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(3x−2y)³ + (2y−4z)³ + (4z−3x)³ 

Let (3x−2y) = a, (2y−4z) = b , (4z−3x) = c 

a + b + c = 3x − 2y + 2y − 4z + 4z − 3x = 0 

We know, a³ + b³ + c³ − 3abc = (a + b + c)(a² + b² + c² − ab − bc − ca) 

⇒ a³ + b³ + c³ −3abc = 0 

or a³ + b³ + c³ = 3abc

⇒ (3x − 2y)³ + (2y − 4z)³ + (4z − 3x)³ = 3(3x − 2y)(2y − 4z)(4z − 3x)

(i) 3x² -4x+15 is a polynomial of one variable x. 

(ii) y² -2√3 is a polynomial of one variable y. 

(iii) 3√x +√2x is not a polynomial as the exponents of 3√x is not a positive integer. 

(iv) x - 4/x is not a polynomial as the exponent of -4/x is not a positive integer. 

(v) x¹² + y³ + t⁵⁰ is a polynomial of three variables x, y, t.

(2x − 3y)³ + (4z − 2x)³ + (3y − 4z)³ 

Let 2x – 3y = a , 4z – 2x = b , 3y – 4z = c 

a + b + c= 3x − 2y + 2y − 4z + 4z − 3x = 0 

We know, a³ + b³ + c³ −3abc = (a + b + c)(a² + b² + c² − ab − bc − ca) 

⇒ a³ + b³ + c³ − 3abc = 0 

(2x − 3y)³ + (4z − 2x)³ + (3y − 4z)³ = 3(2x − 3y)(4z − 2x)(3y − 4z).

Eastern Ghats is a discontinuous and irregular one. It is dissected at many places by the rivers, which drain into the Bay of Bengal. Its height ranges from 1,100 to 1,600 metres.

x/2 - 1/5 = x /3 + 1/4

L.C.M. of the denominators, 2, 3, 4, and 5, is 60.

Multiplying both sides by 60, we obtain

60( x/2 - 1/5 ) = 60( x/3 + 1/4 )

⇒ 30x − 12 = 20x + 15 (Opening the brackets)

⇒ 30x − 20x = 15 + 12

⇒ 10x = 27

⇒ x = 27/10

Kalrayan hill is located in Eastern Ghats.

The correct answer is (C)  2.25.

Correct Answer is: (c) 39

The correct answer is 

(A) 3/5 = 12/20

(B) 4/18 = 2/9

(C) 8/10. = 3.2/4

(D) 18/45 = 16/40 = 24/60

(E) 16/36 = 28/63 = 36/81 = 52/17

(i) Given 16: 18 = x: 96

In proportion we know that product of extremes = product of means

16/18 = x/96

On cross multiplying

x = (18 × 96)/ 16

x = 256/3

(ii) Given x: 92 = 87: 116

In proportion we know that product of extremes = product of means

x/ 92 = 87/116

On cross multiplying

x = (87 × 92)/ 116

x = 69

1. Always eat breakfast.

2. Eat healthy food.

3. Chew your food properly.

4. Keep away from fast food and soft drinks.

5. Have a fiber – filled diet which includes whole grains, vegetables and fruits.

6. Eat more vegetables and fruits.

7. Prefer water over other beverages.

8. Wash hands with soap and clean water, before having meals.

(d) all of these

1. Oil – It is an important ingredient of our food. It is obtained from various parts of the plant. It is the source of energy. It is obtained mainly from seeds and fruits of various plants

e.g. soybean, coconut, mustard, groundnut, sesame, sunflower, etc.

2. Energy arink – Tea and coffee are known as energy drinks. Tea is prepared by drying the leaves of tea plant. The seeds of coffee plant are used to make coffee powder.

Various types of food ingredients are obtained directly or indirectly from animals, like milk, eggs, honey, meat, etc.

1. Milk and milk product – We get milk from cow, buffalo, goat, sheep etc. Curd, buttermilk, maava, ghee, cheese, etc. are prepared from milk. 

2. Honey – We get honey from honeybees.

3. Eggs – Eggs are obtained from hen.

4. Meat – Meat is obtained from goat, hen, fish etc

No, different organisms and animal have different physical requirements.

Yes, some animals obtain their food from both plants and animals.

No, animals are not the only source of food for all animals.

No, plants are not the only source of food for all animals

Various parts of plants like root, stem, leaves, fruits, flowers, etc. are used as vegetables.

Table: various part of the plants as the source of vegetables

Food items eaten by us during a day.

No, all animals do not eat the same type of food materials.

We get honey from honeybees. It is sweet in taste.

From roots – carrot, beetroot, sweet potato.

From stem – potato, Sugarcane.

From leaves – spinach, fenugreek, cabbage.

Curd, butter milk, ghee, maava, cheese, etc.

We consume food in the form of products obtained from different parts of the plants, which are mentioned below: 

1. Cereals 

2. Pulses 

3. Vegetables 

4. Fruits 

5. Sugar 

6. Oils 

7. Spices

8. energy drinks

Cereals are important plant products for all human beings. They are used as a food ingredient. 

They are the main source of carbohydrates and provide energy. 

Example – wheat, corn, rice, millet, barley, etc. 

Two types of sugar are :

Jaggery and Sugar. These are the products obtained from sugarcane. These are prepared by using the sweat juice of sugarcane. Apart from sugarcane, sugar is also made from beetroot.

Two cereals wheat, rice.

Correct Answer is : (b) Loo

Oil is obtained mainly from seeds and fruits of various plants.

Idli – dosa is the famous food of south India.

(c) human being

Wolf is a carnivorous animal.

Eggs are obtained from hen.

Calcium in eggs.

Our body needs food because :

1. Food provides energy for various activities of the body. 

2. Food keeps body healthy and also helps in growth and development of the body.

3. Food maintains the ability to fight disease (disease resistance) in the body.

Magnetite is the best quality iron ore.

Yes, if there is an earthquake, where I live, my house would be in danger. The following damage could happen: 

(i) The various household equipment such as TV, radio, utensils, eatables etc. Could get destroyed.

(ii) If there would be a very severe earthquake, even the people would get crushed under the fallen houses and die. 

Guwahati, Aug1, 2005 The flood situation in Assam has worsened with death of about 500 people in the last three days. Due to the heavy monsoons, the river water level of the adjoining Brahmaputra river has further risen above the danger mark. The Regional Meteorological Centre here warned of more rain and thundershowers.

Aerial survey of the place was conducted to estimate the loss. The area has about 8000 houses under water, two hundreds of dead bodies of man and animals floating in the water. The state government has opened 2500 temporary camps besides lodging the flood hit, sad and homeless people in trying their best to provide help and support to the trapped people. They have been provided with food packets, drinking water, milk etc. Doctors are working voluntarily to provide free treatment to the injured and ill people and also providing
measures to prevent water borne diseases.

Government has announced to pay Rs. 2 lakh to the family members of the deceased and Rs. One lakh to all the flood hit families, as compensation.

Odisha hit by drought
Thursday 2 nd July, 2010
After a year Odisha has been hit by a severe drought again. More than 5,000 families living in the coastal area have been affected. Officials say the state has incurred a huge loss in its paddy crops worth more than 500 crores. There is scarcity of food and drinking water in the affected area. The people are dying due to starvation.
The State Minister said that the government had taken all the measures it could to ensure that the food and drinking water is available to those affected. Various NGO’s have also come to provide help and support to the people by providing food, water, milk, clothes etc. to the affected people. A leading state environmentalist said, the destruction of forest land and the lack of water conservation policy were two key factors responsible for the drought. Government has announced to pay Rs. 25,000 to the affected family as compensation.

If my house would have been all alone at a place, then
(i) There would have been no one to help us during any problem, calamities, or disasters like earthquake, flood, fire, theft, major illness etc.
(ii) There would be no one with whom I could play.
(iii) There would be no one with whom we could celebrate various festivals and special occasions.
(iv) I would have felt scared also.

Yes, these houses would be comparatively safer than before in case there is an earthquake. This is because these are now prepared according to the suggestions and designs explained by the engineers

The people who came to Jasma’s village for help were: 

(i) People from the cities.

 (ii) Scientists, architect and engineers. 

(iii) Non-government and Voluntary organizations

(iv) Some doctors 

(v) State Minister and other political leaders These people helped the villagers in a number of ways, such as: 

(i) People from the cities with food, medicines and clothes. They also helped to put up the tents. 

(ii) The scientists tried to find out which areas have more chances of having earthquake and they gave an alarming signal to the villagers to keep them away from these places. 

(iii) The engineers and architects showed them some special designs for houses that would not get much damaged in an earthquake. 

(iv) The non-government voluntary organizations helped the people by providing them foods, clothes, tents to make huts etc.

 (v) Doctors and nurses provided them free first aid and treatment. 

(vi) The state minister and other political leaders provided the people various basic things like food grains, vegetables, compensatory money etc.

The list of the people who had provided help at that time is as follows:

 (i) The neighbours helped each other.

 (ii) People from the cities.

 (iii) The local leaders. 

(iv) The political leaders.

 (v) Various non-government organizations of that area.

 (vi) Doctors and nurses of the hospitals of that place. 

(vii) Few shopkeepers

Yes, few years back, few houses in our area got burnt. At that time all the neighbours helped them and provided them all possible support.

Yes, we were told in our school about what should be done in case of an earthquake. We were told to go out in an open place if possible or sit under a strong object like a table and hold it firmly.