Explanation

Factors are (x - m)(x - n) = x² - (m + n)x + mn  

So m + n = p and mn = 30  

Numbers that multiply to 30 and differ by 1: 5 and 6, or -5 and -6  

So p = 5 + 6 = 11 or p = -5 + (-6) = -11

Last verified on 09-05-2026

Explanation

(a + bi)(a - bi) = a² - (bi)² = a² - b²i²

Since i² = -1, this becomes a² - b²(-1) = a² + b²

Given (a + bi)(a - bi) = 29, so a² + b² = 29

Last verified on 09-05-2026

Explanation

• Link canals are built to transfer water from one river or canal system to another.

• Their main purpose is to balance water distribution between different river basins.

• They help manage water shortages in some areas by diverting surplus water.

Last verified on 09-05-2026

Explanation

• Turkey is described as the first Islamic state to recognize the Republic of China (ROC).

• Diplomatic relations were established in 1934.

• At that time, the Republic of China was the internationally recognized government of China.

• This recognition reflects early diplomatic ties between Turkey and China.

Last verified on 09-05-2026

Explanation

• The Lesser Himalaya is a middle mountain range of the Himalayas.

• Its average height ranges from 1,500 to 3,000 metres.

• It lies between the Higher Himalaya and the Siwalik Hills.

• This region has deep valleys and forested mountain slopes.

Last verified on 09-05-2026

Explanation

Key Provincial Sex Ratios (2017 Census):

• National Average → 104.91

• Punjab → 103.41

• Khyber Pakhtunkhwa → 102.54

• Sindh → 108.29

• Balochistan → 110.82

• Islamabad (ICT) → 110.68

Population Summary (2017):

• Total Population → ~207.68 million

• Males → ~106.3 million

• Females → ~101.3 million

Last verified on 09-05-2026

Explanation

• The 1971 conflict (Pakistan–India war leading to East Pakistan separation) marked the final collapse of unity.

• It resulted in the breakup of united Pakistan into two countries.

• East Pakistan became an independent state after the conflict.

• Political, economic, and social tensions had already weakened unity before 1971.

• The war confirmed the failure of national integration between the two wings.

Last verified on 09-05-2026

Explanation

• The most critical issue between East and West Pakistan was economic disparity.

• East Pakistan contributed more to foreign exchange earnings (especially through jute exports).

• Despite this, West Pakistan received a larger share of development funds and resources.

• This created feelings of inequality and political dissatisfaction in East Pakistan.

• Economic imbalance became a major factor leading to tensions between the two wings.

Last verified on 09-05-2026

Explanation

• A seaport becomes economically important when it is well connected with international trade routes and global markets.

• Strong connectivity increases import and export activities.

• It attracts trade, investment, and industrial development in nearby areas.

Last verified on 09-05-2026

Explanation

• Water losses in canals (through seepage, evaporation, and leakage) significantly reduce effective water availability.

• A large portion of irrigation water is lost before reaching the fields.

• Poor maintenance of canal systems increases water wastage.

Last verified on 09-05-2026