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

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H$moS> Z . Code No. amob Z . 430/4/1 narjmWu H$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 > 19 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 19 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 (~w{Z`mXr) MATHEMATICS (BASIC) {ZYm [aV g_` : 3 K Q>o A{YH$V_ A H$ : 80 Time allowed : 3 hours .430/4/1 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$s{OE : (i) Z-n Mma I S>m| _| {d^m{OV {H$`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| _|, 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$m h & Z g `m 1 go 10 _| ghr {dH$ n Mw{ZE & 1. 2. {X`m J`m h HCF (156, 78) = 78 (A) 156 (B) 78 (C) 156 78 (D) 156 2 h , Vmo Xmo g_ $n { ^wOm| H$s ^wOmAm| H$m AZwnmV (A) 4:9 (B) 2:3 (C) 81 : 16 (D) 16 : 81 .430/4/1 LCM (156, 78) 4:9 2 H$m _mZ h h & BZ { ^wOm| Ho$ jo \$bm| H$m AZwnmV h General Instructions : Read the following instructions very carefully and strictly follow them : (i) This question paper comprises four sections A, B, C and D. This question paper carries 40 questions. All questions are compulsory. (ii) Section A : Question Numbers 1 to 20 comprises of 20 questions of one mark each. (iii) Section B : Question Numbers 21 to 26 comprises of 6 questions of two marks each. (iv) Section C : Question Numbers 27 to 34 comprises of 8 questions of three marks each. (v) Section D : Question Numbers 35 to 40 comprises of 6 questions of four marks each. (vi) There is no overall choice in the question paper. However, an internal choice has been provided in 2 questions of one mark, 2 questions of two marks, 3 questions of three marks and 3 questions of four marks. You have to attempt only one of the choices in such questions. (vii) In addition to this, separate instructions are given with each section and question, wherever necessary. (viii) Use of calculators is not permitted. SECTION A Question numbers 1 to 20 carry 1 mark each. Choose the correct option in question numbers 1 to 10. 1. 2. Given that HCF (156, 78) = 78, LCM (156, 78) is (A) 156 (B) 78 (C) 156 78 (D) 156 2 Sides of two similar triangles are in the ratio 4 : 9. Areas of these triangles are in the ratio (A) 4:9 (B) 2:3 (C) 81 : 16 (D) 16 : 81 .430/4/1 3 P.T.O. 3. q~X Am| (A) (B) (C) (D) 4. ( 1, 3) VWm 61 BH$mB 37 BH$mB 5 BH$mB 17 BH$mB (5, 2) Ho$ ~rM H$s X ar h { KmV g_rH$aU 2x2 4x + 3 = 0 H$m {d{d $H$a (A) 8 (B) 10 (C) 8 (D) 2 2 (discriminant) AWdm { KmV g_rH$aU 2x2 4x + 3 = 0 Ho$ _yb h (A) dm V{dH$ VWm ~am~a (B) dm V{dH$ VWm {^ (C) dm V{dH$ Zht (D) dm V{dH$ 5. {XImB JB AmH ${V-1 Ho$ AZwgma, ~h nX p(x) AmH ${V-1 (A) 3 (B) 2 (C) 1 (D) 0 .430/4/1 4 Ho$ ey `H$m| H$s g `m h h 3. The distance between the points ( 1, 3) and (5, 2) is (A) 61 units (B) 37 units (C) 5 units (D) 4. 17 units The discriminant of the quadratic equation 2x2 4x + 3 = 0 is (A) 8 (B) 10 (C) 8 (D) 2 2 OR Roots of the quadratic equation 2x2 4x + 3 = 0 are 5. (A) real and equal (B) real and distinct (C) not real (D) real Number of zeroes of the polynomial p(x) shown in Figure-1, are Figure-1 (A) 3 (B) 2 (C) 1 (D) 0 .430/4/1 5 P.T.O. 6. EH$ nmgo H$mo EH$ ~ma \|$H$m OmVm h & EH$ {df_ g `m AmZo H$s m{`H$Vm h (A) (B) (C) (D) 7. k H$m _mZ {OgHo$ {bE g_rH$aU H$mo ` $ H$a|, h (A) (B) (C) (D) 8. 9. 10. 1 1 2 4 6 2 6 3x y + 8 = 0 6x + ky = 16 g nmVr aoImAm| 1 2 1 2 2 2 `{X sin A = cos A, (A) 30 (B) 60 (C) 0 (D) 45 g_m Va loT>r (A) 50 (B) 45 (C) 44 (D) 41 0 A 90 5, 8, 11, ..., 47 h , Vmo H$moU (A) 3 r2 (B) 2 r2 (C) 4 r2 (D) 2 3 r 3 A ~am~a h H$m A {V_ nX go ( W_ nX H$s Amoa) X gam nX h EH$ R>mog AY Jmobo H$m Hw$b n >r` jo \$b h .430/4/1 VWm 6 6. A dice is thrown once. The probability of getting an odd number is (A) 1 1 (B) 2 4 (C) 6 2 (D) 6 7. The value of k for which the equations 3x y + 8 = 0 and 6x + ky = 16 represent coincident lines, is 1 (A) 2 1 (B) 2 (C) 2 (D) 8. 9. 10. 2 If sin A = cos A, 0 A 90 , then the angle A is equal to (A) 30 (B) 60 (C) 0 (D) 45 The second term from the end of the A.P. 5, 8, 11, ..., 47 is (A) 50 (B) 45 (C) 44 (D) 41 Total surface area of a solid hemisphere is (A) 3 r2 (B) 2 r2 (C) 4 r2 (D) 2 3 r 3 .430/4/1 7 P.T.O. Z g `m 11 go 15 _| [a $ WmZ ^[aE & 11. g_rH$aU x2 + bx + c = 0 Ho$ _yb ~am~a h , `{X ___________ h & 12. q~X Am| 13. {H$gr ~m q~X go d m na ItMr JB ne -aoImAm| H$s b ~mB`m 14. 100 15. { KmV ~h nX ( 3, 3) VWm ( 3, 3) H$mo Omo S>Zo dmbo aoImI S> H$m _ `-q~X _________ __________ h & hmoVr h & ojUm| dmbo EH$ ~ Q>Z Ho$ go H$_ H$ma H$m VmoaU VWm go A{YH$ H$ma H$m VmoaU q~X (58, 50) na {V N>oX H$aVo h & Bg ~ Q>Z H$m _m `H$ __________ h & t2 16 Ho$ ey `H$m| H$m `moJ\$b _________ h & Z g `m 16 go 20 _| {Z Z{b{IV Ho$ C ma Xr{OE : 16. g_m Va loT>r 7, 4, 1, 2, ... 17. x-Aj 18. `{X cosec = H$m 26dm nX {b{IE & na Cg q~X Ho$ {ZX}em H$ kmV H$s{OE Omo q~X Am| (2, 3) VWm dmbo aoImI S>> H$mo 1 : 2 Ho$ AZwnmV _| {d^m{OV H$aVm h & 5 4 h , Vmo cot (5, 6) H$mo Omo S>Zo H$m _mZ kmV H$s{OE & AWdm sin 42 cos 48 H$m _mZ kmV H$s{OE & 19. ^y{_ Ho$ EH$ q~X C go, Omo _rZma Ho$ nmX-q~X go 60 _r. H$s X ar na h , _rZma AB Ho$ {eIa H$m C `Z H$moU 30 h , O go {H$ AmH ${V-2 _| {XIm`m J`m h & _rZma H$s D $MmB kmV H$s{OE & AmH ${V-2 .430/4/1 8 Fill in the blanks in question numbers 11 to 15. 11. The roots of the equation, x2 + bx + c = 0 are equal if __________ . 12. The mid-point of the line segment joining the points ( 3, 3) and ( 3, 3) is ____________ . 13. The lengths of the tangents drawn from an external point to a circle are ___________ . 14. For a given distribution with 100 observations, the less than ogive and more than ogive intersect at (58, 50). The median of the distribution is ___________ . 15. In the quadratic polynomial t2 16, sum of the zeroes is __________ . Answer the following question numbers 16 to 20. 16. Write the 26th term of the A.P. 7, 4, 1, 2, ... . 17. Find the coordinates of the point on x-axis which divides the line segment joining the points (2, 3) and (5, 6) in the ratio 1 : 2. 18. If cosec = 5 , find the value of cot . 4 OR Find the value of sin 42 cos 48 . 19. The angle of elevation of the top of the tower AB from a point C on the ground, which is 60 m away from the foot of the tower, is 30 , as shown in Figure-2. Find the height of the tower. Figure-2 .430/4/1 9 P.T.O. 20. AmH ${V-3 _|, Ho$ O dmbo d m na, q~X P go ItMr JB ne -aoIm PQ H$s b ~mB kmV H$s{OE, O~{H$ {X`m J`m h {H$ OP = 12 go_r VWm OQ = 5 go_r & AmH ${V-3 I S> I$ Z g `m 21 go 26 VH$ `oH$ Z 2 A H$m| H$m h & 21. 32 go_r D $Mr Am a AmYma { `m 14 go_r dmbr EH$ ~obZmH$ma ~m Q>r aoV> go nyar Vah ^ar h B h & aoV H$m Am`VZ kmV H$s{OE & ( = 22 `moJ H$s{OE) 7 22. AmH ${V-4 _|, ABC VWm XYZ Xem E JE h & `{X AB = 3.8 go_r, AC = 3 3 go_r, BC = 6 go_r, XY = 6 3 go_r, XZ = 7.6 go_r, YZ = 12 go_r VWm A = 65 , B = 70 hmo, Vmo Y H$m _mZ kmV H$s{OE & 3 3 go_r 6 3 go_r AmH ${V-4 23. 24. 25. AWdm `{X Xmo g_ $n { ^wOm| Ho$ jo \$b ~am~a hm|, Vmo Xem BE {H$ `o { ^wO gdm Jg_ hmoVo h & `{X sec 2A = cosec (A 30 ), 0 < 2A < 90 h , Vmo A H$m _mZ kmV H$s{OE & Xem BE {H$ `oH$ YZm _H$ g_ nyUm H$ 2q Ho$ $n H$m hmoVm h VWm `oH$ YZm _H$ {df_ nyUm H$ 2q + 1 Ho$ $n H$m hmoVm h , Ohm q H$moB nyUm H$ h & Xmo A H$m| dmbr {H$VZr g `mE 6 go {d^m ` h ? AWdm EH$ g_m Va loT>r _| `h {X`m J`m h {H$ gmd A Va 5 h VWm BgHo$ W_ Xg nXm| H$m `moJ\$b 75 h & g_m Va loT>r H$m W_ nX kmV H$s{OE & .430/4/1 10 20. In Figure-3, find the length of the tangent PQ drawn from the point P to a circle with centre at O, given that OP = 12 cm and OQ = 5 cm. Figure-3 SECTION B Question numbers 21 to 26 carry 2 marks each. 21. 22. A cylindrical bucket, 32 cm high and with radius of base 14 cm, is filled 22 completely with sand. Find the volume of the sand. (Use = ) 7 In Figure-4, ABC and XYZ are shown. If AB = 3.8 cm, AC = 3 3 cm, BC = 6 cm, XY = 6 3 cm, XZ = 7.6 cm, YZ = 12 cm and A = 65 , B = 70 , then find the value of Y. 3 3 cm 6 3 cm Figure-4 OR If the areas of two similar triangles are equal, show that they are congruent. 23. If sec 2A = cosec (A 30 ), 0 < 2A < 90 , then find the value of A. 24. Show that every positive even integer is of the form 2q and that every positive odd integer is of the form 2q + 1, where q is some integer. 25. How many two-digit numbers are divisible by 6 ? OR In an A.P. it is given that common difference is 5 and sum of its first ten terms is 75. Find the first term of the A.P. .430/4/1 11 P.T.O. 26. {Z Z{b{IV gmaUr EH$ df _| A nVmb _| ^Vu hmoZo dmbo amo{J`m| H$s Am`w Xem Vr h : 5 15 15 25 25 35 35 45 45 55 55 65 Am`w (dfm] _|) : 60 110 210 230 150 50 amo{J`m| H$s g `m : Bg ~ Q>Z H$m ~h bH$ kmV H$s{OE & I S> J$ Z g `m 27 go 34 VH$ `oH$ Z 3 A H$m| H$m h & 27. gr_m Ho$ nmg EH$ 10 _r. 10 _r. gmBO H$m {H$MZ JmS> Z h , Omo CgH$s agmoB Ho$ gmW gQ>m h Am h & dh Cg 10 10 Ho$ {J S> _| Hw$N> Eogr gp O`m VWm O S>r-~y{Q>`m CJmZm MmhVr h Omo CgH$s agmoB _| amoO `moJ hmoVr h & dh Cg_| {_ >r VWm ImX S>mbH$a Cg_| q~X A na har {_M H$m nm Ym, B na EH$ Y{ZE H$m nm Ym VWm C na EH$ Q>_mQ>a H$m nm Ym bJmVr h & CgH$s ghobr Hw$gw_ CgHo$ JmS> Z _| AmVr h VWm dhm CJmE JE nm Ym| H$s gamhZm H$aVr h & dh H$hVr h {H$ em`X `h nm Yo EH$ hr aoIm _| h & ZrMo {XE JE {M H$mo `mZ go n T>H$a {Z Z{b{IV Zm| Ho$ C ma Xr{OE : .430/4/1 12 26. The following table shows the ages of the patients admitted in a hospital during a year : Age (in years) : 5 15 15 25 Number of 60 110 patients : Find the mode of the distribution. 25 35 35 45 45 55 55 65 210 230 150 50 SECTION C Question numbers 27 to 34 carry 3 marks each. 27. Seema has a 10 m 10 m kitchen garden attached to her kitchen. She divides it into a 10 10 grid and wants to grow some vegetables and herbs used in the kitchen. She puts some soil and manure in that and sows a green chilly plant at A, a coriander plant at B and a tomato plant at C. Her friend Kusum visited the garden and praised the plants grown there. She pointed out that they seem to be in a straight line. See the below diagram carefully and answer the following questions : .430/4/1 13 P.T.O. 28. (i) 10 10 (ii) H$s{OE & X ar gy `m {H$gr A ` gy go Om M H$aHo$ kmV H$s{OE {H$ `m `h q~X maoIr h >& {J S> H$mo {ZX}em H$ Aj boVo h E, q~X Am| A, B VWm C Ho$ {ZX}em H$ kmV AmH ${V-5 _|, EH$ { ^wO ABC Ho$ A VJ V EH$ d m Bg Vah ItMm J`m h {H$ dh ^wOmAm| BC, CA VWm AB H$mo H $_e q~X Am| P, Q VWm R na ne H$aVm h & `{X AB = 10 go_r, AQ = 7 go_r, CQ = 5 go_r hmo, Vmo BC H$s b ~mB kmV H$s{OE & AmH ${V-5 AWdm AmH ${V-6 _|, Ho$ O dmbo EH$ d m na ~m q~X T go Xmo ne -aoImE JB h & {g H$s{OE {H$ PTQ = 2 OPQ & AmH ${V-6 29. {g H$s{OE {H$ 30. {g H$s{OE {H$ 2 EH$ An[a_o` g `m h & : (cosec cot )2 = .430/4/1 1 cos 1 cos 14 TP VWm TQ ItMr 28. (i) Write the coordinates of the points A, B and C taking the 10 10 grid as coordinate axes. (ii) By distance formula or some other formula, check whether the points are collinear. In Figure-5, a circle is inscribed in a ABC touching BC, CA and AB at P, Q and R respectively. If AB = 10 cm, AQ = 7 cm, CQ = 5 cm, find the length of BC. Figure-5 OR In Figure-6, two tangents TP and TQ are drawn to a circle with centre O from an external point T. Prove that PTQ = 2 OPQ. Figure-6 29. Prove that 30. Prove that : 2 is an irrational number. (cosec cot )2 = .430/4/1 1 cos 1 cos 15 P.T.O. 31. 5 n|{gbm| VWm 7 noZm| H$m Hw$b _y ` < 250 h O~{H$ 7 n|{gbm| VWm _y ` < 302 h & EH$ n|{gb VWm EH$ noZ H$m _y ` kmV H$s{OE & AWdm {Z Z{b{IV g_rH$aU `w _ H$mo dO -JwUZ {d{Y go hb H$s{OE : 5 noZm| H$m Hw$b x 3y 7 = 0 3x 5y 15 = 0 32. 52 33. ^wOm 14 go_r dmbo EH$ dJ ABCD Ho$ `oH$ H$moZo go 3.5 go_r { `m dmbo d m H$m EH$ MVwWm e H$mQ>m J`m h VWm ~rM _| 4 go_r { `m H$m EH$ d m ^r H$mQ>m J`m h O gm {H$ AmH ${V-7 _| {XIm`m J`m h & dJ Ho$ eof (N>m`m {H$V) ^mJ H$m jo \$b kmV H$s{OE & n mm| H$s A N>r H$ma go \|$Q>r JB Vme H$s EH$ J >r _| go EH$ n mm `m N>`m {ZH$mbm OmVm h & {Z Z{b{IV H$mo m H$aZo H$s m{`H$Vm kmV H$s{OE : (i) bmb a J H$m ~mXemh (ii) B Q> H$s ~oJ_ (iii) EH$ B $m AWdm EH$ ~m g _| 90 {S> H$ (discs) h {OZ na 1 go 90 VH$ H$s g `mE A {H$V h & `{X Bg ~m g go EH$ {S> H$ `m N>`m {ZH$mbr OmVr h , Vmo BgH$s m{`H$Vm kmV H$s{OE {H$ Bg {S> H$ na A {H$V hmoJr (i) Xmo A H$m| H$s EH$ g `m & (ii) EH$ nyU dJ g `m & (iii) 15 go N>moQ>r EH$ A^m ` g `m & AmH ${V-7 34. 3 go_r { `m H$m EH$ d m It{ME & d m Ho$ Ho$ O go P go Bg d m na Xmo ne -aoImAm| H$s aMZm H$s{OE & .430/4/1 16 7 go_r H$s X ar na p WV EH$ q~X 31. 5 pencils and 7 pens together cost < 250 whereas 7 pencils and 5 pens together cost < 302. Find the cost of one pencil and that of a pen. OR Solve the following pair of equations using cross-multiplication method : x 3y 7 = 0 3x 5y 15 = 0 32. One card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting (i) a king of red colour. (ii) the queen of diamonds. (iii) an ace. OR A box contains 90 discs which are numbered from 1 to 90. If one disc is drawn at random from the box, find the probability that it bears 33. (i) a two-digit number. (ii) a perfect square number. (iii) a prime number less than 15. In Figure-7, ABCD is a square of side 14 cm. From each corner of the square, a quadrant of a circle of radius 3.5 cm is cut and also a circle of radius 4 cm is cut as shown in the figure. Find the area of the remaining (shaded) portion of the square. Figure-7 34. Draw a circle of radius 3 cm. Take a point P outside the circle at a distance of 7 cm from the centre O of the circle and draw two tangents to the circle. .430/4/1 17 P.T.O. I S> K$ Z g `m 35 go 40 VH$ `oH$ Z 4 A H$m| H$m h & 35. {g H$s{OE {H$ {H$gr g_H$moU { ^wO _| H$U H$m dJ , A ` Xmo ^wOmAm| Ho$ dJm] Ho$ `moJ\$b Ho$ ~am~a hmoVm h & 36. ~h nX x3 + 3x2 3x + 5 H$mo ~h nX x2 + x 1 go {d^m{OV H$s{OE VWm {d^mOZ Eo Jmo[a _ H$s g `Vm H$s Om M H$s{OE & AWdm ~h nX p(x) = 2x4 3x3 3x2 + 6x 2 Ho$ A ` ey `H$m| H$mo kmV H$s{OE `{X BgHo$ Xmo ey `H$ 2 VWm 2 kmV h & 37. ^y{_ Ho$ EH$ q~X go EH$ 20 _r. D $Mo ^dZ Ho$ {eIa na bJr EH$ g Mma _rZma Ho$ Vb Am a {eIa Ho$ C `Z H$moU H $_e 45 Am a 60 h & _rZma H$s D $MmB kmV H$s{OE & ( 3 = 1.73 `moJ H$s{OE) 38. EH$ ~m Q>r e Hw$ Ho {N> H$ Ho$ AmH$ma H$s h & Bg ~m Q>r Ho$ {ZMbo VWm D$nar d mmH$ma {gam| H$s { `mE H $_e 10 go_r VWm 20 go_r h VWm BgH$s D $MmB 30 go_r h & Bg ~m Q>r H$s Ym[aVm kmV H$s{OE & ( = 3.14 `moJ H$s{OE) AWdm 6 _r. Mm S>r Am a 1.5 _r. Jhar EH$ Zha _| nmZr 10 {H$_r/K Q>m H$s Mmb go ~h ahm h & 30 {_ZQ> _|, `h Zha {H$VZo jo \$b H$s qgMmB H$a nmEJr `{X qgMmB Ho$ {bE 4 go_r Jhao nmZr H$s Amd `H$Vm hmoVr hmo ? 39. {Z Z{b{IV ~ Q>Z Ho$ {bE go A{YH$ H$ma H$m VmoaU It{ME ^ma ({H$J m _|) : 40 44 44 48 48 52 52 56 N>m m| H$s g `m 40. : 4 10 30 24 : 56 60 60 64 64 68 18 12 2 EH$ aobJm S>r EH$g_mZ Mmb go 360 {H$_r H$s X ar V` H$aVr h & `{X `h Mmb 5 {H$_r/K Q>m A{YH$ hmoVr, Vmo dh Cgr `m m _| 1 K Q>m H$_ g_` boVr & aobJm S>r H$s _yb Mmb kmV H$s{OE & AWdm Xmo dJm] Ho$ jo \$bm| H$m `moJ\$b 468 dJ _r. h & `{X CZHo$ n[a_mnm| H$m A Va 24 _r. hmo, Vmo XmoZm| dJm] H$s ^wOmE kmV H$s{OE & .430/4/1 18 SECTION D Question numbers 35 to 40 carry 4 marks each. 35. In a right-angled triangle, prove that the square of the hypotenuse is equal to the sum of the squares of the remaining two sides. 36. Divide polynomial x3 + 3x2 3x + 5 by the polynomial x2 + x 1 and verify the division algorithm. OR Find other zeroes of the polynomial p(x) = 2x4 3x3 3x2 + 6x 2 if two of its zeroes are 2 and 2. 37. From a point on the ground, the angles of elevation of the bottom and the top of a transmission tower, fixed at the top of a 20 m high building, are 45 and 60 respectively. Find the height of the tower. (Use 3 = 1.73) 38. A bucket is in the form of a frustum of a cone of height 30 cm with the radii of its lower and upper circular ends as 10 cm and 20 cm respectively. Find the capacity of the bucket. (Use = 3.14) OR Water in a canal 6 m wide and 1.5 m deep, is flowing with a speed of 10 km/hr. How much area will it irrigate in 30 minutes if 4 cm of standing water is needed ? 39. Draw a more than ogive for the following distribution : Weight (in kg) : Number of Students : 40. 40 44 44 48 48 52 52 56 56 60 60 64 64 68 4 10 30 24 18 12 2 A train travels 360 km at a uniform speed. If the speed had been 5 km/hr more, it would have taken 1 hour less for the same journey. Find the original speed of the train. OR Sum of the areas of two squares is 468 m2. If the difference of their parameters is 24 m, find the sides of the two squares. .430/4/1 19 P.T.O.

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