Class 12th

Let X be a random variable with distribution.

x                    -2                 -1                 -3                 4                   6

P(X = x)       $\frac{1}{5}$                    a   $\frac{1}{3}$                                                $\frac{1}{5}$ b

If the mean of X is ${\sigma }^2,$ 2.3 and variance of X is then $100{\sigma }^2$  is equal to:

The passage below is accompanied by a set of questions. Choose the best answer to each question.
Mirabai was a great saint and devotee of Sri Krishna. Despite facing criticism and hostility from her own family, she lived an exemplary saintly life and composed many devotional bhajans. Historical information about the life of Mirabai is a matter of some scholarly debate. The oldest biographical account was Priyadas's commentary in Nabhadas' Sri Bhaktammal in 1712. Nevertheless there are many aural histories, which give an insight into this unique poet and Saint of India. 
Mira was born around the start of the 16th Century in the Chaukari village in Merta, Rajasthan. Her father was Ratan Singh a descendent of Rao Rathor, the founder of Jodhpur. When Mirabai was only 3 years old, a wandering Sadhu came to her family's home and gave a doll of Sri Krishna to her father. Her father took this is as a special blessing, but was initially unwilling to give it to her daughter, because she felt she would not appreciate it. However Mira had, at first sight, become deeply enamoured with this doll. She refused to eat until the doll of Sri Krishna was given to her. To Mira, this figure of Sri Krishna, embodied his living presence. She resolved to make Krishna her lifelong friend, lover, and husband. Throughout her turbulent life she never wavered from her youthful commitment.
On one occasion when Mira was still young she saw a wedding procession going down the street. Turning to her mother she asked in innocence, “Who will be my husband?” Her mother replied, half in jest, half in seriousness. “You already have your husband, Sri Krishna.” Mira's mother was supportive of her daughter's blossoming religious tendencies, but she passed away when she was only young.
At an early age Mira's father arranged for her to be married to Prince Bhoj Raj, who was the eldest son of Rana Sanga of Chittor. They were an influential Hindu family and the marriage significantly elevated Mira's social position. However, Mira was not enamoured of the luxuries of the palace. She served her husband dutifully, but in the evening,she would spend her time in devotion and singing to her beloved Sri Krishna. Whilst singing devotional bhajans, she would frequently lose awareness of the world, entering into states of ecstasy and trance.
However, her new family did not approve of her piety and devotion to Krishna. To make things worse Mira refused to worship their family deity Durga. She said she had already committed herself to Sri Krishna. Her family became increasingly disproving of her actions, but the fame and saintly reputation of Mirabai spread throughout the region. Often, she would spend time discussing spiritual issues with Sadhus and people would join in the singing of her bhajans. However, this just made her family even more jealous. Mira's sister-in- law Udabai started to spread false gossip and defamatory remarks about Mirabai. She said Mira was entertaining men in her room. Her husband, believing these stories to be true, tore into her room with sword in hand. However, he saw Mira only playing with a doll. No man was there at all. Yet throughout these hysterical slanders Mirabai remained unmoved by both the criticism and praise of the world.

Which of the following statements is TRUE according to the passage?

The passage below is accompanied by a set of questions. Choose the best answer to each question.

Mirabai was a great saint and devotee of Sri Krishna. Despite facing criticism and hostility from her own family, she lived an exemplary saintly life and composed many devotional bhajans. Historical information about the life of Mirabai is a matter of some scholarly debate. The oldest biographical account was Priyadas's commentary in Nabhadas' Sri Bhaktammal in 1712. Nevertheless there are many aural histories, which give an insight into this unique poet and Saint of India.
Mira was born around the start of the 16th Century in the Chaukari village in Merta, Rajasthan. Her father was Ratan Singh a descendent of Rao Rathor, the founder of Jodhpur. When Mirabai was only 3 years old, a wandering Sadhu came to her family's home and gave a doll of Sri Krishna to her father. Her father took this is as a special blessing, but was initially unwilling to give it to her daughter, because she felt she would not appreciate it. However Mira had, at first sight, become deeply enamoured with this doll. She refused to eat until the doll of Sri Krishna was given to her. To Mira, this figure of Sri Krishna, embodied his living presence. She resolved to make Krishna her lifelong friend, lover, and husband. Throughout her turbulent life she never wavered from her youthful commitment.
On one occasion when Mira was still young she saw a wedding procession going down the street. Turning to her mother she asked in innocence, “Who will be my husband?” Her mother replied, half in jest, half in seriousness. “You already have your husband, Sri Krishna.” Mira's mother was supportive of her daughter's blossoming religious tendencies, but she passed away when she was only young.
At an early age Mira's father arranged for her to be married to Prince Bhoj Raj, who was the eldest son of Rana Sanga of Chittor. They were an influential Hindu family and the marriage significantly elevated Mira's social position. However, Mira was not enamoured of the luxuries of the palace. She served her husband dutifully, but in the evening,she would spend her time in devotion and singing to her beloved Sri Krishna. Whilst singing devotional bhajans, she would frequently lose awareness of the world, entering into states of ecstasy and trance.
However, her new family did not approve of her piety and devotion to Krishna. To make things worse Mira refused to worship their family deity Durga. She said she had already committed herself to Sri Krishna. Her family became increasingly disproving of her actions, but the fame and saintly reputation of Mirabai spread throughout the region. Often, she would spend time discussing spiritual issues with Sadhus and people would join in the singing of her bhajans. However, this just made her family even more jealous. Mira's sister-in- law Udabai started to spread false gossip and defamatory remarks about Mirabai. She said Mira was entertaining men in her room. Her husband, believing these stories to be true, tore into her room with sword in hand. However, he saw Mira only playing with a doll. No man was there at all. Yet throughout these hysterical slanders Mirabai remained unmoved by both the criticism and praise of the world.

The passage mainly deals with

There is a sentence that is missing in the paragraph below. Look at the paragraph and decide in which blank (option 1, 2, 3, or 4) the following sentence would best fit.

Sentence: This regime of direct taxes is manned by a cadre of Indian Revenue Services (IRS).

In India, like any other country, the government draws its income from two heads: tax revenue and non-tax revenue. (1)___________. Tax revenue has two components: direct tax which comprises Income Tax and Corporate Tax; and Indirect Taxes which has GST, Customs and other taxes. (2)__________. The Income Tax Department in India collects the direct taxes portion of the tax revenue for the government of India. (3)____________.  Most of these are highly technical, professional and tech-savvy cadre. However, the services rendered by the IRS in the nation-building hardly gets recognised. The work of an IRS officer is quite challenging and interesting. They are the earner of the nation-family. (4)_________.  IRS recruits enter the cadre at Assistant Commissioner Level through the civil services examination.

There is a sentence that is missing in the paragraph below. Look at the paragraph and decide in which blank (option 1, 2, 3, or 4) the following sentence would best fit.

Sentence: Such earthquakes are related to industrial activities.

The Pawnee earthquake followed the dramatic increase of seismic events in the central United States beginning in 2009, associated with the increase of underground wastewater disposal by oil and gas operators. (1)__________. This and other events in the area raised public concerns and led governmental agencies to shut down injection wells and establish new regulations regarding wastewater injections. (2)_________. While human-caused earthquakes have been documented for more than a century, their increasing number reported worldwide has drawn much scientific, social and political attention. (3)________. Some of the examples are mining, construction of water dams, injection of liquids such as waste water and carbon dioxide, and extractions associated with oil and gas exploitation. (4)____________. With the ever-increasing demand for energy and mineral supplies worldwide, the number of human-caused earthquakes is expected to rise in the upcoming years.

The four sentences (labelled 1, 2, 3 and 4) below, when properly sequenced, would yield a coherent paragraph. Decide on the proper sequencing of the order of the sentences and choose the correct option.

1. On 17 August 2017, three leading activists, aged 19 to 24, who had served their community service sentences for civil disobedience, were imprisoned following the Hong Kong government's unprecedented appeal of the ruling.
2. Hong Kong's version of “Occupy Wall street”, the Umbrella movement against Beijing politics was the most important protest in recent years, lasting three months.
3. As hundreds paid homage to the 2014 protests on September 29 in Hong Kong, the challenges facing the new generation of activists are not how to mobilise mass protests, but how to wrestle with the state's innovative strategy to manage society.
4. But three years later, Hong Kong's democracy is still kept at bay.