Explore topic-wise InterviewSolutions in Current Affairs.

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1.

two ships are approaching a lighthouse from opposite directions.the angle of depression of the ships from the top of a lighthouse are 30°and 45°.if the distance between the two ships is 100m,find the height of the lighthouse.(use /3=1.732.)

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2.

7. From the top of the lighthouse, an observerlooks at a ship and finds the angle of depressionto be 30°. If the height of the lighthouse is 100metres, then find how far the ship is from thelighthouse.Solution:

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3.

From the top of a lighthouse, an observer looking at a ship makes angle ofdepression of 60o. If the height of the lighthouse is 90 metre, then find how farthe ship is from the lighthouse. (3 1.73)

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4.

26. Two ships are approaching a lighthouse from opposite directions. The angles ofdepression of the two ships from the top of the lighthouse are 30° and 45°. If thedistance between the two ships is 100 m, find the height of the lighthouse.[Use /3 = 1.732]

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AB = 100Let AC = xLet BC = 100-xLet CD = hInΔEAD,EA = DCED = ACtan 45° = EA/ED1 = h/xx = hIn ΔDFBFB = CDDF = CBtan 30° = FB/DF1/√3 = h/100-x1/√3 = h/100-h100-h =√3h100-h = 1.732h2.732h = 100h = 100/2.732h = 36.603mh = 36.6m

5.

Practice set 6.2A person is standing at a distance of 80m from a church looking at its top.The angle of elevation is of 45°. Find the height of the church.From the top of a lighthouse, an observer looking at a ship makes angle ofdepression of 60°. If the height of the lighthouse is 90 metre, then find how farthe ship is from the lighthouse. (3-1.73)

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2)tan∅ = AB/BC

tan60° = 90/BC

√3 = 90/BC

BC×√3 = 90

BC = 90/√3

BC. = 90/1.73

BC = 52.023 m (approximate)___________________________________so ship 52.023 meter far from the light house.

6.

окThe angles of depression of two ships from the top of a lighthouse and on the same sideare found to be 45e and 30°. If the ships are 200 mof tapart, find the height of the lighthousecoins are tossed simultaneously, find the probability of getting

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7.

25. The angles of depression of the top and bottom of a 10 m high buildingfrom the top of a multi-storey building are 30° and 45° respectively.Find the height of the multi-storey building and the distance betweenthe two buildings. [Take 3 -1.732]

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8.

subtract 16 from 79 ones

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79 - 16 = 63

9.

Subtract the sum of 5.39 and 8.06 from 16.

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sum of 5.39 and 8.065.39+8.06 = 13.45ow subtraction16-13.45 = 2.55

thank you mam

10.

A) Subtract the following.1) -16 - (+24)4) 75 - 46

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1. -402. 29 is the correct answer

11.

If m th term of an AP is 1/n and nth term is 1/m then find the sum of itsfirst mn terms.

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thsnks

12.

63-jilmn+1)If the mth term of an AP is 1/n und nth term is 1'm. then show that the sum of mn terms is

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Given that, mth term=1/n and nth term=1/m.then ,let a and d be the first term and the common difference of the A.P.so a+(m-1)d=1/n...........(1) and a+(n-1)d=1/m...........(2).subtracting equation (1) by (2) we get,md-d-nd+d=1/n-1/m=>d(m-n)=m-n/mn=>d=1/mn. again if we put this value in equation (1) or (2) we get, a=1/mn.then, let A be the mnth term of the APa+(mn-1)d=1/mn+1+(-1/mn)=1 hence proved

13.

From the top and foot of a 40 m high tower, the angles of elevation of the top of alighthouse are found to be 30 and 60" respectively. Find the height of the lighthouseAlso find the distance of the top of the lighthouse from the foot of the tower

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1

2

at last why we put sin tita

or tan tita is wrong?

why please tell me the reason

ohh ok sir I understood

tnq

14.

From the top of a 7m high building, the angle of elevation of the top of a cable tower is600 and the angle of depression of the foot of the tower is 300. Find the height of the tower.

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15.

. Watching from the top of a 80 m high hill, theangle of elevation of the top of a tower is 30and the angle of depression of the base of thetower is 45. Find the height of the tower.

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16.

(iv) If sin(2e+15°)-cos3θ, then the value of e is

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Sin(90-3theta)= sin(2theta+15°)90-3theta= 2 theta+155 theta = 75theta= 15°

17.

4cmFrom the adjacent figure, find the values ofi) 3 sin θ + 4cos θii) 1- cos2iii) sec 2e-tan 2 θReom the given A ARC find the values of5cm13cm12cm

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18.

Find the principal values ofCOSI (- )cosTV2

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3pi/4 since cosinv(-x) = pi - cosinv(x)

If the principal value of cos−1 x is θ then we know, 0 ≤ θ ≤ π.

Therefore, If the principal value of cos−1 (-1/√2) be θ then cos−1 (-1/√2) = θ

⇒ cos θ = (-1/√2) = cos π/4 = cos (π - π/4) [Since, 0 ≤ θ ≤ π]

Therefore, the principal value of cos−1 (-1/√2) is π - π/4 = 3π/4

19.

V2. Find the principal values of the following functions :(a) cos? +2 sin

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20.

and the 25th teml.17. If mth term of an AP is 1and nth termisthen find the sum of itsfirst mn terms.CBSE 2017]

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Given that, mth term=1/n and nth term=1/m.then ,let a and d be the first term and the common difference of the A.P.so a+(m-1)d=1/n...........(1) and a+(n-1)d=1/m...........(2).subtracting equation (1) by (2) we get,md-d-nd+d=1/n-1/m=>d(m-n)=m-n/mn=>d=1/mn. again if we put this value in equation (1) or (2) we get, a=1/mn.then, let A be the mnth term of the APa+(mn-1)d=1/mn+1+(-1/mn)=1 hence proved.

21.

12 Name the technigucs to separatea Cream from Milkb. Dyes in the black inAmmonium Chloride and common salt.Or

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The process ofcentrifugationis used in dairies to separate cream from milk .Centrifugationis a method for separating the suspended particles of a substance from a liquid in which the mixture is rotated at a high speed in a centrifuge machine.

Chromatography is the separation technique which can be use to separate dyes in the black ink . This could be possible with the whatman’s filter paper.

There are way in separating mixtures of chlorides salts such as that of sodium chloride and ammonium chloride. It can be done by crystallization, filtration orsublimation. The easiest method among the three is separation bysublimation. Ammonium chloride sublimes uponheating.

There are way in separating mixtures of chlorides salts such as that of sodium chloride and ammonium chloride. It can be done by crystallization, filtration orsublimation. The easiest method among the three is separation bysublimation. Ammonium chloride sublimes uponheating.

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22.

from the ground.Orof depression of the top andFrom the top of a building 60 m high, the anglesa tower are observed to be 30° and 60. Find the height of the towerbottom ofof100% SUCCESSINMATHEMATİCS-1026

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23.

26. The angle of depression of a car parked on the road side from the top of a 150m high tower is30 Find the distance of the car from the tower.

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24.

Đź-rroduct or the two given numbers.14. If one zero of a polynomial 3x2-8x 2k +1 is seven times the other, find the value of k.

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25.

Eight persons stand in a line at random.What is the probability that two personX and Y don't stand together.6.

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a cyclist travel 0.9 km in 3 minute . find his speed in km per hour

26.

* डक कप 10 ¥ k¥ 2E केS o L 1९: ७

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इस समीकरण में एक्स की घात 2 का गुणांक माइनस वन है

27.

Find all pairs of consecutive even positive integers, both of which are largeran 5 such that their sum is less than 23.

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28.

Is (2e-3) a factor of p(2)--27-9II + a, i

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29.

Find all pairs of consecutive even positive integers, both of which are larger than 5 suchthat their sum is less than 23.

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30.

14. If one zero of a polynomial 3x2 8x + 2k + 1 is seven times the other, find the value of k.15. Solve the following pair of linear equations by substitution method:

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3x²-8x+2k+1 a=3, b=-8 ,c=2k+1suppose the zeroes of the equation are α and β . by the given condition α=7βas we know , α+β=-b/a7β+β=-(-8)/38β=8/3β=8/3×1/8=1/3αβ=c/a7β×β=2k+1/37×1/3×1/3=2k+1/37/9=2k+1/321/9=2k+121/9-1=2k12/9=2k4/3=2k4/6=k2/3=k

31.

ETT?37123 x 43144 x 57226 x 32127 x 5251 m şorts at 1a(A) 6(B) 5(C) 4(D) 3

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32.

Find all pairs of consecutive even positive integers, both of which are larger than5 such that their sum is less than 23

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33.

Findallpairsofconsecutiveevenpositive integers, both of which are larger than5 such that their sum is less than 23

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34.

+15ii)Find the value of the expression 2e + 2x2-7x + 72 when x=2

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35.

24Savita and Hamida are friends. What is the probabilitythat both will have (a) different birthdays? (b) the samebirthday ? (ignoring a leap year).

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Out of two friends, one girl say, Savita's bday can be any day of the year. Now, Hamida's bday can also be on any day out of 365 days in the Year.

We assume that these 365 outcomes are equally likely.(i) If Hamida's bday is different from savita's, the no. Of favorable outcomes for her bday is 365-1= 364

So, P(Hamida' bday is diffrent from Savita's bday)=364/365

(ii) P(Savita and Harmida have the same bday)= 1-P(Both have diffrent bdays)=1-(364/365) [ using P(not event)=1-P(E)]=1/365

36.

Find compound interest oncompounded annually2600 for 2 years at 10% per annum

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37.

ettaate amodnt and compound interest(i)12600 for 2 years at 10% p.a, compounded annually

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38.

painting with dimensions 140 cm by 80 cm is to be framed with a 10 cm wide frame all anedges. Ifaround7 Athe framed painting is to be backed by hardboard, what is the area of the hardboard to be2 mTn

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l= 140 cm b=80 cm therefore Area =l×B=140 ×80 =11200 Sq.cmHence ,11200 Sq. . cm is the area of required hardboard.

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39.

Marbles of diameter 1.4 cm are dropped into a beaker containing some water and are fullysubmerged. The diameter of the beaker is 7 cm. Find how many marbles have been dropped in itthe water rises by 5.6 cm

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40.

A sector containing an angle of 120 is cut off from a circle of radius 21 cm and folderinto a cone by joining the radii. Find the curved surface area of the cone.

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41.

. Marbles of diameter 1.4 cm are dropped into acylindrical beaker containing some water and are fullysubmerged. The diameter of the beaker is 7 cm. Howmany marbles have been dropped in it, if the water

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42.

9.35 ,AODC-AOBA,2BOC=125° और ZCDO=70° है।ZDOGC,2DCGऔर ZOAB ज्ञात कीजिए।3. समलंब ABCD, जिसमें AB | DCहै, के विकर्णAC और BD परस्पर पर प्रतिच्छेद करते हैं। दो| त्रिभुजों की समरूपता कसौटी का प्रयोग करतेहुए, दर्शाइए कि OA = OB है।OC OD 2

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sorry i didn't understand math in hidi language. please like

43.

9. In Fig. 10.13, XY and X'Y' are two parallel tangents to a circle with centre O andanother tangent AB with point of contact Cintersecting XY at A and X'Y' at B. Provethat < AOB = 90°.

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44.

3. In Figure 8, AO B0 and ZA 4B.Prove that ΔΑ0C Ξ ΔΒ0DIs ZACO BDO? Give reasons.Fig, 8

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45.

169. A milk container is in the form of a frustum of a cone of height 18 cmwith radii of its upper and lower ends as 8 cm and 32 cm respectivelyFind the amount of milk which can completely fill the container and its[CBSE 20070cost at the rate of20 per litre. Use π3.14.

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46.

1~ 100+ 99809 i ‘{I — ue} - ःहू 809

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SinA/secA+tanA-1+cosA/cosecA+cotA-1=sinA/(1/cosA+sinA/cosA-1)+cosA/(1/sinA+cosA/sinA-1)=sinA/{(1+sinA-cosA)/cosA}+cosA/{(1+cosA-sinA)/sinA}=sinAcosA/(1+sinA-cosA)+sinAcosA/(1+cosA-sinA)=sinAcosA[(1+cosA-sinA+1+sinA-cosA)/(1+sinA-cosA)(1+cosA-sinA)]=2sinAcosA/(1+sinA-cosA+cosA+sinAcosA-cos²A-sinA-sin²A+sinAcosA)=2sinAcosA/{1+2sinAcosA-(sin²A+cos²A)}=2sinAcosA/(1+2sinAcosA-1)=2sinAcosA/2sinAcosA=1 (Proved)

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47.

)/ A man borrowed4000 at a certain rate of interest and1050 as interest in 3 years. Find the two rates at which he l5000 at 2% lower thanIn all, he paidthe money.

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suppose 4000 at rate of x so rate for 5000 is x-2 both are for 3 years total interest is 1050 (4000×x×3)/100 + (5000(x+2)3)/100 = 1050 120x + 150x + 300 = 1050 270x = 750 x = 27/75 = 9/25 = 0.36% and second rate is 2.36%

48.

рем 809 * x7 500 * # 809.

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Cosxcos2xcos3x=or, (2cosxcos3x)(2cos2x)=1or, (cos4x+cos2x)(2cos2x)=1or, 2cos4xcos2x+(2cos²2x-1)=0or, 2cos4xcos2x+cos4x=0or, cos4x(2cos2x+1)=0Either, cos4x=0or, 4x=(2n+1)π/2or, x=(2n+1)π/8Or, 2cos2x+1=0or, 2cos2x=-1or, cos2x=-1/2or, cos2x=cos(-π/3)or, cos2x=cosπ/3 [neglecting the negative sign for cos]or, 2x=2nπ⁺₋π/3or, x=nπ⁺₋π/6(⁺₋ means plus-minus)

49.

at what rate per annum will rupees 800 amount to Rs 882 in 2 years compound annually

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here the amount is 882 the principle is 800 and time is 2 years , let r be the rate.

so, A = p(1+r)ⁿ=> 882 = 800(1+r)²=> (1+r)² = 88/80 = 11/10 = 1.1=> 1+r = √1.1 = 1.048

so, r = 0.048 or 4.8%

50.

=430350 x 100122 85

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