Slant height of cone = radius of sector = 12 cm

Radius of cone = \(\frac{120}{360}\) of radius of sector = 12 x \(\frac{120}{360}\) = 4 cm

Given function (x) = x³ + x ² − 1 is polynomial of degree 3. 

Therefore, given function (x) = x ³ + x ² − 1 is defined for every real value of . 

Let us the continuity of function (x) = x ³ + x ² − 1 at arbitrary point x = c. 

The left hand limit of function at x = c is (c⁻) = \(\lim \limits _{x \to c^+}\) f(x) = \(\lim \limits _{h \to 0}\) f(c − ℎ) 

= \(\lim \limits _{h \to 0}\) (c − ℎ)³ + (c − h)² − 1 

= (c − 0)³ + (c − 0)² − 1 = c³ + c² − 1. (By putting the limit ) 

The right hand limit of function at x = c is f(c⁺) 

= \(\lim \limits _{x \to c^+}\) f(x) =\(\lim \limits _{h \to 0}\) f(c + h) 

= \(\lim \limits _{h \to 0}\) (c + h)³ + (c + h)² − 1 = (c + 0)³ + (c + 0)² − 1 = c³ + c² − 1. (By putting the limit ) 

And the functional value of function f(x) = x³ + x² − 1at x = c is f(c) = c³ + c² − 1. 

Hence, the left hand limit of function at x = c = the right hand limit of function at x = c = f(c). 

i.e., f(c⁻) = f(c ⁺) = f(c) = c³ + c² − 1. 

Therefore, the function f(x) =x³+ x² − 1is continuous at x = c, 

which is arbitrary point. 

Hence, f is continuous for each x ∈ R.

Correct option is C) considered

Correct option is A) crying / spilt

Correct answer is (d) Assertion and reasoning both are correct

(1) A. balanced in our emotions.

(2) C. respect the origins from where we have grown.

(3) D. Everyone is dependent on each other

(4) C. Selfless assistance to help others.

(5) B. remaining hidden.

(6) B. workaholic (work+ alcoholic)

(7) C. (1), (4) and (5)

(8) D. Nothing lasts forever.

(9) D. Having free time for ourselves.

(10) B. Look deep into nature, and then you will understand everything better. - A. Einstein

(2)Respect the origins form where we have grown 

(3)Everyone  is dependent on each other 

1. Basketball is the most popular game in the school. 

2. True. 

3. 35 students play only cricket. 

4. Don’t look down upon the poor.

The purpose of an essay is to present a coherent argument in response to a stimulus or question, and to persuade the reader that your position is credible (i.e. believable and reasonable).

Meena has made use of the library the most.

The milk that is collected from various sources needs to be tested in the dairy for its purity. After it’s tested, it’s pasteurized so that when it is marketed and shelved, it does not easily get spoilt. The pasteurized milk is cooled before it’s bottled and packed. It is distributed to wholesale dealers who in turn sell it to retailers. The milk is then sold in booths and shops to customers.

The correct answer is Regur.

• Black Soils are commonly referred to as regur but are widely known as “black cotton soils,” as cotton has been the most common conventional crop in areas where they are found.
• This type of soil is typically found in the Deccan Trap (Basalt) region which spreads over the northwest Deccan plateau and is made from lava flows.
• The Black soil or Regur is found on the plateaus of Maharashtra, Saurashtra, Malwa, Madhya Pradesh, Chhattisgarh and stretch in the Southeast direction along the Godavari and the Krishna Valleys.
• The properties of such soils include the following: high compressibility, low bearing capacity, and low shearing strength.
• The Black soils are made up of clayey materials and are widely known for their capacity to hold moisture.
• The Black soils are highly prosperous in calcium carbonate, magnesium, potash, and lime.

Vasant is a good example to show how good and bad habits can make or mar a man. Vasant was very irregular to school and so lagged behind in studies. He had problems with attendance too. Even when the Headmaster advised him and warned him, he paid no heed. He only grew to be more irregular. Naturally he could not perform well in the exam and failed miserably. Fortunately, at least then he realized his mistake and corrected his ways. The next year it was a reformed Vasant everyone saw. He studied earnestly and as a result, he not only passed but also earned a I class.

Recently when eight of us went to Bandipur forest it was an awe inspiring experience. We got to see lovely peacocks dancing away to glory and majestic elephants climbing up the hill as though they were the lords of the hills. We played in the water of the stream flowing in the valley. In the evening we glimpsed the spectacular sunset. We jumped for joy looking at the beautiful scenery. We sang and danced being one with nature. We returned in the evening although we felt like spending more time in the natural surroundings. We have decided to have more such visits in the future.

Gandhiji was the greatest Indian of the 20th century. It is remarkable that he led India in its freedom movement at a critical juncture with nothing else but truth and non-violence as his weapons. However, although this was his greatest contribution, there were other remarkable achievements as well. Gandhiji strove relentlessly for Hindu-Muslim unity. His attempts to form a casteless society are praiseworthy indeed. The annals of Indian history will be incomplete if the accomplishments of this noble apostle of peace are forgotten. Although Gandhiji – the Father of the Nation – was assassinated soon after India got freedom, his principles have remained the guiding light of India.

The correct answer is All of the above.

• Rishi Agastya was an eminent saint of Rigvedic time, Lopamudra was the wife of the sage Agastya. 
• Vishwavara of the Atri family is ascribed a hymn of six verses. She was a married woman.
• Rigveda also mentions another woman Apala.
• She was also a married woman, but then her husband discarded her because she was suffering from an incurable skin disease.
• Ghosha Indian female philosopher from the ancient Vedic period.

• Vishwavara is famous for approaching the blazing sacrificial fire at dawn with her face towards the East, offering oblations to the gods, and praying for love and happiness in wedded life.
• Lopamudra is also known as Kaushitaki and Varaprada.
• Ghosha was also known as a Brahmavadini.

Women scholars such as Lopamudra, Gargi and Maitreyi are mentioned in the vedic literature.

1. Economic advantage 

2. Protection of members

Answer is (a) I and II

• To strengthen the process of economic development of rural women and create a conducive environment for social change. 
• To form a self-help group based on thrift and credit principles which builds self-reliance and enable women, to have greater access and control over resources.

b. Disappointment and anxiety 

• Tribes have paid disproportionate price for the development of the rest of the Indian society 
• National developments started in Nehruvian era involving the building of large dams, factories and mines were undertaken at the cost of dispossessing tribes of their land. 
• The loss of forests, community based collective ownership on which tribal communities depended has been a major blow 
• Heavy immigration of non-tribals threaten to disrupt their culture

According to M.N. Srinivas “A caste is dominant when it preponderates numerically over the other castes, when it also wields preponderant economic and political power, and when it enjoys a high ritual status in local caste hierarchy”.

a) They preferred children to work in farms. 

Dilapidated and Poor Houses, High Density of Population and Housing.

1. Hindu Marriage Act of 1955.

2. Domestic Violence Act of 2005.

• Commercialization of agriculture led to the growth of migrant agricultural labour that circulated between their home villages and more prosperous areas.
• Migrants were more easily exploited by the wealthy farmers and were usually not paid the minimum wages. 
• These migrant workers were terms as’ footloose labour’ by Jan Breman. • Migration and lack of job security have created very poor working and living conditions for these workers.

A. Mahnavami Dibba was part of ‘The King’s Palace Complex’.

Matriarchical and Patriarchical Joint Family.

Matriarchal joint family and patriarchal joint family.

Preponderates Numerically over other castes and high.

1. Ritual status in local. 

2. hierarchy

Alcohol, gambling, spend thriftness, Failure of crops, Chromic illness, Debt burden, loss in non-agricultural activities.

Answer is B. Tuluva

A. Thinkers of the world tried to understand mysteries of existence

Modernization in India is undergoing the following processes:

1. At the economic level, there is a persistent and growing tendency to adopt the rational, mechanized industrial economy in place of older communal — familistic tool economy. This is even responsible for the breakdown of traditional systems like jajmani system.

2. At the political level, the change in the power structure is being introduced through the abolition of semi-feudal group-oriented power structure of the past and by replacing it by a rational parliamentary democratic structure of power.

3. At the cultural level, the change in the realm of values is from sacred value system to secular value system.

4. At the social level, there is a decline in the traditional principle of ascribed status and role to achieve status and role. Yogendra Singh in his work “Modernization of Indian Tradition” is of the opinion that a unique feature of modernization in India is that it is being carried forward through adaptive changes in the traditional structures rather than structural dissociation or breakdown.

Unity implies oneness or a sense of we-ness.

1. High density of population and housing.

2. Lack of public utilities and facilities.

Small in size and importance to primary relation.

The term Demography is derived from two Greek words i.e. demos (people) and graphein (describe), implying the description of people.

Women Empowerment is the act of empowering women i.e. to give them the power or authority. The term Empowerment has different meanings to women of different classes.

A Self-help Group comprises a group of micro enterpreneurs having homogenous social and economic backgrounds, all voluntarily coming together to save regularly small sums of money, mutually agreeing to contribute to a common fund and to meet their emergency needs from that fund on the basis of mutual help.

Theodore Levitt.

Sathya Shodaka samaja.

1. Tribal groups refused to be absorbed. 

2. Special problem posed by strong ethnic groups.

Holayas and Bhories.

A . R . Desai.

Sathya Shodaka samaja.