Explanation

Let the factors be (x - m) and (x - n)

Then:

m + n = p

m * n = 90

|m - n| = 9

Using (m - n)^2 = (m + n)^2 - 4mn:

9^2 = p^2 - 4*90

81 = p^2 - 360

p^2 = 441

p = ±21

Last verified on 25-05-2026

Explanation

(a + bi)(a - bi) = a² - (bi)² = a² - b²i² = a² - b²(-1) = a² + b²

So (a + bi)(a - bi) = a² + b² = 73

Last verified on 25-05-2026

Explanation

• The Balochistan Plateau has low rainfall and rugged mountainous terrain.
• Water scarcity limits agricultural activities in the region.
• Most farming depends on tube wells and seasonal rainfall.
• Population density is also low due to harsh conditions.
• The area mainly supports dry farming and livestock.

Last verified on 25-05-2026

Explanation

• Interior regions of Pakistan are mostly dry and arid.
• These areas are far from the sea and receive less moisture.
• Maritime influence helps bring humidity and rainfall.
• Lack of sea winds increases dryness and temperature extremes.
• Deserts like Thar are examples of arid interior regions.

Last verified on 25-05-2026

Explanation

• National integration means unity among people despite differences.
• A shared ideology creates common goals and identity.
• It strengthens patriotism and social harmony.
• Countries remain stable when citizens unite around common principles.
• In Pakistan, ideology played a major role in nation-building.

Last verified on 25-05-2026

Explanation

• Muslim nationalism in South Asia was based on separate religious and cultural identity.
• Muslims considered themselves a distinct nation from Hindus.
• Their traditions, laws, history, and values were different.
• This idea later developed into the Two-Nation Theory.
• It became the ideological basis for the creation of Pakistan.

Last verified on 25-05-2026

Explanation

• Muslims of the subcontinent feared domination under Hindu majority rule.
• They wanted protection of their political, religious, and cultural identity.
• The Two-Nation Theory emphasized Muslims as a separate nation.
• This demand eventually led to the creation of Pakistan in 1947.
• Political representation and security were central concerns.

Last verified on 25-05-2026

Explanation

• Energy is not continuous; it exists in small packets.
• These packets are called quanta (singular: quantum).
• Light energy is carried in quanta called photons.
• This idea is part of quantum theory.
• It explains atomic and subatomic behavior of energy.

Last verified on 24-05-2026

Explanation

• Threshold frequency is a concept of the photoelectric effect.
• It is the minimum frequency of light needed to remove electrons from a metal surface.
• Below this frequency, no electrons are emitted.
• Different metals have different threshold frequencies.
• This concept was explained by Albert Einstein in 1905.

Last verified on 24-05-2026

Explanation

• Tidal forces are mainly caused by the Moon’s gravitational pull.
• The Moon attracts Earth’s oceans, creating high and low tides.
• The Sun also affects tides but less than the Moon.
• Tides occur regularly due to Earth-Moon interaction.
• Coastal areas experience noticeable tidal changes daily.

Last verified on 24-05-2026