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When new resources are explored and new technology is discovered,PPC wouldexpand,indicating larger and larger flow of goods &services in the economy.But our wants are limited, so scarcity of resources in relation to human wants will always exist.And,so long as limited resources are to colliding with unlimited wants,central problems can never be solved once for all. 

Micro ecomics is the study of an individual economic unit like a firm, a consumer.

Production possibility curve shows different combinations of two goods which can be produced with given resources and technology.

It is the value of a factor in its next best alternative use.

It is the rate at which output of good Y is to be sacrificed for every additional unit of good X.

PPC slopes downward from left to right. And PPC is concave to the origin. 

An economic problem arises because resources are limited,our wants are unlimited and resources have alternative uses.

Given- 

Two numbers are 3 and 12

Calculation-

Let the number be x which should be added to 3 and 12.

According to Question-

(3 + x)/(12 + x) = 2 : 5

⇒ 15 + 5x = 24 + 2x

⇒ 3x = 9

⇒ x = 3

∴ 3 should be added to 3 and 12 in order to make them in the ratio of 2 : 5.

Correct option is a) banking 

Correct option is c) Time 

Theme park 

There are children playing in a theme park. Two girls are playing by the swing each hand in hand. A boy is playing with a colourful boy. Some children are playing on the giant wheel. A circus show is also being performed there. The park is full of trees and flowers.

Correct answer is (b) Can you 

Nest

I see a bird and two nestlings in the picture. The nestlings are seemed to be in hungry. The mother bird has fetched some food. It is sitting near the nestlings. The nestlings eagerly open their beaks for the food.

It indicates growth of resources or technological improvement or both resulting in increased productivity.

The bloodless bodies of the poor children are referred to as ‘slag heap’.

A child’s foot offers many contrasing descriptions in the poem. At the child’s age, it does not realise that it was a foot, but after facing many difficulties in life, it understands that it was a prisoner inside a man’s shoe. It felt the darkness inside the shoe that it couldn’t even get an opportunity to communicate with the other foot. When the man grows old, it also grows old, becomes rough and gets age related diseases and understands that it cannot stay young forever. The man must end his life one day or the other, but the foot is unaware of all these happenings.

Explanation:

• Igor Stimac is appointed the head coach of the men’s senior national football team by the All India Football Federation (AIFF) in 2019.
• Igor Stimac was a former professional footballer in Croatia.
• Sunil Chhetri is the captain of the Indian football team.
• The current FIFA ranking of the Indian football team is 108.

The third Buddhist council was held during his reign is NOT correct.

• ​The third Buddhist Council was held in 250 BC in Patliputra under the patronage of Ashoka and was presided by Moggaliputta Tissa.
  • The council recommended the ruler Ashoka to expel sixty thousand Brahmanic spies as well as to reevaluate the Pāli Canon.
  • It was presided over by the elder monk Moggaliputta-Tissa and one thousand monks participated in the Council.
  • The council is recognized and known to both the Theravada and Mahayana schools, though its importance is central only to the Theravada.
  • The Third Buddhist Council is reported to have been to rid the Sangha of corruption in the form of enemies who in the guise of supporters had infiltrated the Sangha, as well as monks who held heretical views.

• Buddhist Councils:
  • Buddhist Councils marked important turning points in early Buddhism.
  • These councils resulted in sectarian clashes and the eventual Great Schism that resulted in the two major schools, Theravada and Mahayana.
• First Buddhist Council:
  • It was held soon after the Mahaparinirvan of the Buddha, around 483 BC under the patronage of King Ajatshatru, and was presided by Mahakasyapa, a monk.
  • The council was held in the Sattapani cave at Rajgriha.
  • The council was held with the purpose of preserving Buddha’s teachings (Sutta) and rules for disciples.
  • During this council, the teachings of Buddha were divided into three Pitakas.
• Second Buddhist Council:
  • It was held in Vaishali, a village in Bihar under the patronage of king Kalasoka in 383 BC.
  • It was presided by Sabakami.
• Fourth Buddhist Council:
  • It was held in 72 AD at Kundalvana, Kashmir.
  • It was presided by Vasumitra, while Asvaghosa was his deputy under the patronage of King Kanishka of the Kushan Empire.
  • Buddhism was divided into two sects namely Mahayana and Hinayana.

The correct answer is Prakrit.

• The Satavahanas were an ancient Indian dynasty in the Deccan region.
• Simuka was the founder of the Satavahana Dynasty.
• Satavahana's official language was Prakrit and its script was Brahmi.
  • Hence, option 2 is correct.
• They patronised Prakrit more than Sanskrit.
• The golden age for Prakrit was the reign of King Hala of Satavahanas.
• The inscriptions of Satavahanas are mostly in Prakrit.

• The Satvahanas were not matriarchal or matrilineal yet they used matronyms like Gautamiputra and Vaishishthiputra.
• They are known for starting the practice of giving royal grants of land to Brahmans and Buddhist monks.
• Some of the great rulers of the dynasty are Gautamiputra Satakarni, Vashishthiputra Pulumayi, Yajna Sri Satakarni.
• They assumed the title of Dakshinapatha Pati.

The correct answer is Digboi.

• First oil refinery in India was set up in Digboi, a town in Tinsukia district of Assam. 
• Digboi is also known as oil city. 
• The commission of this refinery started on 11 December 1901. 
• It stands as the first and oldest oil refinery in entire Asia continent.
• The oil was found accidentally in the Digbol district in 1867 while laying railway line.
• In 1889 the process of digging of oil started and refinery was established in 1901.

The correct answer is Karnataka.

• The Belgaum airport is located 10 kilometers to the east of Belgavi, which is a city in the Indian state of Karnataka.
• The airport is spread across 440 acres and a second taxiway connecting the emergency service enclave to the main apron is currently under construction.

The correct answer is Odisha.

• Chandipur beach is located in Odisha.
• The beach is about 16 km from Balasore and has been listed by Lonely Planet (the world’s renowned travel expert) as one of world’s most unusual beaches.
• The Chandipur coast has attained global popularity for its ‘Vanishing Sea’ phenomenon. 
• Chandipur is home to a wide range of biodiversity.
• Apart from a variety of fish species, the rare Horseshoe crab and tiny red crabs are often spotted on the beach. 

The correct answer is lie detection.

• Polygraph is a device commonly used by law enforcement agencies for lie detection.

• It is a device or procedure that measures and records several physiological indicators such as blood pressure, pulse, respiration, and skin conductivity while a person is asked and answers a series of questions.
• The belief is that the use of the polygraph is that deceptive answers will produce physiological responses that can be differentiated from those associated with non-deceptive answers.
• Instruments like cardio-cuffs or sensitive electrodes are attached to the person for the test.
• A numerical value is assigned to each response to conclude whether the person is telling the truth, is deceiving, or is uncertain.

The correct answer is Kaushambi.

The correct answer is Visakhapatnam dockyard.

• Goa Shipyard Limited (GSL) -
  • It is established in 1957 on the west coast of India, is functioning under the administrative control of the Ministry of Defense, Government of India.
  • GSL is strategically located on the banks of the Zuari River in Goa.
  • It was started with a small boat manufacturing yard.
  • At present time GSL has the distinction of being one of the most sophisticated shipbuilders in the country.
• Visakhapatnam dockyard -
  • The Visakhapatnam dockyard is located in Andhra Pradesh. 
  • This is one of the most important dockyards in India, after the Bombay Dockyard.
  • It was set up as a "Boat Repair Workshop" in Visakhapatnam to support the Indian army units in Burma in 1941.​
• Bombay dockyard -
  • It is a shipbuilding yard in Mumbai. 
  • It was established in 1735 by the East India Company.
• Mazagon Dock Limited -
  • Mazagaon Dock Shipbuilders Limited is India's leading shipyard.
  • Its main function is to build submarines and warships in Mumbai and Nhava Yard.

• Harbor defense systems have been inducted into the Navy to enhance the surveillance capability of the Indian Navy.
• Integrated Submerged Harbor Defense and Surveillance System (IUHDSS) -
  • It is a multisensor system that can detect any threat to the port of Visakhapatnam, detect it, issue warnings, and alert defense equipment. 

Criminal tribes act

The correct answer is Criminal tribes act

• Meena movement was started in Jaipur, Alwar, Kota, and Bundi region.
• Meena’s were declared criminal tribes under the 1924’s Criminal Tribal Act and Jarayam Pesha kanun 1930 which was the main reason for this movement.
• On 4^th may 1946 government exempted women and children from the Jarayam Pesha law in Jaipur state and finally in 1952 this law was abolished.

Chipko movement - 

• It is primarily a forest conservation movement.
• It was started in 1970 aimed at protecting trees.
• It was started in the northern Himalayan segment i.e. Uttarakhand.

• Sunderlal Bahuguna is a prominent environmentalist from Garhwali, and member of the Chipko movement.
• The idea of the Chipko movement was of his wife and he took the action.
• He has been fighting for forest protection in the Himalayas for years, first as a leader of the Chipko movement in the 1970s, and then led the Anti-Tehri Dam campaign from the 1980s until early 2004.
• The Chipko movement was awarded the Right Livelihood Award in 1987 "for its commitment to conserving, preserving and ecologically sustainable use of the natural resources of India."
• Chipko-type movements date back to 1730 AD when 363 Bishnois sacrificed their lives in the village of Prasanna Khamkar in Rajasthan to save the Khejri trees.

Hence, it could be concluded that the Chipko Movement took place to prevent trees.

The correct answer is Ghori Dynasty

​

• Ghori Dynasty did not rule Delhi Sultanate directly.
• Mohammad Ghori's slaves ruled over India after his death.
• Muhammad Ghori was defeated by Prithviraj in the First Battle of Tarain in 1191
• The second battle of Tarain was fought between Muhammad Ghori and t Prithvi Raj Chauhan in 1192. The battle saw the defeat of Prithvi Raj Chauhan.

The correct answer is Delhi and Ajmer.

• Quwwat-ul-Islam Mosque:-
  • It is in the Qutb Minar enclosure of Delhi.
  • The initial construction was built by Qutb-ud-din Aibak.
  • It is built of red sandstone, grey quartz, and white marble.
  • The expansion of the mosque continued after the death of Qutb.
  • Just to the west of the expanded mosque, Iltutmish built his own tomb, the first to be erected for the Delhi Sultanate.
• Arhai Din Ka Jhonpra:-
  • It is in Ajmer, Rajasthan.
  • It is one of the oldest mosques in India.
  • A large number of architectural members and sculptures of temples are lying inside the verandah of the complex.
  • It was built by Qutub-ud-Din-Aibak.
  • Iltutmish had subsequently beautified it in AD 1213.

Lag-Lead Compensator :

The lag-lead compensator is the combination of a lag compensator and a lead compensator. The lag section is provided with one real pole and one real zero, the pole being to the right of zero, where as the lead section has one real pole and one real came with the zero being to the right of the pole.

(a) The force between two conducting spheres is not exactly given by the expression, Q₁Q₂/4πε_or ², because there is a non-uniform charge distribution on the spheres. 

(b) Gauss’s law will not be true, if Coulomb’s law involved 1/r³ dependence, instead of 1/r², on r. 

(c) Yes, If a small test charge is released at rest at a point in an electrostatic field configuration, then it will travel along the field lines passing through the point, only if the field lines are straight. This is because the field lines give the direction of acceleration and not of velocity. 

(d) Whenever the electron completes an orbit, either circular or elliptical, the work done by the field of a nucleus is zero. 

(e) No Electric field is discontinuous across the surface of a charged conductor. However, electric potential is continuous.

(f)The capacitance of a single conductor is considered as a parallel plate capacitor with one of its two plates at infinity. 

(g)Water has an unsymmetrical space as compared to mica. Since it has a permanent dipole moment, it has a greater dielectric constant than mica.

Steady State Response: 

The steady state response is the part of the total response that remains after the transient has died out. For a position control system, the steady state response when compared to with the desired reference position gives an indication of the final accuracy of the system. If the steady state response of the output does not agree with the desired reference exactly, the system is said to have steady state error.           

Time response = Transient response + Steady state response

Time Response Analysis & Design :

• Two types of inputs can be applied to a control system 

• Command Input or Reference Input yr(t) 

• Disturbance Input w(t) (External disturbances w(t) are typically uncontrolled variations in the load on a control system) 

• In systems controlling mechanical motions, load disturbances may represent forces.

• In voltage regulating systems, variations in electrical load area major source of disturbances.

• Goal: Determining whether the system is stable or unstable from a characteristic equation in polynomial form without actually solving for the roots 

• Routh’s stability criterion is useful for determining the ranges of coefficients of polynomials for stability, especially when the coefficients are in symbolic (non numerical) form 

• To find Kmar & ω

• A necessary condition for stability of the system is that all of the roots of its characteristic equation have negative real parts, which in turn requires that all the coefficients be positive.

• A necessary (but not sufficient) condition for stability is that all the coefficients of the polynomial characteristic equation are positive & none of the co-efficient vanishes.

• Routh’s formulation requires the computation of a triangular array that is a function of the coefficients of the polynomial characteristic equation.

• A system is stable if and only if all the elements of the first column of the Routh array are positive

Method for determining the Routh array 

Consider the characteristic equation

a(s) = a₀sⁿ + a₁s^n-1 + a₂s^n-2 + ....+ a_n-1s¹ + a_ns⁰

Root locus Technique:

• Introduced by W. R. Evans in 1948 

• Graphical method, in which movement of poles in the s‐plane is sketched when some parameter is varied 

• The path taken by the roots of the characteristic equation when open loop gain K is varied from 0 to ∞ are called root loci 

• Direct Root Locus = 0 < k < ∞  

• Inverse Root Locus = ‐ ∞ < k < 0

Root Locus Analysis: 

• The roots of the closed‐loop characteristic equation define the system characteristic responses 

• Their location in the complex s‐plane lead to prediction of the characteristics of the time domain responses in terms of:

o damping ratio, ζ

o natural frequency, w_n

o damping constant, σ → first‐order modes

o Consider how these roots change as the loop gain is varied   from 0 to ∞ 

Case 1: All the elements of a row in a RA are zero 

• Form Auxiliary equation by using the co-efficient of the row which is just above the row of zeros 

• Find derivative of the A.E. 

• Replace the row of zeros by the co-efficient of dA(s)/ds 

• complete the array in terms of these coefficients 

• analyze for any sign change, if so, unstable 

• no sign change, find the nature of roots of AE 

• non-repeated imaginary roots - marginally stable 

• repeated imaginary roots – unstable 

Case 2: First element of any of the rows of RA is

• Zero and the same remaining row contains at least one non-zero element 

• Substitute a small positive no. “ε‘ in place of zero and complete the array. 

• Examine the sign change by taking Lt ε = 0

Answer: Relieving severe visceral pain, e.g. myocardial infarction, cancer pain condition, renal or biliary colic