ae ibe Series WX1YZ/1 SET~2 me 80/12. tiered wea ts St age qe-ye w sae fered | ‘andidates must write the Q.P. Code nn the title page of the answer-book. wafote (arte) — Beatiares MATHEMATICS (Standard) - Theory fates era: 3 372 HTETH FE : 80 Time allowed : 3 hours Maximum Marks : 80 az / NOTE: (i) rar ate a ot fe 3a ea 99 FAB 7S 23 B | Please check that this question paper contains 23 printed pages. Weta HE TBA BTL BD BNC RU TE MEAT IS BY TATE TH YRTBT FS-TS fer 1 Q.P. Code given on the right hand side of the question paper should be written on the title page of the answer-book by the candidate. per ate at ot Pe $e eA A B3 MET | Please check that this question paper contains 38 questions. A MEA BHT TA AAA BPR HCA BY TECH, TAR PETAL HIE ET HATE HAP FS | Please write down the serial number of the question in the answer- book before attempting it, ger we awh ge & Pee 15 Pe aor ear Rar me & | eae wr Pen af 10.15 WP LRAT ATOM 1:10.15 FAB 10.30 FA TH TT BACT VIVA BI TED BIR FA TARY & chars ose gfere 1 IS see Te P| 15 minute time has been allotted to read this question paper. The question paper will be distributed at 10.15 a.m. From 10.15 a.m. to 10.30 a.m., the candidates will read the question paper only and will not write any answer on the answer-book during this period. FREE son 104 B ERAN oreat PTO.Frcaferteaa fica at aga erat a aee sie TIFF BT : (Fa MeA- VA H38 wea e | at EF sire e | (ii) Were are ast # fase B 1 avs %, G7, TAME | (iii) Gas — wa wed eT 1 B18 aH AeA Te eT TET 19 Vs 20 stir UT BRT TTMIRG CBR HF H IEF B | (iv) Bs @ Aye AEM AI G25 TH HPI TY FILL (SA-L) VOR & BA HH) B MET # (ve) @ue— 1A e4 FEAT 26 831 FH oY TAAL (SA-I]) WR H alta—At sree) H ET a (vi) @rs— wt NET GET 32 G35 aH Gel sala WH VIII HH] VETS | (vii) wes FF 939 AEA 36 H38 THT sHaEI/ BBE STG AR-AR HTH eI B | areas Fae aah ate) a 794 Rear wear @ | (viii) wer BT Te @/ rere, ae. watt, we SL a, wea 42 wea Hae ass & 3 ea F amrattes Peed aT TATA Fea TAT B | (ix) et arraeer Bi eaves omrgphal ware | ate area BF a a = 2 a (x) Herter ar seein attr 2 | B0/1/2 ww Page 2aa General Instructions : Read the following instructions carefully and follow them : () This question paper contains 88 questions. All questions are compulsory. (ii) This Question Paper is divided into FIVE Sections - Section A, B, C, D and E. (iii) In Section-A question number I to 18 are Multiple Choice Questions (MCQs) and question number 19 & 20 are Assertion-Reason based questions of 1 mark each. (iv) In Section-B question number 21 to 25 are Very Short-Answer-I (SA-D) type questions of 2 marks each. (v) In Section-C question number 26 to 31 are Short Answer-II (SA-I)) type questions carrying 8 marks each (vi) In Section-D question number 32 to 85 are Long Answer (LA) type questions carrying 5 marks each. (vii) In Section-E question number 36 to 38 are Case Study / Passage based integrated units of assessment questions carrying 4 marks each. Internal choice is provided in 2 marks question in each case-study. (viii) There is no overall choice. However, an internal choice has been provided in 2 questions in Section-B, 2 questions in Section—C, 2 questions in Se tion-D and 3 question in Section-E. 2 ix) Draw neat figures wherever required. Take 2 = 22. wherever required i 7 not stated. (x) Use of calculator is NOT allowed. 30/1/2 ww Page 3 P.T.O,Es ws (aefrancda 7) wee we 1 sim aT? | fags AG, 6) 7 BC12, —3) #1 Siga aTe Vanes F1 xa fea aaa A feorfre wre? (A) 1:2 @®) 1:4 (©) 4:1 @) 2:1 ‘dng angie #, Sy O ae ga PQ UH eit z | AG ZAOB = 95°, a ZABQ ara am: A> a Wp (A) 475° @B) 425° (C) 85" @) 95° a2 tan A=32,q SEBA+3 O84 Shae 4sinA-3cosA 7 1 (A) = (A) @) We © 3 (D) Aye? | 20 wafer & wa wag 4, 5 cule ae ae wae S| ale ew cafe argesar gar sia B, at sae ot aaa A) orem ah: 3 1 @ > ®s 1 © 1 OF B0/1/2 ww Page 4is ® 3 SECTION - A (Multiple Choice Questions) Each question is of 1 mark. 1. In what ratio, does x-axis divide the line segment joining the points A(B, 6) and BC-12, 3)? (A) 1:2 @®) 1:4 () 4:1 @) 2:1 2. In the given figure, PQ is tangent to the circle centred at O. If ZAOB = 95°, then the measure of ZABQ will be %Q (A) 47.5° (B) 42. (C) 85° @) 95° 3. If2 tan A=8, then the value of 48D A+ Se0s A 4sinA-—3cosA 1 (A) — © Te ® TB © 3 ©) does not exist 4, Ina group of 20 people, 5 can’t swim. If one person is selected at random, then the probability that he/she can swim, is 3 1 aire ® 3 1 © 1 OF 30/1/2 ww Page 5 P.T.O,a 28 & fre fear gan daw 80 Parental ara, wae ae A, req staat aby carta 2 [sree 10 8H |20 Faw] 30 BH] 40 BH] 50 VaH] 60 aa] [Ferenfekat =ft erat 3 12 27 57 75 30 | Ba Sea agers TTA (A) 10-20 (B) 20-30 (©) 30-40 ) 50-60 FFT 7 cm Sik SATS 24 cm % UH aig HI aH A Ha’ : (A) 528 cm? (B) 1056 em? (C) 550 cm? (D) 500 cm? We Fa we one & aif fig (2, 4) se 3, -1) 8 ga ee @) 25 ® 345 © 38 @) 52 Prorat fe fears agra aa 2 sh o8? ®) 3x(x-5) ©) 2 , y= Pp) @) 3 : ®) 1 © 2 @) 0 kar ae am, fred fore afta & aa ke = y + 2 7eT 6x = Qy + 3% sakes ST a FAH TATE, 2: (A) k=321 @®) wyeAe | (©) k=-321 @) k=421 B0/1/2 ww Page 6is etiae 5. The distribution below gives the marks obtained by 80 students on a test : Marks Less | Less | Less | Less | Less | Less than 10|than 20|than 30 than 40|than 50|than 60) [Number of Students[ 3 2 27 57 75. 80 ‘The modal class of this distribution is : (A) 10-20 ®) 20-30 (©) 30-40 () 50-60 6. The curved surface area of a cone having height 24 cm and radius 7 em, is (A) 528 cm? (B) 1056 cm? (C) 550 em? (@) 500 em? 7. ‘The end-points of a diameter of a cirele are (2, 4) and (-3, -1). The radius of the circle is (A) 2v5 © pz @) 5y2 8. Which of the following is a quadratic polynomial with zeroes (A) 8x(3x—5) @B) 3x(x—5) (Cc) @-= © 3 9. The graph of y = p(a) is given, for a polynomial p(a). The number of zeroes of p() from the graph is x a x y y~ Pe) () 3 . ®) 1 © 2 @) 0 10. The value of k for which the pair of equations kx = y + 2 and 6x = 2y +3 has infinitely many solutions, (A) isk (B) does not exist (©) isk= ) isk=4 30/1/2 ww Page7 P.T.O,‘af@ a, b, ¢ Uh ALP. ard & fared ard sea ‘a’ 2, a (a — 2b —c) BVA ST (A) 2a+4d (B) 0 (C) -2a-4d (D) -2a-3d aR Ue BRERA ied wale Mes a 3A ake we dt ore, Gh atte ar ae (A) seer? | ®) tsHafeatante () Ae sraig aa? () anargig aot? | |. Um Beal afed ara = wifepaT ‘p’ sik Tas a wes AY wifewaT ‘q’ 2, Alp’ AK ‘q’ BT wae A) pta=l ®) p=laq= (©) p=q-l @) ptat1=0 Ge SFI rT she @ fe cited H sees were qeeHK shat at wifsepaT 0.08 8 | afe Her 6000 feasd Farhi A, at cigahl 3 Pra foams aes aft 2 (a) 40 (B) 240 (©) 480 @) 750 amg pe) =x LSE asi ph at aera @ 1 @©-a | ear ae rH eres , Fare fare, feera enflaw 2x2 + ke 4 = OF UATE, B: (A) £22 @®) 2 (©) #2 @) v2 3 sec” 60° tan” 60° + cos” 45° | Hate 1 (a) @) 3 © o o> 1 5 cm Sarg & Ue aera 1 am Ys awe 94.2 cm? 2 | ea Fe HI eT? : (x= 3.14 aif |) (A) 2em ®) 38cm (©) 29cm ©) 6em B0/1/2 ww Page 8ae TI" If, b,c form an AP. with common difference d, then the value of a - 2b—c is equal to (A) 2a+4d ®) 0 (©) -2a-4d (D) -2a-3d 12. If the value of each observation of a statistical data is increased by 3, then the mean of the data (A) remains unchanged (B) increases by 3 (©) increases by 6 (D) increases by 3n 13. Probability of happening of an event is denoted by p and probability of non-happening of the event is denoted by q. Relation between p and q is (A) pt+q=l (B) p=1,q=1 (© peaq-1 @) p+q+1=0 14. A girl calculates that the probability of her winning the first prize in a lottery is 0.08. If 6000 tickets are sold, how many tickets has she bought ? (A) 40 (B) 240 (C) 480 (@) 750 15. Ifa, Bare the zeroes of a polynomial p(x) = 22 + x—1, then 141 equals to a @ 1 ®) 2 © A » 2 2 16. The least positive value of k, for which the quadratic equation 2x2 + kx—4=0 has rational roots, is (A) +22 (®) 2 (©) #2 @) v2 17. ec” 60° — tan? 60° + cos” 45° | is equal to ® 8) © 0 @) 4 18. Curved surface area of a cylinder of height 5 em is 94.2 em®. Radius of the cylinder is (Take m= 3.14) (A) 2em (B) 3em (C) 2.9em @) Gem 30/1/2 ww Page 9 P.T.O.is ® 3 20. 21 22, 23. 24. aaftraer—arent arentta 94 yea Her 19 ear 20 Twa afro (A) % ae wh wT (R) surfed Hera fear 2 8 Race are Ta adh fewer fie : (A) (A) eat R) abit wea Baer R), sefhrapera (A) ol ae eater aT 2 1 (B) (A) tH (R) Set ae, TT (R), gefirers (A) ht aA aT Ta SrA? | (C) (A) aer2, a(R) Ha? (D) (A) sar? TaPe (R) aT? | afiraert (A); sirpht a fae re fay AABC ar afta oH afta GET? | erm (R) : atta densi & ait ar arrest ww site der a2 A 2em| aiftrrert (A) : Fig P(O, 2), Wat 3x + 2y = 4 Sit y.set a whee fag 2 | ‘are (R) : fag P(O, 2) Ha xa a 2 gH? | wea (ga as F aifa g Seta (SAT) ware wea E | ee HT 2 iw z |) ae ota 8 wt den ai SHifre fa 12, 16 sit 24 a fans BA wee fafa F 7a | wm 92H 4 ore, 3 tet site 2 chef Fe | ww He Gar 8 argeoen Franc sft ze | sara sitet afore 5 2g Fe (i) ere & Gi) eA S| (a) atteecT ga x = 5 sity = 7 Br arha fate a eet aAihare | Herat (b) ait fa as soit aed, area ane fas ae aces a x = O aie y = —B Tae are (a) af@ sin 6 + cos 6 = V3 2, Wisin O -cos 0 FIA Ta Ff | aot ) af sina = # aitt cot B=V3 2, a cosec a+ cosee B wT AT aa FAT | B0/1/2 ww Page 10is ® 3 Assertion-Reason Type Questions In Question 19 and 20, an Assertion (A) statement is followed by a statement of Reason (R). Select the correct option out of the following (A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A), (B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A), (©) Assertion (A) is true but Reason (R) is false. (D) Assertion (A) is false but Reason (R) is true. 19. Assertion (A) : The perimeter of ABC is a rational number. Reason (R) : The sum of the squares of two rational numbers is always rational, A NN 2em c RB Bem 20. Assertion (A) : Point P(0, 2) is the point of intersection of y-axis with the line 3x + 2y = 4. Reason (R) : The distance of point P(0, 2) from x-axis is 2 units SECTION - B (This section comprises of Very Short Answer (SA-I) type questions. Every question is of 2 marks.) 21. Find the least number which when divided by 12, 16 and 24 leaves remainder 7 in each case. 22. A bag contains 4 red, 3 blue and 2 yellow balls, One ball is drawn at random from the bag. Find the probability that drawn ball is () red (i) yellow 23. (a) Solve the pair of equations nd y = 7 graphically. OR () Using graphical method, find whether pair of equations x = 0 and y =-3, is consistent or not. 24, (a) Ifsin 0 + cos 0 = V3, then find the value of sin 0 «cos 0. OR (b) Ifsin a = —~ and cot 8 =43, then find the value of cosec a + cosec ft 30/1/2 ww Page 11 P.T.O,‘amg arpfa H, XZ || BC, AZ = 3 cm, ZC = 2 cm, BM= 3 cm 3X MC=5 cm? 1 XY #1 evard ara aifare | wg - 7 (ga Gus Fag Satta (SA-I]) were & wea F | weds WAS 3 awe I) 26, Wh Fa wl Ag (Qa, a— 7) 2 | ‘a’ BI AM are Sify she ae ga fg (11, -9) A eter aren ait gat fae 5 V2 om BI 27. (@) Oma ga R wa fig TS 3 eater TP sik TQ Gist aE Z| fag Fife f& ZPTQ = 220PQ. (b) && 9a GH aa ABCD 4 sifea 2, fre 2B = 90° @ 1 afe AD = 17 cm, AB = 20 em 3% DS = 3 cm @, at ga Ft fsa ara Hite | DS 28. ot dena sek HI HT 22 | eel GeN HS wll Ge H ST HI Are 132 | tome ara Fife | 30/1/2 ww Page 12In the given figure, XZ is parallel to BC. AZ = 3 em, ZC =2 cm, BM=3em and MC = 5 em. Find the length of XY. A SECTION - C (This section comprises of Short Answer (SA-II) type questions of 3 marks each.) 26. The centre of a circle is (2a, a — 7). Find the values of a’ if the circle pas: through the point (11, 9). Radius of the circle is 27. (a) Two tangents TP and TQ are drawn to a circle with contre O from an external point T. Prove that ZPTQ = 2Z0PQ. oR () In the given figure, a circle is inscribed in a quadrilateral ABCD in which ZB = 90°, If AD = 17 em, AB = 20 em and DS = 3 em, then find the radius of the cirele. DS \’ 28. Half of the difference between two numbers is 2. The sum of the greater number and twice the smaller number is 13. Find the numbers. 30/1/2 ww Page 13 P.T.O,ae Stet 29. 30. 32. . Fra tifa: (cosec A—sin A) (see A—cos A) = (a) WH om G& Fem & aren ar 2 fas oo ww shies tag sean 2 | athia & aren #1 fren, jena fet A Sad A one 2 | afe wat A (2408 ns ena, dara Sa ar (- 2 ctf (ar) xr (bo) & Grad ve A Hou 3 cm HK SAE 12 cm 2 | gH VG 4 orga ee HR se seg Br fe seg Baar (2) 8, ore wei wet ag 2 ig oH UH Heats aren F argeshta | sTgEReTA HT sree are AIP, | (x = 3.14 efifere, |) fir aifiry fi V5 ww sraftia ere | 1 cot A+tan A ag -a (ga Gs Ftd seta (LA) weer & wea E | eee AS 5 gies ZI) wm adh yf 8 45° lor ae uw dae | al gs 2 1 ale ail ar, dae a gf A ean 4, 4m Fo 8 Gin ret @, a ae yf a 30° a1 SI are 8 Tas gee Soe fit 3m He aH ara 2 | afr a gas Sad RR A sift Sars cen ait AI cars at sits | B0/1/2 ww Page 14ae sae: 29. (a) A room is in the form of cylinder surmounted by a hemi-spherical dome. The base radius of hemisphere is one-half the height of 1408) eylindrical part. Find total height of the room if it eontains { v2) of air. (Take n= 2) iS 7) OR (©) Anempty cone is of radius 3 em and height 12 em. Ice-cream is filled th in it so that lower part of the cone which is (2) of the volume of \ the cone is unfilled but hemisphere is formed on the top. Find volume of the ice-cream. (Take 14) 30. Prove that 5 is an irrational number. 31. Prove that (cosec A~ sin A) (sec A—cos A) SECTION - D (This section comprises of Long Answer (LA) type questions of 5 marks each.) 32, A ladder set against a wall at an angle 45° to the ground. If the foot of the ladder is pulled away from the wall through a distance of 4 m, its top slides a distance of 3 m down the wall making an angle 30° with the ground. Find the final height of the top of the ladder from the ground and length of the ladder, 30/1/2 wen Page 15 P.T.O.ae 3 (a) WAP. % aie a1 174 ye a gad 3: 42 | AP. 5d eT QI ea carga ara fine | yee 5 aah aS aed 21 wh Sd ar sega A a afar | aaa (b) 250 agai (logs) #1 2 & wa 8 ga eR VET TTT? aad Ara arett daa F 22 igs, saa arrett fat T 21 cis, saa ainefi afer A 20 ‘aad, seme (arpa Qaw) 2 250 aes fire afertt H ya (bo) @7 apf 4, CD ait RS wee: Gras ABC ait fy PQR AM wfBrend & | cafe AABC ~ APQR 8, @ fitg Afar fH @ AADC~ APSR Gi) ADxPR=ACxPS A D&B R 35. 1d om fsa are th ge A ww Sat ga Sy M CO’ sr HM ware B | Sra TY TT ars a dave ar Fife | ora: ae qa avs Hr Gare Hi aa fae | B0/1/2 ww Page 1633. (a) The ratio of the 11" term to 17 term of an AP. is 3: 4. Find the ratio of 5' term to 21* term of the same A-P. Also, find the ratio of the sum of first 5 terms to that of first 21 terms. OR (6) 250 logs are stacked in the following manner 22 logs in the bottom row, 21 in the next row, 20 in the row next to it and so on (as shown by an example). In how many rows, are the 250 logs placed and how many logs are there in the top row ? 7 (Example) 34. (a) PA, QB and RC are each perpendicular to AC. If AP = x, QB RC=y, AB=a and BC =b, then prove that 4 x mr ™~ R © Ye = y — : a Bb © OR (6) In the given figure, CD and RS are respectively the medians of AABC and APQR. If AABC ~ APQR then prove that : @ AADC ~ APSR: (i) AD x PR=ACxPS C R 35. A chord of a circle of radius 14 cm subtends an angle of 60° at the centre. Find the area of the corresponding minor segment of the circle. Also find the area of the major segment of the circle. 30/1/2 ww Page 17 P.T.O,is ® 3 ial wes (Fa ave F 3 re aeTEA/Uitede srenita sya S | eres ITA a 4 at EI) RR SA Sea th oss tet wear @ fare oe wertie sem thee a ware eT 2 | waehig UH ah SE ever 3g ae aa een, foe a Giger & wt ae, waa week Be aT age Fi aa He eT | Langont line dng arpa 4, 3 0 are aft 75 om fen aa Fak AB teh Gi Uw ERI’, ZABO = 30° 3K PQ || OA. sailed Gea } STU: (a) ABS) read ara Fifa | 1 (b) OB A erearg ara =ifere, | 1 (© AP Fava gra fifa | 2 awa PQ A orang ara Fife | B0/1/2 ww Page 18is ® 3 SECTION - E (In this section, there are 3 case study/passage based questions. Each question is of 4 marks.) Case Study 36. The discus throw is an event in which an athlete attempts to throw a discus. The athlete spins anti-clockwise around one and a half times through a circle, then releases the throw. When released, the discus travels along tangent to the circular spin orbit. ‘angont line In the given figure, AB is one such tangent to a circle of radius 75 cm. Point O is centre of the circle and ZABO = 30°. PQ is parallel to OA. O . 2 =< 190m) 5 p A Based on above information : (a) find the length of AB. 1 (b) find the length of OB. 1 (©) find the length of AP. 2 oR find the length of PQ. 30/1/2 ww Page 19 P.T.O,ce age Ae Tere fags ae a, US flies Vos oe Aaa Pe HS BaHe F1 Gal er & fore feral Fars wel St cians ak ters 1 x gers ar far eT @ | AST ‘Brat 18 em weal 3H 12 em HZ | sriaa & sen wt fer weit & ser dif : CD) sataa arent BY eat aren wep after atten fenfeae, | (i) ata faera afte a ars eo F feta | (ID 33 ee Hal} se eT a afer ? x 18cm School 12em Photo. ls awa RH x HTT GAA A, A BAHT HY 220 cm? SH ATK AAT THT VP 38, aca them fergra fern ent aa} favs satis fee ad than otk atts oat ea? | B0/1/2 ww Page 2037. While designing the school year book, a teacher asked the student that the length and width of a particular photo is inereased by x units each to double the area of the photo. The original photo is 18 em long and 12 cm wide. Based on the above information, answer the following questions @) Write an algebraic equation depicting the above information. 1 (il) Write the corresponding quadratic equation in standard form. 1 (I) What should be the new dimensions of the enlarged photo ? 2 ey 18em r School 1em Photo x OR Can any rational value of x make the new area equal to 220 cm? ? 38. India meteorological department observes seasonal and annual rainfall every year in different sub-divisions of our country. 30/1/2 wr Page 21 P.T.O.a ® 2 ae Se shore Ay ger sit faryerao el A seg area @ | Ar At ng rferasr sa—Aserae 2018 Hahah (arrga) aot (faah. 4) fare agi (mm #) wate A ee 200-400 2 400-600 4 600-800 7 800-1000 4 10 00, 2 1200-1400, 3 1400-1600 1 1600-1800 1 sated Gat aren, fet wea & ser difare : (age art ferfize | () fear sifest ar arene ara fare | ga dite 9 9g area af sara afte | (CD af arrga & dee 3 a SH 1000 mm asi ara sys &) areal asl area Sa-Hset AMAT STAT @, ch Pat Sa-sett H sre al es? B0/1/2 ww Page 22Es It helps them to compare and analyse the results. The table given below shows sub-division wise seasonal (monsoon) rainfall (mm) in 2018 Rainfall (mm) | Number of Sub-divisions 200-400 2 400-600 600-800 800-1000 4 1000-1200 2 1200-1400 3 1400-1600 1 1600-1800 1 Based on the above information, answer the following questions (Write the modal class. (II) Find the median of the given data. OR Find the mean rainfall in this season. (I) If sub-division having at least 1000 mm rainfall during monsoon season, is considered good rainfall sub-division, then how many sub- divisions had good rainfall ? 30/1/2 wwa ® 3 B0/1/2 ne Page 24