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1251.

If $ \frac{\cos \alpha}{\cos \beta}=m, \quad \frac{\cos \alpha}{\sin \beta}=n $ show that $ \left(m^{2}+n^{2}\right) \cos ^{2} \beta=n^{2} $

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L.H.S= (m^2+n^2)cos^2b

= {(cosa/cosb)^2+(cosa/sinb)^2}cos^2b

= {(cos^2a/cos^2b) +(cos^2a/sin^2b)}cos^2b

= (cos^2a.sin^2b +cos^2a.cos^2b / cos^2b.sin^2b)cos^2b

= cos^2a(sin^2b+cos^2b) / sin^2b

= cos^2a / sin^2b

R.H.S= n^2

=(cosa/sinb)^2

= cos^2a / sin^2b

1252.

that runs into the sea per minute15. A pit 5 m long and 3.5 m wide is dug to a certain depth. If the volume of earth taken out of tヘ, is 14 m 3, what is the depth of the pit?he leIf the axcalled a

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thank you

1253.

\frac \cos \alpha \cos \beta = m \text and \frac \cos \alpha \sin \beta = n \text ,then prove that ( m ^ 2 %2B n ^ 2 ) \cos ^ 2 \beta = n ^ 2

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1254.

eceipt of a company during a year was 20956480. Next year, it increased by76709570. What was the total sale receipt of the company during these two years?

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48622530 is the right answer....

1255.

6. In a particular year a company produced 8765435 bicycles. Next year. The numberbicycles produced was 1378689 more than those produced in the preceding yearHow many bicycles were produced during the second year?How many bicycles were produced during these two years?20956480. Next year. It increasedThe sale receipt of a company during a year was6709570. What was the total sale receipt of the company during these two years?8. The total population of a city is 28756304. If the number of males is 16987059. And benumber of females in the city.

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1256.

15. Water is being pumped into a water tank of dimensions 10 m x 7.5 m x 4 m at the rate of400 L per minute. What is the time taken to fill the tank completely?

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1257.

7. The sale receipt of a company during a year was 20956480. Next year, it increased by6709570. What was the total sale receipt of the company during these two years?

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Total sale receipt in two years is = Rs 20956480 + Rs 27666050 = Rs 48622530

1258.

Example 3: Locate 2 on the number line.Solution: It is easy to see ow the Grealks might have discovered

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1259.

21.Locate/3 on the number line

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1260.

2, Locate /3 on the number line.

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1261.

school admission is 698781, find the total population of the statt.6. In a particular year a company produced 8765435 bicycles. Next year, the number ofbicycles produced was 1378689 more than those produced in the preceding year.How many bicycles were produced during the second year?How many bicycles were produced during these two years?namnany during a year was * 20956480. Next year, it increased by

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1262.

In a school the total number of students is 1500. If the number of girls is 50 more than that of thethen find the separate number of boys and girls in the school.boys

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total 1500 B + G = 1500 G = B + 50 B + B + 50 = 1500 2B = 1450 B = 725 G = 775

1263.

A plot of land costs 1,0 0,00 0 The land value appreciates by 5% the first year and the valueappreciates by 8% the next year. What is the cost of the land after two years?furth8

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For first year = 100000(1+(5/100)) =100000*21/20 =105000

For second year = 105000(1+(8/100)) = 105000*27/25 = 113400

The Cost of land after 2 years will be Rs.113400

1264.

In a particular year a company produced 8765435 bicycles. Next year, the number ofbicycles produced was 1378689 more than those produced in the preceding year.How many bicycles were produced during second year?How many bicycles were produced during these two years?

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1265.

m sin A-n cos An, find the valuc of n cos At m sin AIf m cot A

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1266.

07. If one zero of the polynomial (a+ 9) a + 13k + 6a is reclprocal of the other,find the valuc of a

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If one of the zero is reciprocal of the other,let one zero beαother zero will be 1/α

Product of roots = c/a⇒α× 1/α = 6a/(a²+9)⇒ 1 = 6a/(a²+9)⇒ a² + 9 = 6a⇒ a² - 6a + 9 = 0⇒ a² - 3a - 3a + 9= 0⇒ a(a-3) -3(a-3) = 0⇒ (a-3)(a-3) = 0⇒ (a-3)²= 0⇒ a = 3

Value of a is 3.

1267.

7. Express the following speeds in metres per second:(a) 118 km/hours(b) 51.5 km/hours

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1 km = 1000 m 1 hr = 3600 seconds1) 118 km/h = 118×1000/3600 = 295/9 m/s 2) 5.15 km/h = 5.15×1000/3600 = 51.5/36 m/s

If you find this answer helpful then like it.

1268.

5. Express each of the following speeds in km/h.(a)60 m per minute15 m per second

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1269.

9 Express each of the following speeds in m/min.:(a) 54 km/hour(b) 63 km/hour(c) 135 km/hour

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1270.

( 4 z ^ { 3 } + 14 z ^ { 3 } + 6 z ) b y ( z + 3 )

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the divident should be 4z^3 + 14z^2 + 6z

1271.

DEPRESENTING REAL NUMBERS ON THE NUMBER LINE (SUCCESSIVEMAGNIFICATION)EXAMPLE 5Locate 3.895 on the number line.

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1272.

3 132. Re32 Represent',VTV8 on the number line,Vi,vo on the number line.

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1273.

how the following numbers on a numberline. Draw a separate number line for eachexample:3 53

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1274.

10. Draw a number line and answer the following:(a) Which number will we reach if we move 4 numbe(b) Which number will we reach if we move 5 numbe(c) If we are at - 8 on the number line, in whichreach - 13?(d) If we are at - 6 on the number line, in whichreach 1?

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we should __________ in the library

1275.

1/Visualise 3.765 on the number line, using successive magnification.2. Visalise 4.26 on the number line, up to 4 decimal places.

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1276.

EXERCISE - 1.3 S(1. Visualise 2.874 on the number line, using successive magnification.(2) Visualilse 5.28 on the number line, upto 3 decimal places.

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1277.

1)Visualise 3,765 on the number line, using successive magnification.2)Visualise 4.26 on the number line, up to 4 decimal pluces.tions am Real Numbers

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2)

1278.

2.Writetheprincipalvalucofcosec(D)

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Let cosec-¹(2) = ∅ where ∅ is the principal branch of cosec-¹(2) therefore cosec∅ = 2 since the range of principal value of branch of cosec-¹x is [+π/2,π/2] -{0} therefore -π/2≤∅≤π/2, ∅≠0

Now cosec∅ = 2 = cosecπ/6 thus ∅ = π/6 as cosecπ/6 = 2 and π/6 € [-π/2,π/2]-{0}

1279.

cr te number line.8. Find the solution set of -x-2x-1>531,xe W. Also, graph the solution on the number line,if possible. D

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1280.

m e r Ull the number line.Example 11 : Visualize the representation of 5.37 on the number line upto 5 decimalplaces, that is, up to 5.37777.

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1281.

Three bells ring at intervals of 15 s, 21sand 16 s, respectively. All bells ringsimultaneously at 12: 00 noon. They willagain ring simultaneously at

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1282.

6.Four bells toll after an interval of 8, 9, 12 and and 15 seconds respectively. When will they tollagain?

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we have to find at which time all will ring together so we have to find L.C.M. of all 4 numbers8=2×2×29=3×312=3×2×215=3×5so L.C.M.=2×2×2×3×3×5=360so after 360 seconds they all toll.

1283.

2. Four bells begin tolling together and toll at interval of 2,6,10,14 secondsrespectively. After how many seconds will they toll together?

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18 seconds will they toll together

1284.

Two bells toll at intervals of 120 and 180s, respectively. If they toll together at 12 noon, then what isthe earliest time at which they toll together?

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They both need to be toll together, so we have to take LCM of both the timingsso here that is 360sso after 3 minutes both will toll together.so at 12:03 they both will toll together.

1285.

Give one advantageWhat is primary key?

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Aprimary key, also called aprimarykeyword, is akeyin a relational database that is unique for each record. It is a unique identifier, such as a driver license number, telephone number (including area code), or vehicle identification number (VIN). A relational database must always have one and only oneprimary key.

1286.

| 8f of a number exceeds itsø 1, find the number.

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21

(1/3)x=(2/7)x+1(1/3-2/7)x=1(7-6)x/21=1x/21=1x=21Explanation:1/3 of 27 is 7, which exceeds 2/7 of 27 (that is 6) by one

1287.

une number.Some pat of a journey of 780 km was made by car with a speedof 60 km/h and the remaining journey was made by train withspeed of 100 km/. If total time required was 9 hours, find thetime taken by train ad distance covered by train.

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1288.

Ut12. 19241610. v1795611. 19600une least number which must be subtracted from 2509 LOwuch must be subtracted from 2509 to make it a perfect14. Find the least number which must be suhtratFind this na

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Solution :-

First of all we have to find the square root of 2509 using the long division method.

50 ____________ 5 | 2509 5 | 25 |______100| 09 |

Here, the remainder is 9.

Hence, 50² < 2509

And we know that, 50² = 2500

Hence, the number to be subtracted is 2509 - 2500 = 9

So, 9 should be subtracted from 2509 to make it a perfect square.

after subtracting 9 in 2509 it become perfect square of 50

1289.

8. Ifof a number exceeds its, find the number,

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(1/3)x=(2/7)x+1(1/3-2/7)x=1(7-6)x/21=1x/21=1x=21Explanation:1/3 of 27 is 7, which exceeds 2/7 of 27 (that is 6) by one

1290.

A number exceeds 8,59,470 by 3,00,999. What is the number?

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thank you for helping me in homework

1291.

116- of a number exceeds itsby 44, find the number

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1292.

2 Drawa pie chart for the following data.Education SFood Health ClhngEltem ofexpenditure12007500mount spent in rupees 3750 1875 1875

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1293.

4. A number exceeds 79,36,542 by 1,90,71,749. What is the number?

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749 hai iska answer to

1294.

cular year a company produced 8765435 bicycles.Nextyear,thenumberof6. Io ayeare produced in the preceding yearbicycles produced was 1378689 mHow many bicycles were próduced during the second year?How many bicycles were produced during these two years?

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1295.

The following table shows monthly expenditure of a family. Draw a pie chart fothe data.ItemsAmount (in Rupees) 1500RentFood Clothing Education Others3600 12002100 2400

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1296.

The following table shows monthly expenditure of a family. Draw a piethe data.107Food Clothing Education Others2400ItemsRent120021003600Amount (in Rupees)1500

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1297.

\frac { 1875 } { 16200 } =

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1875/16200=(75×25)/(648×25)=(25×3)/(216×3)=25/216(basic multiplication)

1298.

Find: ) the euge ul U18. The square on the diagonal of a cube has an area of 1875 cm2. Calculate(ii) the total surface area of the cube.ooe of guhoid are x y and z sa. units, If the volume i(i) the side of the cube,

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1299.

EXERCISE 24A28800. The monthly expenditure o4. the monthly income of a family isvarious items is given below!ItemRentFoodClothingEducationSavingsExpenditurefin )80001080056003600800Represent the above data by a pie chart.

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1300.

following data show the expenditure of an individual over various itemsEducation food16003200 4000 24003200Rent Clothing OthersDraw a pie chart

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