Question Discussion & Solution

CONCEPT:

Equilibrium of a rigid body:

• A rigid body is said to be in mechanical equilibrium if both its linear momentum and angular momentum are not changing with time, or equivalently, the body has neither linear acceleration nor angular acceleration.
• Condition for the mechanical equilibrium:
  1. The total force, i.e. the vector sum of the forces, on the rigid body is zero.
  2. The total torque, i.e. the vector sum of the torques on the rigid body is zero.

⇒ \(\rm\vec{F_1}+\vec{F_2}+...+\vec{F_n}=0\)

⇒ \(\rm \vec{τ_1}+\vec{τ_2}+...+\vec{τ_n}=0\)

• If the forces on a rigid body are acting in the 3 dimensions, then six independent conditions to be satisfied for the mechanical equilibrium of a rigid body.
• If all the forces acting on the body are coplanar, then we need only three conditions to be satisfied for mechanical equilibrium.
• A body may be in partial equilibrium, i.e., it may be in translational equilibrium and not in rotational equilibrium, or it may be in rotational equilibrium and not in translational equilibrium.

EXPLANATION:

• A rigid body is said to be in mechanical equilibrium if both its linear momentum and angular momentum are not changing with time, or equivalently, the body has neither linear acceleration nor angular acceleration.
• We know that the linear acceleration and the angular acceleration of a stationary body are zero.

A book is kept on a table:

• In this case, the book will be stationary so it is an example of the equilibrium of a body.

A ball is moving downward freely under gravity:

• We know that when a ball moves freely under gravity, then only the gravitational force will act on the ball due to which the ball accelerates downward.
• Therefore ball is moving downward freely under gravity is not an example of the equilibrium of a body.
• Hence, option 1 is correct.

The correct answer is Karauli.

• The princely state of Karauli was founded by the Yaduvanshi ruler Arjun Singh under the name Kalyanpuri in Vikram Samvat 1405 (1348 AD), which later became Karauli in the period.

Key Points

• The ruler of Karauli, Harvakshpal Singh, made a treaty with the British.
• Karauli was the first princely state of Rajasthan, which made the first treaty with the British.
• Anjani Mata is the local deity of the princely state of Karauli.

Additional Information

• Karauli State was a princely state in India.
  • It existed from 1348 to 1949.
  • It is located in the Braj region.
  • Its capital was Karauli city.
• The important towns associated were Mandrayal or Mandrail.
• The 32nd district of Karauli Rajasthan was created on 19 July 1997, separated from Sawai Madhopur.
• Ramgopal Vijayvargiya was a well-known painter from Karauli, who started the solo painting exhibition tradition.

Important Points

• Lootmar Holi / Lathmar Holi of Mahavir Ji (Karauli) is very famous.
• Shivaratri Cattle Fair - This fair starts on Phalgun Krishna Trayodashi.
  • This fair is famous for the purchase and sale of cows of the Haryanvi breed.

The correct answer is Accumulator.

Key Points

• An accumulator is a type of register present in a CPU (Central Processing Unit).
• It works as a temporary storage location that keeps an intermediate value in logical and mathematical calculations.
• Intermediate results of execution are progressively stored in the accumulator, replacing the previous value.

Additional Information

• An IR (Instruction Register) saves machine instruction that is currently under execution. It is a register that sits at the top of the memory hierarchy. A variety of registers fulfills different operations in a central processing unit (CPU) – the function of the IR is to keep that currently stacked instruction for use.
• A PC (program counter) is a CPU register that has the address stored for the next instruction to be processed from memory. It is a digital counter required for quicker execution of tasks as well as to keep track of the current execution point. 
• The MAR (Memory Address Register) is the register in the control unit that holds the address of a register to receive or store from or to the storage. The Memory Address Register is half of an interaction between a microprogram and storage.

The correct answer is Bahlul Khan Lodhi.

Key Points

• Bahlul Khan Lodhi is the founder ruler of the Lodhi Dynasty.

Additional Information 

• Lodi Dynasty (1451 to 1526)
  • Bahlul Khan Lodi (1451-1489 AD)
    • He was the founder of the Lodi dynasty.
    • He served as the Subedar (Governor) of Lahore and Sirhind during the reign of Muhammad Shah.
    • He tried to re-establish the greatness of the Delhi Sultanate, hence he had recaptured the areas around Delhi.
    • His most successful war was against the ruler of Jaunpur "Mahmud Shah Sharki".
    • The territories conquered by Bahlol Lodi were Mewat (Ahmed Khan), Sambhal (Dariya Khan), Kol (Isa Khan), Suket (Mubarak Khan), Manipur and Bhongaon (Raja Pratap Singh), Rewari (Qutub Khan), Etawah And Chandawar.
    • In 1498 AD, the able son of Bahlol Lodi, Nizam Shah, came to power in the name of "Sultan Sikandar Shah".
  • Sikandar Shahi (1489-1517 A.D.)Ibrahim Lodi (1518-1526)
    • He was the most qualified of three Lodi rulers who had conquered the king of Bihar and Tirhut.
    • Sikandar Lodi expanded his empire by conquering areas like Dholpur and Chanderi.
    • He kept a strict vigil on his nobles and jagirdars and strictly suppressed the rebellion carried out by them.
    • He had established an efficient espionage system and also arranged for the checking of government accounts.
    • He reduced the restrictions placed on trade, which boosted the economic prosperity of the people. For the measurement of agricultural land, he introduced a "Gaja-e- Sikandari" (Alexander Yard)  or 32 inches.
    • He shifted his capital from Delhi to Agra, which was established by him.
  • Ibrahim Lodi
    • Ibrahim Lodi was stubborn and intolerant which were not good qualities in a ruler.
    • Nobles were killed cruelly and many nobles were humiliated by Ibrahim Lodi.
    • He also treated his son Dilwar Khan Lodi cruelly.
    • Invasion of India was done by Kabul ruler, Babur, at the behest of Daulat Khan, a very powerful noble from Punjab.
    • In the 1st battle of Panipat in the year 1526 A.D, Ibrahim Lodi faced defeat at the hands of Babur

Concept:

System modelling is the process of developing abstract models of a system and each model presenting a different view or perspective of that system. 

Explanation:

Concept that has to be considered while modelling a new system are:

Abstraction: at highest level of abstraction, a solution is stated in broad terms while at the lowest level of abstraction a more detailed solution is provided.

Modularity: it is the single attribute of the software that allows a program to be individually manageable.

Information hiding in this algorithms and data contained within a module are inaccessible to to other modules.

Some other factors that are considered are: architecture, pattern, functional independence, refinement, refinement.