Explanation

Given the proportion:

a³ - b³ : a² - b² :: a² + ab + b² : x

We know a³ - b³ = (a - b)(a² + ab + b²) and a² - b² = (a - b)(a + b)

So, the proportion becomes:

(a - b)(a² + ab + b²) : (a - b)(a + b) :: a² + ab + b² : x

Canceling (a - b):

(a² + ab + b²) : (a + b) :: a² + ab + b² : x

This implies x = a + b.

Explanation

کسب کے لغوی معنی ہیں کمانا، خاص طور پر رزق کمانا۔

یہ لفظ عموماً محنت یا کسی چیز کو حاصل کرنے کے لیے استعمال ہوتا ہے۔

Explanation

Dr. Ruth Pfau

• Date of Birth: 9 September 1929
• Date of Death: 10 August 2017
• Other Name: Mother Teresa of Pakistan (due to her work for leprosy patients)

Major Awards:

• Hilal-e-Imtiaz (Pakistan)
• Hilal-e-Pakistan
• Nishan-e-Quaid-i-Azam
• Staufer Medal (Germany)
• Dame of the Order of St. Gregory the Great (by Pope)

Explanation

حضرت ابو بکر رضی اللہ عنہ کا اصل نام عبداللہ تھا۔

آپ کو ابو بکر کے لقب سے پکارا جاتا تھا، جو آپ کے والد کے نام "بکر" سے منسلک ہے۔

Explanation

Bahadur Shah of Gujarat occupied Gujarat during the reign of Humayun, leading to conflicts between them.

Humayun later defeated him and temporarily took control of Gujarat.

Explanation

In 1916, Quaid-e-Azam played a key role in the Lucknow Pact, where he united Hindus and Muslims on common political demands.

He effectively represented Muslim rights, gaining recognition for separate electorates and other constitutional safeguards.

Explanation

Lenore Hetrick was an American poet known for writing simple, nature-themed poems for children.

"Golden Sun" is one of her popular works that reflects appreciation for nature’s beauty.

Explanation

الممیت اللہ کے اسماء الحسنیٰ میں سے ایک ہے، جس کے معنی ہیں موت دینے والا۔

یہ اسم اللہ تعالیٰ کی اس خصوصیت کو ظاہر کرتا ہے کہ وہ ہی زندگی اور موت کا مالک ہے۔

Explanation

In the Islamic state system, non-Muslim minorities are given equal civic rights and protection.

They are allowed to practice their religion freely.

They are safeguarded under Islamic law.

Explanation

The word "must" indicates a strong obligation or necessity, meaning it is required to wear a seatbelt.

This sentence conveys a rule or command, stressing that wearing a seatbelt is mandatory for safety.