CLASS10BOARDSMATHSSOLUTIONS

YEAR2018

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1

CLASS10BOARDSMATHSSOLUTIONS-2018

Given if thenfind

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2

CLASS10BOARDSMATHSSOLUTIONS-2018

Whatisthevalueof

?

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3

CLASS10BOARDSMATHSSOLUTIONS-2018

FindthedistanceofpointP(x,y)fromtheorigin

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△ ABC~ △ P QR =AB

PQ

13

ar △ ABC

ar △ P QR

(cos2 67 ∘ − sin2 23 ∘

)

4

CLASS10BOARDSMATHSSOLUTIONS-2018

Ifx=3isonerootofthequadraticequation ,thenfindthevalueofk

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5

CLASS10BOARDSMATHSSOLUTIONS-2018

WhatistheHCFofthesmallestprimenumberandthesmallestcompositenumber?

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6

CLASS10BOARDSMATHSSOLUTIONS-2018

InanA.P., if thecommondifference(d)=-4andtheseventhterm is4thenfindthefirstterm

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7

CLASS10BOARDSMATHSSOLUTIONS-2018

An integer ischosenat randombetween1and100.Find theprobability that it is (i)divisibleby8(ii)notdivisibleby8

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CLASS10BOARDSMATHSSOLUTIONS-2018

x2 − 2kx − 6 = 0

(a7)

8Twodifferentdicearetossedtogether.Findtheprobability(i)ofgettingadoublet(ii)ofgettingasumof10,ofthenumbersontwodice

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9

CLASS10BOARDSMATHSSOLUTIONS-2018

Find the ratio in which (4,m) divides the line segment joining A(2,3) and B(6,-3).Hencefindm

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10

CLASS10BOARDSMATHSSOLUTIONS-2018

Giventhat isairrationalprovethat isanirrationalnumber

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11

CLASS10BOARDSMATHSSOLUTIONS-2018

InFig.1.ABCDisarectangle.Findthevaluesofxandy

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12

CLASS10BOARDSMATHSSOLUTIONS-2018

Findthesumoffirst8multiplesof3

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√2 (5 + 3√2)

13

CLASS10BOARDSMATHSSOLUTIONS-2018

While boarding an aeroplane, a passenger got hurt. The pilot showing promptnessandconcern,madearrangementstohospitalisethe injuredandsotheplanestartedlate30minutestoreachthedestination,1500kmawayintime,thepilotincreasedthespeedby100km/hr.Findtheoriginalspeed/houroftheplane.

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14

CLASS10BOARDSMATHSSOLUTIONS-2018

Provethattheareaofequilateraltriangledescribedonthesideofasquareishalftheareaoftheequilateraltriangledescribedonitsdiagonal.

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15

CLASS10BOARDSMATHSSOLUTIONS-2018

Iftheareasoftwosimilartrianglesareequal,provethattheyarecongruent.

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16

CLASS10BOARDSMATHSSOLUTIONS-2018

Prove that the length of the tangents drawn from an external point to a circle areequal.

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17

CLASS10BOARDSMATHSSOLUTIONS-2018

Awoodenarticlewasmadebyscoopingoutahemispherefromeachendofasolidcylinder.Iftheheightofthecylinderis10cm,anditsbaseisofradius3.5cm,findthetotalsurfaceareaofthearticle.

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CLASS10BOARDSMATHSSOLUTIONS-2018

18Aheapofriceisintheformofaconeofbasediameter24mandheight3.5m.Findthevolumeoftherice.Howmuchcanvasclothisrequiredtojustcovertheheap

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19

CLASS10BOARDSMATHSSOLUTIONS-2018

The table below shows Salary of persons. Calculate the median salary of thedata.

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20

CLASS10BOARDSMATHSSOLUTIONS-2018

If evaluate

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21

CLASS10BOARDSMATHSSOLUTIONS-2018

If

where isanacuteangle,findthevalueof

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22

CLASS10BOARDSMATHSSOLUTIONS-2018

Findtheareaof theshadedregion inFig.3,wherearcsdrawnwithcentresA,B,CandDintersectinpairsatmid-pointsP,Q,RandSofthesidesAB,BC,CDandDArespectivelyofasquareABCDofside12cm.[Use ]

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280

4 tan θ = 34 sin θ − cos θ + 14 sin θ + cos θ − 1

tan 2A

= cot(A − 180),2A A.

π = 3.14

23

CLASS10BOARDSMATHSSOLUTIONS-2018

Of

aretheverticesfaparallelogram,findthevaluesof

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24

CLASS10BOARDSMATHSSOLUTIONS-2018

If

aretheverticesofaquadrilateral,findtheareaofthequadrilateralABCD.

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25

CLASS10BOARDSMATHSSOLUTIONS-2018

FindHCFandLCMof404and96andverifythat productofthetwogivennumbers

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26

CLASS10BOARDSMATHSSOLUTIONS-2018

Findallzeroesofthepolynomial

iftwoofitszeroesare and

A( − 2, − 1),

B(a, 0),

C(4, b)andD(1, 2)aandb.

A(5, \ 7),

\ B( − 4, \ − 5),

\ C( − 1, \ − 6)\

and\ D(4, \ 5)

HCF × LCM =

2x4 − 9x3 + 5x2

+ 3x − 1

2 + √3 2 − √3

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27

CLASS10BOARDSMATHSSOLUTIONS-2018

ThesumoffourconsecutivenumbersinA.P.is32andtheratiooftheproductofthefirstandlasttermtotheproductoftwomiddletermsis7:15.Findthenumber

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28

CLASS10BOARDSMATHSSOLUTIONS-2018

In an equilateral triangle ABC, D is a point on side BC such that .

Provethat .

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29

CLASS10BOARDSMATHSSOLUTIONS-2018

(Pythagoras's Theorem) Prove by vector method that in a right angled triangle, thesquareofthehypotenuseisequaltothesumofthesquaresoftheothertwosides.

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30

CLASS10BOARDSMATHSSOLUTIONS-2018

Amotorboatwhosespeed is18km/hmstillwater takes1hourmore togo24kmupstreamthantoreturndownstreamtothesamespot.Findthespeedofthestream.

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31

CLASS10BOARDSMATHSSOLUTIONS-2018

Atrain travelsatacertainaveragespeed foradistanceof63kmand then travelsadistanceof72kmatanaveragespeedof6 km/hrmore than itsoriginal speed. If ittakes3hourstocompletethetotaljourney,whatisitsoriginalaveragespeed?

BD = BC13

9AD2 = 7AB2

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32

CLASS10BOARDSMATHSSOLUTIONS-2018

Asobservedfromthetopofa100mhighlighthousefromthesealevel,theanglesofdepressionoftwoshipsare and Ifoneshipisexactlybehindtheotheroneonthesamesideofthelighthouse,findthedistancebetweenthetwoships.

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33

CLASS10BOARDSMATHSSOLUTIONS-2018

Abucketopenatthetop,andmadeupofametalsheetisintheformofafrustumofacone. The depth of the bucket is 24 cm and the diameters of its upper and lowercircularendsare30cmand10cmrespectively.FindthecostofmetalsheetusedinitattherateofRs10per .

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34

CLASS10BOARDSMATHSSOLUTIONS-2018

Themeanofthefollowingdistributionis18.FindthefrequencyfoftheclassClass11-13,13-15,15-17,17-19,19-21,21-23,23-25 frequency3,6,9,13,f,5,4

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35

CLASS10BOARDSMATHSSOLUTIONS-2018

The followingdistributiongives thedaily incomeof workersofa factory:Convertthedistributionabovetoa lessthantypecumulativefrequencydistributionanddrawitsogive

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30 ∘ 45 ∘

100cm2

19 − 21/n

50

36

CLASS10BOARDSMATHSSOLUTIONS-2018

Provethefollowingidentity,wheretheanglesinvolvedareacuteanglesforwhichtheexpressionsaredefined.(vii)

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= tan θ

sin θ − 2 sin3 θ

2cos3 θ − cos θ