Key Points

• Silver is a metallic element with the chemical symbol Ag and atomic number 47 and Chlorine is an element with the symbol Cl and atomic number 17.
• Ag+ contains silver ions with an anion whose silver salt is soluble. The Cl- contains chloride ions with a cation whose chloride is soluble.
• When the two solutions are combined, a white precipitate of silver chloride is formed. Hence option 3 is correct.

Ag⁺ + Cl^- → AgCl.

• Silver chloride is a chloride of silver that occurs naturally as the mineral chlorargyrite and is used to make photographic paper and pottery glazes.
  • It is also found in stained glass colourants, bandages, and other wound healing products, and may be used as an antidote to mercury poisoning.
• Silver chloride is prepared when sodium chloride is added to silver nitrate solution a white precipitate of silver chloride occurs.
• Silver chloride undergoes a decomposition reaction in the presence of sunlight to form silver and chlorine.

Additional Information

• Pure silver is the best conductor of heat and electricity, so it is sometimes used in making solder, electrical contacts, and printed circuit boards.
• Silver is also the best reflector of visible light known, but silver mirrors must be given a protective coating to prevent them from tarnishing.
• Argon appears as a colourless odourless noncombustible gas. Heavier than air and can asphyxiate by displacement of air. Exposure of the container to prolonged heat or fire can cause it to rupture violently and rocket.
  • If liquefied, contact with the very cold liquid with water may cause violent boiling.
• Chloride is a mineral naturally found in various foods, but our main dietary source is sodium chloride, otherwise known as table salt.
  • It carries an electric charge and therefore is classified as an electrolyte, along with sodium and potassium.

Given:

2x + 3y = 9 and xy = 3

Concept used:

(a + b)² = a² + b² + 2ab

a³ + b³ = (a + b)(a² - ab + b²)

Calculation:

2x + 3y = 9

on squaring both side we get

(2x + 3y)² = 9²

⇒ 4x² + 9y² + 12xy = 81

⇒ 4x² + 9y² + 12 × 3 = 81

⇒ 4x² + 9y² = 45

now,

8x³ + 27y³ = (2x)³ + (3y)³

⇒ (2x)³ + (3y)³ = (2x + 3y)(4x² - 6xy + 9y²)

⇒ (2x)³ + (3y)³ = 9 × (45 - 6 × 3)

⇒ 243

∴ The answer is 243.

Alternate Method

a³ + b³ = (a + b)³ - 3ab(a + b)

8x³ + 27y³ = (2x + 3y)³ - 3 × 2x × 3y(2x + 3y)

⇒ 9³ - 18 × 3 × 9

⇒ 729 - 486

⇒ 243

∴ The answer is 243.

The least possible Venn diagram for the given statement is:

Conclusions:

I. Some brushes are tables → Does not Follow (As, all brushes are easels and some easels are tables. So, it is possible but not definitely true.)

II. Some paints are easels → Follow (As, some paints are brushes and all brushes are easels. So, whole brushes comes in easels and have some part common with paints therefore it is definitely true.)

III. Some easels are brushes → Follow (As, all brushes are easels. So, whole brushes comes in easels therefore it is definitely true.)

So, Only conclusions II and III follow.

Hence, the correct answer is "Only conclusions II and III follow".

The correct answer is A - (ii), B - (iii), C - (iv), D - (i).

Important Points

• Champaran Satyagraha:
  • Many movements were made in our country against the British under the leadership of Gandhiji.
  • One of these movements was named Champaran Satyagraha, which was associated with the farmers.
  • It was started on April 19, 1917
  • The reason for the beginning of this movement was the forced cultivation of indigo by the British.
  • Because by cultivating indigo, the land of the farmers was getting spoiled.
• Rowlatt Satyagraha:
  • This law was passed in March 1919 by the Imperial Legislative Council which gave them the power to arrest any person without any trial.
  • To abolish this act, Gandhi and the other leaders called for a Hartal (suspension of work) to show Indians' objection to this rule, called the Rowlatt Satyagraha.
• Kheda Satyagraha:
  • The Kheda Satyagraha began on March 11, 1918, exactly four days after the major mill strike in Ahmedabad.
  • Although Mahatma Gandhi was its spiritual head, the Kheda Satyagraha was mainly led by Sardar when the agricultural economy was devastated by famine, cholera and plague in the region.
  • In view of such a situation, there should have been a waiver of rent, but the government officials were not ready to listen to this point of the farmers.
  • When all the prayers of the farmers became fruitless, then Mahatma Gandhi announced the 'Kheda Movement' on March 22, 1918 and took over the reins of it.
• Bardoli Satyagraha: 
  • The Bardoli Satyagraha, 1928 was a movement in the independence struggle led by Sardar Vallabhai Patel for the farmers of Bardoli against the unjust raising of taxes.

In News

• Rahul Singh, a senior bureaucrat and a 1996-batch IAS officer of the Bihar cadre, has been appointed as the new chairperson of the Central Board of Secondary Education (CBSE).

Key Points

• Singh is currently serving as the Additional Secretary in the Department of Personnel and Training (DoPT).
• Nidhi Chhibber, the outgoing CBSE chairperson, has been appointed as Advisor to the Niti Aayog.
• The Appointments Committee of the Cabinet (ACC) approved Singh's appointment, as per an order issued by the Personnel Ministry.

Additional Information

• A P Das Joshi, a 1994-batch IAS officer of the Assam-Meghalaya cadre, will replace Singh as the new Additional Secretary in DoPT.
• Rajeev Kumar Mital has been appointed as the Director General of the National Mission for Clean Ganga under the Ministry of Jal Shakti.
• Gyanesh Bharti will take over as the Additional Secretary in the Ministry of Women and Child Development, while Deepak Narain has been named as the Additional Secretary and Financial Advisor in the Ministry of Information and Broadcasting.

Given:

The average weight of 14 students = 30 kg.

2 students of weight = 20 kg & 24 kg respectively, joined

Concept Used:

Average = Sum of observations/Total no. of observations

Calculations:

Total weight of 14 students = 14 × 30 = 420 kg

When 2 students joined then,

New total weight = 420 + 20 + 24 = 464 kg

New total number of students = 14 + 2 = 16

Then, the new average weight of the class = 464/16 = 29 kg.

Hence, the correct answer is 29 kg.

The pattern followed here is,

Hence, the correct answer is "5160".

Important Points

• Devaprayag is the place of confluence of the Bhagirathi and Alaknanda River.
• Vishnuprayag is the place of confluence of the Dhauliganga  and Alaknanda River.
• Rudraprayag is the place of confluence of the Mandakini and Alaknanda River.
• Karnaprayag is the place of confluence of the Pindar and Alaknanda River.
• Nandaprayag is the place of confluence of the Nandakini and the Alaknanda River.

Additional Information

• Alaknanda river is one of the headstreams of the Ganga.
• It rises at the confluence and feet of the Satopanth and Bhagirath glaciers in Uttarkhand.
• It meets the Bhagirathi River at Devprayag after which it is called as the Ganga.
• Its main tributaries are the Mandakini, Nandakini, and Pindar rivers.
• Bhagirathi river is one of the two most important headstreams of the Ganga which meets the Alaknanda at Devprayag to form the Ganga
• It rises at the foot of Gangotri Glacier, at Gaumukh, at an elevation of 3892m at the base of Chaukhamba peak in the Uttarkashi district of Uttarakhand.
  • Dhauliganga river originates from Vasudhara Tal, perhaps the largest glacial lake in Uttarakhand.
• It is one of the important tributaries of Alaknanda, the other being the Nandakini, Pindar, Mandakini and Bhagirathi.
• Dhauliganga is joined by the Rishiganga river at Raini.
• At Devprayag, the Bhagirathi meets the Alaknanda. Hereafter, it is known as the Ganga.
• The Alaknanda has its source in the Satopanth glacier above Badrinath.
• The Alaknanda consists of the Dhauli and the Vishnu Ganga which meet at Joshimath or Vishnu Prayag.
• The other tributaries of Alaknanda such as the Pindar join it at Karna Prayag while Mandakini or Kali Ganga meets it at Rudra Prayag.
• The Ganga enters the plains at Haridwar.

Key Points

Samudrayaan:

• Recently, ​The National Institute of Ocean Technology (NIOT) has completed a key test for India’s first manned submersible mission called Samudrayaan. 
• It is India’s first manned mission to explore the deep ocean. 
• Nodal Ministry: Ministry of Earth Sciences (MoES) 
• It aims to develop a self-propelled manned submersible to carry three human beings to a water depth of 6,000 meters in the ocean. Hence, option 3 is the correct answer.
• It will also develop a suite of scientific sensors and tools for deep ocean exploration. 
• It is designed to study the deep ocean resources and conduct biodiversity assessments as well. 
• The mission will not disturb the ecosystem as the submersible is used solely for exploration purposes. 
• The project is part of the larger Deep Ocean Mission, which supports the Central Government’s Blue Economy policy.

MATSYA 6000:

• It is a manned submersible vehicle developed by the National Institute of Ocean Technology (NIOT), Chennai. 
• It was developed under the Samudrayaan mission to facilitate humans in the deep ocean in exploring mineral resources.
• It has an endurance of 12 hours of operational period and 96 hours in case of emergency.

Additional Information

Deep Ocean Mission:

• It is a mission-mode project to support the Blue Economy Initiatives of the Government of India.
• It has been launched as a Central Sector Scheme of the Ministry of Earth Sciences.
• It aims to develop technologies to harness living and non-living resources from the deep oceans.

Calculation:

The denominators are 10, 9, 15,

5, and 3. Their LCM is 90. 

Now,

7/10 × 90 = 63

4/9 × 90 = 40

2/15 × 90 = 12

3/5 × 90 = 54

2/3 × 90 = 60

Now, you can compare the numerators of these equivalent fractions

to find the largest and smallest fractions:

So, the smallest fraction is 2/15 and the largest fraction is 7/10.