rd] fQj Q ls S rd] F cy vkjksfir djds lrg ds vuqfn'k pykdj ys tk;k tkrk gSA ;g cy F bl iFk ds izR;sd fcUnw ds Li'kZ js[kh; fn'kk esa gSA ;fn ?k"kZ.k xq.kkad gks rks CykWd dks v)Zxksys f=kT;k R dh lrg ds vuqfn'k P ls S rd ys tkusa esa cy F }kjk fd;k x;k dk;Z Kkr dhft,A

(A) 2mgR (B) mgR (C) mgR (D) mgR



SCIMATHTP-XI-6

5th Edition


15. A block of mass M is suspended by a string. Bullets each of mass m are fired vertically upwards towards the centre of the block at speed u. If the bullets rebound after striking the block and coefficient of restitution for each collision is same and equal to e, how many bullets per second are to be fired so that the string just becomes slack ?

(A) Mu(1 e)mg (B) Mg(1 e)

mu

(C) Mgmu(1 e)

(D) None of these

,d M nzO;eku dk CykWd jLlh dh lgk;rk ls yVdk gqvk gS m nzO;eku R;sd ds fy, dh

xksfy;k u pky ls /okZ/kj ij dh vksj CykWd ds dsUnz dh vksj nkxh tkrh gS ;fn xksfy;k CykWd ls Vdjkdj iqu% ykSV vkrh gS ,oa izR;sd VDdj ds fy, izR;koLFku xq.kkad e gks rks izfr lSd.M fdruh xksfy;k nkxh tk,a rkfd jLlh



SCIMATHTP-XI-7

5th Edition


18. A smooth chain AB of mass m rests on a quarter circular fixed smooth surface of radius r as shown in figure. When released the chain slides in vertical plane on the circular surface. If the length of the chain is exactly equal to the length of the quarter circular path, then find its velocity when the complete part of the chain comes over the horizontal smooth surface.

,d ?k"kZ.kghu m nzO;eku dh pSu AB fp=kkuqlkj r f=kT;k ,d pkSFkkbZ ds o`kh; ?k"kZ.kghu fLFkj Hkkx ij fLFkr gS tgk ls bls fQlyus ds fy, /okZ/kj ry esa eqDr fd;k tkrk gSA pSu dh yEckbZ, o`k dh ,d pkSFkkbZ yEckbZ ds Bhd cjkcj gSA pSu dk osx ml {k.k Kkr dhft, tc bldk lEiw.kZ Hkkx ?k"kZ.kjfgr {kSfrt lrg ij vk tk;sA

(A) 2gr4

(B) 12gr 1 (C) 22gr 1

(D) 2gr 1

19. Power of the only force acting on a particle of mass m = 1 kg moving in straight line depends on its

velocity as P = v2 where v is in m/s and P is in watt. If initial velocity of the particle is 1 m/s, then the displacement of the particle in n2 seconds will be :

ljy js[kk esa xfr dj jgs m = 1 kg nzO;eku ds d.k ij dk;Zjr dsoy ,d cy dh 'kfDr blds osx ij P = v2 ds vuqlkj fuHkZj djrh gS tgk v, m/s esa gS rFkk P okWV esa gSA ;fn d.k dk izkjfEHkd osx 1 m/s gSA rc n2 lsd.M esa d.k dk foLFkkiu gSA

(A) (n2 1)m (B) (n2)2 m (C) 1 m (D) 2 m 20. A uniform sheet of mass M is lying on coordinate axis as shown in the figure. What is coordinate of

centre of mass of sheet.

(A) 3( 3 1)b3 , 3( 3 1)b

3 (B) 3( 3 1)b

3 , 3( 3 1)b

3

(C) (2 3 1)b3( 3 1)

, 3b

3( 3 1) (D) None of these

X ,d le:i M nzO;eku dh ifdk funsZ'k rU=k esa fp=kkuqlkj j[kh gqbZ gSA ifdk ds nzO;eku dsUnz ds funsZ'kkad D;k

gksaxsA

(A) 3( 3 1)b3 , 3( 3 1)b

3 (B) 3( 3 1)b

3 , 3( 3 1)b

3

(C) (2 3 1)b3( 3 1)

, 3b

3( 3 1) (D) buesa ls dksbZ ugha



SCIMATHTP-XI-8

5th Edition


PART - II (CHEMISTRY) Hkkx- II jlk;u foKku



21. In an H like species when electron make back transition to first excited state from nth orbit emits photon of 23 eV energy and when electron make back transition from the same nth orbit to 2nd excited state emits photon of 6 eV energy. What is the maximum wavelength required to just ionise the sample from ground state. [hc = 1240 nm eV]

,d H ds leku Lih'kht es ;fn bysDVkWu nth d{kk ls 23 eV QksVksu dh tkZ mRlftZr dj izFke mRrsftr voLFkk esa i'p lae.k djrs gS rFkk bysDVkWu leku nth d{kk ls 6 eV QksVksu dh tkZ dk mRltZu dj f}rh; mRrsftr voLFkk esa vkrs gS] rks bl uewus dks vk| voLFkk ls vk;fur djus ds fy;s vko';d vf/kdre rjaxnS/;Z D;k gksxh \

[hc = 1240 nm eV] (A) 10.13 nm (B) 22.7 nm (C) 91.18 nm (D) 5.7 nm 22. Magnetic moments of V (Z = 23), Cr (Z = 24), Mn (Z = 25) are x, y, z respectively. Hence : V (Z = 23), Cr (Z = 24), Mn (Z = 25) ds pqEcdh; vk?kw.kZ e'k% x, y, z gSa] rks (A) x = y = z (B) x < y < z (C) x < z < y (D) z < y < x

23. The correct order of bond lengths in the following is (A) H2 < H2+ < He2+ (B) O22 > O2 > O2 > O2+ > O2++ (C) CO3 > CO2 > CO (D) all of them are correct fuEu ds fy, ca/k yEckbZ dk lgh e gksxk & (A) H2 < H2+ < He2+ (B) O22 > O2 > O2 > O2+ > O2++ (C) CO3 > CO2 > CO (D) mi;qDr lHkh lgh gSa 24. According to molecular orbital theory which of the following is correct : (A) LUMO level for C2 molecule is a 2p orbital (B) Mixing of 2s and 2p orbitals is observed in M.O. of C2. (C) In 22C ion there is one and two bonds (D) all the above are correct. v.kq d{kd fl)kUr (MOT) ds vuqlkj fuEu esa ls lgh gS& (A) C2 v.kq ds fy, LUMO ry ,d 2p d{kd gSA (B) C2 ds M.O. esa 2s o 2p d{kdksa dk feJ.k izsf{kr gksrk gSA (C) 22C vk;u esa ,d rFkk nks cU/k gksxsa (D) mijksDr lHkh lgh gSaA 25. Name of a newly discovered element which belongs to a period number 7 and group number 8 is : ,d u;s [kkst fd;s x;s rRo dk uke fyf[k;s tks fd vkorZ la[;k 7 o oxZ la[;k 8 ls lEcfU/kr gS % (A) unnilnilium (mufuyfufy;e) (B) unniloctium (mufuyvkWfDV;e) (C) ununbium (mumufc;e) (D) ununhexium (mumugsfDl;e)

26. What volume of HCl solution of density 1.2 g/cm3 and containing 36.5% by weight HCl, must be allowed to react with zinc (Zn) in order to liberate 4.0 g of hydrogen ?

1.2 g/cm3 ?kuRo rFkk Hkkj dk 36.5% HCl j[kus okys HCl foy;u dk fdruk vk;ru (Zn) ds lkFk vfHkdr` djk;k tk, fd 4.0 g gkbMkstu eqDr gks ?

(A) 333.33 ml (B) 500 ml (C) 614.66 ml (D) None of these (buesa ls dksbZ ugha)



SCIMATHTP-XI-9

5th Edition


27. During the test of sulphur in organic compound, the purple colour formed by adding sodium nitroprusside to Lassaignes extract is due to

dkcZfud ;kSfxd esa lYQj ds ifj{k.k ds nkSjku ySlkus fu"d"kZ esa lksfM;e ukbVksizqlkbM feykus ij fuEu esa ls fdlds dkj.k gYdk cSaxuh jax curk gS %&

(A) Na4 [Fe(CN)5NO] (B) Na4 [Fe(CN)5NOS] (C) Na3 [Fe(CN)5NS] (D) Fe4 [Fe(CN)6]3 28. IUPAC name of the given compound is : fuEu ;kSfxd dk IUPAC uke gS %

OH

OH (A) Dec-8-en-4-yne-3,6-diol (B) Dec-2-en-6-yne-5,8-diol (C) 3, 6-dihydroxydec-8-en-4-yne (D) 5,8-dihydroxydec-2-en-6-yne

(A) Msd-8-bZu-4-vkbu-3,6-MkbvkWy (B) Msd-2-bZu-6-vkbu-5,8-MkbvkWy (C) 3, 6-MkbgkbMkWDlhMsd-8-bZu-4-vkbu (D) 5,8-MkbgkbMkWDlhMsd-2-bZu-6-vkbu 29. Which amongs the following can be the structure of molecular formula C5H8O2. v.kqlw=k C5H8O2 okys ;kSfxd dh nh xbZ lajpukvksa esa ls dkSulh lajpuk ;kSfxd dh gS\

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

30. Consider the following compound fuEu ;kSfxd ij fopkj dhft,

OCH3N

P

The locant number for the OCH3 in above compound is mijksDr ;kSfxd esa OCH3 ds fy, ekadu la[;k gS % (A) 5 (B) 6 (C) 2 (D) 3 31. Three oxides of a certain hypothetical element contain 50%, 33.33% and 25% element by mass

respectively. The simplest ratio of the valencies of element in the three oxides is: (A) 2 : 3 : 4 (B) 3 : 4 : 6 (C) 1 : 2 : 3 (D) None of these ,d dkYifud rRo ds rhu vkWDlkbMksa esa e'k% Hkkjkuqlkj 50%, 33.33% rFkk 25% rRo mifLFkr gSA bu rhuksa

vkWDlkbMksa esa rRo dh la;kstdrkvksa dk ljyre vuqikr gS : (A) 2 : 3 : 4 (B) 3 : 4 : 6 (C) 1 : 2 : 3 (D) buesa ls dksbZ ugha 32. An electron is accelerated from rest by a certain potential difference and it has wavelength of 1.41 . By

how much amount should potential difference be dropped, so that wavelength associated with electron becomes 1.73 :

fojke voLFkk ls ,d bysDVkWu dks ,d fuf'pr foHkokUrj }kjk Rofjr fd;k tkrk gS rFkk bldh rjax nS/;Z 1.41 gSA rc fdruh ek=kk esa foHkokUrj dks de fd;k tk;s] fd bysDVkWu ls lEcfU/kr rajx}S/;Z 1.73 gks tk;s %

(A) 25 V (B) 50 V (C) 75 V (D) 12.5 V



SCIMATHTP-XI-10

5th Edition


33. The correct sequence of the ionic radius of the following is : fuEu esa ls fdlesa] Lih'kht dh vk;fud f=kT;kvksa dk vuqe lgh gS % (A) Br > Cl > S2 > O2 > F (B) Br > S2 > Cl > O2 > F (C) Br > S2 > Cl > F > O2 (D) S2 > Br > Cl > O2 > F 34. In which of the following species, the bond length, is expected to be the longest ? fuEu esa ls fdl iztkfr esa] cak yEckbZ lcls cM+h gksrh gSA (A) O22 (B) O2 (C) O2 (D) O2+ 35. Given a compound XeO2F2, the hybridisation of Xe and shape of molecule respectively are : (A) sp3d, see-saw (B) sp3, tetrahedral (C) sp3, see-saw (D) sp3d, tetrahedral ,d ;kSfxd XeO2F2 fn;k x;k gS] Xe dk ladj.k rFkk v.kq dh vkd`fr e'k% fuEu gSa % (A) sp3d, >qys tSlh vkd`fr (see-saw) (B) sp3, prq"Qydh; (C) sp3, >qys tSlh vkd`fr (see-saw) (D) sp3d, prq"Qydh; 36. In the preparation of iron form haematite (Fe2O3) by the reaction with carbon Fe2O3 + C Fe + CO2 How much 80% pure iron could be produced from 120 kg of 90% pure Fe2O3? dkcZu ds lkFk vfHkf;k }kjk gsesVkbV (Fe2O3) ls vk;ju ds fuekZ.k esa Fe2O3 + C Fe + CO2

90% 'kq) (Fe2O3) ds 120 Kg ls mRikfnr 80% 'kq) vk;ju fdruk gS\ (A) 94.5 kg (B) 60.48 kg (C) 116.66 kg (D) 120 kg

37. Observe each pair of cations. In which case (s) first is more stable than the second : fuEufyf[kr izR;sd /kuk;u ;qXeksa dk izs{k.k dhft,] buesa ls dkSuls ;qXe dk izFke /kuk;u f}rh; ls vf/kd LFkk;h gS

(W) ,

(X)

,

(Y)

,

(Z)

,

(A) Only in W (B) Only in X and Y (C) Only in Z (D) Only in W and Z (A) dsoy W esa (B) dsoy X rFkk Y esa (C) dsoy Z esa (D) dsoy W rFkk Z esa



SCIMATHTP-XI-11

5th Edition


38. Give the correct IUPAC name of the following compound is :

(A) 1-Bromo-1-ethyl-2-fluoro-2-iodo-1-nitroethane.

(B) 3-Bromo-4-fluoro-4-iodo-3-nitrobutane. (C) 2-Bromo-1-fluoro-1-iodo-2-nitrobutane.

(D) 1-Fluoro-1-iodo-2-bromo-2-ethyl-2-nitroethane. fuEu ;kSfxd dk lgh IUPAC uke gS %

(A) 1-czkseks-1-,fFky-2-yksjks-2-vk;ksMks-1-ukbVks,Fksu

(B) 3-czkseks-4-yksjks-4-vk;ksMks-3-ukbVksC;wVsu (C) 2-czkseks-1-yksjks-1-vk;ksMks-2-ukbVksC;wVsu

(D) 1-yksjks-1-vk;ksMks-2-czkseks-2-,fFky-2-ukbVks,Fksu 39. Which of the following pairs contain functional isomers? fuEu esa ls dkSulk ;qXe f;kRed leko;ork j[krk gS\

(A) ,

(B) ,

(C) , (D) ,

40. During addition of HCl over propene in the presence of peroxide, intermediate formed is : ijkWDlkbM dh mifLFkfr esa] izksihu ij HCl dks feykus ds nkSjku] fuEu esa ls dkSulk e/;orhZ curk gS :

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



SCIMATHTP-XI-12

5th Edition


PART - III (MATHEMATICS) Hkkx- III xf.kr



41. Let A = {1, 2, {3, 4}, 5}. Which of the following is correct ? ekuk A = {1, 2, {3, 4}, 5} rc fuEu esa ls dkSulk lgh gS ? (A) {{3, 4}} A (B) A (C) {3, 4} A (D) {1, 2, 5} A 42. Given that X = A B and Y = A B. The number of subsets of B is four times the number of subsets of

A, while the number of subsets of A is four times the number of subsets of X. It is given that n(X) = 5. Let p, q, r, s be the number of subsets of A, B, X and Y respectively. Then from the following

(i) n(A) = 7 (ii) n(B) = 9 (iii) n(Y) = 11 (iv) pq = rs, the number of correct statements is (are)

fn;k x;k gS X = A B vkSj Y = A B gSA B ds mileqPp;ksa dh la[;k] A ds mileqPp;ksa dh la[;k ls pkj xquk vf/kd gS tcfd A ds mileqPp;ksa dh la[;k] X ds mileqPp;ksa dh la[;k dk pkj xquk gSA ;g fn;k x;k gS fd n(X) = 5. ekuk A, B, X rFkk Y ds mileqPp;ksa dh la[;k e'k% p, q, r, s gSA rc fuEu esa ls

(i) n(A) = 7 (ii) n(B) = 9 (iii) n(Y) = 11 (iv) pq = rs, lgh dFkuksa dh la[;k gS& (A) 1 (B) 2 (C) 3 (D) 4

43. The sum of the series 360

n 1

1n n 1 (n 1) n

is equal to

Js



SCIMATHTP-XI-13

5th Edition


47. If sin xsin y

= 12

, cos xcos y

= 32

, where x, y 0,2

, then the value of tan(x + y) is equal to :

;fn sin xsin y

= 12

, cos xcos y

= 32

, tgk x, y 0,2

, rc tan(x + y) dk eku cjkcj gS&

(A) 13 (B) 14 (C) 17 (D) 15 48. If more than two values of x satisfying the equation

A 10

x2 + A 5

5B 7

x + 4B 7

13C 70

= 0, then which one of the following is

INCORRECT ? ;fn lehdj.k

A 10

x2 + A 5

5B 7

x + 4B 7

13C 70

= 0 ds fy, x ds nks ls vf/kd eku larq"B gksrs gS]

rc fuEu esa ls dkSulk vlR; gS ?

(A) tan A = tan A (B) tan A tan B = 1 (C) cot A2

= cot A2

(D) cot A cot B = 1

49. The general solution of the equation tan2 tan = 1, is lehdj.k tan2 tan = 1 dk O;kid gy gS&

(A) = (2n + 1) 4 , n (B) = (2n + 1)

6 , n

(C) = (2n + 1) 3 , n (D) = n

3 , n

50. The length of a rectangle is three times the breadth. If the minimum perimeter of the rectangle is

160 cm, then (A) breadth > 20 cm (B) length < 20 cm (C) breadth 20 cm (D) length 20 cm vk;r dh yEckbZ] bldh pkSM+kbZ ls rhu xquh gSA ;fn vk;r dk U;wure ifjeki 160 lseh gS rc, (A) pkSM+kbZ > 20 lseh (B) yEckbZ < 20 lseh (C) pkSM+kbZ 20 lseh (D) yEckbZ 20 lseh

51. The value of a such that the sum of the squares of the roots of the equation x2 (a 2) x (a + 1) = 0 is least is

a dk eku gksxk tcfd lehdj.k x2 (a 2) x (a + 1) = 0 ds ewyksa ds oxksZ dk ;ksxQy U;wure gks - (A) 5 (B) 3 (C) 1 (D) 0

52. If z = 17

50( 3 i)(1 i)

, then principal value of argument of z is equal to

;fn z = 17

50( 3 i)(1 i)

, rc z ds dks.kkad dk eq[; eku cjkcj gS&

(A) 3 (B) 2

3 (C) 2

3 (D) 5

3

53. The number of arrangements which can be made out of the letters of the word 'ALGEBRA' without

changing the relative order (positions) of vowels and consonants, is : 'kCn 'ALGEBRA' ds v{kjksa ds Lojksa vkSj O;atuksa dk lkisf{kd e esa ifjorZu fd, fcuk cuk, x, ep;ksa dh la[;k gS &

(A) 72 (B) 54 (C) 36 (D) 48



SCIMATHTP-XI-14

5th Edition


54. If a, b, c are the sides of a triangle, then ab c a

+ bc a b

+ ca b c

;fn a, b, c f=kHkqt dh Hkqtk,a gks] rks ab c a

+ bc a b

+ ca b c

(A) 3 (B) < 3 (C) 1 (D) 2

55. Let tr = 2r/2 + 2r/2. Then 10

2r

r 1

t is equal to

ekuk tr = 2r/2 + 2r/2. rc 10

2r

r 1

t cjkcj gS&

(A) 21

10

2 12

+ 20 (B) 21

10

2 12

+ 19 (C) 21

10

2 12

1 (D) 210 + 101

2+ 2 10

56. Suppose A1, A2,..A30 are thirty sets with five elements and B1 , B2, .Bn are n sets each with three

elements, where 30 n

i ji 1 j 1

A B S

. Assume that each element of S belong to exactly ten of the Ai's and to exactly nine of the Bj's then value of n is

(A) 44 (B) 45 (C) 46 (D) 50 ekuk fd A1, A2,..A30 rhl leqPp; gS ftlesa izR;sd esa 5 vo;o gS rFkk B1 , B2, .Bn , n leqPp; gS ftuesa izR;sd

esa 3 vo;o gS tgk 30 n

i ji 1 j 1

A B S

ekuk fd S dk izR;sd vo;o Ai ds Bhd 10 dks j[krk gS rFkk Bj ds Bhd ukS dks j[krk gSA rc n dk eku gS -

(A) 44 (B) 45 (C) 46 (D) 50 57. Value of cos56 + cos58 cos66 4cos28 cos29 sin33 equal to cos56 + cos58 cos66 4cos28 cos29 sin33 dk eku cjkcj gS - (A) 0 (B) 1 (C) 1 (D) 2

58. If f(n) = 13 + 23 + 33 +. upto n terms, then n

3

r 1

(1 2r) =

;fn f(n) = 13 + 23 + 33 +. n in rd gS rc n

3

r 1

(1 2r) =

(A) 8f(n) f(2n) (B) f(2n) 8f(n) (C) f(n) f(2n) (D) f(2n) + 8f(n) 59. The number of ways of selecting four card of an ordinary pack of playing cards so that exactly 3 of them

are of the same denominations is (A) 2496 (B) 13C3 4C3 48 (C) 52C3 48 (D) None of these rk'k dh lk/kkj.k xM~Mh ls pkj ikksa dks pquus ds ep; gS tcfd muesa ls Bhd rhu leku vad@v{kj ds gS& (A) 2496 (B) 13C3 4C3 48 (C) 52C3 48 (D) buesa ls dksbZS ugha 60. The last digit of (1! + 2! + .... + 2005!)500 is (1! + 2! + .... + 2005!)500 dk vfUre vad gS - (A) 9 (B) 2 (C) 7 (D) 1



SCIMATHTP-XI-15

5th Edition


61. The modulus of 1 i3 i

+ 4i5

is : 1 i3 i

+ 4i5

dk ekikad gS&

(A) 5 (B) 115

(C) 55

(D) 125

62. Which of the following set of values of x satisfies the equation

3 3 sin3x + cos3x + 3 3 sin x cos x = 1 lehdj.k 3 3 sin3x + cos3x + 3 3 sin x cos x = 1 dks larq"B djus okys x ds ekuksa dk leqPp; gS&

(A) 2n, n (B) (2n + 1) 3 , n (C) (2n + 1)

4 , n (D) 2n

3 , n

63. The values of the parameter 'a' for which the quadratic equations (1 2a)x2 6ax 1 = 0 and

ax2 x + 1 = 0 have at least one root in common are izkpy a dk eku gksxk ftlds fy, f}?kkr lehdj.ksa (1 2a)x2 6ax 1 = 0 vkSj ax2 x + 1 = 0 esa de ls de

,d ewy mHk;fu"B gS&

(A) 0, 12

(B) 12

, 29

(C) 29

(D) 0, 12

, 29

64. Which of the following is the correct principle of mathematical induction : (A) Let P(n) be a statement such that n be any integer and P(1) is true also P(m) is true for, any natural

number then P(n) is true for all integers n (B) Let P(n) be a statement involving natural number n such that P(1) is true and P(m) is true whenever

P(n) is true for every n m, then P(n) is true for all n N (set of natural numbers) (C) Let P(n) be a statement where n N such that P(1) is true and P(n), P(n + 1) also holds then P(n)

is true n N (D) Let P(n) be a statement involving natural number n, such that P(1) is true and P(m + 1) is true for all

n m. Then P(n) is true for all n N

fuEu esa ls dkSulk dFku xf.krh; vkxeu dk fl)kUr ds fy, lgh gS - (A) ekuk P(n) dFku gS tcfd n dksbZ iw.kkZd gS rFkk P(1) lR; gS rFkk P(m) Hkh lR; gS fdlh izkdr` la[;k ds fy,

rc lHkh n iw.kkZad ds fy, P(n) lR; gS (B) ekuk n izkd`r la[;k ds fy, P(n) ,d dFku bl izdkj gS fd P(1) lR; gS vkSj P(m) lR; gS tcfd

n m, ds fy, P(n) lR; gS rc lHkh n N (lHkh izkd`r la[;kvksa dk leqPp;) ds fy, P(n) lR; gSA (C) ekuk P(n) ,d dFku gS tgk n N tcfd P(1) lR; gS rFkk P(n), P(n + 1) Hkh lR; gS rc P(n),

n N ds fy, lR; gSA (D) ekuk P(n) izkdr` la[;k n ds fy, dFku bl izdkj gS fd P(1) lR; gS rFkk P(m + 1) lR; gS lHkh n m ds

fy, rc lHkh n N ds fy, P(n) lR; gSA

65. Let x be the arithmetic mean and y, z be the two geometric means between any two positive numbers,

then the value of 3 3y zxyz is

ekuk fdlh nks /kukRed la[;kvksa ds e/; ,d lekUrj ek/; x rFkk nks xq.kkskj ek/; y vkSj z gS] rc 3 3y zxyz dk eku gS&

(A) 2 (B) 3 (C) 1/2 (D) 3/2

66. If n = 12m, (m N), nC0 n

22

C(2 3)

+n

44

C(2 3)

n

66

C(2 3)

+..... = (1)mn

P2 Q

then P Q is

;fn n = 12m, (m N), nC0 n

22

C(2 3)

+n

44

C(2 3)

n

66

C(2 3)

+.... = (1)mn

P2 Q

rc P Q gS -

(A) 4 (B) 5 (C) 6 (D) 20



SCIMATHTP-XI-16

5th Edition


67. Let R and S be two non-void relations on set A. which of the following statement is false ? (A) R and S are transitive implies R S is transitive (B) R and S are transitive implies R S is transitive

(C) R and S are symmetric implies R S is symmetric (D) R and S are reflexive implies R S is reflexive

ekuk R vkSj S leqPp; A ij nks vfjDr leqPp; gS rc fuEu esa ls dkSulk dFku xyr gS ? (A) R rFkk S laked gS rc R S Hkh laked gSA (B) R rFkk S laked gS rc R S laked gSA

(C) R rFkk S lefer gS rc R S lefer gSA (D) R rFkk S LorqY; gS rc R S LorqY; gSA

68. If straight lines 2x + 3y 1 = 0, x + 2y 1 = 0 and ax + by 1 = 0 form a triangle with origin as

orthocentre, then (a, b) is equal to ;fn ljy js[kk,a 2x + 3y 1 = 0, x + 2y 1 = 0 vkSj ax + by 1 = 0 ,d f=kHkqt cukrh gS ftldk yEcdsUnz]

ewy fcUnq gS] rc (a, b) cjkcj gS& (A) (6, 4) (B) (3, 3) (C) (8, 8) (D) (0, 7) 69. Value of sin25 + sin210 + sin215 + .......... + sin285 + sin290 is sin25 + sin210 + sin215 + .......... + sin285 + sin290 dk eku gS&

(A) 3 (B) 9 (C) 192

(D) 92

70. For n 2, , (1 i)12

21 i1

2

221 i12

. . . . . 201021 i1

2

= (1 + i ) n211

2

the

value of n is

n 2, ds fy, (1 i)12

21 i12

221 i12

.....201021 i1

2

= (1 + i) n211

2

rc n dk eku gS -

(A) 2011 (B) 2009 (C) 2010 (D) 2012 71. The quadratic x2 + ax + b + 1 = 0 has roots which are positive integers then (a2 + b2) can be equal to

f}?kkr x2 + ax + b + 1 = 0 ds ewy] /kukRed iw.kkd gS rc (a2 + b2) dk eku cjkcj gks ldrk gS& (A) 50 (B) 37 (C) 61 (D) 19 72. z1 and z2 are two distinct points in an argand plane. If a|z1| = b|z2| (where a, b R), then the point

1 2

2 1

az bzbz az

is a point on the

(A) line segment [2, 2] of the real axis (B) line segment [2, 2] of the imaginary axis. (C) unit circle |z| = 1 (D) line with arg z = tan1 2

lfEeJ lery esa z1 vkSj z2 nks fofHk fcUnq gSA ;fn a|z1| = b|z2| (tgk a, b R), rc ,d fcUnq 1 22 1

az bzbz az

ij gS&

(A) okLrfod v{k ds js[kk[k.M [2, 2] ij (B) dkYifud v{k ds js[kk[k.M [2, 2] ij (C) bdkbZ o`k |z| = 1 ij (D) dks.kkad arg z = tan1 2 dh js[kk ij



SCIMATHTP-XI-17

5th Edition


73. Let a (0, 1] satisfies the equation a2008 2a + 1 = 0 and S = 1 + a + a2 + .. + a2007 sum of all possible value(s) of S is

ekuk a (0, 1] lehdj.k a2008 2a + 1 = 0 vkSj S = 1 + a + a2 + .. + a2007 dks larq"B djrs gS rc S ds lHkh laHkkfor ekuksa dk ;ksxQy gS&

(A) 2010 (B) 2009 (C) 2008 (D) 2 74. Let n N; n > 25. Let A,G,H denote the arithmetic mean, geometric mean and harmonic mean of 25

and n. The least value of n which A,G,H {25, 26, 27,.n} ekuk n N; n > 25 ekuk A,G,H 25 vkSj n ds lekUrj ek/;] xq.kkskj ek/;] vkSj gjkRed ek/; dks O;Dr djrk gSA

n dk U;wure eku tcfd A,G,H {25, 26, 27,.n} gSA (A) 49 (B) 81 (C) 169 (D) 225 75. n is selected from the set {1, 2, 3,100} and the number 2n + 3n + 5n is formed. Total number of

ways of selecting n so that the formed number is divisible by 4 is equal to leqPp; {1, 2, 3,100} ls n la[;kvksa dks pquk tkrk gSA rFkk la[;k 2n + 3n + 5n cukbZ tkrh gSA pquh xbZ n

la[;kvksa dh dqy la[;k tcfd cukbZ xbZ la[;k 4 ls foHkkftr gS& (A) 50 (B) 49 (C) 48 (D) 100

ANSWER KEY Stream : Science-Maths 1. (C) 2. (A) 3. (B) 4. (D) 5. (B) 6. (C) 7. (C)

8. (A) 9. (B) 10. (D) 11. (B) 12. (A) 13. (B) 14. (A)

15. (C) 16. (B) 17. (B) 18. (C) 19. (C) 20. (C) 21. (A)

22. (C) 23. (D) 24. (D) 25. (B) 26. (A) 27. (B) 28. (A)

29. (D) 30. (B) 31. (C) 32. (A) 33. (B) 34. (A) 35. (A)

36. (A) 37. (D) 38. (C) 39. (B) 40. (A) 41. (B) 42. (A)

43. (B) 44. (D) 45. (D) 46. (C) 47. (D) 48. (D) 49. (D)

50. (A) 51. (B) 52. (B) 53. (A) 54. (B) 55. (B) 56. (B)

57. (C) 58. (A) 59. (A) 60. (D) 61. (C) 62. (A) 63. (C)

64. (C) 65. (A) 66. (D) 67. (B) 68. (C) 69. (C) 70. (C)

71. (A) 72. (A) 73. (A) 74. (D) 75. (B)

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