My Work Book on€¦ · 6. Find the value of k if x + 2 2is a factor of 4x4 + 2x3 - 3x + 8x + 4k....

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Class X

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Mathematics & Science

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Teachers Forum -3-

Work Book - Class X

1. REAL NUMBERS2 MARKS

1. GiventhatLCM(77,99)=693,findtheHCF(77,99).

2. UseEuclid’sdivisionalgorithmtofindtheHCFof216and1176

3. Checkwhether(12)ncanendwiththedigit0foranynaturalnumbern.

4. IftheHCF(24,x)=6andLCM(24,x)=144,thenfindthevalueofx.

5. Show thatsquareofanypositiveodd integer isof the form8k+1,wherek isaninteger.

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Work Book - Class X

6. Thedeimalexpansionoftherationalnumber43

24 . 53 willterminateafterhowmanyplacesofdecimal?

7. Showthatanypositiveoddintegerisoftheform4q+1or4q+3,whereqissomeinteger.

8. FindtheHCFof867and255usingEuclid’sdivisionalgorithm.

9. State wheather the following rational numbers will have a terminating decimalexpansion or non-terminating repeating decimal expansion (performing the longdivisionisnotallowed):

(a) 151600

(b) 29343

10. Explainwhy5x4x3x2x1+3isacompositenumber.

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Work Book - Class X

11. Withoutthelongdivision,statewhetherthefollowingrationalnumberswillhavetheterminatingornon-terminatingrepeatingdecimalexpansion:

(a) 27x334x23x52 (b) 129

23x52x32

3 MARKS

12. FindtheHCFbyusingEuclid’sdivisionalgorithmofthenumbers92690,7378and7161.

13. FindtheHCFandLCMof306and54.VerifythatHCFxLCM=productofthetwonumbers.

14. Euclid’sdivisionalgorithmtofindtheHCFofthefollowing:

(a) 180,192 (b)27,36 (c)210and55.

15. UseEuclid’sdivisionalgorithmtofindtheHCFof10224and9648.

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Work Book - Class X

16. FindtheHCFandLCMofthefollowingnumbersbyapplyingtheprimefactorisationmethod:

(a) 96and128 (b)225and450

17. Showthatsquareofanypositiveintegercannotbeoftheform5q+2or5q+3foranyintegerq.

18. Write the denominator of911250

in the form of 2m.5n wherem, n are non-negative

integers.Alsowriteitsdecimalexpansionwithoutactualdivision.

19. Provethat√6 +√2 isirrational.

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Work Book - Class X

20. Provethat5√2 isirrationalnumber.

21. Provethat√2 +√5 isirrational:

22. Provethat3√2

5isirrational.

23. Expressthenumber0.3178withformofrationalnumber.

24. Provethatthesquareofoddpositiveintegerscanneverbeoftheformof7k+1.

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Work Book - Class X

25. Findthegreatestnumberof6digitsexactlydivisibleby24,15and36.

4 MARKS

26. Provethat√2 isanirrationalnumber.Henceshowthat5+3√2 isalsoanirrationalnumber.

27. Provethat√5 isanirrationalnumber.Henceshowthat3-√5 isalsoirrational.

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Work Book - Class X

Choose the correct answer :

28. IftheHCFof408and1032isexpressibleintheform1032m-408x5,thenmwillbe

(a)-2 (b)2 (c)4 (d)-4

29. Theproductoftwoconsecutivenaturalnumbersisalwaysa

(a) evennumber(b)oddnumber(c)primenumber(d)noneofthese

30. TheHCFof17and3is

(a) 17 (b)3 (c)51 (d)1

31. IftheHCFoftwonumbers216and1176is24,thentheirLCMwillbe

(a) 10584 (b)254016 (c)28224(d)noneofthese

32. p is

(a) arationalnumber (b)anirrationalnumber

(c) aninteger (d)anaturalnumber

AnSweR Key

1. 11 2. 24 4. 36

6. four 8. 51

9. (a)Terminatingdecimal (b)Non-terminating

11. (a)Terminating (b)Non-Terminating

12. 31 13. 18,918

14.(a)12(b)9(c) 5 15. 144

16. (a)HCF=32,LCM=384 (b) HCF=225,LCM=450

18. 0.0728 23.6351998

25.999720 28. (b)

29. (a) 30.(d)

31. (a) 32. (b)

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Work Book - Class X

2. POLYNOMIALS2 MARKS

1. Showthat3and-34arethezerosofthepolynomial4x2-9x-9.

2. Findthequadraticpolynomial,sumofwhosezeroes is-3andtheirproduct is-10.Hencefindthezeroesofthepolynomial.

3. Ifαand 1α arethezeroesofthepolynomial4x2-2x+k-4,findthevalueofK.

4. Ifthesumandproductofthezeroesofthepolynomialf(x) = 4x2-27x+3k2areequal,findthevalue(s)ofk.

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Work Book - Class X

5. Ifoneofthezeroesofthepolynomialp(x) = 2x2-8x-mis 52 ,findmandtheother

zero.

6. Findthevalueofkifx+2isafactorof4x4+2x3-3x2+8x+4k.

7. Ifαandβarethezeroesofthepolynomialf(x) = kx2+4x+4suchthatα2+β2 = 24, findthevalueofk.

8. Ifpandqarezeroesofpolynomialf(x) = 2x2-7x+3,findthevalueofp2+q2.

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Work Book - Class X

9. Findaquadraticpolynomialwhosezeroesare4+√5 and4-√5 .

10. Ifmandnarethezeroesofthepolynomial3x2+11x-4,findthevalueof mn + nm .

11. Divide(6+23x+25x2+6x3)by(3+7x+2x2)andverifydivisionalgorithm.

3 MARKS

12. Ifα andβ are zeroes of the polynomial p(x) = 3x2 - 4x - 7 then forma quadraticpolynomialwhosezeroesare 1

α and 1β .

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Work Book - Class X

13. Divide6x3+2x2-4x+3by3x2-2x+1andverifythedivisionalgorithm.

14. Findthezeroesof thequadraticpolynomial5x2+8x -4andverifytherelationshipbetweenthezeroesandthecoefficientsofthepolynomial.

15. Ondividingthepolynomialp(x) = 5x4-4x3+3x2-2x+1byanotherpolynomialg(x) = x2+2,ifthequotientisax2+bx+c,finda,bandc.

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Work Book - Class X

16. Find the zeros of the following quadratic polynomials and verify the relationshipbetweenthezerosandtheircoefficients:

(a) 4x2-4x+1 (b)x2-8x+12

17. Dividethegivenf (x)byg (x)andfindthequotientandremainder:

f (x) = x4+x2+x, g (x) = x2+x+1

18. If(x+a)isafactoroftwopolynomialsx2+px+qandx2+mx+n,thenprovethat a = n-qm-p

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Work Book - Class X

19. whatmustbeaddedtox3-4x2+x -6sothatx2+2x-3becomesitsfactor.

20. Ondividingthepolynomialp(x) = 9x4-4x2+4byg(x) = 3x2+x-1,theremainderisax-b.Findaandb.

21. Showthat 12 and -32 are thezeroesof thepolynomial4x2+4x -3andverify the

relationshipbetweenzeroesandcoefficientsofpolynomial.

22. Checkbydivisionwhetherx2-2isafactorofx4+x3+x2-2x-3.

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Work Book - Class X

23. If 12 and1arezeroesof2x4-3x3-3x2+6x-2,findtheotherzeroes.

24. Forwhatvalueofk,-8isazeroofthepolynomialx2-x-(5k+2)?Alsofindtheotherzero.

25. Ifαandβarethezeroesofthepolynomialx2-5x+6,thenfindthepolynomialwhosezeroesare 1

α and 1β .

26. Dividethegivenf (x)byg (x)andfindthequotientandremainder:

f (x) = x3-6x2+11x-6,g (x) = x+2

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Work Book - Class X

27. Ifαandβarethezerosofthepolynomialf (x) = x2-5x+k such α-β=1,findthevalue

ofk.

28. Findthezerosofx2-53andverifytherelationshipbetweenitszerosanditscoefficients.

29. Find thezerosof thequadraticpolynomialx2+7x+10andverify the relationshipbetweenthezerosandcoefficientsofthepolynomial.

30. Findthevalueofpforwhichthepolynomialx3+4x2-px+8isexactlydivisiblebyx-2.

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Work Book - Class X

31. Whatmustbeaddedto6x3+5x2+5sothatitisexactlydivisibleby3x+4?

32. Findthezerosofx2+3x+2.

4 MARKS

33. Ifαandβarethezeroesofthequadraticpolynomialp(x) = 3x2-5x-2,thenevaluate:

(i) 1α + 1

β (ii) α3β+αβ3

34. Usingdivisionalgorithm,findthequotientandremainderondividing8x4+14x3-2x2 +8x-12by4x2+3x-2.

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Work Book - Class X

35. Ifα andβ arethezeroesof2x2+5x+kandα2+β2+αβ = 214 ,findthevalueofk.Anu

saysthatthezeroesofthegivenpolynomialarereciprocaltoeachother.Issheright?Justify.

36. Applythedivisionalgorithmtofindthequotientandremainderof x3-6x2+11x-6

x2-4x+3

37. Applythedivisionalgorithmtofindthequotientandremainderof

10x4+17x3-62x2+30x-32x2 +7x+1

38. Whatmustbesubstractedoraddedtop(x)=8x4+14x3-2x2+8x-12Sothat4x2+3x-2isafactorofp(x)?

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Work Book - Class X

39. Byapplyingdivisionalgorithm,checkwhetherornotx2+3x+1isafactorof3x4+5x3 -7x2+2x+2.

40. Divide21x-12x2-30+8x4+8x3by3x+2x2-5andverifydivisionalgorithm.

41. Ifthepolynomialf(x) = 3x4+3x3-11x2-5x+10iscompletelydivisibleby3x2-5,findallitszeroes.

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Work Book - Class X

42. Findthevaluesofaandbsothatx4+x3+8x2+ax+bisexactlydivisiblebyx2+1.

43. Findallthezeroesof2x4+7x3-19x2-14x+30iftwoofitszeroesare√2 and-√2 .

44. Obtainallotherzeroesof2x4-6x3+3x2 -2iftwoofitszeroesare1

√2and-

1√2

.

45. Ifthepolynomialx4-6x3+16x2-25x+10isdividedbyx2-2x+k,theremaindercomesouttobex+a,findkanda.

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Work Book - Class X

46. Ifαandβarezeroesofthepolynomialp(x) = 6x2-5x+ksuchthatα-β = 16 ,findthe

valueofk.

47. Findthezeroesofthequadraticpolynomial2x2+x–10.Alsoverifytherelationshipbetweenzeroesandcoefficients.


48. Thedegreeofpolynomialx5-x4+7is

(a) 5 (b)4 (c)2 (d)0

49. Ifα, βarezerosofthepolynomialf (x) = x2+x+1,then 1α+ 1

βisequalto

(a) 1 (b)-1 (c)0 (d)Noneofthese.

50. Productofthezerosof-2x2+kx+6is

(a) -3 (b)3 (c)k2 (d)-k

2

51. If1isoneofthezerosofpolynomialx2-x+k,thevalueofk is

(a) -2 (b)0 (c)2 (d)4

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Work Book - Class X

AnSweR Key

2. x2+3x-10 3. 8 4. ±3

5. -152 , 3

2 6. k=-5 7. -1, 23

8. 374 9. x2-8x+11 10. -145

12

12. 7x2+4x-3 13. -2, 25 15. 5,-4,-7

16. (a) 12 (b)6,2 17. x2-x+1 19. 24+16x

20. -1,-4 22. No. 23. √2 ,-√2

24. k=14,0=9 26. Quotient=x2-8x+27,Remainder=-60

27. k=6. 28. √53 ,-√5

3 29. -2,-5

30. 16 31. 7. 32. -1,-2

33. (i) -52 , (ii) -7427 34. Quotient=2x2+2x-1,Remainder=15x-14

35. k=2,yes 36. Quotient=x-3,Remainder=0

37. Quotient=5x2-9x-2,Remainder=53x-1 38. 15x - 14 or -15x +

14 39. Yes 40.Q=4x2-2x+7,R=-10x+5

41. ± √ -52 ,-2 42. 1,6 43. √2 ,-√2 ,-5, 32

44. 1

√2, -1√2

,1,2 45. k=5,a=-5 46. 1

48. (a) 5 49. (b)-1 50. (a) -3

51.(a)-2

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Work Book - Class X

3. PAIR OF LINEAR EQUATIONSIN TWO VARIABLES

2 MARKS

1. Solve: 99x+101y =499;101x+99y=501

2. Forwhatvaluesofaandb,thefollowingsystemsofLinearequationshaveaninfinitenumberofsolutions?

(iii) 2x+y-5=0,(a+b)x+(a-2b)y-15=0

3. Isthesystemoflinearequations2x+3y-9=0and4x+6y-18=0consistent?Justifyyouranswer.

4. Solve: 4x +5y = 7, 3

x +4y = 5

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Work Book - Class X

5. Findthevalueofk forwhichthegivensystemofequationshasauniquesolution:

x-ky = 2, 3x+2y=-5

6. Forwhatvalueofk,thepairoflinearequationskx+3y = k-3,12x+ky = khasuniquesolution.

7. Twoshopkeeperssellelectronicgoodsofsamekind.Theirsalesfortwoitemsarerepresentedbytwoequations3x+y=9and7x+2y=20.Findthesalepriceofeachitembythetwoshopkeepers.

8. Forwhatvalueof'a',thefollowingpairoflinearequationshasinfinitelymanysolution?

2x+5y=8;ax+(3a-2)y = 4a

3 MARKS

9. Thesumofthedigitsofatwodigitnumberis12.Thenumberobtaimedbyinterchangingthetwodigitsexceedsthegivennumberby18.Findthenumber.

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Work Book - Class X

10. Findthevalueofαandβforwhichthefollowingpairoflinearequationshaveinfinitenumberofsolutions.

2x+3y=7,2aα+(α +β)y=28

11. Findwhetherthefollowingpairoflinearequationshasauniquesolutionornot.Ifyes,findthesolution.

7x-4y=49,5x-6y = 57

12. Twoyearsago,thefatherwasfivetimesasoldashisson.Twoyearslater,hisagewillbe8morethanthreetimestheageoftheson.Findthepresentagesofthefatherandson.

13. Thesumofthedigitsofatwodigitnumbreis8andthedifferencebetweenthenumberandthatformedbyreversingthedigitsis18.Findthenumber.

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Work Book - Class X

14. Thesumofthedigitsofatwo-digitnumberis15.Thenumberisdecreasedby27ifthedigitsarereversed.Findthenumber.

15. Findthevalueofkforwhichthefollowingsystemofequationshasnosolution:

3x-4y+7=0,kx+3y-5=0

16. FindthefouranglesofacyclicquadrilateralABCDinwhich∠A=2x-1°,∠B = y+5°,∠C = 2y+15°and∠D = 4x-7°.

17. 3chairsand2tablescost`700and5chairsand3tablescost`1100.Whatisthecostof2chairsandtwotables.

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Work Book - Class X

18. Solveforxandy:7(y+3)-2(x+2)=14,4(y-2)+3(x-3)=2

19. Solveforxandy:x +yxy

= 2, x -yxy

= 6

20. Solvethefollowingsystemofequationsbythemethodofcross-multiplication:

5x +y

- 2x -y

+1=0, 15x +y

+ 7x -y

-10=0

21. 4menand6boyscanfinishapieceofworkin20days,while3menand4boyscanfinishitin28days.Findthetimetakenbyonemanaloneandoneboyalonetofinishthatwork.

22. 2menand7boyscandoapieceofworkin4days.Itisdoneby4menand4boysin3days.Howlongwouldittakeforonemanoroneboytodoit?

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Work Book - Class X

23. Forwhatvaluesofaandbdoesthefollowingpairoflinearequationshaveaninfinitenumberofsolutions.

2x+3y=7;a(x+y)-b(x-y)=3a+5-2

24. Aboat goes16 kmupstreamand24 kmdownstream in6hrs. Also it covers12kmupstreamand36kmdownstreaminthesametime.Findthespeedoftheboatupstreamanddownstream.

25. Solve: 2x + 3

y = 13, 5x - 4 y =-2,x,y≠0

26. Solveforuandvbychangingintolinearequations

2(3u-v)=5uv;2(u+3v)=5uv

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Work Book - Class X

27. Solvethefollowingsystemoflinearequationsbycrossmultiplicationmethod:

2(ax-by)+(a+4b)=0;2(bx+ay)+(b-4a)=0

28. Solveforxandy.

a2

x + b2

y =0; a2bx +b

2ay = a+b , x ≠0;y ≠0

29. Solveforxandy;x+12 + y-13 = 9 ; x-13 +y+12 =8

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Work Book - Class X

30. Drawthegraphoftheequations:2x+3y=12andx-y = 1

Shadetheregionbetweenthetwolineasandx -axis.Alsodeterminetheverticesofthetrianglesoformed.

31. Afractionbecomes 911 ,if2isaddedtobothitsnumeratorandthedenominator.If3is

addedtobothitsnumeratoranddenominatoritbecomes 56 .Findthefraction.

4 MARKS

32. Aboatcovers32kmupstreamand36kmdownstreamin7hours.Alsoitcovers40kmupstreamand48kmdownstreamin9hours.Findthespeedoftheboatinstillwaterandthatofthestream.

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Work Book - Class X

33. Solveforxandy: 5x-1 +

1y-2 = 2, 6

x-1 -3

y-2 = 1

34. Solveforxandy:2(3x-y) = 5xy, 2(x+3y) = 5xy

35. Solvethefollowingsystemoflinearequationsgraphically.

2x+y = 6, 2x-y=-2

Also,findtheareaoftheregion(triangle)formedbythesetwolinesandx-axis.

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Work Book - Class X

36. Solvethefollowingsystemoflinearequationsgraphically.

3x+y+1=0,2x-3y+8=0

Shadetheregionboundedbythelinesandthex-axis.

37. Solvethefollowingsystemsoflinearequations:

8x-9y = 6xy, 10x+6y = 19xy

38. TwoplacesAandBare120kmapartfromeachotheronahighway.AcarstartsfromAandanotherfromBatthesametime.Iftheymoveinthesamedirection,theymeetin6hoursandiftheymoveinoppositedirections,theymeetin1hour12minutes.Findthespeedofcars.

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Work Book - Class X

39. Amantravels600kmtohishomepartlybytrainandpartlybycar.Hetakes8hoursifhetravels120kmbytrainandandtherestbycar.Hetakes20minuteslongerifhetravels200kmbytrainandandtherestbycar.Findthespeedofthetrainandthecar.

40. Solvethefollowingsystemsofequationsgraphically

3x-5y+1=0,2x-y+3=0

41. Showgraphicallythefollowingsystemofequationshasinfinitelyamnysolutions.

2y = 4x-6,2x = y+3

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Work Book - Class X

42. Drawthegraphsofthefollowingequations:

2x-3y+6=0

2x+3y-18=0

y-2=0

Findtheverticesofthetrianglesoobtained.Also,findtheareaofthetriangle.

43. Solveeachofthefollowingforxandy:mx -

ny = a, qx-py=0;x, y≠0

44. Solvexandy:x + yxy

= 2, x - yxy

= 6

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Work Book - Class X

45. Solvethepairoflinearequationsgraphically:2x+3y=12andx-y=1

FindtheareaoftheragionboundedbythetwolinesrepresentingtheaboveequationsandY-axis.

46. Thesumofatwodigitnumberandthenumberobtainedbyreversingtheorderofthedigitis99.Ifthedigitsofthenumberdifferby3,findthenumber.

47. 8menand12boyscanfinishapieceofworkin10days,while6menand8boyscanfinishitin14days.Findthetimetakenbyonemanaloneandoneboyalonetofinishthework.

48. Findgraphicallythesolutionsoftheequations:x+2y=8,y-x = 1

FindthecoordinatesofthepointswherethetwolinesmeetY-axis.

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Work Book - Class X

49. Solvex-y=1and2x+y=8graphicallyandfindtheareaoftheregionboundedbytheselinesandtheX-axis.

50. Solve: 2x+2y + 1

x-2y = -57

; 1x+2y - 2

x-2y = 157

51. Amotorboatcantravel30kmupstreamand28kmdownstreamin7hours.Itcantravel21kmupstreamandreturnin5hours.Findthespeedoftheboatinstillwaterandthespeedofthestream.

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Work Book - Class X

52. Inabagcontainingredandwhiteballs,halfthenumberofwhiteballsisequaltoone-thirdthenumberofredballs.Thricethetotalnumberofballsexceedsseventimesthenumberofwhiteballsby6.Howmanyballsofeachcolourdoesthebagcontain?

53. Theratioofincomesoftwopersonsis11:7andtheratiooftheirexpenditureis9:5.Ifeachofthemmanagestosave`400permonth,findtheirmonthlyincome.

54. Inaclasstest,thesumofRamesh’smarksinMathematicsandEnglishis40.Hadhegot3moremarksinMathematicsand4markslessinEnglish,theproductofhismarkswouldhavebeen360.Findhismarksinthetwosubjectsseparately.

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Work Book - Class X

55. Solveforx: 1 x+4

- 1 x-7

= 11 30

, x ≠ -4,7


56. Thevalueofkforwhichthesystemofequations.kx-y = 2, 6x-2y=3hasauniquesolution,is

(a) =3 (b)≠3 (c)≠0 (d)=0

57. Ifintheequationx+2y=10,thevalueofxis-2,thenthevalueofywillbe

(a) 4 (b)5 (c)6 (d)8

58. Thegraphoftheequationx+y=10isa

(a) verticalline (b)horizontalline (c)straightline(d)noneofthese

59. thegraphofx =5isalineparalleltothe

(a) x -axis (b)y -axis (c)bothx andy axis(d)noneofthese

60. Twoequationsintwovariablestakentogetherarecalled

(a)simpleequations (b)quadraticequations (c) simultaneous equations (d)noneofthese

AnSweR Key

1. 3,2 2. a=5,b=1 3. Yes

4. 13 ,-1 5. k≠ -2

3 6. K≠ ±6

7. `. 2, `3 8.K= ±2 9. 57

10. 4,8 11. Yes,3,-7

Teachers Forum -40-

Work Book - Class X

12. 42yearsand10yearsrespectively.

13. 53 14. 10 15. k =-2.25

16. ∠A=65°,∠B = 55°,∠C=115°and∠D=125°. 17. `600

18. x = 5, y = 1 19. x = -12

, y = 14 20. x = 3, y = 2

21. 140,280 22. 15,60 23.5,1

24. 8km/h,4km/h 25. 12 , 1

3 26. 2, 1

27. -12 ,2 28. a2,b2 29. 13, 7

30. (3,2),(6,0),(1,0) 31. 79 32. 10km/h,2km/h

33. 4, 5 34. 2, 1

35. x = 1,y=4,area=8sq.units.

36. x=-1,y = 2 37. x = 32

, y = 23 38.60km/h,40km/h

39. 60km/h,80km/h 40. x=-2,y=-1;

42. (3,4),(0,2),(6,2);Area=6sq.units. 43.x = mp - nqap

, y = mp - nqaq

44. x = -12

, y = 14 45. 7.5sq.unit 46. 47

47. 140,280 48. (2,3) 49. (3,2),3sq.unit

50. 2,3 51. 10,4 52. 18,12

53. `2200,`1400 56. (b) 57. (c)

58. (c) 59. (b) 60. (c)

Teachers Forum -41-

Work Book - Class X

4. QUADRATIC EQUATIONS2 MARKS

1. Solveforx:10x- 1x

= 3, x ≠0

2. FindthevaluesofPforwhichthequadraticequation4x2+px+3=0hasequalroots.

3. Solvefor:2x2+ax-a2=0.

4. Findtherootsofthefollowingquadraticequation:15x2-10√6 x+10=0

Teachers Forum -42-

Work Book - Class X

5. Findtherootsofthequadraticequation5x2-2√10x+2=0

6. Usingquadraticformulasolvethefollowingquadraticequationforx:abx2+(b2-ac)x-bc=0.

7. Ifanumberisaddedtotwiceitssquare,theresultis21.Findthenumber.

8. Findwhetherthequadraticequationx2-x-2=0hasrealrootsornot.Ifyesfindtheroots.

Teachers Forum -43-

Work Book - Class X

9. Findthevalueofkforwhichthequadraticequation(k+4)x2+(k+1)x+1=0hasequalroots.

10. Findthevalueofpsothattheequation3x2-5x+2p=0hasequalroots.Alsofindtheroots.

11. Theproductoftwoconsecutiveintegersis20.Findthenumbers,iftheirsumis9.

12. Findthevalueofa,suchthatthequadraticequation

(a-3)x2+2(a-4)x+4=0hasequalroots.

Teachers Forum -44-

Work Book - Class X

13. Ifx=2andx=3aretherootsoftheequation3x2-2kx+2m=0,findthevaluesofkandm.

14. Determinewhetherx = 12andx=2arethesolutionsofthequadraticequation

2x2-5x+2=0.

3 MARKS

15. Solveforx: 4x-3= 5

2x+3 ; x ≠0, -3

2

16. Forwhatvalueofk,therootsofthequadraticequationkx(x-2√5 )+10=0areequal.

Teachers Forum -45-

Work Book - Class X

17. Findtherootsoftheequation2x2+x-4=0bythemethodofcompletingthesquare.

18. Iftherootsofthequadraticequation(a-b)x2+(b-c)x+(c-a)=0,a ≠ bareequal,thenprovethatb+c = 2a.

19. Thesumofages(inyears)ofasonandhisfatheris35yearsandproductoftheiragesis150years.Findtheirages.

20. Forwhatvaluesofk,doesthequadraticequation(4-k)x2+(2k+4)x+8k+1=0haveequalroots?

Teachers Forum -46-

Work Book - Class X

21. Solvethequadraticequation9x2-15x+6=0bythemethodofcompletingthesquare.

22. Solveforx:(x-1)2-5(x-1)-6=0

23. Usingquadraticformula,solvethefollowingquadraticequations:

x2-4ax+4a2-b2=0

Teachers Forum -47-

Work Book - Class X

24. Solveforx: x -1x -2

+x - 3x -4

= 3 13

; x≠2,4

25. Solveforx: 4x-3= 5

2x+3;x≠0,-3

2

26. If-5isarootofthequadraticequation2x2+px-15=0andquadraticequation p (x2+x)+k=0hasequalroots,findthevalueofk.

27. Iftwonumbersaredifferby4andtheirproductos192,findthenumbers.

Teachers Forum -48-

Work Book - Class X

28. Atwodigitnumberisfourtimesthesumof itsdigitsandisalsoequaltotwicetheproductofitsdigits.Findthenumber.

29. Therearethreeconsecutivepositiveintegerssuchthatthesumofthesquaresofthefirstandtheproductoftheothertwois154.Findtheintegers?

30. Solveforx: 1x -3

- 1x +5

= 16

(x≠3,-5)

31. Theproductoftwosuccessivemultiplesof5is300.Determinethemultiples.

Teachers Forum -49-

Work Book - Class X

32. Findthewholenumberwhichwhendecreasedby20isequalto69timesthereciprocalofthenumber.

4 MARKS

33. Astudentscoredatotalof32marksinclasstestinmathematicsandscience.Hadhescored2markslessinscienceand4moreinmathematics,theproductofhismarkswouldhavebeen253.Findhismarksintwosubjects.

34. Ifthepriceofabookisreducedby`5,apersoncanby5morebooksfor`300.Findtheoriginallistpriceofthebook.

Teachers Forum -50-

Work Book - Class X

35. Atakes6dayslessthanthetimetakenbyBtofinishapieceofwork.IfbothAandBtogethercanfinishitin4days,findthetimetakenbyBtofinishthework.

36. Thedifferenceoftwonumbersis5andthedifferenceoftheirreciprocalsis 110

.Findthenumbers.

37. If1isrootoftheequation3x2+ax-2=0andthequadraticequationa(x2+6x)-b=0hasequalroots,findthevalueofaandb.

Teachers Forum -51-

Work Book - Class X

38. Thesumofthesquaresoftwoconsecutivemultiplesof7is637.Findthemultiples.

39. 250applesweredividedequallyamongacertainnumberofstudents.Iftherewere25morestudents,eachwouldhavereceivedhalfapples less.Find thenumberofstudents.

40. Asailorcanrowaboat8kmdownstreamandreturnbacktothestartingpointin1hour40minutes.Ifthespeedofthestreamis2km/hr,findthespeedofboatinstillwater.

Teachers Forum -52-

Work Book - Class X

41. Afasttraintakes3hourslessthanaslowertrainforajourneyof600km.Ifthespeedoftheslowertrainis10km/hlessthanthatofthefasttrain,findthespeedofthetwotrains.


42. Ifax2+bx+c=0hasequalroots,thencisequalto

(a) -b2a

(b) b2a

(c) -b2

4a (d) b

2

4a

43. Inaquadraticequation,sumoftherootsis

(a) coefficientofxcoefficientofx2 (b)- coefficientofx

coefficientofx2

(c) coefficientofx2

coefficientofx (d)- constantterm

coefficientofx

44. Everyquadraticpolynomialcanhaveatthemost

(a) onezero (b)twozeros (c)threezeros(d)noneofthese

45. Therootsofax2+bx+c=0,a≠0arerealandunequal,ifb2-4acis

(a) =0 (b)>0 (c)<0 (d)noneofthese

46. Therootsofax2+bx+c=0,a≠0arereal,ifb2-4acis

(a) =0 (b)≥0 (c)≤0 (d)noneofthese

Teachers Forum -53-

Work Book - Class X

AnSweR Key

1. - 15

, 12

2. ± 4√3 3. -2,1

4. √2√3

, √2√3

5. √25

, √25

6. cb

, -ba

7. 3or- 72 8. 1 ± 3

2 9. k=5,-3

10. roots=56

, p = 2524

11. 4and5 12. a=8

13. k = -152

& m=9 14. Yes 15. 1,-2

16. 2 17. -1± √314

19. 5,30

20. 3,0 21. 1, 23 22. 7,0

23. x = 2a +b, x = 2a-b 24. x = 5, x = 52

25. x=-2,x = 1

26. k = 74 27. 12,16or-12,-16 28. 36

29. 8,9,10 30. -9,7 31.15,20or-15,-20.

32. 23 33. (i)7,25(ii)19,13 34. 20

35.12days 36. 10,5 37. 1,-9

38. 14,21 39. 100 40. 10km/hr

41. 50km/h,40km/h 42. (d) 43. (b)

44. (b) 45. (b) 46. (b)

Teachers Forum -54-

Work Book - Class X

5. ARITHMETIC PROGRESSIONS2 MARKS

1. ThefirstandlasttermofanA.Pare5and45respectively.Ifthesumofallitstermis400,finditscommondifference.

2. IffivetimesthefifthtermofanA.Pisequaltoeighttimesitseighthterm,showthat13thtermiszero.

3. Howmanythreedigitnaturalnumbersaredivisibleby7.

4. Findthevaluesofa,bandcsuchthatthenumbersa,10,b,c,31areinA.P.

Teachers Forum -55-

Work Book - Class X

5. Ifx-2,4x-1and5x+2areinA.Pfindthevalueofx.

6. FindthemiddletermoftheA.P:-11,-7,-3,......,45.

7. TheanglesofaquadrilateralareinA.P,whosecommondifferenceis10o.Finditsfourangles.

8. HowmanytermsofA.P18,16,14..............shouldbetakensothattheirsumiszero.

Teachers Forum -56-

Work Book - Class X

9. Determineksothatk +2,4k -6and3k -2arethethreeconsecutivetermsofanA.P.

10. Determinek sothat4k +8,2k2+3k+6,3k2+4k +4arethethreeconsecutivetermsofanA.P.

11. Writethefirstthreetermsofthesequencean = n2+1.

12. Showthata-b,aanda+baretheconsecutivetermsofanA.P.

Teachers Forum -57-

Work Book - Class X

3 MARKS

13. FindthesumoffirstseventeentermsofanA.Pwhose4thand9thtermsare-15and-30respectively.

14. ThecommondifferenceofanA.Pis-2.Finditssumiffirsttermis100andlasttermis-10.

15. ThesumoffirstntermsofanA.PisgivenbySn = 3n2-4n.DeterminetheA.Pandthe12thterm.

16. Findthe20thtermofanA.Pwhose3rdtermis7andtheseventhtermexceedsthreetimesthe3rdtermby2.

Teachers Forum -58-

Work Book - Class X

17. ThesumofalltermsoftheA.P-4,-1,2,5......,xis437.Findx.

18. Thesumoffirst7termsofanAPis10andthatofnext7termsis17.FindtheA.P.

19. HowmanytermsoftheA.P:9,17,25............mustbetakentogetasumof450?

20. Findthe31sttermofanA.Pwhose11thtermis38and16htermis73.

Teachers Forum -59-

Work Book - Class X

21. The 7thtermofanA.P.is20andits13thtermis32.FindtheA.P.

22. The8thtermofanA.P.is37andits12thtermis57.FindtheA.P

23. IfthesumoffirstntermsofanA.P.isgivenbySn = 4n2-3n,findthenthterm.

24. Ifthesumofn termsofanA.P.isgivenbySn = 2n2+5n,findthenthterm

Teachers Forum -60-

Work Book - Class X

25. The nthterm(tn)ofanA.P.isgivenbytn = 5n -3.Findthesumofthelast20termsoftheA.P.

26. Ifthenth termofanA.P.is2n+1,findthesumofthefirsttwoterms.

27. HowmanytermsoftheA.P.54,51,48,......shouldbetakensothatthesumbe513?

4 MARKS

28. Ifthesumoffirst'm'termsofanA.Pissameasthesumofitsfirstnterms.Showthatthesumofthefirst(m+n)termsiszero.

Teachers Forum -61-

Work Book - Class X

29. FindthenumberoftermsofA.P-12,-9,-6,.....,21.If1isaddedtoeachtermofthisA.P,thenfindthesumofallthetermsoftheA.Pthusobtained.

30. IfSndenotesthesumoffirstntermsofanA.P,provethatS30 = 3(S20-S10)

31. ProvethatnthtermoftermofanA.Pcannotben2+1.Justifyyouranswer.

32. Theratioofthe5thand3rdtermsofanA.Pis2:5.Findtheratioofthe15thand7th terms.

Teachers Forum -62-

Work Book - Class X

33. InanA.P,6thtermishalfthe4thtermand3rdtermis15.Howmanytermsareneededtogiveasumthatisequalto66?

34. ThesumoffirstmtermsofanA.Pis4m2-m.Ifitsnthtermis107,findthevalueofn.Alsofindthe21sttermofthisA.P.

35. Thesumoffirst6termsofanA.Pis42.Theratioof10thtermtoits30thtermis1:3.Calculatethefirsttermand13thtermofA.P.

Teachers Forum -63-

Work Book - Class X

36. Calculatethesumofthefirst24termsofthelistofnumberswhosenthtermis an = 2n+3.

37. IfthefirsttermofanA.P.is2andthesumofthefirstfivetermsisequaltoone-fourthofthesumofthenextfiveterms,findthesumofthefirst30terms.


38. IfthesumofntermsofanA.P.is3n2 -n anditscommondifferenceis6,thenitsfirsttermis

(a) 2 (b)3 (c)1 (d)4

39. If7thand13thtermsofanA.P.are34and64respectively,thenits18thtermis

(a) 87 (b)88 (c)89 (d)90

40. IfthesumofptermsofanA.P.isq andthesumofq termsp,thenthesumofp +q termsis

(a) 0 (b) p - q (c) p+1 (d)-(p + q)

41. Ifthesumofn termsofanA.P.is2n2+5n, then its nthtermis

(a) 4n-3 (b)3n-4 (c)4n+3 (d)3n+4

42. IftheratioofthesumofntermsoftwoA.P.’sis(3n +4):(5n +6),thentheratiooftheir5thtermis

(a) 2131

(b)3141

(c) 3151

(d)1131

Teachers Forum -64-

Work Book - Class X

AnSweR Key

1. 1. 83 3. 128 4. 3,17,24

5. 1 6. 17 7. 75o,85o,-95o,105o

8. 19 9. 3 10. 0,2

11. 2, 5, 6 13. -1363

15. 65

16. 75 17. 50 18. 1, 87

, 97

19. 10 20. 178 21. 8,10,12

22. 2,7,12,.... 23. 8n-1 24. 4n+3

25. 990 26. 8 27. 18or19

29. 12,54 32. 13:1 33. 4or11

34. 14, 163 35. 2, 26 36. 672

37. S30=-2550 38. (a) 39. (c)

40. (d) 41. (c) 42. (c)

Teachers Forum -65-

Work Book - Class X

6. TRIANGLES2 MARKS

1. Averticalpolewhichis2.25mlongcastsa6.75mlongshadowontheground.Atthesametime,avericaltowercastsa90mlongshadowontheground.Findtheheightofthetower.

2. In ∆ABC,DandEarepointsonABandACrespectivelysuchthatDE||BCandAD=x-2,AE=x-1,BD=x+1andCE=x+3.Findx.

A

D E

B C

x-2 x-1

x+1 x+3

3. Ifareasoftwosimilartrianglesareequal,provethattheyarecongruent.

Teachers Forum -66-

Work Book - Class X

4. Inthefigure,ABCandAMParetworighttiangles,rightangledatBandMrespectively.ProvethatCAxMP=PAxBC.

M

C

A BP

5. Inanequilateral∆ABC,ADisdrawnperpendiculartoBCmeetingBCinD.ProvethatAD2 = 3 BD2.

6. Inthefigure,in∆PQR,ST||QRandPSSQ

= 35andPR=28cm.FindPT.

P

S

Q

T

R

Teachers Forum -67-

Work Book - Class X

7. ABCDisarhombus.Provethat4BC2=AC2+BD2.

8. InthefigurefindPK.

24cm

26cmQ R

P

8cm

9. Inthefigure∆ ABC~∆ PQR.Area(∆ ABC)=4area(∆ PQR).IfBC=12cm,findQR.

A

B C

P

Q R

Teachers Forum -68-

Work Book - Class X

10. Twopolesofheights6metresand11metresstandonaplaneground.Ifthedistancebetweentheirfeetis12metres,findthedistancebetweentheirtops.

11. In thegivenfigure, themeasurementsaregiven in centimetres.Find thevalueofy.

A

B CP 4

y

16

3 MARKS

12. Inanequilateral∆ABC,DisapointonsideBCsuchthatBD= 13

BC.Provethat9AD2=7AB2.

Teachers Forum -69-

Work Book - Class X

13. In thegivenfigurePQRS isa rhombussuch thatRQ isproduced toEandSE isjoined.SEandPRintersectatD.ProvethatSD.RE=SR.DE.

P

S RD

Q

E

14. Twoisoscelestriangleshaveequalverticalanglesandtheirareasareintheratio16:25.Findtheratiooftheircorrespondingheights.

15. In ∆PQR,SandTarepointsonsidesPQandPRrespectivelysuchthatPSSQ

= PTTR

and∠PST = ∠PRQ.ProvethatPQRisanisoscelestriangle.

Teachers Forum -70-

Work Book - Class X

16. Ifonediagonalofatrapeziumdividestheotherdiagonalintheratio1:2,provethatoneoftheparallelsidesisdoubletheother.

17. ADisanaltitudeofanequilateral∆ABC.OnADasbase,anotherequilateralADEisconstructed.Provethatar(∆ADE):ar(∆ABC)=3:4.

18. InthefigureABDisatriangleinwhich∠DAB=90oandAC⊥BD.ProvethatAB2=BCxBD.

DC

A B

Teachers Forum -71-

Work Book - Class X

19. Inthefigure∆ABCisrightangledatCandCD= 13

BC.Showthat AB2=AD2+8CD2.

D C

A

B

20. InthefigureAD⊥BCandBD= 13

BC.Provethat2AC2=2AB2+BC2.

A

B CD

21. Inthefigure PAAQ

= PBBR

=3.iftheareaof∆PQRis32cm2,findtheareaofthe

quadrilateralAQRB.

BR

A

P

Q

Teachers Forum -72-

Work Book - Class X

22. IfthediagonalBDofaquadilateralABCDbisectsboth∠Band∠D,showthat ABBC

=ADCD

.

23. InthegivenfigureDE||ACandDC||AP.ProvethatBEEC

=BCCP

.

AD

B E C P

24. ∠Aofanisoscelesof∆ABCisacuteinwhichAB=AC,andBD⊥AC.ProvethatBC2=2ACxCD.

Teachers Forum -73-

Work Book - Class X

25. ABCisatrianglewith∠C=90°and∠AC=√3 BCandDisthemid-pointofAB.Provethat ∠ABC=60°.

26. InaparallelogramABCD,EisanypointonAD,ACandBEintersecteachotheratF.ProvethatBFxFA=EFxFC.

4 MARKS

27. Inthegivenfigure,∆PQRisrightangledatQ.XandYarethepointsonPQandQRsuchthatPX:XQ=1:2andQY:YR=2:1.Provethat9(PY2+XR2) = 13 PR2.

P

RYQ

X

Teachers Forum -74-

Work Book - Class X

28. Inthefigure,in∆ABC,XY||ACandXYdividesthe∆ABCintotworegionssuchthatar(BXY)=2ar(ACYX).Determine AX

AB.

B

CAYX

29. Provethatinarighttriangle,thesquareofthehypotenuseisequaltothesumofthesquaresoftheothertwosides.

30. InthegivenfigureifOE||BCandAD:DB=5:4,find ar(∆DFE)ar(∆CFB)

B C

A

ED

F

Teachers Forum -75-

Work Book - Class X

31. IntrapeziumABCD,AB||DCandDC=2AB.EF||ABwhereEandFlieonBCandAD

respectivelysuchthat BEEC

= 34.DiagonalDBintersectsEFatG.Provethat

7EF=11AB.

32. Inthefigure,ABCisanisoscelestrianglerightangledatB.

TwoequilateraltrianglesareconstructedwithsideBCandAC.Provethatar(∆BCD) = 1

2 ar(∆ACE)

A B

D

E C

33. Inthegivenfigure,l||mandlinesegmentsAB,CDandEFareconcurrentatP.Provethat AE

BF = AC

BD = CE

FD l

AEC

lDFB

P

Teachers Forum -76-

Work Book - Class X

34. Inanisosceles∆ABC,thebaseBCisproducedboththewaystoPandQsuchthatPCxBQ=AC2.Provethat∆PCA∼ ∆ABQ.

35. Inthefigure,∆ABC∼ ∆PQR,ADBC,PS⊥QRandAD:PS=4:9.Find ar(∆ABC)ar(∆PQR)

.

A

B CD

p

Q RS

36. Inthegivenfigure,DandEtrisectBC.Provethat8AE2=3AC2+5AD2.

A

BD E C

Teachers Forum -77-

Work Book - Class X

37. Inarighttriangle,provethatthesquareonthehypotenuseisequaltothesumofthesquaresontheothertwosides.

Usingabove,solvethefollowing:

A

B

C

D

6m

12m

11m

FromtheadjoiningfigurefindthelengthofCA,ifCD⊥DBandAB⊥ DB.

AnSweR Key

1. 30m 2. 5 6. 10.5cm

8. 6cm 9. 6cm 10. 13m

11. 8cm 14. 4:5 21. 14cm2

28.√3-√2

√3 30. 25:81 37. 13m.

Teachers Forum -78-

Work Book - Class X

7. COORDINATE GEOMETRY2 MARKS

1. IfthepointP(x,y)isequidistantfromA(5,1)andB(-1,5),thenprovethat3x=2y.

2. Thepoint(4,2)dividesthelinesegmentjoining(5,-1)and(2,y)intheratio1:2.Findy.

3. If the vertices of∆ABCareA(5, -1), B(-3, -2),C(-1, 8), find the length ofmedianthroughA.

4. IfthepointsA(1,2),B(0,0)andC(a,b)arecollinearthenfindarelationshipbetweenaandb.

Teachers Forum -79-

Work Book - Class X

5. InwhatratioisthelinesegmentjoiningthepointsP(-2,-3)andQ(3,7)dividedbytheY-axis?

6. FindthedistancebetweenthepointsP( sinθ2

,0)andQ(0,cosθ2 ).

7. Findthevaleofkforwhichthepoints(3,2),(4,k)and(5,3)arecollinear.

8. IfthepointP(x, y)isequidistantfromthepointsA(5,1)andB(-1,5),provethat 3x = 2y.

Teachers Forum -80-

Work Book - Class X

9. Showthatthepoints(2,-2),(-3,8)and(-1,4)arecollinear.

10. FindtheareaofthetriangleformedbythepointsA(5,2),B(4,7)andC(7,-9).

11. Ifthepoint(x,2)isequidistantfromthepoints(8,-2),(-2,-2),findthevalueofx.

12. ABisadiameterofacirclewithcentre(1,1).IfAis(4,5),findB.

Teachers Forum -81-

Work Book - Class X

13. If(3,2),(-3,5)and(x, y)arecollinear,showthatx +2y -7=0.

3 MARKS

14. IfthepointsA(-2,1),B(a,b)andC(4,1)arecollinearanda-b=1,findaandb.

15. ThelinesegmentjoiningthepointsA(3,2)abdB(5,1)isdividedbyatthepointPintheratio1:2andPliesontheline3x-18y+k=0,findthevalueofk.

16. FindthevalueofPforwhichthepoints(p+1,2p-2),(p-1,p)and(p-3,2p-6)arecollinear.

Teachers Forum -82-

Work Book - Class X

17. IfthepointsA(-1,-4),B(b,c)andC(5,-1)arecollinearand2b+c=4findthevaluesofbandc.

18. IfthepointsA(x,y),B(a,0),C(0,b)arecollinear,provethat xa+ y

b = 1

19. FindthecoordinatesofthepointswhichdividethelinesegmentjoiningA(-2,2)andB(2,8)intofourequalparts.

Teachers Forum -83-

Work Book - Class X

20. ABCisatriangleandG(4,3)isthecentroidofthetriangle.IfA,BandCarethepoints(1,3),(4,b)and(a,1)respectively,findthevaluesofaandb.AlsofindthelengthofsideBC.

21. Find the ratio inwhich the line segment joiningpoints (a+b,b+a)anda-b, b-a) isdividedbydividedbythepoints(a,b).

22. Usingdistanceformula,showthatthepointsA(-6,0)B(0,5)andC(6,10)arecollinear.

Teachers Forum -84-

Work Book - Class X

23. Findthecoordinatesofthepointswhichtrisectthelinesegmentjoining(1,-2)and (-3,4)

24. If(3,0),(2,a)and(b,6)aretheverticesofa∆ABCwhosecentroidis(2,5)findthevaluesofaandb.

25. Findtheareaofthequadilateral,thecoordinatesofwhosevcerticesare(1,2),(6,2),(5,3)and(3,4)

26. Determine,whether thepoints (-2,1), (2, -2)and (5,2)are theverticesofa righttriangle.

Teachers Forum -85-

Work Book - Class X

27. Iftheverticesofanequilateraltriangleare(0,0)and(3,√3 ),findthethirdvertex.

28. Inwhatratiodoesthex-axisdividethelinesegmentjoiningthepoints(2,-3)and(5,6)?Also,findthecoordinatesofthepointofintersection.

29. Findthecoordinatesofthecentroidofatrianglewhoseverticesare(0,6)(8,12)and(8,0).

30. Inwhatratioisthelinesegmentjoiningthepoints(-2,-3)and(3,7)dividedbythey-axis.Alsofindthecoordinatesofthepointofdivision.

Teachers Forum -86-

Work Book - Class X

31. Determinetheratioinwhichthepoint(-6,9)dividesthejoinofA(-3,-1)andB(-8,9).Alsofindthevalueofa.

32. Determinetheratioinwhichthelinesegmentjoiningthepoints(-3,10)and(6,-8)isdividedby(-1,6)

33. Twoverticesofatriangleare(1,2)and(3,5).Ifthecentroidofthetriangleisattheorigin,findthecoordinatesofthethirdvertex.

34. Ifthepoints(10,5)(8,4)and(6,6)arethemid-pointsofthesidesofatriangle,finditsvertices.

Teachers Forum -87-

Work Book - Class X

4 MARKS

35. ThethreeverticesofaparallelogramABCDareA(3,-4),B(-1,-3)andC(-6,2).FindthecoordinateofvertexDandfindtheareaofABCD.

36. Find theratio inwhich thepointP(x,2)divides the linesegment joining thepointsA(12,5)andB(4,-3).Alsofindx.

37. Provethat thepoints(0,0),(5,5)and(-5,5)aretheverticesofan isoscelesrightangledtriangle.Findthelengthofthehypotenusandalsofinditsarea.

Teachers Forum -88-

Work Book - Class X

38. Thelinesegmentjoining(2,-2)and(-7,4)istrisectedatthepointsPandQ.ifthecoordinatesofPandQare(a,0)and(-4,b)respectively,findthevaluesofaandb.Alsofindthelengthofthelinesegmentjoining(2,-2)and(-7,4).


39. Ifpoints(t,2t),(-2,6)and(3,1)arecollinear,thent=

(a) 34 (b)4

3 (c) 5

3 (d)3

5

40. Ifthedistancebetweenthepoints(4,p)and(1,0)is5,thenp=

(a) ±4 (b)4 (c)-4 (d)0

41. Thelinesegmentjoiningpoints(-3,-4),and(1,-2)isdividedbyy-axisintheratio.

(a) 1:3 (b)2:3 (c)3:1 (d)3:2

42. If(x,2),(-3,-4)and(7,-5)arecollinear,thenx =

(a) 60 (b)63 (c)-63 (d)-60

43. Ifthepoints(k, 2 k), (3k, 3k)and(3,1)arecollinear,thenk =

(a) 13 (b)-1

3 (c) 2

3 (d)-2

3

44. Ifthecentroidofthetriangleformedby(7,x), (y,-6)and(9,10)isat(6,3)

then (x, y) =

(a) (4,5) (b)(5,4) (c)(-5,3) (d)(5,2)

Teachers Forum -89-

Work Book - Class X

AnSweR Key

2. 8 3.√64 units 4. 2a=b

5. 2:2 6. 12

units 7. k = 52

10. 2sq.units 11. x =5 12. (-2,-3)

14. 2,1 15. 19 17. 3,-2

19. (-1, 72 ),(0,5),(1, 13

2 ) 20. 7,5;5units 21. 1:1

23. (-13 ,0) and(-53 ,0). 24. a=9,b=1 25. 112sq.units.

26. yes 27.(0,2√3 or(3,-√3 ) 28. 1:2,(3,0)

29. (2, 23 ) 30. 2:3,(0,1) 31. 3:2,a = 5

32. 2:7 33. (-4,-7)

34. (4,5)(8,7)(1,2,3) 35. (-2,1),15sq.units 36. 3:5,9

37. 10units,25sq.units 39. (b) 40. (a)

41. (c) 42. (c) 43. (b)

44. (d)

Teachers Forum -90-

Work Book - Class X

8. INTRODUCTION TO TRIGONOMETRY2 MARKS

1. Withoutusingtrigonometrictables,provethat

cos2 49o+cos2 41o

sin2 31o+sin2 59o +2tan35o tan 55o = 3.

2. Provethat1+ tan2 θ1+secθ

= secθ.

3. Ifsin3A=cos(A-26o)where3AisanacuteanglefindthevalueofA.

4. IfA,BandCaretheinterioranglesof∆ABC,thusprovethattanA+B2

=cot C2

.

Teachers Forum -91-

Work Book - Class X

5. IfsinA=√3 2,findthevalueof2cot2A-1.

6. If√2 sinθ=1,findthevalueofsec2θ-cosec2θ.

7. Inthefigure,AOBisadiameterofcirclewithcentreO.FindtanA.tanB.

A

C

BO•

8. Evaluate: 6 sin23o+sec79o+3tan48o

cosec11o+3cot42o+6cos67o

Teachers Forum -92-

Work Book - Class X

9. Findthevalueofcos2θof2sin2θ = √3.

10. IftanA= 512

,findthevalueof(sinA+cosA).secA.

11. IftanA= 724

,findthevaluesofsinAandcosA.

12. Ifcosα = 12andtanβ =

1 √3

,findsin(α+β)whereαandβarebothacuteangles.

Teachers Forum -93-

Work Book - Class X

13. Withoutusingtrigonometrictables,provethat:

tan1o. tan 11o . tan21o . tan 69o, tan 79o.tan89o = 1

14. Provethat(tanθ+ 1tanθ )2

= sec2θ+cosec2θ.

15. Evaluatethefollowing:cos70°sin20°

+ cos55°cosec35°tan 5°tan25°tan65°tan85°

16. Showthat tanA(1+tan2A)2

+ cotA(1+cot2A)2

=sinAcosA

Teachers Forum -94-

Work Book - Class X

17. Showthatsec4 θ-sec2 θ = tan4 θ+tan2 θ

18. Showthat sin θ-2sin3θ2cos3 θ -cosθ

= tan θ

19. IfsinA= 35,findcosAandtanA.

20. Provethat:(1+tan2θ)(1-sinθ)(1+sinθ) = 1.

Teachers Forum -95-

Work Book - Class X

21. Ifcosθ = 35,evaluatecosθ +cosecθ.

22. Ifx=45°,verifythat:

(i) sin 3x = 3 sin x-4sin3x

(ii) cos3x=4cos3x-3cosx

23. Evaluate 23(cos430°-sin445°)-3(sin260°-sec245°)+ 1

4cot2 30°.

3 AMRKS

24. Provethat: cot(90o-θ)

tanθ+ cosec(90

o-θ)sinθtan(90o-θ)

= secθ

Teachers Forum -96-

Work Book - Class X

25. Ifcosθ-sinθ = √2 sinθ,provethatcosθ+sinθ = √2cosθ.

26. Verify:√ 1-cosθ1+cosθ = sin θ

1+cosθ,for=60o.

27. Ifsin3θ=cos(θ-60o),findthevalueofθ.

28 Provethat: sinθ-cosθsinθ +cosθ

+ sinθ+cosθsinθ -cosθ

= 22 sin2θ-1

Teachers Forum -97-

Work Book - Class X

29. Findthevalueoftan30ogeometrically.

30. Evaluate:2cos260o+3sec230o-2tan245o

sin230o+cos2 45o.

31. Ifsin(A+B+C)=1,tan(A-B)= 1√3

andsec(A+C)=2,findA,BandC.

32. Showthat 11+sin(90-θ)

+ 11-sin(90-θ)

=2cosec2θ.

Teachers Forum -98-

Work Book - Class X

33. Provethat:(cosecθ-cotθ)2 = 1-cosθ1+cosθ

34. Ifx=bsecθ+atanθandy=btanθ+asecθ.Provethatx2-y2=b2-a2.

35. IfA,B,CareinterioranglesofatriangleABC,provethattanA+B-C2

=cotC.

4 AMRKS

36. If2cosθ-sinθ=andcosθ-3sinθ=y,provethat2x2+y2-2xy=5.

Teachers Forum -99-

Work Book - Class X

37. Provethat:√1+cosA1-cosA =cosecA+cotA.

38. Provethat:sinA(1+tanA)+cosA(1+cotA)=secA+cosecA.

39. Provethat:sin6θ+cos6θ=1-3sin2cos2θ.

40. Provethat: tanθ1-cotθ

+ cotθ1-tanθ

=1+secθ.cosecθ.

Teachers Forum -100-

Work Book - Class X

41. IftanA=√2-1,showthatsinA.cosA=√2 4

42. IftanA=2,evaluatesecA.sinA+tan2A-cosecA.

43. IftanA= 1√3

, ∆ABCisrightangledatB,findthevalueofsinAcosC+cosAsinC.

44. Evaluate:4(sin430o+cos460o)-3(cos2 45o-sin290o)


Work Book - Class X

45. Ifsinθ = c√c2+d2

andd>0,findthevaluesofcosθandtanθ.

46. Iftan= 1√5

.

(i)Evaluate: cosec2θ -sec2θcosec2θ+sec2θ

(ii)Verifytheidentity:sin2θ+cos2θ = 1

47. If15tan2θ+4sec2θ=23,findthevalueof(secθ+cosecθ)2-sin2θ.


Work Book - Class X

48. Provethat: tanθ +sinθtanθ -sinθ

= secθ +1secθ -1

.

49. Provethat:(1+cotA-cosecA)(1+tanA+secA)=2.

50. In∆ABC,rightangledatB,AC-BC=8cmandAB=12cm.FindthevalueofsecC+4cotA.


Work Book - Class X

51. ThealtitudeADofa∆ABC,inwhich∠Aisanobtuse,is10cm.IfBD=10cm,CD=10√3cm,find∠A.

A

B CD

10cm

10cm 10√3cm

52. Evaluate:secθcosec(90o-θ)-tanθ.cot(90o-θ)+sin2 55o+sin2 35o

tan10otan20otan60otan70otan80o

53. Ifsecθ+tanθ = p,showthat p2-1

p2+1 = sin θ.


Work Book - Class X

54. Provethat: cosA1-tanA

- sin2 AcosA-sinA

=sinA+cosA

55. IfcosecA=√2 ,findthevalueof2 sin2 A+3cos2 A4 tan2A-cos2A

.

56. Provethat:tan θ-cotθsin θcos θ

= tan2 θ-cot2 θ.


Work Book - Class X

57. Provethat 1sec θ+tanθ

= sec θ-tanθ.

58. ProvethatsecA(1-sinA)(secA+tanA)=1.


59. Iftan245°-cos230°=xsin45°cos45°,thenxisequalto

(a) 2 (b)-2 (c)-12 (d)1

2

60. Thevalueofcos217°-sin2 73°is

(a) 1 (b)13 (c)0 (d)-1

61. 2tan30°1+tan230°

isequalto

(a)sin60° (b)cos60° (c)tan60° (d)sin30°

62. Thevalueoftan10°tan15°tan75°tan80°is

(a) -1 (b)0 (c)1 (d)noneofthese

63. Thevalueoftan1°tan3°.........tan89°is

(a) 1 (b)-1 (c)0 (d)noneofthese


Work Book - Class X

64. 2tan30°1-tan230°

isequalto

(a) cos60° (b)sin60° (c)tan60° (d)sin30°

65. Iftanθ = 125,thevalueof1+sinθ

1-sinθ is

(a) 5 (b)0 (c)25 (d)-25

66. 9 sec2A-9tan2Aisequalto

(a) 1 (b)9 (c)8 (d)0

67. Ifsinθ+sin2 θ=1,thencos2 θcos4 θisequalto

(a) -1 (b)1 (c)0 (d)Noneofthese

68. IfcosA+cos2A=1,thensin2A+sin4 A

(a) -1 (b)0 (c)1(d)Noneofthese

AnSweR Key

3. 29o 5. - 13 6. 0

7. 1 8. 1 9. 12

10. 1712

11. 725

, 2425

15. 2

19. cosA= 45,tanA= 3

4 21. 37

20 23. 113

24

27. 24o 31. 60o,30o,0o. 46. (i) 23

47. 152 50. 61

5 51. 105o

52. 2

√3 55. 8

7. 59. (a)

60. (c) 61. (a) 62. (c)

63. (a) 64. (c) 65. (c)

66. (b) 67. (b) 68. (c)


Work Book - Class X

9. SOME APPLICATIONS OF TRIGONOMETRY

2 MARKS

1. Findtheangleofdepressionofapointonthegroundatadistanceof10√3 mfromthebaseofthetower,fromthetopofatowerwhoseheightis10m.

2. Theratiooflengthoftheverticallystandingrodtoitsshadowis√3 :1.Findtheangleofelevationofthesun.

3 MARKS

3. Theanglesofelevationofthetopofatowerfromtwopointsatdistances10mand5mfromthebaseofthetowerandinthesamestraightlinewithitarecomplementary.Findtheheightofthetower.


Work Book - Class X

4. Asobservedfromthetopofa60mhighlighthousefromthesea-level,theangleofdepressionoftwoshipsare30oand45o.Ifoneshipisexactlybehindtheotheronthesamesideofthelighthouse,findthedistancebetweenthetwoships.(√3 = 1.732)

5. Amanobserves the angle of elevation of a bird to be30o.He thenwalks 100mtowardsthebirdwhichisstationaryandfindsthattheangleofelevationis60o.Findtheheightatwhichthebirdissitting.(√3 = 1.732)

6. Two ships are approaching a light house from opposite directions. The angle ofdepressionoftwoshipsfromtopofthelighthouseare30oand45o.Ifthedistancebetweentwoshipsis100m,findtheheightofthelighthouse.


Work Book - Class X

7. A1.6mtallgirlstandsatadistanceof3.2mfromalamppostandcastsashadowof4.8montheground.Findtheheightofthelamppost.

8. Twomenstandingonoppositesidesofatowermeasuretheangleofelevationofthetopofthetoweras30oand60orespectively.iftheheightofthetoweris20m,findthedistancebetweenthetwomen.

4 MARKS

9. Theangleofelevationoftopofatowerfromapointonthegroubdis60o.Atapoint40mverticallyabovethefirstpointofobservation,theangleofelevationis30o.Findtheheightoftoweranddistancebetweenthetowerandfirstpointofobservation.


Work Book - Class X

10. There are temples, one on each bank of a river just opposite to each other.Onetempleis50mhight.Fromthetopofthistemple,theanglesofdepressionoftopandfootoftheothertempleare30oand60orespectively.Findthewidthoftheriverandtheheightoftheothertemple.

11. TheangleofelevationofthetopBofatowerABfromapointXonthegroundis60o. AtapointY,40mverticallyaboveX,theangleofelevationis45o.FindtheheightofthetowerABandthedistanceXB.

12. Fromthetopofa15mhighbuilding,theangleofelevationofthetopofatowerisfoundtobe30°.Fromthebottomofthesamebuilding,theangleofelevationofthetopof the tower is found tobe60°.Find theheightof the towerand thedistancebetweenthetowerandbuilding.


Work Book - Class X

13. Fromthe topofa60mhighbuilding, theanglesofdepressionof the topand thebottomofatowerareobservedtobe30°and60°.Findtheheightofthetower.

14. TheangleofelevationofthetopofatowerfromapointAonthegroundis30°.Onmovingadistanceof20metrestowardsthefootofatowertoapointB,theangleofelevationincreasesto60°.FindtheheightofthetoweranddistanceofthetowerfromthepointA.

15. Abirdissittingonthetopofatree,whichis80mhigh.Theangleofelevationofthebirdfromapointonthegroundis45°.Thebirdfliesawayfromthepointofobservationhorizontallyandremainsatconstantheight.After2seconds,theangleofelevationofthebirdfromthepointofobservationchangesto30°.Findthespeedofthebird.


Work Book - Class X

16. TheangleofelevationofajetplanefromapointAonthegroundis60°.Afteraflightof15seconds, theangleofelevationchangesto30°. If the jetplane is flyingataconstantheightof1500√3 m.Findthespeedofthejetplane.

17. Twomenareonoppositesidesofatower.Theymeasuretheangleofelevationofthetopofthetoweras45°and60°respectively.Theheightofthetoweris30m.Findthedistancebetweenthetwomen.

18. Theangleofelevationofthetopofahillfromthefootoftoweris60°andtheangleofelevationofthetopofthetowerfromthefootofthehillis30°.Iftheheightofthetoweris50m,findtheheightofthehill.


Work Book - Class X

19. Anaeroplaneatanaltitudeof200metresobservestheangleofdepressionoftheoppositepointsonthetwobanksofarivertobe45°and60°.Findthewidthoftheriver.

20. Anaeroplaneflyinghorizontallyataheightof2500mabovethegroundisobservedatanangleofelevationof60°.Ifaftertheflightof15seconds,theangleofelevationisobservedtobe30°,findthespeedoftheaeroplaneinkm/h.

21. Thelengthoftheshadowofa6mtallflagstaffplacedontopofatoweris2√3 malongtheground.Whatangledoesthesunmakewithground?


Work Book - Class X


22. Theangleofelevationofthesun(sun’saltitude)whenthelengthofashadowofaverticalpoleisequaltoitsheightis

(a) 30° (b)45° (c)60° (d)90°

23. Thetopsoftwopolesofheight20mand14mareconnectedbyawire.Ifthewiremakesandangleof30°withhorizontal,thenthelengthofthewireis

(a) 12m (b)10m (c)8m (d)6m

24. Fromthetopofa25mhighdiff,theangleofelevationofatowerisfoundtobeequaltotheangleofdepressionofthefootofthetower.Theheightofthetoweris

(a) 25m (b)50m (c)75m (d)100m

AnSweR Key

1. 30o 2. 60o 3. 5√2 m

4. 43.92m 5. 86.6m 6. 36.6m

7. 2.67m 8. 80√33

m 9. 60m,40√3 m

10. 50√3√3

m,33.33m 11. 20(√3 +3)m,40(1+√3 )m

12. Height=22.5m,distance=12.975m 13. 40m.

14. 17.32m,30m 15. 29.28m/s 16. 720km/h

17. 47.3m 18. 150m 19. 315.4metres

20. 400√3 km/h 21. 60° 22. (b)

23. (a) 24. (b)


Work Book - Class X

10. CIRCLES2 MARKS

1. Inthegivenfigure,PQisdiameterandPTisatangentofthecirclewithcentreO. If∠QOS=150o,find∠PTS.

Q

O

T

SP

2. Provethattangentsdrawnfromanexternalpointareequallyinclinedtolinejoiningtheexternalpointandthecentre.

3. IfintheisoscelstiangleABC,AB=AC,showthatBF=FC.

A

GE

BF C


Work Book - Class X

4. PQisatangentatapointRofthecirclewithcentreO.If∠TRQ=30o,findthemeasureof∠RTS.

•

P QR

SO

T30o

5. ThelengthofatangentfromapointAatadistance5cmfromthecentreofcircleis4cm.Findthediameterofthecircle.

6. ABisachordofcirclewithcentreO.AtB,tangentPBisdrawnsuchthatitslengthis24cm.ThedistanceofPfromthecentreis26cm.IfchordABis16cmfinditsdistancefromthecentre.


Work Book - Class X

7. AtangentPQatapointPtoacircleofradius5cmmeetsinalinethroughthecentreOatapointQsuchthatOQ=13cm.FindthelengthofPQ.

8. IfPAandPBaretangentsfromanoutsidepointP,suchthatPA=10cmand∠APB=60°,findthelengthofchordAB.

9. ApointAis13cmfarfromthecentreofacircle.ThelengthofthetangentdrawnfromAtothecircleis12cm.Findtheradiusofthecircle.

3 MARKS

10. IntriangleABC,AB=AC.IftheincircleofABCtowardsthesidesAB,BCandCAatD,E,Frespectively.ProvethatEbisectsBC.


Work Book - Class X

11. Twoconcentriccirclesareofradii6.5cmand2.5cm.Findthelengthofchordofthelargercirclewhichistangenttothesmallercircle.

12. InthegivenfigureABisatangenttoacirclewithcentreO.Provethat∠BPQ=∠PRQ.If∠BPQ=60o,find∠RPQ.

•O

R

Q

PA B

13. Inthefigure,PQisachordoflength8cmofacircleofradius5cm.ThetangentsatpointsPandQintersectatpointT.FindthelengthoftangentTP.

O

P Q

T


Work Book - Class X

14. ApointPis26cmawayfromthecentreOofacircleandthelengthPTofthetangentdrawnfromPtothecircleis10cm.Findtheradiusofthecircle.

15. AcircletouchesallthefoursidesofaquadilateralABCD.Provethat:

AB+CD=BC+DA

16. ABCisarigthtriangle,right-angledatBsuchthatBC=6cmandAB=8cm.Findtheradiusofitsincircle.


Work Book - Class X

4 MARKS

17. Provethatthelengthoftangentstoacirclefromanexternalpointareequal.

18. TwocircleswithcentresOandO|toucheseachotherexternallyatTasshowninthefigure.IfPR=12cm,PO=13cm,O|Q=5cmandSQ=3cm,findthelengthofthelinesegmentPQ.

PO O|

T Q5cm13cm3cm

12cmR

S

• •

19. Inthe figure,∆ABC isdrawn to cirumscribeacircleof radius4 cm, such that thesegmentsBDandDCareoflengths8cmand6cmrespectively.FindABandAC.

A

BD C

O•

8cm 6cm


Work Book - Class X

20. In the figure, XY andX|Y| are two parallel tangents to a circlewith centreO andanother tangentABat thepointofcontactC is intersectingXYatAandX|Y| at B. Provethat∠AOB=90o.

APX Y

O

X|Q B Y|

AnSweR Key

1. 60o 4. 60o 5. 6cm

6. 6cm 7. 12cm 8. 10cm

9. 5cm 11. 12cm 12. 30o

13. 203cm 14. 24cm 16. r=2cm

18. 27cm 19. 15cm,13cm


Work Book - Class X

11. CONSTRUCTIONS1. Construct∆ABCsimilartogivenisoscelestrianglePQRwithQR=5cm,

PR=PQ=6cmandeachofitssidesis34

thofcorrespondingsidesofthe∆ PQR.

2. Dividealinesegmentoflength12cmintheratio7:3.

3. Dividelinesegmentoflength14cmintheratio2:5.Also,justifyyourconstruction.


Work Book - Class X

4. Constructatrianglesimilartoagiven∆ABCsuchthateachofitssidesis(23 )rdofthe

correspondingsidesof∆ABC.ItisgiventhatBC=6cm,∠B=50°and∠C=60°.

5 DrawarighttriangleABCinwhichAC=AB=4.5cmand∠A=90°.Drawatriangle

similarto∆ABCwithitssidesequalto(54 )th

ofthecorrespondingsidesof∆ABC.

6. Drawtwotangentstoacircleofradius3.5cmfromapointPatadistanceof5.5cmfromitscentre.Measurethelengthsofthetangents.


Work Book - Class X

12. AREAS RELATED TO CIRCLES2 MARKS

1. Thecircumferencesof twoconcentriccirclesformingaringare88cmand66cm.Findthewidthofthering.[usep = 22

7]

2. Abicyclewheelofradius35cmismaking25revolutionsin10seconds.Atwhatspeed(inkm/h)isthebicyclemoving?

3. Abicyclewheelmakes5000revolutionsinmoving22km.Findthediameterofthewheel.[usep = 22

7]


Work Book - Class X

4. Thelengthofanarcofacircleofradius12cmis10pcm.Findthecentralangleofthisarc.

5. Iftheareaofasectorofacircleis 518

th oftheareaofthatcircle,thenfindthecentralangleofthesector.

3 MARKS

6. Inthefigure,asquareOABCofside20cmisinscribedinaquadrantOPBQ.Findtheareaofshadedregion.

P

QB

O A

C

20cm

20cm


Work Book - Class X

7. In the given figure, a trapezium shaded wall of a 20 m high bridge displays anadvertisement in theformof twosectorsofangle30oeachandradius12meach.Findtheareaofshadedportion.

30o 30o

50m

20m

70m

8. Afarmerhasacircularfieldofradius120m.Ithasawellinthemiddleofthefiledofradius8metres.Howmuchareashasheforgrowinghiscrops?

9. FindtheareaofthesegmentboundedbyachordABandthearcACBofthecirclewithcentreOhavingradius7cmandsectorangleequalto90o,asshowninthegivenfigure.

A

B

O

C•


Work Book - Class X

10. Atableinarestauranthasatopoftheshapeasshowninthefigure,where∠AOD=120oandOA=OB=OC=OD=60cm.Findtheperimeterofthetopofthetable.(Takep = 3.14)

A

BO

120o

120o

D

C

11. Findtheareaofasemicircularparkwhoseperimeteris360m.[usep = 227

]

12. AchordABofacircleofradius14cmmakesanangleof60°atthecentreofthecircle.

Findtheareaoftheminorsegmentofthecircle.(Use p = 227 )


Work Book - Class X

13. Asquareparkhaseachsideof100m.Ateachcornerofthepark,thereisaflowerbedintheformofaquadrantofradius14masshowninthefigure.Findtheareaof

theremainingpark.(Use p = 227 ).

14m

14m 14m

14m

100m

14. Inthegivenfigure,findtheareaoftheshadedregion.[Usep = 3.14)

8cm6cm

A B

D C

15. Fourequalcircles,eachofradius5cm,toucheachotherasshowninthefigure.Findtheareaincludedbetweenthem.[Usep = 3.14)

5cm 5cm

5cm5cm


Work Book - Class X

16. Theperimeterofasectorofacircleofradius5.2cmis16.4cm.Findtheareaofthesector.[Usep = 3.14]

17. Findtheareaofthesectorofacirclewithradius4cmandangle30°.Also,findtheareaofthecorrespondingmajorsector.[Usep = 3.14]

18. Inanequilateraltriangleofside24cm,acircleisinscribedtouchingitssides.Findtheareaoftheremainingportionofthetriangle.[use√3 = 1.732]


Work Book - Class X

4 MARKS

19. Arectangularparkisofdimensions100mx50m.Itissurroundedbysemi-circularflowerbedsallround.Findthecostoflevellingthesemi-circularbedsat`0.75persquaremetre.(Usep = 3.14)

20. Theareaofacircleis78.5sq.cm.Calculatethecircumferenceofthecircle.(take p = 3.14)

21. Theareaenclosedbetweentwoconcentriccirclesis770cm2.Iftheradiusoftheoutercircleis21cm,findtheradiusoftheinnercircle.


Work Book - Class X


22. Inacircleofradius21cm,anarcsubtendsanangleof60°atthecentre.Thelengthofthearcis

(a) 20cm (b)22cm (c)24cm (d)26cm

23. Amanrunsaroundacircleoftheradius50mataspeedof12km/h.Thetimetakenbyhimforgoiningaroundtentimesis

(a) 10min42s (b)12min35s (c)15min42s(d)10min35s

24. Apathofwidth7mrunsaroundoutsideacircularparkwhoseradiusis18m.Theareaofthepathis

(a) 948m2 (b)960m2 (c)942m2 (d)946m2

25. The areas of the two circles are in the ratio of 4 : 9. The ratio between theircircumferencesis

(a) 1:2 (b)2:3 (c)3:4 (d)4:5

26. Theradiusofacircularfieldis35metres.Howmanyroundsshouldbetakenaroundthefieldsoastocoveradistanceof1540metres?

(a) 7 (b)8 (c)9 (d)10

27. Iftheperimeterofasemicircularprotractoris36m,itsdiameteris

(a) 10cm (b)12cm (c)15cm (d)14cm

AnSweR Key

1. 3.5cm 2. 19.8km/h 3. 1.4m

4. 150o 5. 100o 6.228cm2

7. 1124 47m2 8. 45056m2 9. 14cm2

10. 62.8cm 11. 7700m2 12. 17.80cm2

13. 9384m2 14.30.50cm2 15.21.5cm2

16. 15.6cm2 17. 46.05cm2 18. 98.55cm2

19. `7359.375 20. 141.3cm 21. 14cm

22. (c) 23. (c) 24. (d)

25. (b) 26. (a) 27. (d)


Work Book - Class X

13. SURFACE AREAS AND VOLUMES2 MARKS

1. Howmany lead shots, each 0.3 cm in diameter, can be made from a cuboid ofdimensions9cmx11cmx12cm?[usep = 22

7]

2. Thematerialofaconeisconvertedintotheshapeofacylinderofequalradius.Iftheheightofthecylinderis5cm,findtheheightofthecone.

3. Gayatriwasmakingamathematicalmodel,inwhichsheplaced4cubeseachofedge20cmoneaboveanother.Findthesurfaceareaoftheresultingcuboid.

4. A5cmwideclothisusedtomakeaconicaltentofbasediameter14mandheight24m.Findthecostofclothusedattherateof`25permeter.


Work Book - Class X

5. Asphereofmaximumvolumeiscutoutfromasolidhemisphereofradius6cm.Findthevolumeofthecutoutsphere.

6. Acylinderandaconehavebaderadii5cmand3cmrespectivelyandtheirrespectiveheightsare4cmand8cm.Findtheratiooftheirvolumes.

3 MARKS

7. Solidsheresofdiameter6cmeacharedroppedintoacylindericalbeakercontainingsomewarerandarefullysubmerged.Ifthediameterofthebeakeris18cmandthewaterrisesby40cminthebeaker,findthenumberofsolidspheresdroppedinthewater.

8. Asphereofdiameter6cmisdeoppedinarightcircularcylindericalvesselpartlyfilledwithwater.Thediameterofthecylindricalvesselis12cm.Ifthesphereisexactlyhalfsubmergedinwater,byhowmuchwillthelevelofwaterriseinthecylindricalvessel.


Work Book - Class X

9. Acylindricaltankhasacapacityof6160m3.Diameterofitsbaseis28m.Findthecurvedsurfaceareaofthiscylindricaltank.

10. Usingpapermache,astudentmadearightcircularhollowconeofheight15cmandradiusofbase8cm.Hethenhastopaintthisconefromoutsideandinsideboth.Whatisthetotalsurfaceareathathastobepainted?

11. Agirlemptiesacylindricalbucket,fullofsand,ofbaseradius18cmandheight32cm,onthefloortoformaconicalheapofsand.Iftheheightofthisconicalheapis24cm,thenfinditsslantheightcorrectuptooneplaceofdecimal.


Work Book - Class X

12. Thelargestpossibleshpereiscarvedoutofawoodebsolidcubeofside7cm.Findthevolumeofwoodleft.

13. Thecircumferenceofthebaseofaconicaltentis44m.Iftheheightoftentis24m,findthelengthofthecanvasusedinmakingthetent,ifthewidthofthecanvasis2m.

[Usep = 227

]

14. A solidmetallic sphere of diameter 16 cm ismelted and recast into a number ofsmallerconeseachofradius4cmandheight8cm.Findthenumberofconessoformed.


Work Book - Class X

15. Waterisflowingat47m/sthroughacircularpipeofinternaldiameterof2cmintoacylindricaltank,theradiusofwhosebaseis40cm.Findtheincreaseinwaterlevelin30minutes.

16. Asolidsphereofradius3cmismeltedandthenrecastintosmallsphericalballseachofdiameter0.6cm.Findthenumberofballsthusobtained.

17. Howmany spherical lead shots each 4.2 cm in diameter can be obtained froma

rectangularsolidofleadwithdimensions66cm,42cm,21cm.(use p = 227 ).


Work Book - Class X

18. Waterisflowingattherateof7metrespersecondthroughacircularpipeofinternal

diameter2cmintoacylindricaltankwhoseradiusofbaseis40cm.Determinethe

increaseinthewaterlevelin 12hour.

19. Arectangularwatertankofbase11mx6mcontainswateruptoaheightof5m.Ifthe

waterinthetankistransferredintoacylindricaltankofbaseradius3.5m,findhow

highwillthewaterlevelbeinthecylindricaltank(use p = 227 ).

20. Theinteriorofabuildingisintheformofarightcircularcylinderofdiameter4.2mandheight4msurmountedbyacone.Theverticalheightoftheconesis2.1m.Findthe

outersurfaceareaandvolumeofthebuilding.(use p = 227 ).


Work Book - Class X

21. Avessel is in the formofahemisphericalbowlmountedbyahollowcylinder.Thediameterofthesphereis14cmandthetotalheightofthevesselis13cm.Finditscapacity.

22. Atoyisintheformofacornmountedonahemisphereofradius1.75cm.Ifthetotalheightofthetoyis7.75cm,findthetotalsurfaceareaofthetoy.

23. Ametallicsphereofradius10.5cmismeltedandthusrecastintosmallcones,eachofradius3.5cmandheight3cm.Findthenumberofconessoobtained.


Work Book - Class X

4 MARKS

24. Ifh,candVrespectivelyrepresenttheheight,curvedsurfaceareaandvolumeofa

cone,provethatC2 = 3pVh3+9V2

h2 .

25. Theperimeteroftheendsofafrustumofarightcircularconeare44cmand33cm.Iftheheightoffrustumis16cm,finditsvolumeandtotalsurfacearea.

26. Ahemisphericaldepressioniscutfromonefaceofacubicalblock,suchthatdiameter'l'ofhemisphericalisequaltotheedgeofcube.Findthesurfaceareaoftheremainingsolid.


Work Book - Class X

27. Waterinacanal6mwideand1.5mdeepisflowingwithaspeedof10km/h.Howmuchareainhectareswillitirrigatein30minutesif8cmofstandingwaterisneeded?

28. Waterisflowingattherateof15km/hrthroughacylindricalpipeofdiameter14cmintoacuboidalpondwhichis50mlongand44mwide.Inwhattimethelevelofwaterinpondriseby21cm?

29. Theradiiofthecircularendsofafrustumofconeofheight6cmare14cmand6cmrespectively.Findthelateralsurfaceareaandtotalsurfaceareaofthefrustum.


Work Book - Class X

30. Iftheradiiofthecircularendsofaconicalbucketofheight45cmare28cmand7cm,findthecapacityofthebucket.

31. A12mdeepwellwithdiameter3.5misdugoutandtheearthfromitisspreadevenlytoformaplatformof10.5mx8.8m.Determinetheheightoftheplatform.

32. Iftheradiiofthecircularendsofaconicalbucketofheight45cmare28cmand

7cm,findthecapacity ofthebucket.(use p = 227 ).


Work Book - Class X

33. Iftheradiiofthecircularendsofadrinkingglasswhichisintheshapeofafrustumofaconeare2cmand1cmandtheheightisof14cm,findthecapacityoftheglass.

34. Abucketmadeofaluminiumsheetofheight20cmand itsupperand lowerendsareofradii25cmand10cmrespectively.Findthecostofmakingthebucketifthealuminiumsheetcosts`70per100cm2.

35. Avesselisintheformofaninvertedcone.Itsheightis8cmandtheradiusofitstopwhichisopenis5cm.Itisfilledwithwateruptotherim.Whenledshots,eachofwhichissphereofradius0.5cm,aredroppedintothevessel,onefourthofwaterflowsout.Findthenumberofledshotsdropedinthevessel.


Work Book - Class X

36. Thedifferencebetweenoutsideandinsidesurfaceareasofcylindricalmetallicpipeof14cmlongis44cm2.Ifthepipeismadeof99cm3ofmetal,findtheouterandinnerradiiofthepipe.


37. Thediameterofasphereis6cm.Itismeltedanddrawnintoawireofdiameter2mm.

Thelengthofthewireis

(a) 12m (b)18m (c)36m (d)66m

38. Thenumberofsolidsphere,eachofdiameter6cmthatcouldbemouldedtoforma

solidmetalcylinderofheight45cmanddiameter4cm,is

(a) 3 (b)4 (c)5 (d)6

39. Acircustentiscylindricaltoaheightof4mandconicalaboveit.Ifitsdiameteris105

manditsslantheightis40m,thetotalareaofthecanvasrequiredinm2 is

(a) 1760 (b)2640 (c)3930 (d)7920

40. Iftheareaofthesurfaceofasphereis4pcm2,thediameterofthespherewillbe

(a) 1cm (b)2cm (c)6cm (d)5cm


Work Book - Class X

AnSweR Key

1.84000 2.15cm 3. 7200cm2

4. 110m 5. 113.14cm3 6. 25:6

7. 90 8. 0.5cm 9. 880m2

10. 854.08cm2 11. 43.2cm 12.163.4cu.cm

13. 275m 14. 16 15. 31.5m

16. 1000 17. 1500 18. 787.5cm

19. 8.6metres 20. 72.40m2,65.142m3 21. 1642.66cm3

22. 53.625cm2 23. 126 25. 1899cm3

26. 14(24+p)l2units 27. 56.25hectares 28. 2hrs

29. 7920cm2 30. 48510cm3 31. 1.25m

32. 48510cm3. 33. 102.66cm3 34. ` 2143.05

35. 100 36. 52cm,2cm 37. (c)

38. (c) 39. (d) 40. (b)


Work Book - Class X

14. STATISTICS2 MARKS

1. Calculatethemodeofthefollowingdata:

Class 1-4 4-7 7-10 10-13Frequency 6 12 26 20

2. Findthemissingvaluesfora,b,canddinthefollowingdata:

Class 0-8 8-16 16-24 24-32 32-40 40-48Frequency 15 a b 18 9 cC. f 15 28 43 61 d 80

3. Findthedifferenceoftheupper limitofthemedianclassandthelower limitofthemodalclassofthefollowingdata:

Class 65-85 85-105 105-125 125-145 145-165 165-185 185-205Frequency 4 5 13 20 14 7 5


Work Book - Class X

4. Writetherelationshipconnectingthreemeasuresofcentraltendencies.Hencefindthemedianofthegivendataifmodeis24.5andmeanis29.75.

5. Findthemodeofthefollowingdistribution.

Marks 10-20 20-30 30-40 40-50 50-60No.ofstudents 15 30 45 12 18

6. Themedianofthefollowingobservationsgiveninorder16,18,20,24-x,22+2x,28,30,32is24.Findthevalueofx.


Work Book - Class X

7. Findthemodalheightofthefollowingfrequencydistribution.

Heights(incm) 135-140 140-145 145-150 150-155 155-160No.ofpersons 4 9 12 10 7

8. Inafrequencydistribution,ifa=assumedmean=25,∑ƒi=50and∑ƒi di=-50,thenfindthemeanofthedistribution.

9. Acompanymarketsaparticularbrandofelectricalfans.Thelifeoffans(inmonths)isgiveninthefollowingdistribution.Determinethemodalageoffans.

Age(inmonths) 0-6 6-12 12-18 18-24 24-30 30-36 36-42 42-48

No.offans 15 20 25 40 32 18 20 11


Work Book - Class X

3 MARKS

10. Data regarding height of students of class X ofmodel school, Dehradun is givenbelow.Calculatetheaverageheightofstudentsoftheclass.

Height(incm) 150-156 156-162 162-168 168-174 174-180No.ofstudents 4 7 15 8 6

11. Inastudyonasthmaticpatients,thefollowingfrequencydistributionwasobtained.Findtheaverage(mean)ageatthedetection.

Ageatdetection(inyears) 0-9 10-19 20-29 30-39 40-49

No.ofpatients 12 25 13 10 5


Work Book - Class X

12. The following frequency distribution shows the number of runs scored by somebatsmanofIndiainone-daycricketmatches.

Runsscored 2000-4000 4000-6000 6000-8000 8000-10000 10000-12000No.ofbatsman 9 8 10 2 1

Findthemodefortheabovedatafrequencydistribution.

13. Drawa‘lessthantype’ogiveforthedata.

Class 15-20 20-25 25-30 30-35 35-40 40-49Frequency 13 18 31 25 15 5

14. Heightof50girlsofclassXofaschoolarerecordedasfollows:

Height(incm) 135-140 140-145 145-150 150-155 155-160 160-165No.ofgirls 5 8 9 12 14 2

Drawa‘morethantype’ogivefortheabovedata.


Work Book - Class X

15. Ifthemeanofthefollowingdatais44,findthemissingfrequency(x).

Class 0-20 20-40 40-60 60-80 80-100Frequency 12 x 6 7 9

16. Findthemeanofthefollowingfrequencydistribution. Class interval Frequency

0-10 710-20 520-30 630-40 1240-50 850-60 2

17. Ifthearithmeticmeanofthefollowingfrequencydistributionis53,findthevaluep. Classinterval 0-20 20-40 40-60 60-80 80-100Frequency 12 15 32 p 13


Work Book - Class X

18. Calculatethemedianfromthefollowingdata:Class 0-10 10-20 20-30 30-40 40-50

Frequency 5 25 25 18 7

19. Ifthemedianofthegivenincompletedistributionis35andsumoftheallfrequenciesis170,findthemissingterms.

Variable 0-10 10-20 20-30 30-40 40-50 50-60 60-70Frequency 10 20 x 40 y 25 15

20. Findthemodeofthefollowingdistributions: Class 25-30 30-35 35-40 40-45 45-50 50-55

Frequency 25 34 50 42 38 14


Work Book - Class X

4 MARKS

21. Findthemean,medianandmodeofthefollowingdata:

Class 0-20 20-40 40-60 60-80 80-100 100-120 120-140Frequency 6 8 10 12 6 5 3

22. Convertthefollowingdataintoalessthantypedistributionanddrawitsogive.Alsofixedthemedianfromthegraph.

ClassInterval 100-120 120-140 140-160 160-180 180-200Frequency 12 14 8 6 10

23. Findthevaluesofxandyifthemedianforthefollowingdatais31.

Class 0-10 10-20 20-30 30-40 40-50 50-60 TotalFrequency 5 x 6 y 6 5 40


Work Book - Class X

24. Thefollowingdistributiongivestheannualprofitearnedby30shopsofashoppingcomplex.

Profit(inlakh) 0-5 5-10 10-15 15-20 20-25No.ofshops 3 14 5 6 2

Changetheabovedistributiontomorethantypedistributionanddrawitsogive.

25. Changethefollowingfrequencydistributiontolessthantypedistributionanddrawitsogive.Henceobtainthemedianvalue.

Class 0-10 10-20 20-30 30-40 40-50 50-60Frequency 2 5 7 12 8 6


Work Book - Class X

26. Thefollowingdistributiongivesthedailywagesof50workersofafactory.

Dailywages(in Rs.) 20-40 40-60 60-80 80-100 100-120 120-140 140-160

No.ofworkers 4 6 10 16 12 7 3

Converttheabovedistributiontoalessthantypecumulativefrequencydistribution.Drawitsogiveandfindthemedian.

27. Changethegivendistributiontomorethantypedistributionanddrawitsogive.

Classes 20-25 25-30 30-35 35-40 40-45 45-50Frequency 3 6 12 9 6 4


Work Book - Class X

28. Themedianofthefollowingdatais525.Findthevaluesofxandyifthetotalfrequencyis100.

C I Frequency0-100 2100-200 5200-300 x300-400 12400-500 17500-600 20600-700 y700-800 9800-900 7900-1000 4

29. Draw'lessthanogive'and'morethanogive'forthefollowingdistributionandhencefinditsmedian:

Class 20-30 30-40 40-50 50-60 60-70 70-80 80-90Frequency 10 8 12 24 6 25 15


Work Book - Class X

30. Drawmorethanogiveforthefollowingdistributionandhavefindthemedian.

Classes 0-10 10-20 20-30 30-40 40-50Frequency 10 18 40 20 12

31. Inaclasstest,marksobtainedbythestudents(outof90)areasfollows:

Marks 0-15 15-30 30-45 45-60 60-75 75-90No.ofstudents 5 12 28 x 35 y

Ifthemodeofthedatais63,findthemissingfrequencies,whenitisgiventhatsumoffrequenciesis125.


Work Book - Class X

32. IfthemedianI.Qofthestudentsis135,findthemissingfrequenciesf1andf2 in the followingfrequencydistributionfor220students.

I.Q 100-110

110-120

120-130

130-140

140-150

150-160

160-170

170-180

No.ofstudents 15 35 f1 f2 33 23 19 8

33 Followingtableshowsmarks(outof100)ofstudentsinaclasstest.

Marks no. of studentsMorethanorequalto0 80Morethanorequalto10 77Morethanorequalto20 72Morethanorequalto30 65Morethanorequalto40 55Morethanorequalto50 43Morethanorequalto60 28Morethanorequalto70 16Morethanorequalto80 10Morethanorequalto90 8Morethanorequalto100 0

Draw‘morethantypeogive’.Fromthecurve,findthemedian.Alsocheckmedianbyactualcalculations.


Work Book - Class X

34. Considerthefollowingdistributionofdailywagesofworkersinacompany:

Dailywages 400-500

500-600

600-700

700-800

800-900

900-1000

1000-1100

1100-1200

No.ofworkers 10 15 11 12 13 18 6 4

Darwa‘lessthantype’ogiveand‘morethantype’ogivefortheabovedata.


Work Book - Class X

35. Drawa ‘less than’and ‘more than’ogive for the followingdistributionon thesamegraph:

Marks 30-39 40-49 50-59 60-69 70-79 80-89 90-99No.ofstudents 14 6 10 20 30 8 12

36. Drawa‘lessthan’ogiveforthefollowingdistributionofmarkssecuredbystudentsofaclass:

Marks 0-10 10-20 20-30 30-40 40-50 50-60No.ofstudents 5 8 10 9 6 7


Work Book - Class X

37. Determinethemedianmarksgraphicallyfromthefollowingdata: Marks 50-55 55-60 60-65 65-70 70-75 75-80 80-85

No.ofstudents 6 10 22 30 16 12 15

38. Themeanof the following frequency table is50.But the frequencies f1 and f2 aremissing.Findthemissingfrequencis.

Class 0-20 20-40 40-60 60-80 80-100 TotalFrequency 17 f1 32 f2 19 120


Work Book - Class X

39. Ifthemedianofthefollowingdistributionis28.5,findthevaluesofxandy. Classinterval 0-10 10-20 20-30 30-40 40-50 50-60 TotalNo.ofstudents 5 x 20 15 y 5 60

40. Computethemodeforthefollowingfrequencydistribution: Variable 0-4 4-8 8-12 12-16 16-20 20-24 24-28 28-32 32-36 36-40Frequency 5 7 9 17 12 10 6 3 2 0


Work Book - Class X

41. Themedianoffollowingdatais16.Findthemissingfrequenciesaandbifthetotalofallfrequencies is42.

Classes 0-5 5-10 10-15 15-20 20-25 25-30 30-35 35-40Frequencies 12 a 12 15 b 6 6 4


42. Whichofthefollowingisnotameasureofcentraltendency?

(a) Mean (b)Median (c)Mode (d)standarddeviation

43. Forafrequencydistribution,mean,medianandmodeareconnectedbytherelation

(a) Mode=2Median-3Mean (b)Mode=2Median+3Mean

(c) Mode=3Median-2Mean (d)Mode=3Median+2Mean

44. Modeis

(a) lkeastfrequentvalue (b)middlemostfrequentvalue

(c) mostfrequentvalue (d)noneofthese

45. Whichofthefollowingcannotbedetermindgraphically?

(a) Mean (b)Median (c)Mode (d) None ofthese

46. Theaverageof11resultsis50.Iftheaverageofthefirstsixresultsis49andthatofthelastsixis52,thenthesixthresultis

(a) 53 (b)54 (c)55 (d)56


Work Book - Class X

AnSweR Key

1. 9.1 2. 13,15,10,70 3. 20

4. 28 5. 33.125 6. 2

7. 148 16. 28.75 17. p =28

18. 24 19. 35,25 20. 38.33

21. 62.4, 65, 61.67 22. ` 138.5 23. 8,10

24. 7.5 25. 35 26. 91

28. 9,15 29. 60 30. 25

38. f1=28,f2 = 24 39. x=8,y =7 40. 32.66

42. (d) 43. (c) 44. (c)

45. (a) 46. (d)


Work Book - Class X

15. PROBABILITY2 MARKS

1. Ajigsawpuzzleiscomposedoffiverectangularpieces,threecircularpiecesandfivetriangularpieces. Ifonepieceof thepuzzle is lost,findtheprobability that the lostpieceisacircularone.

2. Abagcontains18balls,outofwhichxballsareredandrestarewhite.Ifoneballisdrawnatrandom,

(a) Whatistheprobabilitythatitisaredball?

(b) Howmanywhiteballsarethere,ifprobabilityofdrawingawhiteballis 13?

3. Twodifferentdicearerolledtogether.Findtheprobabilitythat

(i) Numberoneachdieiseven.

(ii) Sumofnumberappearingontwodiceis5.


Work Book - Class X

4. Abagcontainscardsbearingnumbersfrom11to30.Acardistakenoutfromthebagatrandom.Findtheprobabilitythattheselectedcardhasmultipleof5onit.

5. Adieistossedonce.Findtheprobabilityofgettinganevennumberoramultipleof3.

6. Twodicearethrowntogether.Whatistheprobabilityofgettingadoublet?


Work Book - Class X

7. Findtheprobabitlythataleapyearselectedatrandomwillcontain53sundays.

8. Ticketsnumberedfrom1to20aremixeduptogetherandthenaticketisdrawnatrandom.Whatistheprobabilitythatthetickethasanumberwhichismultipleof3or7?

9. Abagcontains12balls,outofwhichxarewhite.Ifoneballisdrawnatrandom,whatistheprobabilitythatwillbeawhiteball?

10. Inalottery,thereare10prizesand25blanks.Findtheprobabilityofgettingaprize.


Work Book - Class X

11. Theprobabilitythatitwillraintomorrowis0.85.Findtheprobabilitythatitwillnotraintomorrow.

3 MARKS

12. Twocoinsaretossedsimultaneously.Findtheprobabilityofgetting:

(i) Atleastonehead.

(ii) Atmosttwotails.

13. Adieisthrownonce.Findtheprobabilityofgetting:

(A) Anevennumber

(B) Anumbergreaterthan3.

(C) Anumberbetween3and6.

(D) Anumberbetween3and6.

14. Abagcontainscardsnumbered1to49.Findtheprobabilitythatthenumbronthedrawncardis:

(i) anoddnumber

(ii) amultipleof5

(iii) evenprime


Work Book - Class X

15. Twounbiasedcoinsaretossedsimultaneously.Findtheprobabilityofgetting:

(i) atleastonehead

(ii) atmostonehead

(iii) nohead

16. Twodicearethrownatthesametime.Findtheprobabilityofgetting:

(i) samenumberonbothside.

(ii) sumoftwonumbersappearingonboththediceis8.

17. Threecoinsaretossedsimultaneouslyonce.Findtheprobabilityofgetting:

(i) atleastonetail

(ii) notail

18. Ajarcontains54marblesofcolourblue,greenorwhite.Theprobabilityofselecting

abluemarbleatrandomfromthejar is 13,andtheprobabilityofselectingagreen

marbleatrandomis49.Howmanywhitemarblesdoesthejarcontain.


Work Book - Class X

19. Inasinglethrowoftwodice,findtheprobabilityofgetting:

(i) atotalof7

(ii)atotalof11

(iii)adooublet

(iv)sixasaproduct

20. Abagcontains4red,5blackand6whiteballs.Aballisdrawnfromthebagatrandom.Findtheprobabilitythattheballdrawnis:

(i) red

(ii)black

(iii)notblack

21. Adieisthrownonce.Findtheprobabilityofgetting:

(i) anevennumber

(ii)aprimenumber

(iii) anumbergreaterthan4

4 MARKS

22. Alltheredfacecardsareremovedfromapackof52playingcards.Acardisdrawnatrandom,findtheprobabilitythatadrawncardis,

(i) redcolour


Work Book - Class X

(ii) aqueen

(iii) an ace

(iv) afacecard

23. Alltheblackfacecardsareremovedfromapackof52cards.Findtheprobabiltiyofgettinga

(i) facecard

(ii) redcard

(iii) blackcard

(iv) king


24. Abagcontaians8red,6whiteand4blackballs.Aballisdrawnatrandomfromthe

bag.Findtheprobabilitythatthedrawnballis:

(i) redorwhite (b)notblack (iii)neitherwhitenorblack

25. Aboxcontains30cardsnumbered from1 to30.Acard isdrawn from theboxat

random.Findtheprobabilitythatthenumberonthedrawncardis

(i) even (ii)Ppime (iii)amultipleof7

26. Acard isdrawnat randomfromawellshuffleddeckof52playingcards.Find the

probabilitythatthecarddrawnis

(i) acardofspadeoranace (ii)aredking

(iii) neitherakingnoraqueen (iv)eitherkingorqueen


Work Book - Class X

27. Abagcontains5resballs,8whiteballs,4greenballsand7blackballs.Ifoneballis

drawnatrandom,findtheprobabilitythatitis:

(i) black (ii)red (iii)notgreen

28. 100cardsmarkedwiththenumbers2to101areplacedinabagandmixedthoroughly.

Sujathadrawsacardfromthebag.Findtheprobabilitythatthenumberonthecard

drawnis

(i) anoddnumber (ii)anevennumber

(iii) anumberwhichisasquare (iv)aprimenumberlessthan50.

29. Iftheprobabilityofwinningagameis0.3,theprobabilityoflosingitis

(a) 0.5 (b)0.2 (c)0.7 (d)Noneofthese

30. Twodicearethrownsimultaneously.Theprobabilityofgettingamultipleof2onone

dieandamultipleof3ontheotheris

(a) 536

(b) 512

(c) 1136

(d) 112

31. Twocoinsaretossedsimultaneously.Theprobabilityofgettingatleastoneheadis

(a) 14 (b) 1

2 (c) 3

4 (d)0

32. If threecoinsaretossedsimultaneously,thentheprobabilityofgettingat leasttwo

headsis

(a) 14 (b)3

8 (c) 1

2 (d)1

4

33. Theprobabilityofguessingthecorrectanswertoacertaintestquestionisx2 .Ifthe

probabilityofnotguessingthecorrectanswertothisquestionis23

, then x =

(a) 2 (b)3 (c)23 (d)1

3

34. Adieisthrownonce.Theprobabilityofgettinganumber3or4is

(a) 13 (b)2

3 (c)0 (d)1


Work Book - Class X

AnSweR Key

1. 313

3. (i) 14

(ii) 19

4. 15

5. 23

6. 16

7. 27

8. 25

9. x2 10. 2

7

11. 0.15 17. (i) 78

(ii) 18 18. 12

19. 16

, 18

, 16

, 19 20. 7

17, 8

15, 2

5 21. 1

2, 1

2, 1

3

22. (i) 1013

(ii) 123

(iii) 223

(iv) 323

23. Alltheblackfacecardsareremovedfromapackof52cards.

Findtheprobabiltiyof

(i) 323

(ii) 1323

(iii) 1023

(iv) 123

24. (i) 79

(ii) 79

(iii) 49

25. (i) 12

(ii) 13

(iii) 215

26. (i) 413

(ii) 126

(iii) 1113

(iv) 213

27. (i) 724

(ii) 524

(iii) 56

28. (i) 12

(ii) 12

(iii) 9100

(iv) 320

29. (c) 30. (c) 31. (c)

32. (c) 33. (c) 34. (a)


Work Book - Class X

1. CHEMICAL REACTIONS AND EQUATIONS 1. Balancethefollowingchemicalequations:

(a) NaOH+H2SO4 →Na2SO4+H2O

(b) FeCl2+H2S →HCl+FeS

(c) HNO3+Ca(OH)2 →Ca(NO3)2+H2O

(d) Pb(NO3)2 heat PbO+NO2+O2

(e) Fe+H2O →Fe3O4+H2

(f) KI+Pb(NO3)2 →PbI2+KNO3

(g) K+H2O →KOH+H2

(h) H2S+O2 → SO2+H2O

(i) AlCl3+NH4OH→Al(OH)3+NH4Cl


Work Book - Class X

2. ACIDS, BASES AND SALTS1. Completethefollowingreactions.

(a) CaCO3+2HCl→

(b) 2NaHCO3 ∆

(c) 2NaCl+2H2O →

(d) Ca(OH)2+Cl2 →

(e) CaSO4.2H2O 373K

(f) Ca(OH)2+CO2 →

(g) NaCl+H2O+CO2+NH3 →

(h) Na2CO3.10H2O heat

(i) Zn+2NaOH→


Work Book - Class X

3. METALS AND NON METALS1. Completethefollowingreaction.

(a) Zn+FeSO4 →

(b) 2ZnS+3O2 heat

(c) Zn CO3 heat

(d) 3MnO2+4Al→

(e) 2HgS+3O2 →

(f) Al2 O3+6HCl→

(g) Al2 O3+2NaOH→

(h) 3Fe+4H2O →

4. CARBON AND ITS COMPOUNDS1. Drawtheelectrondotstructuresforthefollowing:

(a) propanne (b) H2S


Work Book - Class X

(c) benzene (d) sulphur

2. Drawthestructuresofthefollowing:

(a) Propene (b) chloropropane

(c) Butyne (d) Butanoicacid

(e) cyclohexane

3. Completethefollowingequations:

(a) CH3 -CH2OHAlkalineKmnO4+Heat

(b) CH3CH2OHConc.H2SO4

Heat


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(c) CHCl3+Cl2 Sunlight

(d) 2CH3CH2OH+2Na

(e) CH3COOH+NaOH

(f) CH2=CH2+H2 Ni

(g) CH3COOH+CH3CH2OHAcid

6. LIFE PROCESS1. Drawthediagramsforthefollowing:

(a) NutritioninAmoeba.

(b) Humanrespiratorysystem.


Work Book - Class X

(c) Stomata.

(d) Humanheart.

(e) Strucutureofnephron.

(f) Humanalimentarycanal.

(g) Extretorysysteminhumanbeings.


Work Book - Class X

7. CONTROL AND COORDINATION1. Drawthediagramforthefollowing:

(a) Structureofneuron.

(b) Humanbrain.

8. HOW DO ORGANISMS REPRODUCE ?1. Drawalabelleddiagramsforthefollowing:

(a) BuddinginHydra


Work Book - Class X

(b) RegenerationinPlanaria

(c) Germinatingseed

(d) Humanfemalereproductivesystem

(e) Longitudinalsectionofflower


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(f) Humanmalereproductivesystem

(g) Fertilisationinafloweringplant.

9. HEREDITY AND EVOLUTION1. Explainwith thehelpofadiagramhowsexofachild isdeterminedat the timeof

conceptioninhumanbeings.


Work Book - Class X

10. LIGHT - REFLECTION AND REFRACTION

1. Drawtheimageformedbyaconcavemirrorwhentheobjectisplaced:

(i) Atinfinity

(ii) BeyondC

(iii) AtC

(iv) BetweenCandF

(v) AtF


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(vi) BetweenPandF

2. Drawtheraydiagramfortheimageformedbyaconvexmirror.

3. Drawthediagramfortherefractionoflightthrougharectangularglassslab.

4. Drawtheimageformedbyaconvexlenswhentheobjectisplaced

(i) Atinfinity

(ii) Beyond2F1


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(iii) At2F

(iv) BetweenF1and2F1

(v) AtfocusF1

(vi) BetweenF1andopticalcentreO.


Work Book - Class X

11. HUMAN EYE AND COLOURFUL WORLD

1. Drawthediagramforthefollowing:

(a) Myopiceyeanditscorrection.

(b) Hypermetropiceyeanditscorrection

(c) Pathofrayoflightthroughatriangularglassprism

(d) Dispersionoflight


Work Book - Class X

(e) Rainbowformation

(f) Whysunisvisibleatustwominutesbeforetheactualsun-riseandtwominutesafterthesunset?

12. ELECTRICITY1. Inthecircuitshown,calculate

B

||||(•)

2Ω

3V

4Ω

A

CD E•6Ω

(a) TotalresistanceinthearmCE.

(b) Totalcurrentdrawnfromthebattery

(c) CurrentinthearmsABandCE.


Work Book - Class X

2. ResistivityofamaterialAisintherangeof1010-1014 ΩmwhilethatofBistherangeof10-6-10-8 Ωm.Whichofthesewillbehaveasaninsulatorandwhy?

3. Calculatetheresistanceofa1kmlongaluminiumwireofdiameter5mm.FindtheresistanceofthewiremadeofNichromeofsamelengthanddiameter.

(giveρ aluminium=28x10-8 Ωm,ρmichrome=100x10-6 Ωm)

4. Findtheratioofequivalentresistanceofseriescombinationofnequalresistancestotheequivalentresistanceinparallelcombinationofnresistances.


Work Book - Class X

5. In the given circuit diagram if R1 = R2 = R3 = R4 = R5 = 3Ω, find the equivalentresistanceofthecircuit.

||||

(•)

R1 R2

R5

R3

R4

6. Findtheequivalentresistaneinthegivencircuit.

1Ω

3Ω

||||

(•)

3Ω

1Ω

2Ω

2Ω

7. An electric iron is marked 1000W, 220V. Find the current drawn by iron and theresistanceoftheelectriciron.


Work Book - Class X

8. Anelectricheaterisusedona220Vsupplyandtakesacurrentof5A

(a) Finditspower.

(b) Calculatethecostofusingtheheaterfor1hrif1kWhcosts` 2.

9. DrawtheschematicdiagramtoverifyOhm'slaw.

AnSweR Key

1. (a) 6Ω (b)1A (c)0.5A,0.5A 2. A

3. 56Ω,20000Ω 4. n2

5. 8Ω 6. 7.5Ω

7. 4.55A,48.4Ω 8. (a)1100W(b) 2.20


Work Book - Class X

13. MAGNETIC EFFECT OF ELECTRIC CURRENT 1. Drawthediagramforthefollowing: (a) Magneticfieldlinesaroundabarmagnet.

(b) Magneticfieldlineproducedbyacurrentcarryingcircularloop.

(c) Patternofmagneticfieldlinesaroundacurrentcarryingsolenoid.

(d) Aschematicdiagramofcommondomesticcircuit.


Work Book - Class X

nOTeS


Work Book - Class X

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My Work Book on€¦ · 6. Find the value of k if x + 2 2is a factor of 4x4 + 2x3 - 3x + 8x + 4k....

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