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CBSE Class 10 Board Exam 2020 : Mathematics Standard (Series 4)

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Kendriya Vidyalaya (KV), Kamla Nehru Nagar, Ghaziabad

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H$moS> Z . Code No. amob Z . 30/4/1 narjmWu H$moS >H$mo C ma-nwp VH$m Ho$ _wI-n >na Ad ` {bIo & Roll No. Candidates must write the Code on the title page of the answer-book. (I) ZmoQ> H $n`m Om M H$a b| {H$ Bg Z-n _o _w{ V n > 23 h & (II) Z-n _| Xm{hZo hmW H$s Amoa {XE JE H$moS >Z ~a H$mo N>m C ma-nwp VH$m Ho$ _wI-n > na {bI| & (III) H $n`m Om M H$a b| {H$ Bg Z-n _| >40 Z h & 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| & 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 & (IV) (V) NOTE (I) Please check that this question paper contains 23 printed pages. (II) Code number given on the right hand side of the question paper should be written on the title page of the answer-book by the candidate. (III) Please check that this question paper contains 40 questions. (IV) Please write down the Serial Number of the question in the answer-book before attempting it. (V) 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$) g mp VH$ MATHEMATICS (STANDARD) Theory {ZYm [aV g_` : 3 K Q>o A{YH$V_ A H$ : 80 Time allowed : 3 hours .30/4/1 Maximum Marks : 80 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$s{OE : (i) `h Z-n Mma I S>m| _| {d^m{OV {H$`m J`m h H$, I, J Ed K & Bg Z-n _| 40 Z h & g^r Z A{Zdm` h & (ii) I S> H$ _| Z g `m 1 go 20 VH$ 20 Z h Ed `oH$ Z EH$ A H$ H$m h & (iii) I S> I _| Z g `m 21 go 26 VH$ 6 Z h Ed `oH$ Z Xmo A H$m| H$m h & (iv) I S> J _| Z g `m 27 go 34 VH$ 8 Z h Ed `oH$ Z VrZ A H$m| H$m h & (v) I S> K _| Z g `m 35 go 40 VH$ 6 Z h Ed `oH$ Z Mma A H$m| H$m h & (vi) Z-n _| g_J na H$moB {dH$ n Zht h & VWm{n EH$ -EH$ A H$ dmbo Xmo Zm| _|, Xmo-Xmo A H$m| dmbo Xmo Zm| _|, VrZ-VrZ A H$m| dmbo VrZ Zm| _| VWm Mma-Mma A H$m| dmbo VrZ Zm| _| Am V[aH$ {dH$ n {XE JE h & Eogo Zm| _| Ho$db EH$ hr {dH$ n H$m C ma {b{IE & (vii) BgHo$ A{V[a $, Amd `H$VmZwgma, `oH$ I S> Am a Z Ho$ gmW `Wmo{MV {ZX}e {XE JE h & (viii) H $bHw$boQ>a Ho$ `moJ H$s AZw_{V Zht h & I S> H$ Z g `m 1 go 20 VH$ `oH$ Z 1 A H$ H$m h & Z g `m 1 go 10 VH$ ~h {dH$ nr` Z h & ghr {dH$ n Mw{ZE & 1. {H$gr ~h nX H$s g m h (A) 3 (B) 4 (C) 0 (D) 5 p(x) Ho$ {bE y = p(x) H$m J m $ AmH ${V-1 | {X`m J m h & AmH ${V-1 .30/4/1 2 p(x) Ho$ ey H$m| General Instructions : Read the following instructions very carefully and strictly follow them : (i) This question paper comprises four sections A, B, C and D. This question paper carries 40 questions. All questions are compulsory. (ii) Section A : Question Numbers 1 to 20 comprises of 20 questions of one mark each. (iii) Section B : Question Numbers 21 to 26 comprises of 6 questions of two marks each. (iv) Section C : Question Numbers 27 to 34 comprises of 8 questions of three marks each. (v) Section D : Question Numbers 35 to 40 comprises of 6 questions of four marks each. (vi) There is no overall choice in the question paper. However, an internal choice has been provided in 2 questions of one mark, 2 questions of two marks, 3 questions of three marks and 3 questions of four marks. You have to attempt only one of the choices in such questions. (vii) In addition to this, separate instructions are given with each section and question, wherever necessary. (viii) Use of calculators is not permitted. SECTION A Question numbers 1 to 20 carry 1 mark each. Question numbers 1 to 10 are multiple choice questions. Choose the correct option. 1. The number of zeroes for a polynomial p(x) where graph of y = p(x) is given in Figure-1, is (A) 3 (B) 4 (C) 0 (D) 5 Figure-1 .30/4/1 3 P.T.O. 2. EH$ g m Va loT>r H$m W nX 400 hmo, Vmo nXm| H$s g m h (A) (B) (C) (D) 5 h VWm A {V nX 45 h & {X g^r nXm| H$m moJ\$b 20 8 10 16 AWdm EH$ g m Va loT>r 3. 4. (A) 32 (B) (C) (D) 0 17 13 15, 11, 7, ..., 49 H$m 9dm nX h {X m J m h {H$ q~X A(1, 2), B(0, 0) VWm C(a, b) maoIr h & {Z Z{b{IV g ~ Ym| | go a VWm b Ho$ ~rM H$m H$m Z-gm g ~ Y ghr h ? (A) (B) (C) a = 2b 2a = b a+b=0 (D) a b=0 AmH ${V-2 |, {X TP, TQ Ho$ O dmbo {H$gr d m na ItMr JB Xmo ne -aoImE Bg H$ma h {H$ POQ = 115 h , Vmo PTQ ~am~a h (A) 115 (B) 57 5 (C) 55 (D) 65 AmH ${V-2 AWdm .30/4/1 4 2. The first term of an A.P. is 5 and the last term is 45. If the sum of all the terms is 400, the number of terms is (A) 20 (B) 8 (C) 10 (D) 16 OR The 9th term of the A.P. 15, 11, 7, ...., 49 is 3. 4. (A) 32 (B) 0 (C) 17 (D) 13 It is being given that the points A(1, 2), B(0, 0) and C(a, b) are collinear. Which of the following relations between a and b is true ? (A) a = 2b (B) 2a = b (C) a+b=0 (D) a b=0 In Figure-2, TP and TQ are tangents drawn to the circle with centre at O. If POQ = 115 then PTQ is (A) 115 (B) 57 5 (C) 55 (D) 65 Figure-2 OR .30/4/1 5 P.T.O. EH$ d m na {H$gr ~m q~X Q go ItMr JB ne -aoIm H$s b ~mB H$s d m Ho$ Ho$ go X ar 8 go r h & d m H$s { m h 5. 6. 7. (A) 39 go r (B) 3 go r (C) 39 (D) 7 go r 5 go r h VWm q~X Q go r `{X cos (10 + ) = sin 30 h , Vmo H$m mZ h (A) 50 (B) 40 (C) 80 (D) 20 EH$ W bo | 3 bmb, 5 H$mbr VWm 7 g o$X J|X| h & Bg W bo | go EH$ J|X H$mo m N> m {ZH$mbm OmVm h & {ZH$mbr JB J|X H$mbr Zht h , BgH$s m{ H$Vm h (A) 1 3 (B) 9 15 (C) 5 10 (D) 2 3 a {IH$ g rH$aUm| y = 0 VWm y = 6 Ho$ (A) A{ Vr hb h (B) H$moB hb Zht h (C) AZoH$ hb h (D) {g $ EH$ hb .30/4/1 w H$m EH$ (0, 0) h 6 From an external point Q, the length of the tangent to a circle is 5 cm and the distance of Q from the centre is 8 cm. The radius of the circle is (A) 39 cm (B) 3 cm (C) (D) 5. 6. 7. 39 cm 7 cm The value of for which cos (10 + ) = sin 30 , is (A) 50 (B) 40 (C) 80 (D) 20 A bag contains 3 red, 5 black and 7 white balls. A ball is drawn from the bag at random. The probability that the ball drawn is not black, is (A) 1 3 (B) 9 15 (C) 5 10 (D) 2 3 The pair of linear equations y = 0 and y = 6 has (A) a unique solution (B) no solution (C) infinitely many solutions (D) only solution (0, 0) .30/4/1 7 P.T.O. 8. 9. 10. EH$ ~ Q>Z H$m m VWm m H$ H $ e (A) 16 (B) 17 (C) 18 (D) 13 14 VWm 15 h & AV ~h bH$ H$m mZ hmoJm { KmV g rH$aU x2 4x + k = 0 Ho$ Xmo {^ dm V{dH$ yb hm|Jo {X (A) k=4 (B) k>4 (C) k = 16 (D) k<4 q~X A( 5, 2) a H$m VWm q~X B(4, 6) H$mo Omo S>Zo dmbo aoImI S> H$m -q~X a P , 4 8 h & mZ h (A) 4 (B) 4 (C) 8 (D) 2 Z g `m 11 go 15 _| [a $ WmZ ^[aE & 11. 2 5 3 EH$ _________ g m h & 12. _mZ br{OE {H$ ABC DEF VWm BZ { ^wOm| Ho$ jo $b H $ e 81 go r2 VWm 144 go r2 h & {X EF = 24 go_r h , Vmo ^wOm BC H$s b ~mB _________ go_r hmoJr & 13. q~X Am| 14. {X tan A = 1 h , Vmo 15. { m 8 go r dmbr YmVw H$s EH$ JmobmH$ma J|X H$mo {nKbmH$a 8 g mZ AmH$ma H$s N>moQ>r J|X| ~ZmB JB h & `oH$ ZB J|X H$s { m ___________ go r h & .30/4/1 (a, b) VWm ( a, b) Ho$ ~rM H$s X ar _________ h & 2 sin A cos A = _________ . 8 8. 9. 10. The mean and median of a distribution are 14 and 15 respectively. The value of mode is (A) 16 (B) 17 (C) 18 (D) 13 The quadratic equation x2 4x + k = 0 has distinct real roots if (A) k=4 (B) k>4 (C) k = 16 (D) k<4 a Point P , 4 is the mid-point of the line segment joining the points 8 A( 5, 2) and B(4, 6). The value of a is (A) 4 (B) 4 (C) 8 (D) 2 Fill in the blanks in question numbers 11 to 15. 11. 2 5 3 is _________ number. 12. Let ABC DEF and their areas be respectively 81 cm 2 and 144 cm2. If EF = 24 cm, then length of side BC is _________ cm. 13. The distance between the points (a, b) and ( a, b) is _________ . 14. If tan A =1, then 2 sin A cos A = _________ . 15. A spherical metal ball of radius 8 cm is melted to make 8 smaller identical balls. The radius of each new ball is _________ cm. .30/4/1 9 P.T.O. Z g `m 16 go 20 _| {Z Z{b{IV Ho$ C ma Xr{OE >& 16. {X m J m h {H$ _.g. H$s{OE & (HCF) (135, 225) = 45, 17. AmH ${V-3 |, A N>r Vah go VZr h B EH$ 20 r. b ~r a gr, ^y{ na grYo bJo I ^o Ho$ {eIa go ~ Yr h & {X ^y{ Va Ho$ gmW a gr mam ~Zm m J m H$moU 30 H$m hmo, Vmo I ^o H$s D $MmB kmV H$s{OE & Vmo b.g. (LCM) (135, 225) kmV AmH ${V-3 18. Xmo nmgm| H$mo EH$ gmW |$H$m OmVm h & BgH$s m m{ H$Vm h {H$ XmoZm| nmgm| na AmZo dmbr g mAm| H$m moJ\$b 13 hmo ? 19. {H$VZo Xe bd WmZm| Ho$ ~mX n[a o g m 20. AmH ${V-4 |, AB VWm CD CZ Xmo d mm| H$s C^ {Z R> ne -aoImE h Omo EH$-X gao H$mo q~X D na ne H$aVo h & {X AB = 8 go_r hmo, Vmo CD H$s b ~mB kmV H$s{OE & 229 2 57 AmH ${V-4 .30/4/1 10 2 H$m Xe bd {Z $nU gm V hmoJm ? Answer the following question numbers 16 to 20. 16. Given that HCF (135, 225) = 45, find the LCM (135, 225). 17. In Figure-3, a tightly stretched rope of length 20 m is tied from the top of a vertical pole to the ground. Find the height of the pole if the angle made by the rope with the ground is 30 . Figure-3 18. Two dice are thrown simultaneously. What is the probability that the sum of the two numbers appearing on the top is 13 ? 19. After how many decimal places will the decimal representation of the 229 rational number terminate ? 2 2 57 20. In Figure-4, AB and CD are common tangents to circles which touch each other at D. If AB = 8 cm, then find the length of CD. Figure-4 .30/4/1 11 P.T.O. I S> I$ Z g `m 21 go 26 VH$ `oH$ Z 2 A H$m| H$m h & 21. x Ho$ {bE hb H$s{OE : 6x2 + 11x + 3 = 0 22. Xmo g $n { ^wOm| Ho$ n[a mn H $ e 30 go_r VWm 20 go_r h & {X EH$ { ^wO H$s EH$ ^wOm 9 go_r b ~r h , Vmo X gao { ^wO H$s g JV ^wOm H$s b ~mB kmV H$s{OE & AWdm AmH ${V-5 _|, PQR EH$ g H$moU { ^wO h {OgH$m H$moU P g H$moU h & QR na q~X M Bg H$ma p WV h {H$ PM QR h & Xem BE {H$ PQ2 = QM QR. AmH ${V-5 23. mZ kmV H$s{OE : 2 2 sin 47 cos 30 (sin 60 ) 2 cos 43 cot 30 24. : {Z Z{b{IV ~ Q>Z H$m ~h bH$ kmV H$s{OE dJ : ~ma ~maVm : 0 20 20 40 40 60 60 80 80 100 10 8 12 16 4 AWdm {Z Z{b{IV ~ Q>Z go m H$ kmV H$s{OE dJ : ~ma ~maVm : .30/4/1 : 500 600 600 700 700 800 800 900 900 1000 36 32 32 20 30 12 SECTION B Question numbers 21 to 26 carry 2 marks each. 21. Solve for x : 6x2 + 11x + 3 = 0 22. The perimeters of two similar triangles are 30 cm and 20 cm respectively. If one side of the first triangle is 9 cm long, find the length of the corresponding side of the second triangle. OR In Figure-5, PQR is right-angled at P. M is a point on QR such that PM is perpendicular to QR. Show that PQ2 = QM QR. Figure-5 23. Evaluate : 2 2 sin 47 cos 30 (sin 60 ) 2 cos 43 cot 30 24. Find the mode of the following distribution : Classes : Frequency : 0 20 20 40 40 60 60 80 80 100 10 8 12 16 4 OR From the following distribution, find the median : Classes : Frequency : .30/4/1 500 600 600 700 700 800 800 900 900 1000 36 32 32 20 30 13 P.T.O. 25. AmH ${V-6 _|, H$moB V ~y EH$ ~obZ Ho$ AmH$ma H$m h {Og na EH$ e Hw$ A mamo{nV h & ~obZmH$ma ^mJ H$s D $MmB 2 1 r. VWm e dmH$ma ^mJ H$s {V H$ D $MmB 2 8 r. h & XmoZm| ^mJm| H$s EH$g mZ { m 2 r. h & Bg V ~y H$mo ~ZmZo | w V H $Zdg (canvas) H$m jo $b kmV H$s{OE & ( = 22 `moJ H$s{OE) 7 AmH ${V-6 26. no S> bJmZo H$m A{^ mZ EH$ J wn hmD$qgJ gmogmBQ>r Ho$ 600 gX h {OZHo$ Ka H $ng | h VWm C hm|Zo Zd df Ho$ Adga na no S> bJmZo H$m A{^`mZ {Z M {H$ m & oH$ Ka H$mo B N>mZwgma EH$ nm Ym bJmZo H$mo {X m J`m & {d{^ H$ma Ho$ nm Yo, Omo bJmE JE Wo, dh h (i) Zr 125 (ii) nrnb 165 (iii) H $sna 50 (iv) $bm| Ho$ nm Yo 150 (v) y$bm| Ho$ nm Yo 110 CX KmQ>Z-g_mamoh na, BZm XoZo Ho$ {bE, `m N>`m EH$ nm Ym MwZm J m & Cn`w V AZw N>oX H$mo n T>H$a {Z Z{b{IV Zm| Ho$ C ma Xr{OE : MwZo JE nm Yo H$m {Z Z{b{IV hmoZo H$s m{ H$Vm m h (i) $bm| H$m EH$ nm Ym AWdm y$bm| H$m EH$ nm Ym (ii) Zr H$m nm Ym AWdm nrnb H$m nm Ym .30/4/1 14 ? 25. In Figure-6, a tent is in the shape of a cylinder surmounted by a conical top. The cylindrical part is 2 1 m high and conical part has slant height 2 8 m. Both the parts have same radius 2 m. Find the area of the canvas 22 used to make the tent. (Use = ) 7 Figure-6 26. Tree Plantation Drive A Group Housing Society has 600 members, who have their houses in the campus and decided to hold a Tree Plantation Drive on the occasion of New Year. Each household was given the choice of planting a sampling of its choice. The number of different types of saplings planted were : (i) Neem 125 (ii) Peepal 165 (iii) Creepers 50 (iv) Fruit plants 150 (v) Flowering plants 110 On the opening ceremony, one of the plants is selected randomly for a prize. After reading the above passage, answer the following questions. What is the probability that the selected plant is (i) A fruit plant or a flowering plant ? (ii) Either a Neem plant or a Peepal plant ? .30/4/1 15 P.T.O. I S> J$ Z g `m 27 go 34 VH$ `oH$ Z 3 A H$m| H$m h & 27. {g H$s{OE {H$ 28. EH$ g m Va loT>r Ho$ W 30 nXm| H$m moJ\$b g m Va loT>r H$m 11dm nX kmV H$s{OE & 29. q~X Am| (3, 1) VWm (6, 8) H$mo Omo S>Zo dmbo aoImI S> H$mo g -{ ^m{OV H$aZo dmbo q~X Am| Ho$ {ZX}em H$ kmV H$s{OE & AWdm 5 EH$ An[a o g m h & h & {X Mm Wm nX H$m jo $b kmV H$s{OE {OgHo$ erf -q~X C(4, 0) VWm D(4, 4) na p WV h & MVw^w O 30. ABCD 1920 h , Vmo Bg A(1, 2), B(1, 0), AmH ${V-7 |, XY VWm MN, O Ho$ dmbo {H$gr d m na Xmo g m Va ne -aoImE h Am a ne {~ X C na EH$ X gar ne -aoIm AB, XY H$mo A VWm MN H$mo B na {V N>oX H$aVr h & {g H$s{OE {H$ AOB = 90 h & AmH ${V-7 31. 18 {Z Z{b{IV g rH$aU w H$mo hb H$s{OE : 2 3 5 4 11, 7 x y x y AV 5x 3y H$m mZ kmV H$s{OE & AWdm .30/4/1 16 SECTION C Question numbers 27 to 34 carry 3 marks each. 27. Prove that 5 is an irrational number. 28. The sum of the first 30 terms of an A.P. is 1920. If the fourth term is 18, find its 11th term. 29. Find the co-ordinates of the points of trisection of the line segment joining the points (3, 1) and (6, 8). OR Find the area of a quadrilateral ABCD having vertices at A(1, 2), B(1, 0), C(4, 0) and D(4, 4). 30. In Figure-7, XY and MN are two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersecting XY at A and MN at B. Prove that AOB = 90 . Figure-7 31. Solve the pair of equations : 2 3 5 4 11, 7 x y x y Hence, find the value of 5x 3y. OR .30/4/1 17 P.T.O. EH$ ZJa | Q> gr Ho$ ^m S>o | EH$ {Z V ^m S>o Ho$ A{V[a V Mbr JB X ar na {Z^ a ^m S>m gp _{bV {H$ m OmVm h & 10 {H$ r X ar Ho$ {bE ^m S>m < 75 h VWm 15 {H$_r X ar Ho$ {bE < 110 h & {Z V ^m S>m VWm {V {H$_r H$m ^m S>m m h ? AV 35 {H$ r H$s X ar H$m ^m S>m kmV H$s{OE & 32. {g H$s{OE {H$ : sin cos 1 1 cos sin 1 sec tan 33. AmH ${V-8 |, N>m m {H$V ^mJ H$m jo $b kmV H$s{OE, Ohm ^wOm 14 go r dmbo EH$ g ~mh { ^wO OAB Ho$ erf O H$mo Ho$ mZH$a 7 go r { m dmbm EH$ d mr Mmn ItMm J m h & ( = 22 VWm 3 = 1 73 `moJ H$s{OE) 7 AmH ${V-8 34. 5 go r, 6 go r VWm 7 go r ^wOmAm| dmbo EH$ { ^wO H$s aMZm H$s{OE & { $a EH$ A { ^wO H$s aMZm H$s{OE {OgH$s ^wOmE nhbo dmbo { ^wO H$s g JV ^wOmAm| H$s 2 3 JwZr hm| & AWdm 3 go r { m Ho$ EH$ d m na Eogr Xmo ne -aoImE It{ME Omo na na hm| & .30/4/1 18 60 Ho$ H$moU na PwH$s Taxi charges in a city consist of fixed charges and the remaining charges depend upon the distance travelled. For a journey of 10 km, the charge paid is < 75 and for a journey of 15 km, the charge paid is < 110. Find the fixed charge and charges per km. Hence, find the charge of covering a distance of 35 km. 32. Prove that : sin cos 1 1 cos sin 1 sec tan 33. In Figure-8, find the area of the shaded region where a circular arc of radius 7 cm has been drawn with vertex O of an equilateral triangle OAB 22 of side 14 cm as centre. (Use = and 3 = 1 73) 7 Figure-8 34. Construct a triangle with sides 5 cm, 6 cm and 7 cm. Now construct 2 another triangle whose sides are times the corresponding sides of the 3 first triangle. OR Draw a pair of tangents to a circle of radius 3 cm which are inclined to each other at an angle of 60 . .30/4/1 19 P.T.O. I S> K$ Z g `m 35 go 40 VH$ `oH$ Z 4 A H$m| H$m h & 35. 600 {H$ r H$s hdmB m m |, Iam~ m g H$s dOh go EH$ hdmB Ohm O H$s Mmb H$ H$a Xr JB & `m m H$s Am gV Mmb H$mo 200 {H$ r/K Q>m H$s Xa go KQ>mZo Ho$ H$maU C S>mZ H$m g 30 { ZQ> ~ T> J m & Ama ^ | hdmB Ohm O H$s Am gV Mmb kmV H$s{OE & AWdm Hw$N> { V m| | < 9,000 g mZ $n go ~m Q>o JE & `{X 20 { V Am a hmoVo, Vmo oH$ H$mo < 160 H$ { bVo & Ama ^ | Hw$b {H$VZo { V Wo ? 36. 37. {Z Z{b{IV ~ Q>Z Ho$ {bE go A{YH$ g M`r ~ma ~maVm dH $ It{ME & J m\$ H$s ghm Vm go ~ Q>Z H$m m H$ ^r kmV H$s{OE & ^ma ({H$J m |) : 40 44 N>m m| H$s g m : 7 44 48 48 52 52 56 56 60 60 64 64 68 12 33 47 20 11 5 {X {H$gr { ^wO H$s EH$ ^wOm Ho$ g m Va A Xmo ^wOmAm| H$mo {^ -{^ q~X Am| na {V N>oX H$aZo Ho$ {bE EH$ aoIm ItMr OmE, Vmo {g H$s{OE {H$ o A Xmo ^wOmE EH$ hr AZwnmV | {d^m{OV hmo OmVr h & AWdm EH$ g H$moU { ^wO |, {g H$s{OE {H$ H$U H$m dJ eof Xmo ^wOmAm| Ho$ dJm] Ho$ moJ\$b Ho$ ~am~a hmoVm h & 38. EH$ grYm amO mJ EH$ rZma Ho$ nmX VH$ OmVm h & rZma Ho$ {eIa na I S>m EH$ { V EH$ H$ma H$mo 30 Ho$ AdZ Z H$moU na XoIVm h , Omo {H$ rZma Ho$ nmX H$s Amoa EH$g mZ Mmb go Am ahr h & 50 r. H$s X ar V hmoZo Ho$ ~mX, H$ma H$m AdZ Z H$moU 60 hmo OmVm h & rZma H$s D $MmB kmV H$s{OE & ( 3 = 1 73 moJ H$s{OE) .30/4/1 20 SECTION D Question numbers 35 to 40 carry 4 marks each. 35. In a flight of 600 km, the speed of the aircraft was slowed down due to bad weather. The average speed of the trip was decreased by 200 km/hr and thus the time of flight increased by 30 minutes. Find the average speed of the aircraft originally. OR < 9,000 were divided equally among a certain number of persons. Had there been 20 more persons, each would have got < 160 less. Find the original number of persons. 36. Draw a more than cumulative frequency curve for the following distribution. Also, find the median from the graph. Weight (in kg) : Number of Students : 37. 40 44 44 48 48 52 52 56 56 60 60 64 64 68 7 12 33 47 20 11 5 If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then prove that the other two sides are divided in the same ratio. OR In a right-angled triangle, prove that the square of the hypotenuse is equal to the sum of the squares of the other two sides. 38. A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car at an angle of depression of 30 , which is approaching the foot of the tower with a uniform speed. After covering a distance of 50 m, the angle of depression of the car becomes 60 . Find the height of the tower. (Use .30/4/1 3 = 1 73). 21 P.T.O. 39. EH$ D$na go Iwbr ~m Q>r Ho$ XmoZm| D$nar VWm {ZMbo d mmH$ma {gam| H$s { mE H $_e 40 go r Am a 20 go r h VWm ~m Q>r H$s JhamB 21 go r h & ~m Q>r H$m Am VZ kmV H$s{OE & gmW hr ~m Q>r H$mo ~ZmZo | w V YmVw ({Q>Z) H$s MmXa H$m jo $b ^r kmV H$s{OE & ( = 22 `moJ H$s{OE) 7 40. ~h nX f(x) = 2x4 + 3x3 5x2 9x 3 Ho$ Xmo ey H$ Ho$ eof ey H$ kmV H$s{OE & 3 VWm 3 h & Bg ~h nX AWdm ey H$m| H$s dm V{dH$ JUZm {H$E {~Zm EH$ { KmV ~h nX ~ZmBE {OgHo$ ey H$ ~h nX 5x2 + 2x 3 Ho$ ey H$m| Ho$ w H $ hm| & .30/4/1 22 39. A bucket open at the top has top and bottom radii of circular ends as 40 cm and 20 cm respectively. Find the volume of the bucket if its depth is 21 cm. Also find the area of the tin sheet required for making the 22 bucket. (Use = ) 7 40. Obtain other zeroes of the polynomial f(x) = 2x4 + 3x3 5x2 9x 3 if two of its zeroes are 3 and 3. OR Without actually calculating the zeroes, form a quadratic polynomial whose zeroes are reciprocals of the zeroes of the polynomial 5x2 + 2x 3. .30/4/1 23 P.T.O.

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