निर्देश: निम्नलिखित प्रश्न में, चर X और Y में दो समीकरण दिए गए हैं। आपको इन समीकरणों को हल करना है और X और Y के बीच संबंध निर्धारित करना है।

I. X² – 5x + 6 = 0
 II. Y² – y – 6 = 0

प्रति व्यक्ति आय में वृद्धि बेहतर कल्याण का संकेत देगी यदि इसके साथ हो -

समबाहु त्रिभुज की भुजा और ऊँचाई का अनुपात कितना होता है?

यदि 3sin²θ – cosθ-1=0, 0⁰< θ<90⁰ है, तो cot θ + cosec θ का मान क्या है?

Comprehension: Read the following passage and answer the questions given after it.

Since September, at least 25 people have died and thousands have been made homeless. Every state and territory in Australia has experienced fires this summer. But the biggest fires burn along stretches of the eastern and southern coast, where most of the population lives. This includes areas around Sydney and Adelaide. More than 6.3 million hectares (63,000 sq km or 15.6 million acres) have been burned so far – one hectare is roughly the size of a sports field. To put that in perspective, around 800,000 hectares were engulfed in a bush fire in 2018 in California. Australia has always experienced bushfires – it has a "fire season". But this year they are a lot worse than normal.

Fires are usually caused by lightning strikes or accidentally by a spark – but some fires are also started deliberately. This year, a natural weather phenomenon known as the ‘Indian Ocean Dipole’ has meant a hot, dry spell across the country. This year, Australia twice set a new temperature record: an average maximum of 41.9°C was recorded on 18 December. That comes on top of a long period of drought.

Scientists have long warned that this hotter, drier climate will contribute to fires becoming more frequent and more intense. The more extreme weather patterns and higher temperatures increase the risk of bushfires and allow them to spread faster and wider. Fire fighters are spraying water and fire retardant from planes and helicopters as well as from the ground. But fighting bush fires is extremely difficult and often authorities have to focus on just stopping the spread, rather than putting the fire out. The spread can for instance be best contained by digging earth boundaries to stop the flames from spreading. The priority is saving lives.

Professional fire fighters are the first in line to battle the flames, but they are outnumbered by the thousands of volunteers. Three of them have died. There's also help coming from abroad: the US, Canada and New Zealand have sent fire fighters to help. Australia's police, military and navy are involved in rescue and evacuation efforts. While people can flee the fires and are being evacuated if need be, the flames are devastating wildlife in the affected areas. One study estimated that half a billion animals have died in New South Wales alone.

Zookeepers take animals home to save them from fire, but the fires don't only kill animals directly, they also destroy the habitat, leaving the survivors vulnerable even when the fires have gone. So the true scale of loss isn't yet clear. Experts say more than 100,000 cows and sheep may also have been lost, which is devastating for farmers.

Each state runs its own emergency operation, but Prime Minister Scott Morrison has promised better funding for fire-fighting and payouts for volunteer fire fighters, and an additional A$2billion ($1.4billion; £1billion) for the recovery. But the national government has come under strong criticism from its opponents that it has not been doing enough against climate change. The country is one of the world's biggest per capita greenhouse gas emitters but under international agreements it has committed itself to reduction targets

It can be inferred from the passage that this year’s fire in Australia is mostly a result of:

Read the given passage and answer the questions that follow.

Santiniketan embodies Rabindranath Tagore’s vision of a place of learning that is unfettered by religious and regional barriers. Established in 1863 with the aim of helping education go beyond the confines of the classroom, Santiniketan grew into the Visva Bharati University in 1921, attracting some of the most creative minds in the country.

He developed a curriculum that was a unique blend of art, human values and cultural interchange. Even today, in every step, in every brick and in every tree at Santiniketan, one can still feel his presence, his passion, his dedication and his pride in the institution. In 1862, Maharishi Debendranath Tagore, father of Rabindranath, was taking a boat ride through Birbhum, the westernmost corner of Bengal, when he came across a landscape that struck him as the perfect place for meditation. He bought the large tract of land and built a small house and planted some saplings around it. Debendranath Tagore decided to call the place Santiniketan, or the ‘abode of peace’, because of the serenity it brought to his soul. In 1863, he turned it into a spiritual centre where people from all religions, castes and creeds came and participated in meditation.

In the years that followed, Debendranath’s son Rabindranath went on to become one of the most formidable literary forces India has ever produced. He wrote in all literary genres but he was first and foremost a poet. As one of the earliest educators to think in terms of the global village, he envisioned an education that was deeply rooted in one’s immediate surroundings but connected to the cultures of the wider world.

Located in the heart of nature, the school aimed to combine education with a sense of obligation towards the larger civic community. Blending the best of western and traditional eastern systems of education, the curriculum revolved organically around nature with classes being held in the open air. Tagore wanted his students to feel free despite being in the formal learning environment of a school, because he himself had dropped out of school when he found himself unable to think and felt claustrophobic within the four walls of a classroom. Nature walks and excursions were a part of the curriculum, special attention was paid to natural phenomena and students were encouraged to follow the life cycles of insects, birds and plants.

The rural paradise of Santiniketan, Tagore’s erstwhile home, has become a thriving centre of art, education and internationalism over the years.

What did Santiniketan initially serve as?

Read the following passage carefully and answer the questions given below it. Certain words have been highlighted for your attention.

Most people spend (on average) half of their day tapping away at their hand-held devices. Either, surfing the net or checking notifications. Facebook ranks the highest in all social networking platforms, followed by Twitter, Instagram and so forth.

Social media is addictive- which is why so many people are 'hooked'. Often referred to as Social networking addiction, this phrase is often used to describe someone who spends too much time on Facebook, Twitter, Instagram and other channels. A blog post, Instagram post, tweet, or youtube video can be produced easily by anyone and shared, which can then be viewed by millions for free. Psychologists and scientists have now taken the time to study social media in terms of why they believe it interferes with aspects of our daily life. There is no official medical term that identifies addiction and social networking. It cannot be deemed as a disease or disorder as the cases are not severe and the habit can easily be maintained or prevented. Furthermore, instead of spending long periods of time on social media, we dip into and out of these sites all day long. We check for updates from friends and family as well as news and information. However, the behavior associated with the excessive use of these channels has become the subject of much public and sociological debate. We actively post, like, comment and share personal posts. Not only that, we tend to share and reshare expressions (of either negative or positive) contagiously. But, why?

Scientists believed some years ago that, dopamine was simply a pleasure chemical in the brain. Recent studies have shown that; dopamine actually produces the desire in people to 'want' by drawing out the need for us to -seek and search. Creating the ultimate drive to find what is that what we want.

Dopamine is spontaneous. It’s stimulated by unpredictability and small bits of information as well as reward cues which are the same conditions that social media presents to all users. In addition, the pull of dopamine is so strong that recent studies have shown that tweeting, for example, can be harder to resist than cigarettes and alcohol!

Researchers at Chicago University studied the effects of social media. They concluded quite quickly that people presented higher levels of addiction to social media than the need to smoke or drink. Media cravings ranked higher.

And, let’s not forget oxytocin, many call it the cuddle chemical because the brain releases pleasure chemicals that transpire usually when you kiss and hug- or tweet. It is also known as the hormone that builds the strong yet unique bond between mothers and their babies. Oxytocin is now regarded as the human stimulant of empathy, generosity, trust, and more. These are factors which many advertisers and marketers play on when promoting a brand or business over social media.

Nevertheless, problems have arisen most commonly with school kids - whereby mobile phone devices have been confiscated because exam results have fallen severely due to lack of attention on homework or studies. Schools in many westernized countries have had to take drastic action - banning smartphones, iPad and most portable devices from school premises- as it is claimed to be a huge distraction. Whereas, other schools use it for educational purposes and as a rewards system for their pupils.

Research has also indicated unsurprisingly that Facebook is the most common activity that university students switch to, when studying. Worryingly, it has also found that those who most engage in this type of internet browsing tend to have lower levels of educational achievement.

Also, there have been many cases of students posting or sharing content that is unethical, which has caused parents and academic institutions to limit the use of these online networking channels.

What does the phrase 'Social Networking Addiction' mean?

Direction: In the following passage, some of the words have been left out, each of which is indicated by a number.
Find the suitable word from the options given against each number and fill up the blanks with appropriate words to make the paragraph meaningfully complete. Many of us have a wide variety of responsibilities- familial, employment, educational, social – most of us even have all at the same time. Considering all our duties and the fact that time management is a (A) factor in our mental health, we cannot (B) to ignore any of them. If we plan our time better, we not only get more done, we are more efficient, satisfied and (C) yet relaxed; we are less likely to procrastinate over time. We experience less stress and more self-confidence and self-esteem. Put simply, this way we can attain (D) and reach our goals easily. To do this, firstly it is important to identify what your personal obstacles are. Then write a to-do list of what needs to be done. Start with the most to least important. (E) your work based on your values. Sometimes we won’t get everything done, but if we get the right things done, your day has a good ending. Keep in mind that time management is not about doing everything that needs to be done, at all costs but rather using appropriate time (F). Finally, remember to take a break and know your (G) for stress. Overworking is counterproductive and more often than not results in burnout. Remember, it doesn’t matter what the tasks are, learning to better manage your time to do them will result in less stress and more focus, productivity, efficiency and (in the end) relaxation.

(E) Find out the appropriate word in each case.