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CBSE Class 10 Board Exam 2020 : Mathematics Basic (Series 5)

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CBSE 10
Kendriya Vidyalaya (KV), Kamla Nehru Nagar, Ghaziabad
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H$moS> Z . Code No. amob Z . 430/5/1 narjmWu H$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 .430/5/1 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. `{X a {IH$ g_rH$aUm| H$m EH$ `w _ g JV h , Vmo {Z ${nV aoImE (A) g_m Va h (B) {V N>oXr `m g nmVr h (C) h_oem g nmVr hmoVr h (D) h_oem {V N>oXr hmoVr h 2. q~X Am| (A) (B) (C) (D) .430/5/1 (3, 2) VWm 52 BH$mB 4 10 BH$mB 2 10 BH$mB 40 BH$mB ( 3, 2) Ho$ ~rM H$s X ar h 2 General Instructions : Read the following instructions very carefully and strictly follow them : (i) This question paper comprises four sections A, B, C and D. This question paper carries 40 questions. All questions are compulsory. (ii) Section A : Question Numbers 1 to 20 comprises of 20 questions of one mark each. (iii) Section B : Question Numbers 21 to 26 comprises of 6 questions of two marks each. (iv) Section C : Question Numbers 27 to 34 comprises of 8 questions of three marks each. (v) Section D : Question Numbers 35 to 40 comprises of 6 questions of four marks each. (vi) There is no overall choice in the question paper. However, an internal choice has been provided in 2 questions of one mark, 2 questions of two marks, 3 questions of three marks and 3 questions of four marks. You have to attempt only one of the choices in such questions. (vii) In addition to this, separate instructions are given with each section and question, wherever necessary. (viii) Use of calculators is not permitted. SECTION A Question numbers 1 to 20 carry 1 mark each. Choose the correct option in question numbers 1 to 10. 1. If a pair of linear equations is consistent, then the lines represented by them are (A) parallel (B) intersecting or coincident (C) always coincident (D) always intersecting 2. The distance between the points (3, 2) and ( 3, 2) is (A) 52 units (B) 4 10 units (C) 2 10 units (D) 40 units .430/5/1 3 P.T.O. 3. 4. 8 cot2 A 8 cosec2 A (A) 8 (B) 1 8 (C) 8 (D) 6. 7. 1 8 e Hw$ Ho$ {N> H$ Ho$ AmH$ma Ho$ EH$ {Jbmg H$m g nyU n >r` jo \$b h (A) r1 l + r2 l (B) l (r1 + r2) + r22 (C) 1 h ( r12 + r22 + r1r2) 3 (D) 5. ~am~a h g `m h 2 (r1 r2 )2 120 H$mo A^m ` JwUZI S>m| Ho$ JwUZ\$b Ho$ $n _| ` $ H$aZo na {Z Z m V hmoVm h (A) 5 8 3 (B) 15 23 (C) 10 22 3 (D) 5 23 3 { KmVr g_rH$aU (A) 12 (B) 84 (C) 2 3 (D) 12 4x2 6x + 3 = 0 `{X q~X (3, 6) q~X Am| q~X (x, y) hmoJm (A) (B) (C) (D) .430/5/1 (r1 > r2) (0, 0) H$m {d{d $H$a VWm (x, y) ( 3, 6) (6, 6) (6, 12) 3 ( , 3) 2 4 (discriminant) h H$mo Omo S>Zo dmbo aoImI S> H$m _ `-q~X h , Vmo : 3. 4. 8 cot2 A 8 cosec2 A is equal to (A) 8 (B) 1 8 (C) 8 (D) The total surface area of a frustum-shaped glass tumbler is (r1 > r2) (A) r1 l + r2 l (B) l (r1 + r2) + r22 (C) 1 h ( r12 + r22 + r1r2) 3 (D) 5. 6. 7. 1 8 h 2 (r1 r2 )2 120 can be expressed as a product of its prime factors as (A) 5 8 3 (B) 15 23 (C) 10 22 3 (D) 5 23 3 The discriminant of the quadratic equation 4x2 6x + 3 = 0 is (A) 12 (B) 84 (C) 2 3 (D) 12 If (3, 6) is the mid-point of the line segment joining (0, 0) and (x, y), then the point (x, y) is (A) ( 3, 6) (B) (6, 6) (C) (6, 12) (D) 3 ( , 3) 2 .430/5/1 5 P.T.O. 8. AmH ${V-1 _| {XE JE d m _|, ne -aoIm g `m h (A) (B) (C) (D) 9. Ho$ g_m Va ItMr OmZo dmbr ne -aoImAm| H$s AmH ${V-1 AZoH$ 2 1 {Z Z{b{IV ~ma ~maVm ~ Q>Z Ho$ {bE : 0 5 5 10 dJ : 8 10 ~ma ~maVm : _m `H$ dJ H$s C gr_m h (A) (B) (C) (D) 10. 0 PQ 10 15 15 20 20 25 19 25 8 15 10 20 25 {H$gr Ag ^d KQ>Zm Ho$ hmoZo H$s m{`H$Vm h (A) (B) (C) (D) 1 1 2 n[a^m{fV Zht 0 Z g `m 11 go 15 _| [a $ WmZ ^[aE & 11. 12. 13. 14. 15. {H$gr d m H$mo Xmo q~X Am| na {V N>o{XV H$aZo dmbr aoIm H$mo __________ H$hVo h & `{X ~h nX ax2 2x H$m EH$ ey `H$ 2 h , Vmo a H$m _mZ ___________ h & g^r dJ ____________ hmoVo h & (gdm Jg_/g_ $n) `{X Xmo Jmobm| H$s { `mAm| H$m AZwnmV 2 : 3 h , Vmo BZ Jmobm| Ho$ Am`VZm| H$m AZwnmV _________ hmoJm & `{X PQR H$m jo \$b ey ` h , Vmo q~X P, Q VWm R ______________ h & .430/5/1 6 8. In the given circle in Figure-1, number of tangents parallel to tangent PQ is Figure-1 (A) (B) (C) (D) 9. 0 many 2 1 For the following frequency distribution : Class : Frequency : 0 5 5 10 10 15 15 20 20 25 8 10 19 25 8 The upper limit of median class is (A) 15 (B) 10 (C) 20 (D) 25 10. The probability of an impossible event is (A) 1 1 (B) 2 (C) not defined (D) 0 Fill in the blanks in question numbers 11 to 15. 11. A line intersecting a circle in two points is called a ___________ . 12. If 2 is a zero of the polynomial ax2 2x, then the value of a is ________ . 13. All squares are __________ . (congruent/similar) 14. If the radii of two spheres are in the ratio 2 : 3, then the ratio of their respective volumes is __________ . 15. If ar ( PQR) is zero, then the points P, Q and R are ____________ . .430/5/1 7 P.T.O. Z g `m 16 go 20 _| {Z Z{b{IV Ho$ C ma Xr{OE : 16. AmH ${V-2 _|, ^y{_ Ho$ EH$ q~X B go _rZma AC Ho$ {eIa H$m C `Z H$moU 60 h & `{X _rZma H$s D $MmB 20 _r. hmo, Vmo _rZma Ho$ nmX-q~X go Bg q~X H$s X ar kmV H$s{OE & AmH ${V-2 17. _mZ kmV H$s{OE : tan 40 tan 50 AWdm 18. 19. 20. `{X cos A = sin 42 h , Vmo A H$m _mZ kmV H$s{OE & EH$ {g o$ H$mo Xmo ~ma CN>mbm OmVm h & XmoZm| ~ma {MV AmZo H$s m{`H$Vm kmV H$s{OE & Cg e Hw$ H$s D $MmB kmV H$s{OE {OgH$s { `m 5 go_r VWm {V` H$ D $MmB 13 go_r h & `{X 6, x, 8 EH$ g_m Va loT>r Ho$ H ${_V nX h , Vmo x H$m _mZ kmV H$s{OE & AWdm g_m Va loT>r 27, 22, 17, 12,... H$m 11dm nX kmV H$s{OE & I S> I$ Z g `m 21 go 26 _| `oH$ Z 2 A H$m| H$m h & 21. { KmV g_rH$aU 3x2 4 22. Om M H$s{OE {H$ `m {H$gr mH $V g `m n Ho$ {bE g `m hmo gH$Vr h & AWdm 150 VWm 200 H$m b.g. (LCM) kmV H$s{OE & 23. `{X A .430/5/1 tan (A + B) = VWm B 3 3x+4=0 VWm Ho$ _yb kmV H$s{OE & tan (A B) = Ho$ _mZ kmV H$s{OE & 8 1 3 h , 6n A H$ 0 (ey `) na g_m V 0 < A + B 90 , A > B, Vmo Answer the following question numbers 16 to 20 : 16. In Figure-2, the angle of elevation of the top of a tower AC from a point B on the ground is 60 . If the height of the tower is 20 m, find the distance of the point from the foot of the tower. Figure-2 17. Evaluate : tan 40 tan 50 OR If cos A = sin 42 , then find the value of A. 18. A coin is tossed twice. Find the probability of getting head both the times. 19. Find the height of a cone of radius 5 cm and slant height 13 cm. 20. Find the value of x so that 6, x, 8 are in A.P. OR Find the 11th term of the A.P. 27, 22, 17, 12, ... . SECTION B Question numbers 21 to 26 carry 2 marks each. 21. Find the roots of the quadratic equation 3x2 4 3 x + 4 = 0. 22. Check whether 6n can end with the digit 0 (zero) for any natural number n. OR Find the LCM of 150 and 200. 23. If tan (A + B) = 3 and tan (A B) = 1 , 0 < A + B 90 , A > B, then 3 find the values of A and B. .430/5/1 9 P.T.O. 24. AmH ${V-3 _|, ABC XYZ Xem E JE h & `{X AB = 3 go_r, BC = 6 go_r, AC = 2 3 go_r, A = 80 , B = 60 , XY = 4 3 go_r, YZ = 12 go_r VWm XZ = 6 go_r h , Vmo Y H$m _mZ kmV H$s{OE & VWm 2 3 go_r 4 3 go_r AmH ${V-3 25. 26. {H$gr H$maUde 14 am~ ~ ~, 98 A N>o ~ ~m| _| {_b JE h & Ho$db `h XoIH$a Zht ~Vm`m Om gH$Vm h {H$ H$moB ~ ~ am~ h `m Zht & Bg {_lU _| go EH$ ~ ~ `m N>`m {ZH$mbm OmVm h & {ZH$mbo JE ~ ~ Ho$ A N>m hmoZo H$s m{`H$Vm kmV H$s{OE & {Z Z{b{IV ~ Q>Z H$m _m ` kmV H$s{OE : dJ : 5 15 15 25 25 35 35 45 2 4 3 1 ~ma ~maVm : {Z Z{b{IV ~ Q>Z 100 AWdm H$_ Mm[a`m| Ho$ AmZo-OmZo Ho$ IMm] H$mo Xem Vm h `` (< _|) : 200 400 400 600 600 800 H$_ Mm[a`m| H$s 21 25 19 g `m : Bg ~ Q>Z H$m ~h bH$ kmV H$s{OE & 800 1000 1000 1200 23 I S> J$ Z g `m 27 go 34 _| `oH$ Z 3 A H$m| H$m h & 27. EH$ d m Ho$ n[aJV MVw^w O ABCD ItMm J`m h & {g H$s{OE {H$ AB + CD = AD + BC. .430/5/1 10 : 12 24. In Figure-3, ABC and XYZ are shown. If AB = 3 cm, BC = 6 cm, AC = 2 3 cm, A = 80 , B = 60 , XY = 4 3 cm, YZ = 12 cm and XZ = 6 cm, then find the value of Y. 2 3 cm 4 3 cm Figure-3 25. 14 defective bulbs are accidentally mixed with 98 good ones. It is not possible to just look at the bulb and tell whether it is defective or not. One bulb is taken out at random from this lot. Determine the probability that the bulb taken out is a good one. 26. Find the mean for the following distribution : Classes : Frequency : 5 15 15 25 25 35 35 45 2 4 3 1 The following distribution 100 employees : Expenditure (in <) : Number of employees : OR shows the transport expenditure of 200 400 400 600 600 800 800 1000 1000 1200 21 25 19 23 12 Find the mode of the distribution. SECTION C Question numbers 27 to 34 carry 3 marks each. 27. A quadrilateral ABCD is drawn to circumscribe a circle. Prove that AB + CD = AD + BC. .430/5/1 11 P.T.O. 28. Xmo g `mAm| H$m A Va 26 h VWm ~ S>r g `m, N>moQ>r g `m Ho$ VrZ JwZo go g `mE kmV H$s{OE & AWdm x 29. 30. VWm y Ho$ {bE hb H$s{OE : 2 3 = 13 VWm x y 4 A{YH$ h & 5 4 = 2 x y {g H$s{OE {H$ 3 EH$ An[a_o` g `m h & H $ Um Ho$ nmg EH$ go~m| H$m ~mJ h {OgHo$ gmW EH$ 10 _r. 10 _r. gmB O H$m EH$ {H$MZ JmS> Z h & CgZo Cgo EH$ 10 10 {J S> _| ~m Q>H$a Cg_| {_ >r VWm ImX S>mbr h & CgZo q~X A na EH$ Zt~y H$m nm Ym, q~X B na Y{ZE H$m nm Ym, q~X C na `mO H$m nm Ym VWm q~X D na EH$ Q>_mQ>a H$m nm Ym bJm`m h & CgH$m n{V am_ {H$MZ JmS> Z H$mo XoIH$a Vmar \$ H$aVm h VWm H$hVm h {H$ A, B, C VWm D H$mo {_bmZo na dh em`X EH$ g_m Va MVw^w O ~Z OmE & ZrMo {XE JE {M H$mo `mZnyd H$ XoIH$a {Z Z{b{IV Ho$ C ma Xr{OE : (i) (ii) .430/5/1 {ZX}em H$ Aj Ho$ $n _| 10 10 {J S> H$m Cn`moJ H$aVo h E q~X Am| D Ho$ {ZX}em H$ kmV H$s{OE & kmV H$s{OE {H$ `m ABCD EH$ g_m Va MVw^w O h `m Zht & 12 A, B, C VWm 28. The difference between two numbers is 26 and the larger number exceeds thrice of the smaller number by 4. Find the numbers. OR Solve for x and y : 2 3 5 4 = 13 and = 2 x y x y 29. Prove that 30. Krishna has an apple orchard which has a 10 m 10 m sized kitchen garden attached to it. She divides it into a 10 10 grid and puts soil and manure into it. She grows a lemon plant at A, a coriander plant at B, an onion plant at C and a tomato plant at D. Her husband Ram praised her kitchen garden and points out that on joining A, B, C and D they may form a parallelogram. Look at the below figure carefully and answer the following questions : 3 is an irrational number. (i) Write the coordinates of the points A, B, C and D, using the 10 10 grid as coordinate axes. (ii) Find whether ABCD is a parallelogram or not. .430/5/1 13 P.T.O. 31. 32. `{X {H$gr g_m Va loT>r Ho$ W_ 14 nXm| H$m `moJ\$b 1050 h VWm BgH$m W_ nX 10 h , Vmo Bg g_m Va loT>r H$m 21dm 4 go_r ^wOmAm| dmbo EH$ { ^wO H$s aMZm H$s{OE & {\$a BgHo$ g_ $n go_r, 5 go_r VWm 6 nX kmV H$s{OE & EH$ Am a { ^wO H$s aMZm H$s{OE {OgH$s ^wOmE nhbo { ^wO H$s g JV ^wOmAm| H$s 2 3 JwZr hm| & AWdm 2 .5 go_r { `m H$m EH$ d m It{ME & BgHo$ Ho$ go br{OE & d m na q~X 33. {g H$s{OE {H$ P go AmH ${V-4 _|, P : AB Am a d m H$m `mg h & `{X CD Ho$ O OA = 7 go_r 1 tan A cot A dmbo d m Ho$ Xmo na na b ~ `mg h VWm OD h , Vmo N>m`m {H$V ^mJ H$m jo \$b kmV H$s{OE & AmH ${V-4 AWdm .430/5/1 go_r X a p WV EH$ q~X ne -aoIm `w _ H$s aMZm H$s{OE & (cosec A sin A) (sec A cos A) = 34. 8 14 N>moQ>o 31. If the sum of the first 14 terms of an A.P. is 1050 and its first term is 10, then find the 21st term of the A.P. 32. Construct a triangle with its sides 4 cm, 5 cm and 6 cm. Then construct a 2 triangle similar to it whose sides are of the corresponding sides of the 3 first triangle. OR Draw a circle of radius 2.5 cm. Take a point P at a distance of 8 cm from its centre. Construct a pair of tangents from the point P to the circle. 33. Prove that : (cosec A sin A) (sec A cos A) = 34. 1 tan A cot A In Figure-4, AB and CD are two diameters of a circle (with centre O) perpendicular to each other and OD is the diameter of the smaller circle. If OA = 7 cm, then find the area of the shaded region. Figure-4 OR .430/5/1 15 P.T.O. AmH ${V-5 _|, 7 go_r ^wOm dmbo dJ ^mJ H$m jo \$b kmV H$s{OE & ABCD Ho$ n[aJV EH$ d m ItMm J`m h & N>m`m {H$V AmH ${V-5 I S> K$ Z g `m 35 go 40 VH$ `oH$ Z 4 A H$m| H$m h & 35. ~h nX 2, p(x) = 3x4 4x3 10x2 + 8x + 8 Ho$ A ` ey `H$ kmV H$s{OE, `{X 2 VWm BgHo$ Xmo ey `H$ {XE JE h & AWdm ~h nX g(x) = x3 3x2 + x + 2 H$mo ~h nX x2 {d^mOZ Eo Jmo[a _ H$s g `Vm H$s Om M H$s{OE & 2x + 1 go {d^m{OV H$s{OE VWm 36. g_w Vb go 75 _r. D $Mo bmBQ>hmCg Ho$ {eIa go XoIZo na Xmo g_w r Ohm Om| Ho$ AdZ_Z H$moU 30 VWm 45 h & `{X XmoZm| Ohm O bmBQ>hmCg H$s {dnarV {XemAm| _| hm|, Vmo XmoZm| Ohm Om| Ho$ ~rM H$s X ar kmV H$s{OE & 37. `{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 hmoVr h & AWdm .430/5/1 16 In Figure-5, ABCD is a square with side 7 cm. A circle is drawn circumscribing the square. Find the area of the shaded region. Figure-5 SECTION D Question numbers 35 to 40 carry 4 marks each. 35. Find other zeroes of the polynomial p(x) = 3x4 4x3 10x2 + 8x + 8, if two of its zeroes are 2 and 2 . OR Divide the polynomial g(x) = x3 3x2 + x + 2 by the polynomial x2 2x + 1 and verify the division algorithm. 36. From the top of a 75 m high lighthouse from the sea level, the angles of depression of two ships are 30 and 45 . If the ships are on the opposite sides of the lighthouse, then find the distance between the two ships. 37. If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, prove that the other two sides are divided in the same ratio. OR .430/5/1 17 P.T.O. AmH ${V-6 _|, g_~mh { ^wO ABC _|, AD BC, H$s{OE {H$ 4 (AD2 + BE2 + CF2) = 9 AB2. BE AC VWm CF AB h & {g AmH ${V-6 38. YmVw H$s MmXa go ~Zm Am a D$na go Iwbm EH$ ~V Z e Hw$ Ho$ {N> H$ Ho$ AmH$ma H$m h , {OgH$s D $MmB 14 go_r h VWm {ZMbo Am a D$nar d mr` {gam| H$s { `mE H $_e: 8 go_r VWm 20 go_r h & ~V Z H$s Ym[aVm kmV H$s{OE & 39. Xmo nmZr Ho$ Zb EH$ gmW EH$ hm O H$mo hm O H$mo ^aZo _|, H$_ `mg dmbo Zb 3 K Q>m| _| ^a gH$Vo h & ~ S>o 8 go 10 K Q>o H$_ g_` boVm h & 9 `mg dmbm Zb `oH$ Zb mam AbJ-AbJ hm O H$mo ^aZo H$m g_` kmV H$s{OE & AWdm EH$ Eogo Am`VmH$ma nmH $ H$mo ~ZmZm h {OgH$s Mm S>mB CgH$s b ~mB go 3 _r. H$_ hmo & BgH$m jo \$b nhbo go {Z{_ V g_{ ~mh { ^wOmH$ma nmH $ {OgH$m AmYma Am`VmH$ma nmH $ H$s Mm S>mB Ho$ ~am~a VWm D $MmB 12 _r. h , go 4 dJ _rQ>a A{YH$ hmo & Bg nmH $ H$s b ~mB Am a Mm S>mB kmV H$s{OE & 40. {Z Z{b{IV ~ma ~maVm ~ Q>Z Ho$ {bE go H$_ H$ma H$m VmoaU It{ME dJ : ~ma ~maVm : .430/5/1 : 0 10 10 20 20 30 30 40 40 50 50 60 60 70 70 80 7 14 13 12 18 20 11 15 8 In Figure-6, in an equilateral triangle ABC, AD BC, BE AC and CF AB. Prove that 4 (AD2 + BE2 + CF2) = 9 AB2. Figure-6 38. A container open at the top and made up of a metal sheet, is in the form of a frustum of a cone of height 14 cm with radii of its lower and upper circular ends as 8 cm and 20 cm, respectively. Find the capacity of the container. 39. Two water taps together can fill a tank in 9 3 hours. The tap of larger 8 diameter takes 10 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank. OR A rectangular park is to be designed whose breadth is 3 m less than its length. Its area is to be 4 square metres more than the area of a park that has already been made in the shape of an isosceles triangle with its base as the breadth of the rectangular park and of altitude 12 m. Find the length and breadth of the park. 40. Draw a less than ogive for the following frequency distribution : Classes : Frequency : .430/5/1 0 10 10 20 20 30 30 40 40 50 50 60 60 70 70 80 7 14 13 12 19 20 11 15 8 P.T.O.

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