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We know that, the semi latus-rectum of a parabola is the harmonic mean between the segments of any focal chord of the parabola.

Given that, b and c are lengths of the segments of any focal chord of the parabola y²=4ax

So, Let l is the length of semi-latus rectum of the parabola. 

Then,1/b+1/c=2/l

⇒ l=2bc/(b+c)

Hence, length of latus-rectum=2bc/(b+c)

Correct option is (A) Baking Soda

Sodium hydrogencarbonate (Baking soda), NaHCO₃ is used in the fire extinguishers.

(c) Baking soda

Sodium hydrogen carbonate is known as baking soda because it decomposes on heating to generate bubbles of carbon dioxide (leaving holes in cakes or pastries and making them light and fluffy). Sodium hydrogen carbonate is made by saturating a solution of sodium carbonate with carbon dioxide. The white crystalline powder of sodium hydrogen carbonate, being less soluble, gets separated out. Na₂CO₃ + H₂O + CO₂ → 2NaHCO₃ Sodium hydrogen carbonate is a mild antiseptic for skin infections. it is used in lire extinguishers.

Correct option is (d) Urea

In the presence of metal surfaces or traces of akali (present in glass containers), the reaction is catalysed. It is, therefore, stored in wax-lined glass or plastic vessels in dark. Urea can be added as a stabiliser.

Correct answer is (D) NaHCO₃

Correct answer is (A) Low melting point

Liquation is used to purify metals having lower melting point than impurities present in them.

Correct option is (a) Cu

Cu cannot displace H₂ from mineral acids because it is below hydrogen in electrochemical series.

(d) Ethylene glycol and terephthalic acid

Ethylene glycol and terephthalic acid are monomers which on polymerization gives terylene.

Correct answer is (A) Urea

Urea acts as stabiliser for H₂O₂.

Correct answer is 6.00

PCl₃ , H₂O₂ , SF₄ , XeO₃ , PH4⁺ and [Al(OH)₄]^- are non-planer structures.

Correct option is (a) Cu 

Cu cannot displace H₂ from mineral acids because it is below hydrogen in electrochemical series.

(b) S₁ is correct but S₂ is incorrect.

Emulsions of oil in water are unstable and sometimes they separate into two layers on standing. For stabilization of an emulsion, a third component called emulsifying agent is usually added.

Because LiCl is covalent compound hence dissolves in organic solvent (Ethanol) but NaCl is ionic compound hence insoluble in ethanol.

Correct answer is (B) (A) , (B) and (D) 

2BeCl₂ + LiAlH₄ → 2BeH₂ + LiCl + AlCl₃

Correct answer is 3.00

Magnetic (Fe₃O₄), Siderite(FeCO₃), and Hematite(Fe₂O₃) are ores of iron

(C) Statement I is correct but Statement II is incorrect.

Statement I : Fact 

Statement II: The principle emulsifying agents for O/W emulsions are proteins, gums natural and synthetic soaps etc…

Correct option is (A) (A) and (C) only

(A) Both LiCl and MgCl₂ are soluble in ethanol 

(B) Li and Mg do not form superoxide 

(C) LiF has high lattice energy 

(D) Li₂O is least soluble in water than other alkali metal oxides

Correct option is: (C) Chlorinated Hydrocarbon

Correct answer is 4.

Bauxite — AlO_X(OH)_3–2x(where 0 < x < 1)

✓ Siderite — FeCO₃

Cuprite — Cu₂O

Calamine — ZnCO₃

✓ Haematite — Fe₂O₃

Kaolinite — Al₂(OH)₄Si₂O₅

Malachite — CuCO₃ . Cu(OH)₂

✓ Magnetite — Fe₃O₄

Sphalerite — ZnS

✓ Limonite — Fe₂O₃.3H₂O

Cryolite — Na₃AlF₆

Correct option is (B) Nitrogen

Nitrogen . Around 55% of hydrogen around would goes to ammonia production

(A) (A) - (IV), (B) – (III), (C) – (II), (D) – (I)

The correct answer is Mohandas Karamchand Gandhi.

Mohandas Karamchand Gandhi is known as the 'Father of the Nation' in India.

• The Parliament of Independent India officially recognized Gandhiji as the Father of the Nation. 
• Generally, the first President of an independent country is given such a title. Subhash Chandra Bose chose such a title because he had seen the role of Gandhiji in building India as an independent nation.
• Netaji Subhash Chandra Bose was the first person to call Mahatma Gandhi as a Father of Nation’ from Azad Hind Radio on July 6th, 1944.
• He gave the famous slogan, ”Jai Hind” from Free India Center, Germany.
• He formed the ‘Freedom Army’ which consisted of all prisoners of war captured by Germany with the help of Hitler.
• Mohandas Karamchand Gandhi:-
  • He was a Barrister or Lawyer by profession.
  • In 1888, MK Gandhi went to London, England, to study law.
  • Apart from completing legal education from England, he had to learn Indian law in Bombay.
  • During his first stay in London, from 1888 to 1891, he joined the executive committee of the London Vegetarian Society.

• Bhim Rao Ambedkar:- 
  • He is considered as the Father of the Indian Constitution.
  • He was the chief architect of the Constitution of India.
  • He was appointed Chairman of the Constitution Drafting Committee in 1947.
  • He was independent of India's first Minister of Law and Justice.
• Swami Vivekananda:-
  • He was born in 1863.
  • He founded the Ramakrishna Mission in May 1897.
  • He died in 1902 at Belur Math in West Bengal.
  • He was influenced by Ramakrishna Paramahansa who was also his Guru.
• Mahadev Govind Ranade:- 
  • He was one of India’s Citpavan Brahmans of Maharashtra who was a judge of the High Court of Bombay,
  • He is a noted historian and an active participant in social and economic reform movements.

The correct answer is VK Krishna Menon.

• In 1957, Menon set the record for the longest speech (8 hours) before the U.N. Security Council while defending India's rights to the disputed territory of Kashmir.
• The speech earned him the title of "Hero of Kashmir".
• His statement to the Security Council was given during three meetings on 23rd and 24th January 1957.
• He wrote the first draft of the Preamble to the Constitution of India, initiated the idea of the Constituent Assembly of India, and is considered the architect, and to have coined the name, of the Non-Aligned Movement.

B. only P and R

The antidiuretic hormone is secreted by the hypophysis (also known as pituitary) and it acts in the nephron tubules increasing the resorption of water. When the body needs to retain water, for example, in cases of blood loss and abrupt blood pressure lowering or in cases of abnormally high blood osmolarity, there is stimulus for ADH secretion.

When the body has an excess of water, as in cases of excessive ingestion or in abnormally low blood osmolarity, the secretion of ADH is blocked and the diuresis increases. ADH is also known as vasopressin since it increases the blood volume and thus heightens the blood pressure.

The renal regulator hormone secreted by the heart is the atrial natriuretic factor (or ANF). The ANF increases the excretion of sodium in the nephron tubules causing less resorption of water, more urinary volume, and thus lowering the blood pressure. The atrial natriuretic factor is secreted when there is an increase of the length of the heart muscle fibers in response to high blood pressure. The ANF is a natural antihypertensive substance. Since the health of the heart depends largely upon the stability of the normal blood pressure the evolution should have preserved the atrial natriuretic factor to allow information from the heart to be an additional mechanism for the renal control of the blood pressure.

•  In kidney failure patients’ urea can be removed by a process called hemodialysis. 
•  Blood drained from a convenient artery is pumped into a dialyzing unit after adding heparin. 
•  The unit contains coiled cellophane tubes surrounded by dialyzing fluid having the same composition as that of plasma except nitrogenous wastes. 
•  The porous cellophane membrane of the tube allows the passage of the molecules based on the concentration gradient. 
•  As nitrogenous wastes are absent in dialyzing fluid, these substances freely move out there by clearing the blood. 
•  The purified blood is pumped back through a vein after adding anti-heparin to it.

a. Tsetse flies

Tin Bigha Corridor is an issue, between India and Bangladesh.

China has become famous for its ‘Debt Trap Diplomacy’ in recent times. Under this China provides financial and technical expertise/assistance to help various nations to bring them under its direct or indirect influence. 

The first and the foremost implication of the diplomacy is that Beijing has now become Islamabad’s largest creditor. According to documents released by Pakistan’s finance ministry, its total public external debt stood at $44.35 billion in June 2013, just 9.3 percent of which was owed to China. By April 2021, this external debt had ballooned to $90.12 billion, with Pakistan owing 27.4 percent —$24.7 billion — of its total external debt to China, according to the IMF.

Economic advantages of China Pakistan Economic Corridor (CPEC) to the economy of Pakistan are: 

i. China provided financial and technical expertise to help Pakistan build its road infrastructure, supporting employment and income in the economy 

ii. CPCE has led to a massive increase in power generation capacity of Pakistan. It has brought an end to supply-side constraints in the nation, which had made blackouts a regular phenomenon across the country.

Communist policies – Protest against the autocracy of Chiang – Kai-Shek. Long march Red volunteers – People‘s Republic.

Chiang Kai-Shek ascertained military autocracy in China. He gave opportunity for foreign powers including America to freely interfere in China and did not co-operate with the Communists. Coal and iron industries, banking, and foreign trade were all controlled by foreign countries. The Communists protested against the policy of Chiang Kai-Shek. They were brutally suppressed.

At that time Mao Zedong rose to the leadership of the Communist party. In 1934, under the leadership of Mao Zedong, a journey started from Kiangsi in South China. The adventurous trip ended at Yanan in North-Western China. Throughout the journey, they seized out agricultural land and villages from lords and distributed them among the farmers.

The journey covered around 12000 kms. So it is known as the ‘Long March’. Hence Mao Zedong and the Communist Party became the symbol of struggle of the Chinese against foreign power. Chiang Kai-Shek had to seek political asylum in Taiwan, when the Red Army of Mao Zedong captured the centre of Kuomintang rule. China became the People’s Republic of China on 1^st October 1949 under the leadership of Mao Zedong.

(d) Both (a) and (b)

Prior to 1993, Belgium was a unitary state with most powers concentrated in the central government in Brussels. Following constitutional changes in 1993, it shifted to a more federal form of government by devolving power to the regional governments. The change that took place gave constitutional powers to the regional governments and made them autonomous. This change was motivated by the fact that Belgium has three distinct communities; the Dutch speaking, the French speaking and the German speaking concentrated in three different regions. In order to keep such a diverse nation united, it was felt that more power needs to be given to the regional governments so that they can satisfy the needs and aspirations of the different communities.

The Belgian leaders took a different path. They recognised the existence of regional differences and cultural diversities. Between 1970 and 1993, they amended their constitution four times so as to work out an arrangement that would enable everyone to live together within the same country. 

This measure is not in keeping with Belgium’s power sharing arrangements. The arrangements seek to maintain peace between the French and Dutch-speaking communities. By banning French, the mayor will cause civil unrest. Both the languages should be made acceptable in the town’s schools. This bilingual education system will be a better way to integrate the people of the town.

Ouseph’s statement is the most logical, and thus, should be agreed on. Power sharing not only prevents conflict between various groups in the society but it also inculcates a sense of worth in the citizens. The people will be more satisfied with the government if they have a say in the decision-making process.

"When people participate in the planning and implementation of developmental schemes, they would naturally exercise greater control over these schemes. This would eliminate the corrupt middlemen."