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Class 9 study materials part 5

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Watch the videos and answer the given questions

1)संधि की परिभाषा व उनके भेद उदाहरण सहित दीजिए |
2) स्वर संधि की परिभाषा व भेद उदाहरण सहित दीजिए |
3) स्वर संधि के भेद के पॉच -पॉच उदाहरण लिखें|
4) व्यंजन संधि की परिभाषा उदाहरण सहित दीजिए |
5) विसर्ग संधि की परिभाषा उदाहरण सहित दीजिए |
6) दिए गए शब्दों के संधि विच्छेद कीजिए |
नयन, दिगम्बर, मनोनुकूल, निश्छल, चयन, तपोधन, कपीश, रजनीश, भानूदय, नरेंद्र, स्वागत, लोकेश, परोपकार, सदैव, जलौध, महौज, यद्यपि

https://youtu.be/FcIVPVLt2L4

Science
1) what is Matter? What is its characteristics?
2) What is the Mole concept?
3) Write their definition.
a. Atomic mass. b. Molecular mass c. Molar mass
4) Write and remember Atomic Masses.
5) How do calculating Molecular mass? With their example.
6) What is relation between molar and molar volumes?
7) Calculate number of moles in 392g of H2SO4.
8) Calculate number of moles in 44.8l of Co2 at STP.
9) Calculate number of atoms of the consitutent element in 53g of Co2Co3.
10) Calculate number of moles in 350cm3 of Co2 at 273k and 2atm pressure.
11) Write and remember periodic table.

(i) Name the group of islands lying in the Arabian Sea.

(ii) Name the countries which are larger than India.

(iii) Which island group of India lies to its south-east?

(iv) Which island countries are our southern neighbours?

Answer

(i): India lies in the Northern hemisphere, with the mainland extending between latitudes 8°4’N and 37°6’N and longitudes 68°7’E and 97°25’E. The Tropic of Cancer (23° 30’N) divides the country into almost two equal parts, where the Lakshadweep islands lie in the Arabian Sea to the southwest of the mainland and the Andaman and Nicobar islands lie in the Bay of Bengal to the southeast of the mainland.

(ii): The countries which are larger than India are Russia, Canada, U.S.A, China, Brazil and Australia. Russia is the largest of all countries, with an area of 17.09 sq.km, while India has an area of 3.28 sq.km.

(iii): The Andaman and Nicobar islands lie to the south-east of India in the Bay Of Bengal. India has a land boundary of about 15,200 km. The total length of the coastline, including the islands of the Andaman and Nicobar and the Lakshadweep, is 7,516.6 km.

(iv): The island countries that are our southern neighbours are Sri Lanka and the Maldives. Maldives Islands are situated to the south of the Lakshadweep Islands, whereas Sri Lanka is separated from India by a narrow channel of sea formed by the Palk Strait and the Gulf of Mannar.

3. The sun rises two hours earlier in Arunachal Pradesh as compared to Gujarat in the west but the watches show the same time. How does this happen?

Answer:

The latitudinal and longitudinal extent of India is about 30°. The east-west extent is smaller than the north-south extent. There is a time lag of two hours from Gujarat to Arunachal Pradesh. As Arunachal Pradesh lies to the eastern side of India, the sun rises here earlier when compared to Gujarat. The time along the Standard Meridian of India (82°30’E) passing through Mirzapur (in Uttar Pradesh) is taken as the standard time for the whole country. The latitudinal extent influences the duration of day and night, as one moves from south to north. Therefore, the watches show the same time in all the parts of the country.

4. The central location of India at the head of the Indian Ocean is considered of great significance. Why?

What are the latitudinal and longitudinal extensions of India?
The total area of India and the land boundary.

What are the countries that lie on the eastern coast and the western coast of India?

What are the neighbouring countries of India?

Compute the value of 9×2 + 4y2 if xy = 6 and 3x + 2y = 12.

Solution:

Consider the equation 3x + 2y = 12

Now, square both sides:

(3x + 2y)2 = 122

=> 9×2 + 12xy + 4y2 = 144

=>9×2 + 4y2 = 144 – 12xy

From the questions, xy = 6

So,

9×2 + 4y2 = 144 – 72

Thus, the value of 9×2 + 4y2 = 72

3. Find the value of the polynomial 5x – 4×2 + 3 at x = 2 and x = –1

Solution:

Let the equation be f(x) = 5x – 4×2 + 3

Now, for x = 2,

f(2) = 5(2) – 4(2)2 + 3

=> f(2) = 10 – 16 + 3 = –3

Or, the value of the polynomial 5x – 4×2 + 3 at x = 2 is -3

Similarly, for x = –1,

f(–1) = 5(–1) – 4(–1)2 + 3

=> f(–1) = –5 –4 + 3 = -6

4. Calculate the perimeter of a rectangle whose area is 25×2 – 35x + 12.

Solution:

Given,

Area of rectangle = 25×2 – 35x + 12

We know, area of rectangle = length × breadth

So, by factoring 25×2 – 35x + 12, the length and breadth can be obtained.

25×2 – 35x + 12 = 25×2 – 15x – 20x + 12

=> 25×2 – 35x + 12 = 5x(5x – 3) – 4(5x – 3)

=> 25×2 – 35x + 12 = (5x – 3)(5x – 4)

So, the length and breadth are (5x – 3)(5x – 4).

Now, perimeter = 2(length + breadth)

So, perimeter of the rectangle = 2((5x – 3)+(5x – 4))

= 2(5x – 3 + 5x – 4) = 2(10x – 7) = 20x – 14

So, the perimeter = 20x – 14

5. Find the value of x3 + y3 + z3 – 3xyz if x2 + y2 + z2 = 83 and x + y + z = 15

Solution:

Consider the equation x + y + z = 15

From algebraic identities, we know that (a + b + c)3 = a2 + b2 + c2 + 2(ab + bc + ca)

So,

(x + y + z)2 = x2 + y2 + z2 + 2(xy + yz + xz)

From the question, x2 + y2 + z2 = 83 and x + y + z = 15

So,

152 = 83 + 2(xy + yz + xz)

=> 225 – 83 = 2(xy + yz + xz)

Or, xy + yz + xz = 142/2 = 71

Using algebraic identity a³ + b³ + c³ – 3abc = (a + b + c)(a² + b² + c² – ab – bc – ca),

x3 + y3 + z3 – 3xyz = (x + y + z)(x² + y² + z² – (xy + yz + xz))

Now,

x + y + z = 15, x² + y² + z² = 83 and xy + yz + xz = 71

So, x3 + y3 + z3 – 3xyz = 15(83 – 71)

=> x3 + y3 + z3 – 3xyz = 15 × 12

Or, x3 + y3 + z3 – 3xyz = 180

English

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