Partial preview of the text
Download Class 10 CBSE Sample papers and more Study Guides, Projects, Research Mathematics in PDF only on Docsity!
Series : H4EFG . yea-ua als tera. aP.code 30/4/3 Roll No. — qoanef seq-aa ats al Set-gferar =) Wa-ys 1 saa fed | ss Candidates must write the Q.P. Code | | ill | | HI on the title page of the answer-book. | ale NOTE () Hua sia awe ci fe ga we-aa A afgq |(1) Please check that this question paper Weisel (I) Frat via at ci fF gq yeu A 38 ve él (I) set-aa Fo afet aa Al ake fer ae we-ua als al ueneif sat-gferar Ha-ge 1 fee (IV) Baar wea cat Set fora BS HTS ues, Sat-Uferent A aereerrat ot WET wal wae ataya fered (V) 34 wera at Vet & few 15 fire ar arg fem ran @) sea ar faa yale FH 10.15 a fea rem! 10.15 wt a 10.30 SS teh OA hae WA-Ta HY St ak ga aaf & dhm a sat-gferar alg Sek Aad fra SET ~3 (ml) (i) (Iv) (Vv) contains 15 printed pages. Please check that this question paper contains 38 questions. 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. Please write down the Serial Number of the question in the answer-book at the given place before attempting it. 15 minutes time has been allotted to read this question paper. The question paper will be distributed at 10.15 am. From 10.15 a.m. to 10.30 a.m., the students will read the question paper only and will not write any answer on the answer- book during this period. 2 mitra (ATs ) MATHEMATICS (STANDARD) Rratita ara : 3 qe Time allowed : 3 hours sire He : 80 Maximum Marks : 80 30/4/3 1|Page P.T.O. area Freer : PicafeaRarct ident ah aga areert @ aise sik sree arert aifsTe : @ (ii) (iii) (vy) ) (vi) (vii) (viii) (x) () a yed-a9 8 38 sete) at wea athrare & | we-a ura ael F feria 2 - &, @, 1, TINS! aus w 4 yet Ger 1 & 18 aH aefrHeda Ve (MCOs) TM IF ASM 19 TF 20 afraor wa a& arent 1 se & oe S| Gus @ Ff yet Gem 21H 25 aH Als TY-TAA (VSA) THR H 2 sent H WETS] que 7 HY 797 GET 26 S 31 TH AY-TeA (SA) WHR H 3 seal H eT eS) wus oF yet Ge 32 H 35 aH Aef-salla (LA) VOR HS Heal H WET es Gus 5H Ie GEM 36 o 38 TH TROT Hea Sea 4 Heal aH Vet S| Wea TAT rear H arate fred 2 sient & yet F fear war e | yeaa F aay fered vel fear rer @ 1 zeta, Gus @ H 2 yea H, Gus 7H 2 yea A, ws oh 2 weal Fa Gus SH 2 aial & 3 eal H arate faewed a rae fear 7TH @ | re meer eh, ere orga ree 1 af areas Bat x = = oftre, afe arqer 7 fear wat & 1 depot a svar atta | aus - aH 20x1 = 20 3a ae H 20 ea &, Ad oes 1 aH Te 1. wh 30 m cist Tah Haat Sieh ag chk GT S sft S wea aH ae mg 21 ale Teh sais & 60° ar ar sar 2, ct Ga At Sarg Sh: 1 (a) 10¥3m = (b) 303m (c) 15m (d) 15V¥3 m 7Tcm 3a ae th oa Ht Sad ace B, cast Hl oer Preprerant fisat 0.35 cm % STR WSs STATE STA Sl VS SATE TE Mt At aifrenas Tea ze : 1 (a) 400 (b) 100 (c) 20 (d) 10 Tear At ort & fae geet aman fea at anf At areas al sitset wTeT al ard @ ? 1 (a) mere of am & at (b) Tears at & ote ch at (c) mere af a ved & at (d) ast af afe go atest h UH apa aT sees SR Hers HAT: 13 R11 2, a ETH Wel AT A 2 : 1 (a) 17 (b) 7 (c) 10 (d) 28 30/4/3 A 2|Page 10. 11. 12. 13. omg arefa F, a8 au, faa Sz O 2, aT zara AC 21 AB Bie ga, fareent x of 0 8, c wu el ta @i ae OD =r2, 7 BCA Cal an? : Ae B @ + w = (c) 2r (d) 4r Uh Fa & afera ww ani ways A UH YT 5 cm cet V1 ge GR Va HT aaa 2 : (a) 20cm (b) 20 cm @ 4H (c) 20cma afte wg 40 cm a Fa (d) 40cm fay; ABC 4 ysmsi AB ak AC ® @ fag E sit F ga ver fed @ fr AE AF 1 . .. ER FO 77 el RR Aa Shar date al 8? (a) EF=2BC (b) BC=2EF (c) EF=3BC (d) BC=3EF Ud 3 UH FeIG p(x) & fere Het Hei FS sla-a weal 8? (a) p(x) % afte a afte a fa yee 1 (b) p(x) oH a oH od fa ye ZI (c) p(x) % am fra ye BI (d) p(x) ® afte a afte de fa yee é1 war we Aw: Geel RAS F aen ga von fee Sf A ade WOU fa aK 21S a wa ww ay SS oa SI SH Ta EM A am Hi wT? : 1 1 1 1 (a) 4 (b) 3 (c) rr (d) 36 a x=ab’ sity =a°b%, set a Kb as Heart %, a [HCF (x, y)— LCM (x, y)] aR 2 : (a) 1-a°b? (b) ab (1 —ab) (c) ab-a'b* (d) ab (1 —ab) (1 + ab) (8) (5) (a) earern URAa Ger 81 (b) were yore 21 (c) saree ahaa Gea 21 (d) weorenss sah Ge 21 ‘a’ wr a fares fee ax? +x+a=0 % Ae aoe a ATH &, 2 : @ 2 ® 2 @% @ -5 x-Ha & feig P(1, -1) Ht ate : (a) 1 (b) -1 (©) 0 (d) V2 30/4/3 A 4|Page 5. In the adjoining figure, AC is diameter of larger circle with centre O. AB is tangent to Cc smaller circle with centre O. If OD = r, then Cry] BCi Ito: *) 1 is equal to > A +] a @) Fr (6) > (c) 2r (d) 4r 6. A parallelogram having one of its sides 5 cm circumscribes a circle. The perimeter of parallelogram is : 1 (a) 20cm (b) less than 20 cm (c) more than 20 cm but less than 40 cm (d) 40cm 7. _Eand F are points on the sides AB and AC respectively of a AABC such AE_AF_ 1 : . so sae 2 that EB FC™2: Which of the following relation is true ? 1 (a) EF=2BC (b) BC=2EF (c) EF=3BC (d) BC=3EF 8. Which of the following statements is true for a polynomial p(x) of degree 3? 1 (a) p(x) has at most two distinct zeroes. (b) p(x) has at least two distinct zeroes. (c) p(x) has exactly three distinct zeroes. (d) p(x) has at most three distinct zeroes. 9. Letters A to F are mentioned on six faces of a die such that each face has a different letter. Two such dice are thrown simultaneously. The probability that vowels turn up on both the dice is : 1 1 1 1 1 = = = d — @ 5 (b) 5 © 5 @ 56 10. If x = ab® and y = a’b, where a and b are prime numbers, then [HCF (x, y) — LCM (j, y)] is equal to : 1 (a) 1-a°b? (b) ab (1—ab) (c) ab—a'b* (d) ab (1 —ab) (1 + ab) 2 2 i. (1+¥3) -(1-V3) is: 1 (a) a positive rational number. (b) a negative integer. (c) apositive irrational number. (d) a negative irrational number. 12. The value of ‘a’ for which ax? + x + a =0 has equal and positive roots is : 1 1 1 (a) 2 (b) 2 © 5 @-5 13. The distance of point P(1, —1) from x-axis is : 1 (@) 1 (b) -1 (© 0 @ V2 30/4/3 A 5|Page aie PTO. 14. The number of red balls in a bag is 10 more than the number of black balls. If the probability of drawing a red ball at random from this bag is 3, then the total number of balls in the bag is : (a) 50 (b) 60 (c) 80 (d) 40 15. The value of ‘p’ for which the equations px+3y = p—3, 12x+ py =p has infinitely many solutions is : (a) —6only (b) 6 only (c) +6 (d) Any real number except + 6 16. AABC and APQR are shown R in the adjoining figures. The A ie measure of ZC is : 6V3.em (a) 140° 3.8m 3¥3em 76cm (b) 80° 609 (c) 60° B 6cm c P 12cm Q (d) 40° 17. sec A=2 cos A is true for A= (a) 0° (b) 30° (c) 45° (d) 60° 18. Which of the following statements is true ? (a) sin 20° > sin 70° (b) sin 20° > cos 20° (c) cos 20° > cos 70° (d) tan 20° > tan 70° Directions : In question number 19 and 20, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option : (a) Both, Assertion (A) and Reason (R) are true and Reason (R) is 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). (c) Assertion (A) is true but Reason (R) is false. (d) Assertion (A) is false but Reason (R) is true. 19. Assertion (A): Tangents drawn at the end points of a diameter of a circle are always parallel to each other. Reason (R): The lengths of tangents drawn to a circle from a point outside the circle are always equal. 20. Assertion (A): Unit digit of 3” cannot be an even number for any natural number n. Reason (R): 2 is not a prime factor of 3” for any natural number 7. 30/4/33 7|Page ge PTO. wWs-a ga wus Hi 5 uy Z, fred vets & 2 sis ZI 21. 22. 23. 24, 25. (A) 1.5 m cial U& asa 12 m Sea eg-The (lamp post) % wg 4 2.5 m/sec St what S EM TA Vl 3 sec Ward Sat wren A ceng ara AST awat (B) ania ag ABCD i ys AD at fag E aH aera aa @ sik BE, CD al FR sfcreaied acct 21 fg Fife fe AABE ~ ACFB fig C & Pais aa fife vt ad ee tar ABR ge var fed 2 fH AC = 2BC, ae A ik B& Presa wert: (— 1, 7) ai (4, — 3) BI (A) x= Ar aa Fifer, fora fore (sin A + cosec A)’ + (cos A + sec A)’ =x + tan’ A + cot” A aaat 3 sin30°—4 sin?30° (B) A aa SR: a s0° 42 cost 50" oak faa esi at a7 at 2000, at ue ofa at on, ar 81 one are Alf fm: (i) atta wafer we gal (ii) dat seats fire 21 fra oat fren cat sftsmnfirdia fates @ wa fifi : 73x —37y =109 37x-73y=1 was -7 ga wus F 6 ea @, fra ued & 3 ais FI 26. 27. 28. 29. GH aaa fy PQR, frat araiot ferg Pw @, & efi P (x, y), Q (2, - 3) ak R (2, 3) Gl x ah y & she a dae ara Ae aa: x HS asl wena aia Fifire firs fers y = 22 (A) fate aifire fe cosh ts =cosec A—cot A arat (B) afé cot0+cos0 = p 3 cot0—cos0=q &, at fag fire fp? -q? = 4) pq afe aeqg ax? -x+c % ym a ait BG, A ow aug te sage es ETH a—3 ak B-3 dil 10 cm fsa art wa ga & vita UH Brad ABCD ae 21 fag Sif f& ae aaa ABCD at af @1 a4: ABCD @ aftara aa Aifsra) 30/4/3 A Bae 8|Page 30. (A) fag Ae f& V2 we anita dem 2 aerat (B) aM x sity a fa was der Fh par Yi gan rary p,q ak r et HCE 3 LCM ana Alfie gach Bera ae oh sits Aire fe aa HCF (p, g,r) x LCM (p, g,") =p xq Xr 8 aA 31. UH aaa ar GFT 70 om 2 aiad Al cag, Tey GTA a 5 om sift Z1 ga feafa at sismftrdia at at are wer arta frerra & eo 8 orp Alf) aa: ga Frere at eet Fe) wus - a ya wus Hi 4 oy Z, red vets & 5 sis ZI 32. (A) fiysii ABC ait PQR A ata amd 3:5 & aqua F 1 ADLBC am PSLOR Sat fe fre At arpfcet 4 fear we 2 A P /| BD Cc Qs R (i) fxg fre f& AADC ~ APSR (ii) afe AD=4 cm’, @ PS A cars ara FIfT | (iii) Gi) & ea @ ar (AABC) : ar (APQR) ara Fife aqzat (B) sara saat saa sae! sa wa & sein a Refefaa at fig afar : afe dia ater Yard J, m, n fees Varstt gq an s ae sfredier att 3, ster fe a og apf # fear wm 3, a AB _DE al BC EF 33. we sem Praia art a aka & fee ue ae seen sa ak se H fava aT festa da & weak BT! sft a Um Seren ese H MY SAAR & wT A ot aecl I a ae: cag = 2 m, Aes = 0.5 m, Weg =0.1m SeTaR AMT HI ATG = 0.1 m Serra amt At Sarg = 0.7m aed Heda Se cS! HT ras aa Sif) Fa sect HI He Ysa ara +h ae Alfa 30/4/33 10|Page ae 30. 31. (A) Prove that V2 is an irrational number. OR (B) Let x and y be two distinct prime numbers and p = x* y*, q = xy", r= x° y’. Find the HCF and LCM of p, q and r. Further check if HCF (p, g, r) x LCM (p, q, 7) =p * q Xr or not. The perimeter of a rectangle is 70 cm. The length of the rectangle is 5 cm more than twice is breadth. Express the given situation as a system of linear equations in two variables and hence solve it. SECTION -D This section consists of 4 questions of 5 marks each. 32. 33. (A) The corresponding sides of AABC and APQR are in the ratio 3 : 5. ADLBC and PSLQR as shown in the following figures : A P BD C Q's R (i) Prove that AADC ~ APSR (ii) If AD =4 cm, find the length of PS. (iii) Using (ii) find ar (AABC) : ar (APQR) OR (B) State basic proportionality theorem. Use it to prove the following : If three parallel lines /, m, n are intersected by transversals q and s as shown in the adjoining figure, Cc F on AB _ DE. a \ BC EF A bat manufacturing company made a huge bat for charity and got it signed by world cup winning team. The dimensions of the bat which is in the form of a cuboid with a cylindrical handle at the top are as follows : length = 2 m, width = 0.5 m, thickness = 0.1 m diameter of cylindrical part = 0.1 m height of cylindrical part = 0.7 m Find the volume of wood used in the bat. Also, find the total surface area of the wooden bat. th 30/4/3 “ 11|Page gee PT.O. 34, 35. Following table shows the absentees record of 40 students in an academic year : Number of Days | Number of Students 2-6 ll 6-10 10 10-14 7 14-18 4 18-22 4 22-26 3 26-30 1 Find the ‘mean’ and the ‘mode’ of the above data. (A) The sides of a right triangle are such that the longest side is 4 m more () than the shortest side and the third side is 2 m less than the longest side. Find the length of each side of the triangle. Also, find the difference between the numerical values of the area and the perimeter of the given triangle. OR a -? ; (x #3,5) as a quadratic equation in standard form. Hence, find the roots of the equation so formed. Express the equation SECTION - E This section consists of 3 Case-study based questions of 4 marks each. A drone was used to facilitate movement of an ambulance on the 36. straight highway to a point P on the ground where there was an accident. The ambulance was travelling at the speed of 60 km/h. The drone stopped at a point Q, 100 m vertically above the point P. The angle of depression of the ambulance was found to be 30° at a particular instant. Based on above information, answer the following questions : (i) (ii) Represent the above situation with the help of a diagram. Find the distance between the ambulance and the site of accident (P) at the particular instant. (Use V3= 1.73) (iii) (a) Find the time (in seconds) in which the angle of depression changes from 30° to 45°. OR (iii) (b) How long (in seconds) will the ambulance take to reach point P from a point T on the highway such that angle of depression of the ambulance at T is 60° from the drone ? 2 30/4/3 a 13|Page gee PT.O. 37, Ufa gexeiifern fort aren aitfeiftes sis ghar ch uta wergiat & aa sik aitfeiftis A gram & tafeel Ft son ar sfafificr wea 21 siferties Get & ak A oerTKaT bar & fee qed aan & oat 3 eRe gre arenes fafa afafaterat A ar ferar oral & ta a we ag 3 ee ais F ere A neg S 5 Tera Bed TATU reals Taran sect Bl TA & fore 44 m Teh Al strana ofl oraifeed anit (star faa 4 fara var 2) A ft oral 4 fata Gal ar vexit aed ee Giet aryl ae feat war ef ys OAB GH aHaTg ys @ sik art oraifed aa watran €1 sR AT & stew, Arafeas weit h sax afi : (i) sets eeER weet At eet ara AT! (ii) ZAOB A ary an 8? (iii) (a) oraifea Ba R, at Bae ara ArT! aaat Gii) (b) aerated Gat & art atk ort arch tech A cieng ara Hie 38. fea Reet & hac ar sae wes areca Fa un é| us fet Re R, vast K sre fag @ xitas fag aH daa an Ft want A ‘cars 5000 m@l fra tact HK AR ert @ 3a sara et & fee wed F FAM sete HK GY ME ae ZI amen fag & sect GH Ft et 200 m @ sit ag F GY 150 m H ATK sia K warfia fog sid @1 gach stern, if S sifer Ga At at 300 m 2l sR GT h I HK, TK A aI TRIN ah Fefefad weal h aa afar : (stra ferg @ 10d GA At got ara Aira) Gi) 15d GS atk 25d GAS ste A A are AI (iii) (a) aie Sa aR 5 m/sec M aft A aa We sh aH A Twa, F SUS 15a GY oH ve Fact HK ERT fers Ten aA Fa AIT aerat (ii) (6) Warr > she ome ae Gi Ft Ha Ger ara ifr] 30/4/33 14|Page Ba 30/4/3 A 16|Page 
