elementary_maths - 6* l -v" DO NOT OPEN THIS TEST...

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Unformatted text preview: 6* l -v" DO NOT OPEN THIS TEST BOOKLET UNTIL YOU ARE ASKED TO DO S l T.B.C. : P—DE—A—J—FN Test Booklet Series Serial No. ' 3 8 2. 5 Time Allowed .' Two Hours 1. r“? 10. TE ST BOOKLET ELEMENTARY MATHEMATICS Maximum Marks : 100 INSTRUCTIONS IMMEDIATELY AFTER THE COMMENCEMENT OF THE EXAMINATION, YOU SHOULD CHECK THAT THIS TEST BOOKLET DOES NOT HAVE ANY UNPRINTED 0R TORN OR MISSING PAGES OR ITEMS, ETC. IF SO, GET IT REPLACED BY A COMPLETE TEST BOOKLET. ENCODE CLEARLY THE TEST BOOKLET SERIES A, B, C OR D AS THE CASE MAY BE IN THE APPROPRIATE PLACE THE ANSWER SHEET. You have to enter your Roll Number on the Test Booklet in the Box provided alongside. DO NOT write anything else on the Test Booklet. This Test Booklet contains 100 items (questions). Each item is printed both in Hindi and English. Each item comprises four responses (answers). You will select the response which you want to mark on the Answer Sheet. In case you feel that there is more than one correct response, mark the response which you consider the best. In any case, choose ONLY ONE response for each item. You have to mark all your responses ONLY on the separate Answer Sheet provided. See directions in the Answer Sheet. All items carry equal marks. -’Before you proceed to mark in the Answer Sheet the response to various items in the Test Booklet, you have to fill in some particulars in the Answer Sheet as per instructions sent to you with your Admission Certificate. After you have completed filling in all your responses on the Answer Sheet and the examination has concluded, you should hand over to the Invigilator only the Answer Sheet. You are permitted to take away with you the Test Booklet. Sheets for rough work are appended in the Test Booklet at the end. Penalty {or wrong answers : THERE WILL BE PENALTY FOR WRONG ANSWERS MARKED BY A CANDIDATE IN THE OBJECTIVE TYPE QUESTION PAPERS. (i) There are four alternatives for the answer to every question. For each question for which a wrong answer has been given by the candidate, one-third (0-33) of the marks assigned to that question will be deducted as penalty. (ii) If a candidate gives more than one answer, it will be treated as a wrong answer even if one of the given answers happens to be correct and there will be same penalty as above to that question. (iii) If a question is left blank, i.e., no answer is given by the candidate, there will be no penalty for that question. DO NOT OPEN THIS TEST BOOKLET UNTIL YOU ARE ASKED TO DO SO attaitzagésfianlhflewangfimfifieawwwsl When a natural number is divided by 4, the remainder is 3. What is the remainder when 2n is divided by 4 ? (a) 1 (b) 2 ' (c) 3 (d) 6 What is the last digit in. the expansion of {2457)m '2 (a) 3 (b) 7 (c) 8 (d) 9 If log'6 = m and logr3 = n, then what is logl (r/2) equal to ? (a) m—n'+1 (b) m+n—1 (c) l—m—n (d) l—m+n Consider the following statements : A number a1a2a3a4as is divisible by 9 if 1. aI + a7 + a3 + a4 + a5 is divisible by 9. 2. al — a2 + a3 -— a4 + as is divisible by 9. Which of the above statements is/are conect ? (a) 1 only (b) 2 only (c) Both 1 and 2 ((1) Neither 1 nor 2 What is x(y «— z) (y + z) + y(z — x) _(z+x)+z(x—y)(x+y)equalto? (a) (X+Y)(y+z)(z+x) (b) (x-Y)(X-z)(z-Y) (c) (x-+y)(zfly)(x—z) (d) (VF—tzeylbi-Z) 10. _If the remainder of'the polynomial a0 + alx + a2):2 + ...... .. + aux“ when divided by (x —— l) is 1, then which one of the following is correct ? (a) ao+a2+ ........ ..=a1+a3+ ........ .. (b) ao+az+ ........ ..=1+al+aa+ ........ .. (c) l+ao+az+ ........ ..=—(a1+aa+ ........ ..) (d) l—ao—gir ........ ..=al+a3+ ........ .. When (it3 — 2x2 + px - q) is divided by (X2 — 2x — 3), the remainder is (x — 6). What are the values of p, q respectively ? (a) —2, —6 (b) 2, —6 (c) —2, 6 (d) 2, 6 What are the values of e when the HCF ofx3+cx2—x+2c andx2+cx—20ver the rationals is a linear polynomial ? (a) i] (b) 5:2 (6) *3 (d) :4 If(x + 2) is the HCF of x2 +, ax + b and x2 + cx + d (a at c and b at d), then which one of the following is correct ? @)a+c=b+d (b) 2a+b=2c+d (c) b+2c=2a+d (d) b-2c=2a—d What is the LCM of (xz-yz—zz—Zyz), (xzwy’+z’+2xz)and(x2+y2—z’—2xy)? (a) (x+y+z)(x+y—z)(x—y+z) (b) (x+y+z)(x-y—z)(x-y+z) (c)'(X+Y+Z)(X+Y-z)(X—Y-Z) (d) (X+Y~Z)(X-y-Z)(me+1) - (Contd.) l. Wfi‘fififiinfifi4fifimfifimw 6. fififim3fiwélwznafi4fi WWWfifirfiw-w%? (a)1 (b)2 (6)3 (d)6 2. (2457)”4-4} mm fi' sffim aim arm 3? 7-. (a) 3 (b) 7 (C) 3 (d) 9 3. 1112a logr6=m¢<§ logr3=n€t a} logr(r/2) $ W WT 3 ? (a) m—n+1 (b) m+n~—] (c) lam—n (d) l—m+n 1. al+a2+aj+a4+asfim%9fi 9- 2. al—a2+a3—~a4+asfi‘fififl%9fi aqgafififiafiHHT/fimafi%/%? .(3) W1 (b) W2 (c) lmzafiifi (d) aafilafivraz 5- x(y-z)(y+z)+y(z—x)(z+x)+ z(x—y)(x+y)$WW%? (a) (x+y)(y+z)(z+x) (b) (x—y)(x-z)(z—y) (c) (x+y)(z-y)(x-—z) (d) (y-x)(z—y)(x-z) 10. XW fiW13Wfi§ano+alx+a2xz + ...... ..+anx“31:f (x—l)fifi":flfilfifiim m3, fitfimfiifiafifiafifimvfi %? (a) ao+a2+ ........ ..=al+a3+ ........ .. (b) ao+a1+ ........ ..=l+al+aa+ ........ .. (c) 1+ao+a2+ ........ ..=-(aI +aa+..........) (d)1—ao-—a2+ ........ ..=al+a3+ ........ .. W(x3-2x2+px—q)fi?f(x3—2x—3) I} fi‘mfim W mm %, ‘cfi W (x—6)%I p,q€n‘ m;mfi¢m§? (a) —2,—6 (b) 2,-6 (6) —2,6 (d) 2,6 Wx3+cxl-x+2c1fi x2+cx—2$r HCF‘TW if mas ran-gm firm 3,31 cfififi‘fll‘lfi? ' (a) il (b) i2 (0) i3 (d) :|:4 fix2+ax+b3fi1x2+cx+d(a¢c mb¢d)amHCF(x+2)%,ahfi-sr%fiafi fifiafifima‘é’rfi? (a) a+c=b+d , (b) 2a+b=2c+d (c) -b+2c=2a+d (d) bé2c=2a—d (x2—y2—zz—2yz),(x2—y2+21+2xz)afl1 (x2+y2—23—2xy)?fi LCMWE”? (a) (x+y+z)(x+y-z)(x—ry+z) (b) (x+y+z)(x—y-z)(x—y+z) (c) (x+y+z)(x+y—z)(x-y-z) (d) (x+y-z)(x-y-z)(x-y+z) (Contd.) 11. 12. l3. 14. 15. If 3" + 27(3“) = 12', then what is the value of x ? (a) 1 only (b) 2 only (c) l or 2 (d) O or 1 If x=l+~5 , then what is the value of x“---4x3+4x2 ?- (a) -l (b) 0 (C) 1 (d) 2 What is the magnitude of difference of therootsofx’—ax+b=0? (a) m (b) m 0:) 2M (d) W What is the solution of the equations x — y = 0-9 and 11(x + y)“'= 2 ? (a) x = 3-2 and y = 2-3 (b) x= l andy=0'l (c) x=2andy= 1-1 (d) x = 1-2 and y = 03 Pooja started her job with certain monthly salary and gets a fixed increment every year. if her salary was Rs. 4200 after 3 years and Rs. 6800 after 8 years of ' service, then what are her initial salary and the annual increment reapectively ? (a) 2640, 320 (b) 2460, 320 (c) 2460, 520 (d) 2640, 520 17. 18. 19. 16. A person bought 5 tickets from a station P to a station Q and 10 tickets from the station P to a station R. He paid Rs. 350. If the sum- of a ticket from P to Q and a ticket from P to R is Rs. 42, then what is the fare from P to Q ‘? (a) 12 (b) 14 (c) 16 (d) 18 The product of two alternate odd integers exceeds three times the smaller by 12. What is the larger number ? (a) 3 (b) 5 (c) 7 (d) 9 Ifa"=c‘|=bandct=al=dthenwhich one of the following is correct ? (a) fly = q/z (b) x + y = q + z (c) xy = qz (d) x’ = q‘ A ball is dropped front a height 64 m above the ground and every time ithits the ground it rises to a height equal to half of the previous. What is the height attained after it hits the ground for the 16'“ time ? _ (a) 2'” m (b) 2—” m (c) 2"° m (d) 2" m (Contd.) ll. 12. l3. 14. 15. fi3x+27(3-x)=12%a’rxa-rmw a? (a) W1 (b) #132 (0)1W2 (d) 0m] 115% x=1+J§ %, if x‘—4x3+4x23fi mwfi? (a) -1 (b) 0 (C) I ((1)2 xz—ax+b=0$‘qfif$3ifi‘tmqm €6.03? 00 £2.76 (b) M 0:) 2m w)J?:EE ammx—Foaea‘hmxw—Iez mmwfi? (a) x=3°ZSfiTy=2-3 (b) x=1my=01 (c) x=23mTy=bl (d) x=l-23fi'(y=0‘3 3%: 11f? m an? m a”: 3 6. 42003111 sansf are: a. 6800 m SHEET WM 311? a??? fifth? 36? fig WT: WIT % ? (a) 2640, 320 (b) 2460, 320 (c) 2460.520 (d) 2640, 520 18. 19. 16.@WfiH3WPfiWQfi$i-T sfiwmmpfimakafifi lOfiRfifilwfi‘fidsofifilufiP fiQfififiWsfiTPRfififiw fiWE.42%,?fiPfiQI-T$Wfifl'm .3013? (a) 12 (b) 14 (c) 1 6 (d) I 8 .flufimfiwwfifimmfirfi Wa‘aefiwgfifilzmfimélfit WWWfi? (a) (b) (c) (d) 111% a"=c"=b3fi'( c¥=al=d3 F?! Wfifiafiwmnfifi? (a) xly=qlz 0)x+y=qéz \quw 0:) xy = qz (d) x’ = q2 'wfiwmammmamm #sfiTWWWfiWq-(afi MWfimfiwmfiufi W016fimmfi$mfimfih WWW? (a) 2'um (b) 2—11m (c) 2“°m (d)2'°m 20. 21. 22. 23. 24. What is the value of 2 log(5/8) + log(128/125) + log(5/2) ? (a) 0 (b) 1 (c) 2 (d) 5 If it cos 60° + y cos 0° = 3 and 4x sin 30° — y cot 45" = 2, then what is the value of x ? (a) —1 (b) 0 (C) 1 (d) 2 if the unit of weight is 15/4 kg, what number will 3/2 quintal represent ? (a) 25 (b) 6 (c) 1/9 (d) None of the above A dishonest dealer professes to sell his goods at cost price, but uses a false weight and thus gains 20%. For a kilogram he uses a weight of (a) 700 g (b) 750 g (c) 800 g (d) 850 g If we divide a positive integer by another positive integer, what is the resulting number ? (a) It is always a natural number (b) It is always an integer (c) It is a rational number (d) It is an irrational number x01 25. 26. 27. Nine numbers are Written in ascending order. The middle number is the average of the nine numbers. The average of the first five larger numbers is 68 and that of five smaller numbers is 44. What is the sum of all nine numbers ? (a) 450 (b) 501 (c) 504 (d) 540 What is the value of l 1 1 [W‘WJ‘W—ZTE— '1 1 W+Wl ? (a) 0 (b) 1/3 (c) 1 (d) 5 Two persons P and Q start at the same time from city A for city B, 60 km away. P travels 4 km/hr slower than Q. Q reaches city B and at once turns back meeting P, 12 km from city B. What is the speed of P ? (a) 8 km/hr (b) 12 km/hr (c) 16 km/hr (d) 20 km/hr (Contd.) 20. 21. 22. 23. 24. 2 log(5/8) + 103(128/125) + Inga/2) an 2m If??? xcos60°+ycosO°=33fiT 4xsin30°—ycot45°=2%€fxifiltlfi m g? (a) “"1 (b) 0 (C) 1 (d) .2 fiWfiW15/4kg.%fifififi Wamfia‘mafifimmfi? (a) 25 (b) 6 (c)1/9 (d) Wfififiéafi WWWMmfimafiqfi mafififiwmmgfififiiw WWW20%WWW%IQ$ W$WEWW$WW mm%? (a) 700g (b) 750g (c) 800g (d) 850g afimwmwfifiwtfiw fifiwfiamfifia‘rqfimfimafia mg? (a) fififiwmwg (magsfiwwimfi? (c) WWWW?’ (d)afiflfi?mfiw3 Id 25. 26. 27. Wmfia’rmmmfilfi? Ema-@1133 a’tmfifita’l‘afifil HWHWWWWWéSiafiI WWMWWMng‘hfi WWWW%? (a) 450 (5)501 (c) 504 @540 (a) 0 (b) 1/3 (c) 1 (d) 5 fiwfifipmowfi’rwwmA fiéOkmitmTBfififififiTEyp—W #1 Qfi 4km/hrsfrm Pm?! Q, mbéamaafiTWmaTe-fip afimBfi mum-(man Pafi (Contd.) 28. 29. 30. 3]. A boy walks from his house to school at 2-5 kin/hr and arrives 12 minutes late. The next day he walks at 4 kin/hr and reaches the school 15 minutes earlier. What is the distance fi'om his house to school ? (a) 2 km (b) 25 km (c) 3 km (:1) 3-5 km A and B can do a piece of work in 8 days, B and C can do the same work in 12 days. If A, B and C can complete the same work in 6 days, in how many days can A and C complete the same work ? (a) 8 (b) l 0 (c) l 2 (d) l 6 The compound interest on a sum for 2 years is Rs. 832 and the simple interest on the same sum at the same rate for the same period is Rs. 800. What is the rate of interest ? (a) 6% (b) 8% (c) 10% (d) 12% A person invested‘part of Rs. 45,000 at 4% and the rest at 6%. If his annual income from both are equal, then what is the average rate of interest ? (a) 46% (b) 4-3% (c) 50% (d) 52% 32. 33. 34. 35. What wbuld be the printed price of a watch purchased at Rs. 380, so that after giving 5% discount, there is 25% profit ? (a) Rs. 400 ’ (b) Rs. 450 (c) Rs. 500 (d) Rs. 600 A person A sells a table costing Rs. 2000 to a person B and earns a profit of 6%. The person B sells it to another person C at a loss of 5%. At what price did B sell the table ? I I (a) Rs. 2054 (b) Rs. 2050 (0) Rs. 2024 (at) Rs. 2014 If a:b=1—;—:2% and b:c=2:3% then what is a 1 b : c equal to ? (a) 12 : 8': 21 (b) 8:21 t 12 (c) 8 : 12 :21 (d) 21 :8: 12 A bag contains Rs. 114 in the form of 1 rupee, 50 paisa and 10 paisa coins in the ratio 3 : 4 : 10. What is the number of 50 paisa coins ? (a) 76 (b) 72 (c) 56 (d) 48 28.71.???133fls1'cfi mfifig‘afifi-fi 2-5kmfhrawfiaaafi12fiwaé-fia Wfilmfiww4hn/hréwfi WiZafiIlsfiwzqsfiqi—rmfilm fiagaafiffififiififi? (a)2km (b) 25 km (c) 3 km (d) 3-5 km 29.Amawmafisfififimm 30. “3.1. 3,33fi1cazfimafilzfiwfim W§1HfiABSfiTC3¥fifimffi éfiwfifnmmfifij‘msfitcafi mafifimfifififiwmmg? (208 (b) 10 '(c) 12 (d) 16 wmtfirmzafimafifim ‘6.832€1fiT%5fiT-3'Gfia=rffiTT-Iflfi fifimamaflmm 6. 8003131? Wflwfi? (a) 6% (b) 8% (c) 10% (d) 12% wafiafifi.4s,000%fiflmfi4% ammmmafié‘xufiwf’fiw Wiufisfiififwfifimmm Wfifitsfiafimflfiwfifi? ' (a) 4.6% (b) 4.8% (c) 50% (C!) 5-2% 32. '6. 380iafifia$mgfiawfimm 33. 34. 35. MW, mafingzfiwzm arm fit ? (a) 6. 400 (b) a. 450 (c) a. 500 (d) a. 600 firfifi A,‘6. 2000mm 31?: w 23?! mBafimi‘tah-{mmm 313113633? 5%Enfi'q'tafir'c'ufifi camalsfimmwm W? (a) “6.2054 (b) “6.2050 (0) 6.2024 (d) E. 2014 ‘1 l l :b=l——: — b: =2:3— 111% a 2 24 3111' c 2 3,31 azb:cmwfi? (a) 12:8:21 (b)8:21:12 (c)8:12:21 (d) 21:8:12 magma. 114%m1m, sofifisfitlo'fifimfiffifiswzlo fimfiflsofifiafififiafim min??? (a) 76 (b) 72 (c) 56 (d) 43 36. 3‘7. 38. 39. Two taps can fill a tub in 5 minutes and 7 minutes respectively. A pipe can empty it in 3 minutes. If all the three are kept open simultaneously, when will the tub be full ? (a) 60 min (b) 85 min (c) 90 min (d) 105 min If (x/y) = (21w), then what is (xy + zw)2 equal to ? ‘ (a) (x2 + Z!) (Y2 + W’) (b) x’zy2 + 212w2 (c) xzwz + yzzz (d) (x2 + W) (3’2 + 22) l 2 1009 If fi+m+ 2+1009 =1,thenwhatis thevalueof x + y +—Z_ ? x+l y+2 z+1009_ (a) 0 '(b) 2 (C) 3 (d) 4 Suppose y is equal to the sum of two quantities of which one varies directly as x and the other inversely as x. If y = 6 when x = 4, and y = 10/3 when x = 3, then what is the relation between x and y ? (a) y = x + (4/x) (b) y = —2x + (4/x) (c) y = 2x + (8hr) (d) y = 2x ~ (81x) 40. 41. 42. 43. A train of length 150 111 takes 10 s to cross another train 100 m long coming from the opposite direction. If the speed of first train is 3_0 kmph, what is the speed of second train ? (a) 72 kmph (b) 60 kmph (c) 54 kmph (d) 48 kmph There are some coins and rings of either gold or silver in a box. 60% of the objects are coins, 40% of the rings are of gold and 30% of the coins are of silver. What is the percentage of gold articles ? (a) 16 (b) 27 (c) 58 (d) 70 What is the total number of three digit numbers with unit digit 7 and divisible by 11 ? (a) 6 _ (b) 7 (c) 8 (d) 9 What is the sum of positive integers less than 100 which leave a remainder I when divided by 3 and leave a remainder 2 when divided by 4 ? ‘ (a) 416 (b) 620 (c) 1250 (d) 1314 (Contd .) 36 37. 38. 39. a): 7m was EH 3% m: sfimz aft? “Ifir—IE 1? an m 31 0:55 W 3'8 BWEfimmWEIufiefifi‘Tw am 13% % a‘T w w swim? (a) 601:5??? (b) 35mm: (c) 90%: (d) 105%: I 141% (x/y) = (z/w)%, a‘r (xy + zwyfim‘a mm??? (a) (x1 + 22) (y:I + W) x2y2 + ZZWZ (c) xzwz + yzzz (d) (39+ w!) (312+ 22) 1 2 1009 1112?; +—-—+ . =1, x+1 y+2 z+1009 x + y + 2 WWW??? x+l y+2 2+1009 (a) 0 (b) 2 (C) 3 (d) 4 Wfiiyfiefifinfifia‘wwfiw @fifiwmxa‘a‘fimsfi'tiqfi x$€WWWfifi31ufiy=6m x=4,afi-< y=10/3vrq'x=3 3, ah ny$WWHW%? (a) y=x+(4/x) (b) y = —2x +'(4/x) _(c) y = 2x + (Six) (3) y = 2x — (8/x) 40. 41. 42. 43. @ISOm-cfi’riamé‘rfiq-fiafimaafi mEfiIOOmafir-{afimfiafimm 1? mma-cnal afimmfifi ammmphazhga-fimns‘rafim ‘fifiFfi?? (a) 72kmph (b)60kmph (c) 54kmph (d)48kmph wmfiwwmwga mafimafi’tfifilfitfififia‘f mamiWficIMm-Sx‘fiaafit Wfi30%fi$§lfififififi mummwfi? (a) 16 (b) 27 (c) 53 (d)70 firm eh? a’az‘f afir m fir, W mm7€rafitah llfifimwfif, Fmfifilfifi3? (a)6 (b)? (c) s (d) 9 filoofifirimwfim,firfim 3%fiwfiamfiwfiw 1313141} Wmfimmzmim 2911?? (a) 416 (b) 620 (c) 1250 (d) 1314 44. 45. 46. 47. What is the greatest number which divides 392, 486 and 627 so as to leave the same remainder in each case ? (a) 47 (b) 43 (c) 37 (d) 34 A man walking at the rate 3 [cm/hr crosses a square field diagonally in 1 minute. What is the area of the field ? (a) 1000 m2 (b) 1250 m2 (c) 2500 m2 (d) 5000 m2 The difference between the area of a square and that of an equilateral triangle on the same base is 1/4 cmz. What is the length of side of triangle ? (a) (4-43)”2 cm (19) (4+\/§)”2 cm (c) (Ii—xii)“2 m (d) (4+J3)‘”2 cm A horse is tied to a pole fixed at one corner of a 50 m x 50 m square field of grass by means of a 20 m long rope. What is the area of that part of the field which the horse can graze ? (a) 1256 m2 (b) 942 m2 (c) 628 rn2 ‘ (d) 314 m3 48. 49. 50. Two sides of a parallelogram are 10 cm and 15 cm. If the altitude corresponding to the side of length 15 cm is 5 cm, then what is the altitude to the side of length 10 cm ? I (a) 5 cm (b) 7'5 cm (c) 10 cm (d) 15 cm From a rectangular metal sheet of sides 25 cm and 20 cm, a circular sheet as large as possible is cut-off. What is the area of the remaining sheet ? (a) 186 can2 (b) 144 cm‘I (c) 93 cm2 (d) 72 cm2 Three cubes each of side 5 cm are joined end to end. What is the surface area of the resulting cuboid ? (a) 300 cm! (b) 350 em2 (0) 375 cm2 (01) 400 cm2 51 . The diameter of the moon is approximately one-fourth of that of the earth. What is the (approximate) ratio of the volume of the moon to that of earth ? (a) 1/16 (b) 132 (c) 1/48 (d) 1/64 (Contd.) 44. mm mm, W 392,48630? 627fimfiwmmfimm W3, am 10% ? (a) 47 (b) 43 (c) 37 (d) 34 45.Q$mwfi3kmnufiwatfimanfim fiaafifiwfamfimzifmmi’l fiamémwfi? ' (a) 1000 m2 (b) 1250 m1 (c) 2500 m2 (d) 5000 m2 46.nwramnalfia1fmaw1gfigvra} Wfimlfllcnglfifififiw afifim‘w3? (a) (fit—‘5)”2 cm (b) (tux/i)"2 cm (c) (4—\/§)"’2 cm (d) (4+«5TH2 cm WSOmxso-mmnm$fia% @fifiwfiufifififiqumm mmaamanafi$wmw | ' W,m€mmmafimfi \ a? ‘ (a)1256m2 (b) 942m2 (1::)628m2 ‘ (d) 314m2 47. 48. WWWfiQWIOcmSfiT 49. 50. 51. 15mm?“ 111% 15cmfiil1€figfin $W§ifi5cm$fl Eh lOcmfi‘lTéilfi gm 3|“ m W m 3 ? (a) 5 cm (13) 7-5 cm (c) 10cm (d) 15 cm 25cmSflT20cmWafifiQ$m Wafiw%mwafifia€rw mwmwaumggm mmwa? (a) 186 cm2 (b) 144 cm2 (c) 93 cm2 (d) 72 cm: mfififi,mfifigfi$§m5cm3, mammwmamfim ngmeé? (3) 300cm2 (b) 350cm2 (c) 375cm2 (d) 400cm2 mmmgfira‘ama‘awafim fimfilmfimmgzfi $Wfimmw3? (a) 1/16 (b)1/32 (c) “48 (col/64 (Contd.) S2. 53. 54. 55. 56. What is the area of a right angled isosceles triangle whose hypotenuse is 6J5 cm ? (a) 12 em1 (b) 18 cm2 (c) '24 cm2 (d) 36 cm2 If A is the area of a triangle in cm’, whose sides are 9 cm, 10 cm and 11 cm, then which one of the following is correct ? (a) A < 40 cm2 (b) 40 cm:1 < A-< 45 cm2 (c) 45 cm2 < A < 50 cm2 (d) A > 50 cm2 A roller of diameter 70 cm and length 2 m is rolling on the ground. What is the area covered by the roller in 50 revolutions ? (a mem2 (b) 200m2 (c) 220 m2 (d) 2401n2 A cylindrical rod of length h is melted and cast into a cone of base radius twice that of the cylinder. What is the height of the cone ? (a) 3h/4 (b) 411/3 (c) 2h (d) 11/2 A cylindrical vessel of base radius 14 cm is filled with water to some height. If a rectangular solid of dimensions 22 cm >< 7 cm X 5 cm is immersed in it, what is the rise in water level ? ‘ (a) 0-5 cm (b) 1-0 cm (c) 125 cm ((1) 1-5 cm 57. 58. 59. A lead pencil is in the shape of a cylinder. The pencil is 2] cm long with radius 0-4 cm' and its leadis of radius 01 cm. What is the volume of wood in the pencil ‘? (a) 9 cm3 (b) 94 cm3 (c) 9-9 cm3 (d) 101 cm3 What is the angle (in radian) included between the hands of a clock, when the time is 10 minutes past 5-? (a) 1 71t/36 (b) l 91r/3 6 (c) STE/9 (d) 711/12 ‘ A B Q D In the figure given above ACDQ = 11‘ AB = x, PQ = z and CD = y, then which one of the following is correct ? L’ABD = APQD = l+l_1 (a) X y Z l'+_1._l (b) x z y (c) z y x l+l_2 (d) x y z (Contd.) 52. 53. 54. 55. 56. mefia—gfigfimfimm fificmfi, WW3? (a) 12 cm: (b) 18 am: (e) 24 cm2 (d) 36 cm2 afi9cm,10cm3fi'{ “c:me F3331 ih‘r W A(cm2if)%, EhfiTfifi‘rfiafi fifififimafi%? (a) A<40cm2 (b) 40 cm2<A<4S cm2 (c) 45 cm2<A<SO cm2 ((1) A>500m2 Wm, Wm 70c:me 2m%, gefiwfizfiwfirm-mfil am} 50W 1? WWW‘Ifi-fi W313? (a) 180m2 (b) 200m2 (c) 220m2 (d) 240m2 1:36 hm #1 3mm :93 fl 11mm mfiwfififimmfimfi 3mm Bran W 74% man? fawn afi afi%lm§afiafi1€fifi=fi%? (a) 311/4 (b) 411/3 (0) 2h (d) h/2 Emmi—{maimafimmfiw l4cm%,qfififi§§wfi1€fi$fifim glufiZZCmX'icmXScmfi'minfi Wmmfiwfisfimma Efififiwfififiifififzm? (a) 0-Sem (b) l-Ocm (c)1-25cm (C!) 1-5 cm 57. wwmmaumafim 21cm3flTfiFflTO-4cm3fi13fifi fi-fimn 0-] mm W a} was $1 3mm arm %? (a) 9cm3 (b)'9-4cm3 (c) 9-9::m3 (d) lO-lcm3 58. mafifimsw 10%zm3 aw a'efi ii: We? 3% aha w m (mm fi) arm % ? (a) Fin/36 (b) 191t/36 (c) 5n/9 (d) 7n/12 59. A B 311W 1%?! if AABD = zPQD = ACDQ = Ufa AB=x,PQ=z§ITCD=y§,€IfiWfi-’1fifi if am ET EFF HE?! %? 60. APQR is right angled at Q, PR = 5 cm 61. 62. 63. and QR = 4 cm. If the lengths of sides of another triangle ABC are 3 cm, 4 cm and 5 cm, then which one of the following is correct ? (3) Area of APQR is double that of AABC (b) Area of AABC is double that of APQR (c) fled—Q- 2 (d) Both triangles are congruent Which one of the following figures has only one line of symmetry ? (a) Rhombus (b) Rectangle (c) Isosceles trapezium (d) Parallelogram A ladder 25 m long is leaning against a wall which is perpendicular to the level ground. The bottom of the ladder is 7 m from the base of the wall. If the top of the ladder slips down 4 m, how much will the bottom of the ladder slip ? (a) 7 m (b) 8 m (c) 10 m (d) 15 m If CI and C2 and r1 and r2 are respectively the centroids and radii of incircles of two congruent triangles, then which one of the following is correct ? (a) CI and C2 are the same point and rI = r2 (b) CI and C2 are not necessarily the same point and r1 = r2 (c) Cl and C2 are the same point and rI is not necessarily equal to r2 ((1) Cl and C2 are not necessarily the same point and I1 is not necessarily equal to r2 64. 65. 66. In the figure given above, P is a point on AB and PQ is parallel to AC. What is the number of pairs of distinct similar triangles in the figure ‘? (a) 1 (b) 2 (c) 3 (d) 4 If the medians of two equilateral triangles are in the ratio 3 : 2, then what is the ratio of their sides ? (a) 1:1 (b) 2:3 (c) 3:2 (d) «En/E The centroid and the orthocenter are coincident for which one of the following triangles -? (a) Scalene triangle (b) lsosceles triangle (c) Equilateral triangle (d) Right angled triangle _ (Contd.) 62. 63. '60. 61. APQR,Q‘RW%,PR=S¢m3fi{ "QR=4cml afififiifigfimcifi 331m. 3cm,4cmafi'{ Somm'flfig ffififififfififiafiqmqfififififi? (a) APQRW W, AABC 7% W a £11131 % (b) AABCEFT W, APQRa‘a aha-um % infn % (c) (d) fi-‘fi Fifi? aafim 3' Wfifiafifimwfimfiw Wamafifi? (aJW‘ifi (MW (cJWWiW (mam-{agst wzsmafimafifiamfifi’afifit WWfim3Imwfiw WWWafiafia‘umfi'lmfi 3|ufid’l’rfiafivfidmafimw4m fiffimfia‘lmamfiwm WW1"? (a) 7m (b)8m (c)10m (d) 15m afififiafimfi‘gfifiéfififia“ mmmm:clafi'rczam rIWrzgfiWfififlm @1163? (a) CISfiTCZWEfifigg (magsnamafifiacl figfififiTII=r2 (c)'C13fiT 9113531333 ' Wfi‘éfififirlmrz (magmaswafifiicl'm figfifmufimfifi Emma 64. 65. C a aqgaafiafiABfiqafifignem PQ,Ac$Hfi1‘a—{%Iffi=rwfirg=fi $grrfifiamm%? (3)1 ('13)2 (0)3 ((1)4 A ufifiwgfigxfiafinfmfiwafim fim3:2%,afimgmfiafifim 6w%? 66. (a) 1:1 (b)2:3 (c) 3:2 (d) £45 fififirfiafifirgfifi if a 33? 131 fig?! E? firm—r 23:??? 3M Ham??? firm??? a? ‘ (6mm? mm??? (c) m fagvr (d) fig?! 67. 68. In the figure given above, a circle is inscribed in a quadrilateral ABCD. Given that BC = 38 cm, QB = 27 cm, DC = 25 cm and AD‘is perpendicular to DC. What. is the radius of the circle ? (a) 11 cm (h) 14 cm (c) 15 cm (d) 16 cm In the figure given above, what is ACBA ? (a) 30° (b) 45° .(c) 50° (d) 60" 69. 70. 71. A, B, C; D are four distinct points on a circle whose centre-is at 0. If AOBD - ACDB = ACBD — AODB, then what is 1A equal to ? (a) 45° (b) 60° (c) 120° (11) 135° PQ is a common chord of two circles. APB is a secant line joining points A and B on the tWD circles. Two tangents AC and BC are drawn. If AACB = 45", then what is L’AQB equal to ‘? (a) 75° (b) 90° (c) 120° . (d) 135° ABCD is a concyclic quadrilateralfThe tangents at A and C intersect each other at P. If éABC = 100°, then what is (AFC equal to ? (a) 10° (b) 20° (c) 30° (d) 40° (Could) 67. 68. Wmfiafiamcnfimafiifi i2: BC=38cm,QB=27cm,DC=25cm 3m AD,DCITIEI'H%I afirfififivm fifiF-fi %? (a) 11 cm (b) 14cm (0) 15 cm (d) 16 cm Gag-cm 12133 if ACBA mm ‘3 ? (a) 30° (b) 45° (c) 50° (d) 60° 69. A,B,c,Dartf°I«——rfi'3wgfiw% 70. 71. Who? at“? AOBD-éCDBr— ACBD-zZODB 3, Eh AAW a?» W 3 ? (a) 45° (b) 60° (c) 120° (d) 135° aa—rfiafismfiwsafimpqammw mmaa‘rfifiwfigsfiAafi-t Bfimaia‘rWAcch Emma. ufi: £ACB=45°3EPI AAQB$WTW%? (a) 75° ' (b) 90° (c) 120° (d) 135° ABCDQfi-rfiu aggar %| A373? (:01 W a? $0? a?! P‘Tt $12-01 a. at? AABC =100°,?h zAPC first? a} ma? 3 ? (a) 10° (b) 20" (c) 30° (d) 40° 72. 73. In the figure given above, M is the mid point of the side CD of the parallelogram ABCD. What is ON : OB ? (a) 3:2 (b) 2E1 (0) 3:1 (d) 5:2 E B Q Y A X- In the figure given above, YAX is a tangent to the circle with centre 0. If ABAX = 70° and ABAQ = 40°, then what is AABQ equal to ? (a) 20° (b) 30° (a) 35° (d) 40° 74. 75. In the figure given above, AP = 3 cm, PB=50m,AQ=ZemandQC=x. What is the value of x ? (a) 6 cm (b) 8 cm (0) (d) 12 cm ‘ 10 cm C B In the figure given above, 0 is the centre of a circle oircumscribing a quadrilateral ABC'D. If AB = BC and ABAC = 40", then what is AADC equal to ‘? (a) 50° (b) 60" (0) 70° ((1) 80° (Contd.) 72. 73. wcnmnwfii‘gmfil 0N:013atn %? (a) 3:2 (b) 2:1 (c) 3 :1 ((1) 5:2 E B Q Y A X mm 0' YAXgfiafi, WW 0%, W 3| Ilfi.’ ABAX=70°3fiT ABAQ= 40°? a”: AABQW arm %? (a) 20° (b) 30° (c) 35° (d) 40° 74. 7S. WWfiAP=3cm,PB=Scm, AQ=20mfiTQC=x§lxfiW§m %? (a) 6cm (b) "Scm (c) 10cm (d)120m WmfifiajfiABCDa‘afiqaw $300: afiAB=BCsh ABAC=40° 3 E0 zADCH‘» W 2011 3? (a) 50° (b) 60° (c) 70° (d) 80° (Contd.) 76. 77. 78. 79. Let X13 and XE be two rays intersecting at A. Let D, E be the points lying on ‘A‘B’, It? respectively and P be the point such that P divides the line DE such that. PD : PE = AD : AB. What is the locus of. the point P ? (a) The angle bisector of angle A (b) The angle trisector of angle A (c) The perpendicular bisector of angle A ((1) None of the above What is log (tan 1°) + log (tan 2°) + log (tan 3°) + ..... .. + log (tan 89°) equal to ? (a) 0 (b) 1 (c) 2 (d) —1 Consider the following‘equations : l. coseczx + see: it = cosee2 it set:2 x 2. sec2 x + tan2 x = sec2 x tan2 1:: 3. cosee2 x + tan2 x = cot2 x + see2 it Which of the above statements are correct ? (a) 1 and 2 only (b) 2 and 3 only (c) .1 and 3 only ((1) 1, 2 and 3 If cos x + cos2 x = 1, then what is the value of sin2 x + sin‘I x? (a) 0 (b) 1 (c) 2 (d) 4 80. 81. 82. 83. 84. If sin it cos x = 1/2, then what is the value of sin x — cos x ? (a) 2 '(b) 1 (c) 0 (d) —1 If tan2 y cosec2 x - 1 = tan2 y, then which one of the following is correct ? (a) X—Y=0 (b) x=2_y (c) y=2x (d) X—Y= 1° IfJiL+~=Lwhichone l+cosecx cosecxhl of the following is one of the values of x ? (a) TIE/2 (b) 1t/3 (c) 11/4 (d) n/6 7 Ifx+y=90°andsinxzsiny= Jig], then what is x : y equal to ? (a) l :1 (b) l :2 (c) 2:1 ((1) 3 :2 If cosxzn, Sinxr—m, then what is cosy smy (m2 a n2) sin2 y equal to ? l —,n2 (b) 1 + 11’ 0:) m1 ' (d) n2 (Coma) 7 76.n1-vrafififirfiAqta‘erfi X133??? Efilmmfifiifig 1113mm: A_B,X5tfi3', Pfif'g WDEfifimfiwfiamfifi? PD:PE=AD:AEI figpmtmm %? (a)WAWWWfiW (b)a?rMAmafimerm (QWAWFWW (mangaafffiafiéfifia'é‘f log (tan 1°)+ log (tan 2°)+log (tan 3°)+ + log (tan 89") % WT BRIT 3 ? (A) o (b) 1 ' (C) 2 (d) -1 73WWWWW: . l. nosec2 x + 5m:2 x = cosec2 x scc2 x 77. 2. sec2 x + tanzx = sec2 x tan2 x 3. cosec2x+tan2x=cot2x+sec2x augm$u=fifffizmfiaifi%? (a) aha 125112 (b) W 233? 3 (C) W 131% 3 (d) 1,23%:3 79. aficosx+coszx=13fiTsinlx+sin‘x Emma 3111?? (a) 0 (b)1 (C) 2 (d) 4 80. I1‘17?sinxcosmc=ll2§hE‘Tsinx—msx WWW3? (a) 2 (b) l (c) O (d)-1 81. 1T1? tanzycoseczx—1=tan1y%, E?! Wfifiafifi wwwfi? (a) x-y=0 (b) #:25? (c) y=2x (d) x—.y= 1° COS X COS X 111% ——-——+ =2 E‘- a? I+cosccx cosccx—l Wm ir' a a3? 913$, x a: um- ff % W 3 ? (a) #2 (b) 11/3 (0) n/4 (d) n/6 afix+y=90°3fiTsinx25iny=fizl fifix:y$wwa? (a) 1:] (b) 1:2 (c) 2:1 (d) 3:2 82. 83. COSX __ sinx ..n’ _ . —m smy 84. In? 3 a? cos y (mz—an) sinzyfia‘ WT ET 3? (a) 1 — n1 (b) 1 + n2 (c) m2 (d) n2 (Contd.) 85. 86. 87. If 0 s x 5 11:0, then which one of the following is always correct ? (a) sin2 x < 1/2 and cos2 x > 1/2 (b) sin2 x > 1/2 and cos2 x < 1/2 (c) sin2 x < 1/2 and cos2 x < 1/2 (d) At least one of sin: x, cos2 x is less than I If p = tan2 x + cot2 x, then which one of the following is correct ? (a) p S 2 (b) p 2 2 (c) p < 2 (d) p > 2 What is the value of 5 sin 75° sin 77° + 2 cos 13° cos 15° _ cos 15° sin 77°- 7 sin 81° ? cos 9° (a) —1 (b) 0 (c) l (d) 2 sfi. WA radio transmitter antenna of height 100 m stands at the top of a tall building. At a point on the ground, the angle of elevation of bottom of the antenna is 45° and that of top of antenna is 60". What is the height of the building ? (a) 100 m (b) 50 m (c) sodium (d) 50(J3—1)m 89. 90. 91. The angle of elevation of the top of an unfinished pillar at-a point 150 m from its base is 30°. If the angle of elevation at the same point is to be 45°, then the pillar has to be raised to a height of how many meters ? (a) 59-4 at (b) 61-4 m (6) 62-4 m (d) 63-4 m Which one .of the following represents statistical data ? (a) The names of all owners of shops . located in a shopping complex (b) A list giving the names of all states of India (0) A list of all European countries and their respective capital cities (d) The volume of a rainfall in certain geographical area, recorded every month for 24 consecutive months Ifsinx+siny=aandcosx+cosy=b, what is sinx - siny+cosx-cosyequal to? (a) a+b-ab (b) a+b+ab '(c') a3+b1-2 az+b2—2 (d) ——2—"— (Contd.) 85, fi-OSxSn/2%,€rfi1=1fi~rfiaafffi 86. 87. 88. _ (b) mmfifiaa‘afi%? sin2 x < 1/2 311? cos2 x > 1/2 sin2 x > 1/2 311'? cos2 x < 1/2 sin2 x < 1/2 3111 cos2 x < 1/2 sinzx,coszxiffi$fifififirw, 13133121? afip=tanzx+cotzxfififfifilfifiafi fifififififlfififi%? (a) 1352 (b) p22 (c) p<2 (d) p>2 (a) (c) (d) 5 sin 75° sin 77° + 2 cos 13° cos 15° cos 1 5° sin 77° 7 sin 81° ' cos 9° wmw%? (a)—1 (b)0 (0)1 ((1)2 wmfiafistlOOmmamw mwmwslmsw figwmafiafimwfiw 45°3fi1W$VfifimWafim 60°31mafi3fi1€w%? (a) 100m (b) 50m (c) 50(J§+1)m (d) 50(«5-1)m 89. 90. 9]. @mfia‘fifia‘mfilwmfi wfigwfifi$ufiémmfifim 30°?Ifi3fifififififi$sfififm WW45°W§€IW$W WWWWW? ' (a) 59-4 m _(b) 61-4 m (c) 62-4m (d) 634m Wfifiafifiwmfiafifiam afifimfifimii? (a) @Jfiffiwafi‘ftqfiwffaafimm Wfiwfitfiiw (b) Wfimfififia‘mafiafiw 1?“ (c) afiqfifiuhfiafiafitmm mam-claw (mwfifimafivfimmfim mammfifafiafifafin's‘aufafi trrfin 11131*sirn-t-ii-siny=aev‘?l'{ cosx+cosy=b 3,€fsinx-siny+cosx-cosy$a'{fi'{ inn%? (a) a+b—ab (b) a+b+ab (c) a2+b2-2 a2 +b2 —2 (d) *——-2 92. The arithmetic mean of a set of 10 numbers 93. 94. is 20. If each number is first multiplied by and then increased by 5, then what is the mean of new numbers ? (a) 20 (b) 25 (c) 40 (d) 45 Consider the following types of data : 1. Marks of students who appeared for a test of 100 marks. 2. Collar sizes of 200 shirts sold in a week. 3. Monthly incomes of 250 employees of a factory. For which of the above data, mode is a suitable measure of central tendency ‘? (a) (b) 2 only ' (c) (d) l and 2 only 1 and 3 only i, 2 and 3 The mean of 25 observations is 36. The mean of first 13 observations is 32 and that of last 13 observations is 39. What is the value of 13lh observation ? (a) 20 (b). 23 (c) 32 (d) 40 95. 96. 97. Data on percentage distribution of area of land-in acres owned by households in two districts of a particular state are as follows : Land holding District-A District-B 0-01—4199 5-62 13-53 10—249 18-35 21-34 2-5fl—7-49 47-12 39-32 7-5—1249 19-34 12-15 12-s_19-99 7-21 7-43 20-0-4999 2-36 5-73 What is the appropriate diagram to represent the above data ? (a) Pie diagram (b) Histogram (0) Bar chart (d) None of the above If or is the angle of first quadrant such that cosec‘i or = 17 + cat“ on, then what is the value of sin or ? (a) 1/3 (b) 1/4 (c) 1/9 ((1) 1/16 11‘ x + (1/11) = 2 cos 01., then what is the value of x1 + (1/16) ? (a) 4 cos2 01 (b) 4 cos2 a — l (c) 2 cos2 a — 2 sin2 a. (d) c052 a — sin2 or (Cont/d.) 92. 94. ——___ 93. lomfifiwmmmm 2031mmmfim2fiw ngmmmswm ia‘tmfiimmmw%? (a) 20 (b) 25 (c) 40 (d) 45 fart—1W W % t1? 135111 391W: 1 1. mfimfififimfififirloommfi ' wmfiafi. 2. wwfififizoofié‘fl 2111:1131; 3. ®W$2so$fiafifiafimfi$ 3115133112111 I mafififimfi/fimfimw WWWWWE? (a) whalafitz (b)%aa2 (c) #:3131313 (d) 1,2311-(3 25imfiwmw36%1ww 13fimfi$r 111w 323111 affim 13fiewfiafirmm 39%113’q‘fimafir,mw%? (a) 20 (b) 23 (c) 32 (d) 40 95. 96. 97. qufa$fifififfifia1fifif$ Wfifi—fimqfifimm W3: 51% mm fiat—A fifin—B 001-099 562 13-53 110—2-49 18-35 21-84 25-749 47-12 39-32 7-5—12-49 19-34 _ 12-15 12-5—19-99 7-21 7-43 20-0—29-99 2-36 5-73 WWfifiEfifim—fimm mam%? (a)_m§31fi‘(fi (BMW (0) (#313111? (d) WW,§%3~:E§T§T 111% 92:11 agufm if m afi'm % fi: cosec‘ 01. =17 + cot‘ocfih sin 01331 TNT-T 3311'? ? (a) 1/3 (b) 1/4 (c) ll9 (d) 1/16 If? x+(]/x)=2 cos 01%, 3’! x1+(l/x1) an 1m an % ? (a) 4 005201 (b) 4 cos2 a. —l (c) 2 cos2 a. — 2 sin: a ((1) cos2 a — sin2 a (Contd.) Directions : I Each of the next THREE (03) items consists of two statements, one labelled as the ‘Assertion (A)’ and the other as ‘Reason (R)’. You are to examine these two statements carefully and select the answers to these items using the codes given below : Codes .- (a) Both A and R are individually true and R is the correct explanation of A (13) Beth A and R are individually true but R is not the correct explanation of A (c) A is true but R is false ((1) A is false but R is true 98. Assertion (A) : If two triangles have same perimeter, then they are congruent. : If under a given corres- pondence, the three sides of one triangle are equal to the three sides of the other triangle, then the twotriangles'ate congruent. Reason (R) 99. ABC is a triangle. Let D, E denote the mid points of BC, CA respectively. Let AD and BE intersect at G. Let 0 be a point on AD such that A0 : OD = 2 : 7. Assertion (A) : A0 = (2 GD)/3 Reason (R) : DD = (2 AG)I3 100. ABC is a triangle. AD, BE, CF are altitudes of AABC. Assertion (A): (AB2 + BC2 + CA1) > (AD2 + BE2 + CFZ) (AEz—AFZ)+(BP—BDZ>+ (CD2 — 0132) = 0 Reason (R) . : fié‘w: mazmmmfia‘umfia am%;@a~°r'$fi=r(Ayam§aia?r wmyimw? IEWW mmfiifimwmfimw W fiqgfizafimfi W: F: (a) Aafi-t Ra‘m‘r‘ 96%, am R,A7:Ff (firm? (b) A3111 Rfimfi,mR,Am HEWWWWHE-‘T? (c) AWE}, 1mg Rm % (d) AW%, W Rafi??? 98. mm (A) : W01): 99. ABCQfifi‘gfifilnfiafifirq HEW: BC,CA%Irwfiga?riflfimm%lm am ADSfiT BEfig Gm: W mfilmafifimADwfi30w W3%AO:OD=2:7%I mm (A) : A0 = (2 GD)/3 w (R): OD = (2 AG)/3 100m: figfi ABC a. AD, BE, CF, AABC 3% 911W 3‘! EMF! (A) : (AB2 + BC2 + CA’) > (AD2 + BE2 + CF’) Wm): (AEz—AF‘)+(BFZ—BD")+ (CD2 -— CEz) == 0 SPACE FOR ROUGH WORK 2%: an? % fin”: SPACE FOR ROUGH WORK 65% $115 % fifir mwmvfiwvfiwgfiwfiafifiawmmwamfi fiafixfi. : P—DE—A—J—FN film W 3373111“ in a... WWW mm mm 313%?“ Wmfifi$gwrammwufiawgfiawfimmwfifiawfi fifimw,mmqm§mgtsmmmw€rlufifimtfifia€r WWfiaa'aV-fifiql m—miafimmmfigfimagmAmfimnmwwfiwml wwwmnwfimmfiwfimfi mgfiWfirfim‘glqfimgfiawwaflrfi ? | Wqfimgfiamfimom(m)fiqm%lufi$mfaahfitmafifiw%l mmffafifigfiw(m)fiqm% Iflfiwmfiyfi,fifimafiI—m mafiamwfifilufimfimafifiiwfimwwfiifiww fimfifimufiffiwfil‘fifim$mmqwfimgfimfil mwwwmfifiqmw-mwfiafifimfi%nm-WfifiqmWW: mfimfifi$fiwfil WW%mqfimW$fifiWWfi$Wm-mflsffifim fi,WWW—W$wmfimfimfi€§WW—mfifil mWWWfiW—Wfim$mmufim%wwmafivm afimafifiqilmmmqfimgfimfiafiafimfifil fimfimmqfimm$mfiafifi§| Wm—fifimmmmmafifi%MMfimW| (i) Wwfimwmmfilmmmwfimfiqmww w$fiqmfigmfimmmww—fififi(0-33)av€$6qfi$mml (inufiafia‘mwfim'mwaafifimmwm,wfifiq wmfifiwafitafifimfi,fifiafiwm%mafififimaafim WWWWWWWfiwwmaa-W#wfi Note : English version of the instructions is printed on the front cover of this Booklet. ...
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This note was uploaded on 11/21/2010 for the course MATH 34403 taught by Professor S.k. during the Spring '10 term at University of California, Berkeley.

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elementary_maths - 6* l -v&amp;quot; DO NOT OPEN THIS TEST...

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