Explanation

Old equation: x² - 5x + 6 = 0  

Old roots: (x - 2)(x - 3) = 0 → roots are 2 and 3  

Add 2 to each root  

New roots: 2 + 2 = 4 and 3 + 2 = 5  

New equation: (x - 4)(x - 5) = 0  

x² - 5x - 4x + 20 = 0  

x² - 9x + 20 = 0

Last verified on 04-05-2026

Explanation

Two consecutive integers that add to 7 are 3 and 4  

3 + 4 = 7  

3 × 4 = 12  

So factors are (x - 3)(x - 4) = x² - 7x + 12  

k =  12

Last verified on 04-05-2026

Explanation

(a + bi)(a - bi) = a² + b² = 25  

a + b = 7

Square both sides of a + b = 7  

(a + b)² = 7²  

a² + 2ab + b² = 49  

Put a² + b² = 25  

25 + 2ab = 49  

2ab = 49 - 25  

2ab = 24  

ab = 12

Last verified on 04-05-2026

Explanation

• Pakistan is located at a strategically important geo-political position.
• To its west lie important oil-rich Gulf States.

Gulf States (Oil-rich Countries West of Pakistan):

• Saudi Arabia
• United Arab Emirates (UAE)
• Kuwait
• Qatar
• Oman

Last verified on 04-05-2026

Explanation

• The Karakoram Range is one of the highest mountain ranges in the world.
• Its average height is around 6,100 metres (20,000 feet) above sea level.
• This range is located mainly in Pakistan, India, and China.

Additional information:

• K2 → 8,611 metres (2nd highest in world)
• Gasherbrum I → 8,080 metres
• Broad Peak → 8,051 metres
• Gasherbrum II → 8,035 metres
• Masherbrum → 7,821 metres

Last verified on 04-05-2026

Explanation

• Pakistan (2017): 261 persons/km²
• 1998 census: around 166 persons/km²
• Highest density: Punjab province
• Lowest density: Balochistan province
• Urban areas: much higher than rural areas

Last verified on 04-05-2026

Explanation

• The separation of East Pakistan was finalized in 1971.
• The key event that accelerated this process was armed conflict between East and West Pakistan.
• The war created a rapid political and military breakdown.
• It led to the creation of an independent state of Bangladesh.

Last verified on 04-05-2026

Explanation

• East Pakistan (now Bangladesh) separated in 1971.
• The main reason was lack of political representation and inequality.
• Economic and administrative discrimination increased tensions.

Last verified on 04-05-2026

Explanation

• Ports are vital for a country’s import and export activities.
• Pakistan’s largest and busiest port is the Karachi Port.
• It handles the majority of sea trade, including imports and exports.
• It is located on the Arabian Sea and supports the national economy.

Last verified on 04-05-2026

Explanation

• Irrigation is essential for Pakistan’s agriculture-based economy.
• The main source of irrigation is the extensive canal network.
• These canals distribute water from rivers to agricultural fields.
• It supports major crops like wheat, rice, and cotton.

Last verified on 04-05-2026