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CBSE Class 10 Sample / Model Paper 2024 : Mathematics

23 pages, 133 questions, 0 questions with responses, 0 total responses,

Kishore
Kendriya Vidyalaya (KV) No 2, Thirupparankundram, Madurai

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Series C5ABD/5 SET~1 Z-n H$moS> amob Z . Q.P. Code Roll No. 30/5/1 narjmWu Z-n H$moS> >H$mo C ma-nwp VH$m Ho$ _wI-n >na Ad ` {bIo & Candidates must write the Q.P. Code on the title page of the answer-book. ZmoQ> / NOTE : (i) H $n`m Om M H$a b| {H$ Bg Z-n _o _w{ V n > 23 h & Please check that this question paper contains 23 printed pages. (ii) H $n`m Om M H$a b| {H$ Bg Z-n _| >38 Z h & Please check that this question paper contains 38 questions. (iii) Z-n _| Xm{hZo hmW H$s Amoa {XE JE Z-n H$moS H$mo narjmWu C ma-nwp VH$m Ho$ _wI-n > na {bI| & 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. (iv) H $n`m Z H$m C ma {bIZm ew $ H$aZo go nhbo, C ma-nwp VH$m _| Z H$m H $_m H$ Ad ` {bI| & Please write down the serial number of the question in the answer-book before attempting it. (v) Bg Z-n H$mo n T>Zo Ho$ {bE 15 {_ZQ >H$m g_` {X`m J`m h & Z-n H$m {dVaU nydm _| 10.15 ~Oo {H$`m OmEJm & 10.15 ~Oo go 10.30 ~Oo VH$ N> m Ho$db Z-n H$mo n T>|Jo Am a Bg Ad{Y Ho$ Xm amZ do C ma-nwp VH$m na H$moB C ma Zht {bI|Jo & 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 students will read the question paper only and will not write any answer on the answer-book during this period. J{UV (_mZH$) MATHEMATICS (STANDARD) {ZYm [aV g_` : 3 K Q>o A{YH$V_ A H$ : 80 Time allowed : 3 hours 15-30/5/1 Maximum Marks : 80 Page 1 P.T.O. gm_m ` {ZX}e : {Z Z{b{IV {ZX}em| H$mo ~h V gmdYmZr go n{ T>E Am a CZH$m g Vr go nmbZ H$s{OE : Bg Z-n _| 38 Z h & g^r Z A{Zdm` h & (i) `h Z-n nm M I S>m| _| {d^m{OV h H$, I, J, K Ed L> & (ii) (iii) I S> H$ _| Z g `m 1 go 18 VH$ ~h {dH$ nr` (MCQ) VWm Z g `m 19 Ed 20 A{^H$WZ Ed VH $ AmYm[aV 1 A H$ Ho$ Z h & (iv) I S> I _| Z g `m 21 go 25 VH$ A{V bKw-C mar` (VSA) H$ma Ho$ 2 A H$m| Ho$ Z h & I S> J _| Z g `m 26 go 31 VH$ bKw-C mar` (SA) H$ma Ho$ 3 A H$m| Ho$ Z h & (v) (vi) I S> K _| Z g `m 32 go 35 VH$ XrK -C mar` (LA) H$ma Ho$ 5 A H$m| Ho$ Z h & (vii) I S> L> _| Z g `m 36 go 38 VH$ H$aU A ``Z AmYm[aV 4 A H$m| Ho$ Z h & `oH$ H$aU A ``Z _| Am V[aH$ {dH$ n 2 A H$m| Ho$ Z _| {X`m J`m h & (viii) Z-n _| g_J {dH$ n Zht {X`m J`m h & ` {n, I S> I Ho$ 2 Zm| _|, I S> J Ho$ 2 Zm| _|, I S> K Ho$ 2 Zm| _| VWm I S> L> Ho$ 3 Zm| _| Am V[aH$ {dH$ n H$m mdYmZ {X`m J`m h & (ix) Ohm Amd `H$ hmo d N> AmH ${V`m ~ZmBE & Ohm Amd `H$ hmo p = 22 br{OE, `{X A `Wm 7 Z {X`m J`m hmo & (x) H $ Hw$boQ>a H$m Cn`moJ d{O V h & I S> H$ Bg I S> _| ~h {dH$ nr` Z 1. 2. g_m Va lo T>r (A.P.) (MCQ) 18 , h , {OZ_| `oH$ Z 1 A H$ H$m h & 50 , 98 , H$m AJbm (Mm Wm) nX h : (A) 128 (B) 140 (C) 162 (D) 200 x2 + y 2 H$m _mZ h : `{X x y = 2 sin A, = 2 cos A 3 3 h , Vmo (A) 36 (B) 9 (C) 6 (D) 18 15-30/5/1 Page 2 20 1=20 General Instructions : Read the following instructions very carefully and strictly follow them : (i) This question paper contains 38 questions. All questions are compulsory. (ii) This question paper is divided into five Sections A, B, C, D and E. (iii) In Section A, Questions no. 1 to 18 are Multiple Choice Questions (MCQs) and questions number 19 and 20 are Assertion-Reason based questions of 1 mark each. (iv) In Section B, Questions no. 21 to 25 are Very Short Answer (VSA) type questions, carrying 2 marks each. (v) In Section C, Questions no. 26 to 31 are Short Answer (SA) type questions, carrying 3 marks each. (vi) In Section D, Questions no. 32 to 35 are Long Answer (LA) type questions carrying 5 marks each. (vii) In Section E, Questions no. 36 to 38 are case study based questions carrying 4 marks each. Internal choice is provided in 2 marks questions in each case study. (viii) There is no overall choice. However, an internal choice has been provided in 2 questions in Section B, 2 questions in Section C, 2 questions in Section D and 3 questions in Section E. 22 (ix) Draw neat diagrams wherever required. Take p = wherever required, if not 7 stated. (x) Use of calculator is not allowed. SECTION A This section comprises Multiple Choice Questions (MCQs) of 1 mark each. 1. 2. The next (4th) term of the A.P. 18 , 50 , 98 , is : (A) 128 (B) 140 (C) 162 (D) 200 If x y = 2 sin A, = 2 cos A, then the value of x2 + y2 is : 3 3 (A) 36 (B) 9 (C) 6 (D) 18 15-30/5/1 20 1=20 Page 3 P.T.O. 3. `{X 4 sec q 5 = 0 h , Vmo cot q (A) 3 4 (B) 4 5 (C) 5 3 (D) 4 3 4. g_rH$aU {ZH$m` 3x + 4y = 5 VWm H$s gab aoImE {Z ${nV hmo ahr h ? g_m Va (A) {V N>oXr (B) g nmVr (C) EH$-X gao Ho$ b ~dV (D) 5. { KmV g_rH$aU 6. 7. 8. H$m _mZ h : 5x2 6x + 21 = 0 6x + 8y = 7 mam {Z Z{b{IV _| go {H$g H$ma Ho$ _ybm| Ho$ `moJ\$b VWm JwUZ\$b _| AZwnmV h : (A) 5 : 21 (B) 2:7 (C) 21 : 5 (D) 7:2 `{X Am H$ S>m| 2, 9, x + 6, 2x + 3, 5, 10, 5; H$m _m ` 7 h , Vmo x H$m _mZ h : (A) 9 (B) 6 (C) 5 (D) 3 EH$ W bm, {Og_| 1 go 40 VH$ A {H$V {Q>H$Q>| h , _| go `m N>`m EH$ {Q>H$Q> {ZH$mbr OmVr h & {ZH$mbr JB {Q>H$Q> H$s A {H$V g `m Ho$ 7 H$m JwUO hmoZo H$s m{`H$Vm h : (A) 1 7 (B) 1 8 (C) 1 5 (D) 7 40 { `m dmbo d m Ho$ Cg { `I S>, Omo d m Ho$ Ho$ na H$aVm h , H$m n[a_mn h : 21 cm (A) 22 cm (B) 43 cm (C) 64 cm (D) 462 cm 15-30/5/1 Page 4 60 H$m H$moU A V[aV 3. 4. If 4 sec q 5 = 0, then the value of cot q is : (A) 3 4 (B) 4 5 (C) 5 3 (D) 4 3 Which out of the following type of straight lines will be represented by the system of equations 3x + 4y = 5 and 6x + 8y = 7 ? 5. 6. (A) Parallel (B) Intersecting (C) Coincident (D) Perpendicular to each other The ratio of the sum and product of the roots of the quadratic equation 5x2 6x + 21 = 0 is : (A) 5 : 21 (B) 2:7 (C) 21 : 5 (D) 7:2 For the data 2, 9, x + 6, 2x + 3, 5, 10, 5; if the mean is 7, then the value of x is : 7. (A) 9 (B) 6 (C) 5 (D) 3 One ticket is drawn at random from a bag containing tickets numbered 1 to 40. The probability that the selected ticket has a number which is a multiple of 7 is : 8. (A) 1 7 (B) 1 8 (C) 1 5 (D) 7 40 The perimeter of the sector of a circle of radius 21 cm which subtends an angle of 60 at the centre of circle, is : (A) 22 cm (B) 43 cm (C) 64 cm (D) 462 cm 15-30/5/1 Page 5 P.T.O. 9. 10. 11. 12. 13. { `m dmbo d m H$s EH$ Mmn A V[aV H$moU h : 12 cm 10p cm b ~r h & Bg Mmn mam d m Ho$ H|$ na (A) 120 (B) 6 (C) 75 (D) 150 dh ~ S>r-go-~ S>r g `m Omo h , h : 281 VWm 1249 H$mo ^mJ H$aZo na H $_e: 5 VWm 7 eof\$b XoVr (A) 23 (B) 276 (C) 138 (D) 69 g_m Va lo T>r 3, 6, 9, 12, , 111 Ho$ nXm| H$s g `m h : (A) 36 (B) 40 (C) 37 (D) 30 { `m dmbo EH$ d m H$s EH$ Ordm, d m Ho$ H|$ na g_H$moU A V[aV H$aVr h & Vmo Ordm H$s b ~mB (cm _|) h : 10 cm (A) 5 2 (B) 10 2 (C) 5 2 (D) 5 VrZ g `mAm| 28, 44, 132 H$m b.g. (LCM) h : (A) 258 (B) 231 (C) 462 (D) 924 15-30/5/1 Page 6 9. The length of an arc of a circle with radius 12 cm is 10p cm. The angle subtended by the arc at the centre of the circle, is : 10. (A) 120 (B) 6 (C) 75 (D) 150 The greatest number which divides 281 and 1249, leaving remainder 5 and 7 respectively, is : 11. 12. (A) 23 (B) 276 (C) 138 (D) 69 The number of terms in the A.P. 3, 6, 9, 12, , 111 is : (A) 36 (B) 40 (C) 37 (D) 30 A chord of a circle of radius 10 cm subtends a right angle at its centre. The length of the chord (in cm) is : 13. (A) 5 2 (B) 10 2 (C) 5 2 (D) 5 The LCM of three numbers 28, 44, 132 is : (A) 258 (B) 231 (C) 462 (D) 924 15-30/5/1 Page 7 P.T.O. 14. 15. 16. 17. `{X Xmo gh-A^m ` g `mAm| H$m JwUZ\$b 553 h , Vmo CZH$m _.g. (A) 1 (B) 553 (C) 7 (D) 79 `{X a VWm b ~h nX H$m _mZ h : (A) (C) 3 2 2 3 p(x) = kx2 30x + 45k Ho$ ey `H$ h VWm (HCF) h : a + b = ab h , Vmo k 3 2 (B) (D) 2 3 Xr JB AmH ${V _|, RJ VWm RL, d m na ItMr JB Xmo ne -aoImE h & `{X RJL = 42 h , Vmo JOL H$s _mn h : (A) 42 (B) 84 (C) 96 (D) 138 Xr JB AmH ${V _|, D ABC _|, DE || BC h & `{X AE = 2 cm h , Vmo AC H$s b ~mB h : AD = 2 4 cm, DB = 4 cm (A) 10 cm 3 (B) 3 cm 10 (C) 16 cm 3 (D) 1 2 cm 15-30/5/1 Page 8 VWm 14. 15. 16. 17. If the product of two co-prime numbers is 553, then their HCF is : (A) 1 (B) 553 (C) 7 (D) 79 If a and b are the zeroes of the polynomial p(x) = kx2 30x + 45k and a + b = ab, then the value of k is : (A) (C) 3 2 2 3 (B) (D) 2 3 3 2 In the given figure, RJ and RL are two tangents to the circle. If RJL = 42 , then the measure of JOL is : (A) 42 (B) 84 (C) 96 (D) 138 In the given figure, in D ABC, DE || BC. If AD = 2 4 cm, DB = 4 cm and AE = 2 cm, then the length of AC is : (A) 10 cm 3 (B) 3 cm 10 (C) 16 cm 3 (D) 1 2 cm 15-30/5/1 Page 9 P.T.O. 18. `{X 7 5 m b ~m grYm I S>m I ^m ^y{_ na 5 m b ~r N>m`m ~ZmVm h Am a Cgr g_` EH$ _rZma H$s N>m`m H$s b ~mB 24 m h , Vmo _rZma H$s D $MmB h : (A) 20 m (B) 40 m (C) 60 m (D) 36 m Z g `m 19 Am a 20 A{^H$WZ Ed VH $ AmYm[aV Z h & Xmo H$WZ {XE JE h {OZ_| EH$ H$mo A{^H$WZ (A) VWm X gao H$mo VH $ (R) mam A {H$V {H$`m J`m h & BZ Zm| Ho$ ghr C ma ZrMo {XE JE H$moS>m| (A), (B), (C) Am a (D) _| go MwZH$a Xr{OE & 19. (A) A{^H$WZ (A) Am a VH $ m m H$aVm h & (R) XmoZm| ghr h Am a VH $ (R), A{^H$WZ (A) H$s ghr (B) A{^H$WZ (A) Am a VH $ m m Zht H$aVm h & (R) XmoZm| ghr h , na Vw VH $ (R), A{^H$WZ (A) H$s ghr (C) A{^H$WZ ghr h , na Vw VH $ (R) JbV h & (D) A{^H$WZ (A) JbV h , na Vw VH $ (R) ghr h & A{^H$WZ (A) : (A) ABCD EH$ BC na VH $ (R) : 20. g_b ~ h {Og_| Eogo q~X h {H$ DC || AB h & E VWm F H $_e AD VWm AE BF = EF || AB h & Vmo & ED FC {H$gr g_b ~ H$s g_m Va ^wOmAm| Ho$ g_m Va H$moB aoIm Ag_m Va ^wOmAm| H$mo g_mZwnmV _| ~m Q>Vr h & A{^H$WZ (A) : ey ` ~h nX H$s KmV n[a^m{fV Zht h & VH $ (R) : 15-30/5/1 EH$ ey `oVa AMa ~h nX H$s KmV 0 hmoVr h & Page 10 18. If a vertical pole of length 7 5 m casts a shadow 5 m long on the ground and at the same time, a tower casts a shadow 24 m long, then the height of the tower is : (A) 20 m (B) 40 m (C) 60 m (D) 36 m Questions number 19 and 20 are Assertion and Reason based questions. Two statements are given, one labelled as Assertion (A) and the other is labelled as Reason (R). Select the correct answer to these questions from the codes (A), (B), (C) and (D) as given below. (A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A). (B) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A). 19. (C) Assertion (A) is true, but Reason (R) is false. (D) Assertion (A) is false, but Reason (R) is true. Assertion (A) : ABCD is a trapezium with DC || AB. E and F are points on AD and BC respectively, such that EF || AB. Then AE BF = . ED FC Reason (R) : Any line parallel to parallel sides of a trapezium divides the non-parallel sides proportionally. 20. Assertion (A) : Degree of a zero polynomial is not defined. Reason (R): 15-30/5/1 Degree of a non-zero constant polynomial is 0. Page 11 P.T.O. I S> I Bg I S> _| A{V bKw-C mar` (VSA) H$ma Ho$ Z h , {OZ_| `oH$ Ho$ 2 A H$ h & 21. (a) `{X 3 cm { `m dmbo EH$ d m na ItMr JB Xmo ne -aoImE na na 5 2=10 60 Ho$ H$moU na PwH$s h , Vmo `oH$ ne -aoIm H$s b ~mB kmV H$s{OE & AWdm (b) {g H$s{OE {H$ d m Ho$ {H$gr `mg Ho$ {gam| na ItMr JB ne -aoImE na na g_m Va hmoVr h & 22. _mZ kmV H$s{OE : 2 tan 30 . sec 60 . tan 45 1 sin 2 60 23. `{X a, b ~h nX p(x) = 5x2 6x + 1 Ho$ ey `H$ h , Vmo a + b + ab H$m _mZ kmV H$s{OE & 24. (a) dh AZwnmV kmV H$s{OE {Og_| q~X P( 4, 6), q~X Am| A( 6, 10) VWm B(3, 8) H$mo {_bmZo dmbo aoImI S> H$mo {d^m{OV H$aVm h & AWdm (b) {g H$s{OE {H$ q~X (3, 0), (6, 4) VWm ( 1, 3) EH$ g_{ ~mh { ^wO Ho$ erf h & 25. EH$ {S> ~o _| 60 H$_rO| h , {OZ_| 48 A N>r H$_rO| h , O~{H$ 8 _| _wI Xmof h VWm 4 _| N>moQ>o Xmof h & {ZJ_, EH$ `mnmar, Ho$db A N>r H$_rO| hr drH$ma H$aVm h , O~{H$ EH$ X gam `mnmar AZ_mob , Ho$db C ht H$_rOm| H$mo A drH$ma H$aVm h {OZ_| _wI Xmof hm| & {S> ~o _| go `m N>`m EH$ H$_rO {ZH$mbr JB & m{`H$Vm kmV H$s{OE {H$ {ZH$mbr JB H$_rO AZ_mob H$mo drH$ma h & 15-30/5/1 Page 12 SECTION B This section comprises Very Short Answer (VSA) type questions of 2 marks each. 5 2=10 21. (a) If two tangents inclined at an angle of 60 are drawn to a circle of radius 3 cm, then find the length of each tangent. OR (b) Prove that the tangents drawn at the ends of a diameter of a circle are parallel. 22. Evaluate : 2 tan 30 . sec 60 . tan 45 1 sin2 60 23. If a, b are zeroes of the polynomial p(x) = 5x2 6x + 1, then find the value of a + b + ab. 24. (a) Find the ratio in which the point P( 4, 6) divides the line segment joining the points A( 6, 10) and B(3, 8). OR (b) Prove that the points (3, 0), (6, 4) and ( 1, 3) are the vertices of an isosceles triangle. 25. A carton consists of 60 shirts of which 48 are good, 8 have major defects and 4 have minor defects. Nigam, a trader, will accept the shirts which are good but Anmol, another trader, will only reject the shirts which have major defects. One shirt is drawn at random from the carton. Find the probability that it is acceptable to Anmol. 15-30/5/1 Page 13 P.T.O. I S> J Bg I S> _| bKw-C mar` (SA) H$ma Ho$ Z h , {OZ_| `oH$ Ho$ 3 A H$ h & 26. {g H$s{OE {H$ (a) 3 6 3=18 EH$ An[a_o` g `m h & AWdm {g H$s{OE {H$ ( 2 An[a_o` g `m h & (b) 27. + 3 ) 2 EH$ An[a_o` g `m h , {X`m J`m h {H$ 6 EH$ `{X EH$ g_m Va lo T>r Ho$ nhbo 14 nXm| H$m `moJ\$b 1050 h VWm BgH$m W_ nX 10 h , Vmo Bg g_m Va lo T>r H$m 20dm nX VWm ndm nX kmV H$s{OE & (a) AWdm EH$ g_m Va lo T>r H$m W_ nX 5, A {V_ nX 45 VWm g^r nXm| H$m `moJ\$b h & Bg g_m Va lo T>r Ho$ nXm| H$s g `m VWm gmd A Va kmV H$s{OE & (b) 28. {g H$s{OE {H$ EH$ d m Ho$ n[aJV g_m Va MVw^w O EH$ g_MVw^w O hmoVm h & 29. {g H$s{OE {H$ : 400 tan A cot A + = 1 + sec A cosec A 1 cot A 1 tan A 30. VrZ {Z nj {g Ho$ EH$ gmW CN>mbo JE & {Z Z{b{IV Ho$ m V H$aZo H$s m{`H$Vm kmV H$s{OE : H$_-go-H$_ EH$ {MV (i) _m EH$ nQ> (ii) (iii) Xmo {MV VWm EH$ nQ> 31. { `m dmbo d m H$s EH$ Mmn d m Ho$ H|$ na g_H$moU ~ZmVr h & Vmo g JV XrK { `I S> H$m jo \$b kmV H$s{OE & (p = 3 14 `moJ H$s{OE) 10 cm 15-30/5/1 Page 14 SECTION C This section comprises Short Answer (SA) type questions of 3 marks each. 26. (a) 6 3=18 3 is an irrational number. Prove that OR (b) Prove that ( 2 + 3 ) 2 is an irrational number, given that 6 is an irrational number. 27. (a) If the sum of the first 14 terms of an A.P. is 1050 and the first term is 10, then find the 20th term and the nth term. OR (b) The first term of an A.P. is 5, the last term is 45 and the sum of all the terms is 400. Find the number of terms and the common difference of the A.P. 28. Prove that the parallelogram circumscribing a circle is a rhombus. 29. Prove that : tan A cot A + = 1 + sec A cosec A 1 cot A 1 tan A 30. Three unbiased coins are tossed simultaneously. Find the probability of getting : 31. (i) at least one head. (ii) exactly one tail. (iii) two heads and one tail. An arc of a circle of radius 10 cm subtends a right angle at the centre of the circle. Find the area of the corresponding major sector. (Use p = 3 14) 15-30/5/1 Page 15 P.T.O. I S> K Bg I S> _| XrK -C mar` (LA) H$ma Ho$ Z h , {OZ_| `oH$ Ho$ 5 A H$ h & 32. (a) 4 5=20 k H$m dh _mZ kmV H$s{OE {OgHo$ {bE { KmV g_rH$aU (k + 1)x2 6(k + 1)x + 3(k + 9) = 0, k 1 Ho$ dm V{dH$ Am a g_mZ _yb h & AWdm (b) EH$ `{ $ H$s Am`w AnZo ~oQ>o H$s Am`w Ho$ dJ H$s X JwZr h & AmR> df n MmV , Bg `{ $ H$s Am`w AnZo ~oQ>o H$s Am`w Ho$ VrZ JwZo go 4 df A{YH$ hmoJr & CZH$s dV _mZ Am`w kmV H$s{OE & 33. EH$ ZXr Ho$ nwb Ho$ EH$ q~X go, ZXr Ho$ g _wI {H$Zmam| Ho$ AdZ_Z H$moU H $_e: 30 Am a 60 h & `{X nwb, {H$Zmam| go 4 m H$s D $MmB na hmo, Vmo ZXr H$s Mm S> mB kmV H$s{OE & 34. (a) Xr JB AmH ${V _|, D FEC @ D GDB VWm 1= 2 h & {g H$s{OE {H$ D ADE ~ D ABC. AWdm (b) 15-30/5/1 EH$ D ABC H$s ^wOmE AB Am a AC VWm _mp `H$m AD H $_e: EH$ A ` { ^wO D PQR H$s ^wOmAm| PQ Am a PR VWm _mp `H$m PM Ho$ g_mZwnmVr h & Xem BE {H$ D ABC ~ D PQR. Page 16 SECTION D This section comprises Long Answer (LA) type questions of 5 marks each. 32. (a) 4 5=20 Find the value of k for which the quadratic equation (k + 1)x2 6(k + 1)x + 3(k + 9) = 0, k 1 has real and equal roots. OR (b) The age of a man is twice the square of the age of his son. Eight years hence, the age of the man will be 4 years more than three times the age of his son. Find their present ages. 33. From a point on a bridge across the river, the angles of depressions of the banks on opposite sides of the river are 30 and 60 respectively. If the bridge is at a height of 4 m from the banks, find the width of the river. 34. (a) In the given figure, D FEC @ D GDB and 1 = 2. Prove that D ADE ~ D ABC. OR (b) Sides AB and AC and median AD of a D ABC are respectively proportional to sides PQ and PR and median PM of another D PQR. Show that D ABC ~ D PQR. 15-30/5/1 Page 17 P.T.O. 35. bH$ S>r Ho$ EH$ R>mog ~obZ Ho$ `oH$ {gao na EH$ AY Jmobm ImoX H$a {ZH$mbVo h E, EH$ d Vw ~ZmB JB h , O gm {H$ AmH ${V _| {XIm`m J`m h & `{X ~obZ H$s D $MmB 5 8 cm h Am a BgHo$ AmYma H$s { `m 2 1 cm h , Vmo Bg d Vw H$m g nyU n R>r` jo \$b kmV H$s{OE & I S> L> Bg I S> _| 3 H$aU A ``Z AmYm[aV Z h {OZ_| `oH$ Ho$ 4 A H$ h & 36. 3 4=12 H$aU A ``Z 1 E gob d S> ^maV Ho$ g~go ~ S>o _Zmoa OZ nmH$m] _| go EH$ h Omo g^r C_ Ho$ AmJ VwH$m| Ho$ {bE amo_m MH$ gdmar, Ob AmH$f U Am a _Zmoa OZ {dH$ nm| H$s EH$ {d{dY m Ibm XmZ H$aVm h & `h nmH $ AnZo {Vp R>V dm Q>a qH$JS>_ Ho $ {bE OmZm OmVm h , Omo Bgo nm[adm[aH$ g a Am a _Zmoa OZ Ho$ {bE EH$ bmoH${ ` J V ` ~ZmVm h & nmH $ H$m {Q>H$Q> ew H$ < 150 {V ~ m VWm < 250 {V d` H$ h & EH$ {XZ, nmH $ Ho$ IOm Mr Zo `h nm`m {H$ 15-30/5/1 300 {Q>H$Q> {~H$s h VWm < 55,000 EH$ h E h & Page 18 35. A wooden article was made by scooping out a hemisphere from each end of a solid cylinder, as shown in the figure. If the height of the cylinder is 5 8 cm and its base is of radius 2 1 cm, find the total surface area of the article. SECTION E This section comprises 3 case study based questions of 4 marks each. 36. 3 4=12 Case Study 1 Essel World is one of India s largest amusement parks that offers a diverse range of thrilling rides, water attractions and entertainment options for visitors of all ages. The park is known for its iconic Water Kingdom section, making it a popular destination for family outings and fun-filled adventure. The ticket charges for the park are < 150 per child and < 250 per adult. On a day, the cashier of the park found that 300 tickets were sold and an amount of < 55,000 was collected. 15-30/5/1 Page 19 P.T.O. Cn`w $ Ho$ AmYma na, {Z Z{b{IV Zm| Ho$ C ma Xr{OE : (i) (ii) `{X Cg {XZ AmE ~ m| H$s g `m x VWm d` H$m| H$s g `m p W{V H$mo ~rOJ{UVr` $n _| {b{IE & (a) (b) (iii) Bg _Zmoa OZ nmH $ _| Cg {XZ {H$VZo ~ o AmE ? AWdm Bg _Zmoa OZ nmH $ _| Cg {XZ {H$VZo d` H$ AmE y h , Vmo Xr JB 1 2 ? 2 _Zmoa OZ nmH $ _| `{X 250 ~ o VWm 100 d` H$ AmE, Vmo {H$VZr am{e EH$ hmoJr ? 1 H$aU A ``Z 2 37. EH$ ~JrMm EH$ dJ Ho$ AmH$ma H$m h & _mbr Zo ~JrMo H$s gr_m na EH$-X gao go 1 m H$s X ar na AemoH$ Ho$ no S> Ho$ nm Yo CJmE & dh ~JrMo H$mo Jwbm~ Ho$ nm Ym| go gOmZm MmhVm h & CgZo Jwbm~ Ho$ nm Yo CJmZo Ho$ {bE ~JrMo Ho$ A Xa EH$ { ^wOmH$ma jo MwZm & Cn`w $ p W{V _|, _mbr Zo H$jm 10 Ho$ N>m m| H$s _XX br {O hm|Zo {Z Z H$ma H$m MmQ> ~Zm`m & Cn`w $ Ho$ AmYma na, {Z Z{b{IV Zm| Ho$ C ma Xr{OE : (i) A H$mo _yb-q~X bo H$a, D PQR Ho $ erfm] Ho$ {ZX}em H$ `m h (ii) (iii) 15-30/5/1 (a) X [a`m PQ VWm QR kmV (b) AWdm q~X Am| P VWm R H$mo {_bmZo dmbo aoImI S> H$mo H$aZo dmbo q~X Ho$ {ZX}em H$ kmV H$s{OE & kmV H$s{OE {H$ `m D PQR EH$ ? 1 H$s{OE & g_{ ~mh { ^wO h & Page 20 2 2:1 Ho$ A V: {d^mOZ 2 1 Based on the above, answer the following questions : (i) If the number of children visited be x and the number of adults visited be y, then write the given situation algebraically. 1 (ii) (a) 2 How many children visited the amusement park that day ? OR (b) (iii) 37. How many adults visited the amusement park that day ? 2 How much amount will be collected if 250 children and 100 adults visit the amusement park ? 1 Case Study 2 A garden is in the shape of a square. The gardener grew saplings of Ashoka tree on the boundary of the garden at the distance of 1 m from each other. He wants to decorate the garden with rose plants. He chose a triangular region inside the garden to grow rose plants. In the above situation, the gardener took help from the students of class 10. They made a chart for it which looks like the given figure. Based on the above, answer the following questions : (i) (ii) If A is taken as origin, what are the coordinates of the vertices of D PQR ? 1 (a) 2 Find distances PQ and QR. OR (b) (iii) 15-30/5/1 Find the coordinates of the point which divides the line segment joining points P and R in the ratio 2 : 1 internally. Find out if D PQR is an isosceles triangle. Page 21 2 1 P.T.O. 38. H$aU A ``Z 3 Xm S>Zo `m gmB{H$b MbmZo O gr J{V{d{Y`m VZmd Am a AdgmX O go _mZ{gH$ {dH$ma Ho$ Omo{I_ H$mo H$_ H$aVr h & Xm S>Zo go ghZe{ $ ~ T>mZo _| _XX {_bVr h & ~ m| H$s h{ >`m Am a _m gno{e`m _O~yV hmoVr h Am a CZH$m dOZ ~ T>Zo H$s g ^mdZm H$_ hmoVr h & EH$ Hy$b Ho$ emar[aH$ {ejm {ejH$ Zo AnZo Hy$b n[aga _| EH$ B Q>a- Hy$b aqZJ {V`mo{JVm Am`mo{OV H$aZo H$m {ZU ` {b`m & N>m m| Ho$ g_yh mam 100 m H$s Xm S> _| {b`m J`m g_` ZmoQ> {H$`m J`m, Omo {Z Z H$ma h : g_` (goH$ S> _|) N>m m| H$s g `m 0 20 20 40 40 60 60 80 80 100 8 10 13 6 3 Cn`w $ Ho$ AmYma na, {Z Z{b{IV Zm| Ho$ C ma Xr{OE : (i) D$na {XE JE Am H$ S>m| H$m _m `H$ dJ `m h ? Xm S> nyar H$aZo _| N>m m| mam {b`m J`m _m ` g_` kmV H$s{OE & (ii) (a) AWdm D$na {XE JE Am H$ S>m| H$m ~h bH$ kmV H$s{OE & (b) (iii) 15-30/5/1 {H$VZo N>m m| Zo 60 goH$ S> go H$_ g_` {b`m Page 22 ? 1 2 2 1 Case Study 3 38. Activities like running or cycling reduce stress and the risk of mental disorders like depression. Running helps build endurance. Children develop stronger bones and muscles and are less prone to gain weight. The physical education teacher of a school has decided to conduct an inter school running tournament in his school premises. The time taken by a group of students to run 100 m, was noted as follows : Time (in seconds) Number of students 0 20 20 40 40 60 60 80 80 100 8 10 13 6 3 Based on the above, answer the following questions : (i) What is the median class of the above given data ? 1 (ii) (a) 2 Find the mean time taken by the students to finish the race. OR (b) (iii) 15-30/5/1 Find the mode of the above given data. 2 How many students took time less than 60 seconds ? 1 Page 23 P.T.O.

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