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 Uttarakhand

Key Points

• Nanda Devi is India's second-highest mountain peak, after Kanchenjunga.
  • But it is the highest mountain peak entirely located in India.
  • Height: 7,817 metres
  • Location: Uttarakhand.

Additional Information

About Uttarakhand (as of August 2021):

• Uttarakhand, formerly Uttaranchal, state of India, located in the northwestern part of the country.
  • Uttarakhand was carved out from Uttarpradesh on 9 November 2000 as the 27th State of India.
  • It is bordered to the northwest by Himachal Pradesh, to the northeast by the Tibet Autonomous Region of China, to the southeast by Nepal, and to the south and southwest by the Indian state of Uttar Pradesh.
  • Its capital is the northwestern city of Dehra Dun.
  • Governor: Baby Rani Maurya
  • CM: Pushkar Singh Dhami
  • State flower: Saussurea obvallata
  • State Bird: Alpine musk deer
  • National park: Valley of Flowers National Park (UNESCO sites), Rajaji National Park, Nanda Devi National Park, Gangotri National Park, Jim Corbett (1st National park in India).

The correct answer is Todarmal.

• Todarmal was the last to lead the deputation sent by Akbar to Pratap to negotiate his peaceful subjugation.

Key Points

• Delegation sent to Pratap by Akbar:
  • The very first deputation was sent by Akbar to Maharana Pratap was under Jalal khan Korchi on September 1572 to negotiate his peaceful subjugation but Pratap refused to do so.
  • On April 1573m, Mansingh of Amer was sent to the same agenda but Pratap again refused it. It is said that this deputation was met with Pratap at Gogunda.
  • On September 1573  Bagwantdas of Amer was sent and finally fourth and the last delegation under Todarmal was sent on December 1573.
  • All of the delegations were sent with the same agenda and every time Pratap refused to accept the supremacy of Akbar.

Additional Information

• Battle of Haldighati:
  • After the failure of all of the delegation, the Battle of Haldighati took place on 18 June 1576 in Rajsamand.
  • Mansingh was Commandor of Akbar's army and Hakim khan Suri was commander of Pratap's army.
  • Chetak, the horse of Pratap, was died during this battle at Balicha place.
  • Jhala Bida wore the Pratap crown on the battlefield when Pratap got injured.
  • The Battle of Haldighati is also called the Battle of Tharmopalli by James todd.

If '+' means 'divide by', '-' means 'add to', '×' means 'subtract from' and '/' means 'multiply by',

[{(20 × 6) × (7 / 2)} + (3 - 2)] / 5

We put the right symbol given is the question-

= [{(20 - 6) - (7 × 2)} / (3 + 2)] × 5

Now apply BODMAS rule

= [{14 - 14} / 5] × 5

= [0 / 5] × 5

= 0

Hence, "0" is the correct answer.

The correct answer is Primary key.

Key Points

• The foreign key is not necessarily the primary key in its current table.
  • It only has to contain the same information that is held in another table’s primary key.
  • Foreign keys are the columns of a table that points to the primary key of another table. They act as a cross-reference between tables.

Additional Information​ 

• A report generator is a computer program whose purpose is to take data from a source such as a database, XML stream or a spreadsheet, and use it to produce a document in a format which satisfies a particular human readership.
• The data dictionary is a set of information describing the contents, format, and structure of a database and the relationship between its elements, used to control access to and manipulation of the database.
• Schema objects are logical structures created by users. Objects such as tables or indexes hold data or can consist of a definition only, such as a view or synonym.