### 1. Mathematics
**Question:**
Prove that the sum of the squares of two consecutive positive integers is always odd.
**Answer:**
Let the two consecutive integers be ( n ) and ( n+1 ).
Their squares are ( n^2 ) and ( (n+1)^2 ).
Sum of the squares:
[ n^2 + (n+1)^2 = n^2 + n^2 + 2n + 1 = 2n^2 + 2n + 1 ]
Since ( 2n^2 + 2n ) is even (as it is divisible by 2), adding 1 makes it odd. Thus, the sum is always odd.
### 2. Science (Physics)
**Question:**
State and explain the law of conservation of momentum with an example.
**Answer:**
The law of conservation of momentum states that the total momentum of a closed system remains constant if no external forces act on it.
Example: In a collision between two cars, the total momentum before and after the collision is the same, provided no external force acts on the system.
### 3. Science (Chemistry)
**Question:**
Explain the process of electrolysis of water and its chemical equation.
**Answer:**
Electrolysis of water is the process of using electricity to decompose water into oxygen and hydrogen gas.
Chemical equation:
[ 2H_2O(l) rightarrow 2H_2(g) + O_2(g) ]
At the cathode (negative electrode), reduction occurs:
[ 2H_2O + 2e^- rightarrow H_2 + 2OH^- ]
At the anode (positive electrode), oxidation occurs:
[ 4OH^- rightarrow O_2 + 2H_2O + 4e^- ]
### 4. Science (Biology)
**Question:**
Describe the structure and function of the human heart.
**Answer:**
The human heart is a muscular organ with four chambers: two atria and two ventricles. The right atrium receives deoxygenated blood from the body and pumps it to the right ventricle, which sends it to the lungs for oxygenation. The left atrium receives oxygenated blood from the lungs and pumps it to the left ventricle, which sends it throughout the body. The heart ensures continuous circulation of blood, delivering oxygen and nutrients to tissues.
### 5. History
**Question:**
What were the main causes and impacts of the Indian Independence Movement?
**Answer:**
**Causes:**
– British colonial exploitation and oppressive policies.
– Economic hardship and famines.
– Influence of global movements and wars.
– Rise of nationalist leaders like Mahatma Gandhi.
**Impacts:**
– End of British colonial rule in 1947.
– Partition of India and Pakistan.
– Establishment of a democratic republic in India.
– Significant social and economic reforms.
### 6. Geography
**Question:**
What are the primary factors influencing the climate of a region?
**Answer:**
Primary factors influencing climate:
– **Latitude:** Determines the solar radiation received.
– **Altitude:** Higher altitudes have cooler temperatures.
– **Distance from the sea:** Coastal areas have moderate climates.
– **Ocean currents:** Warm and cold currents affect coastal temperatures.
– **Wind patterns:** Influence temperature and precipitation.
– **Topography:** Mountains can block or direct wind and rain.
### 7. English
**Question:**
Discuss the central theme of the novel “To Kill a Mockingbird” by Harper Lee.
**Answer:**
The central theme of “To Kill a Mockingbird” is racial injustice. Set in the American South, the novel explores the deep-seated prejudice and discrimination against African Americans. Through the eyes of Scout Finch, the story addresses moral growth, the importance of empathy, and the struggle for justice, highlighting the impact of racism on individuals and society.
### 8. Economics
**Question:**
Explain the concept of Gross Domestic Product (GDP) and its importance.
**Answer:**
Gross Domestic Product (GDP) is the total monetary value of all goods and services produced within a country’s borders in a specific time period. It is important because:
– It measures economic performance and growth.
– Indicates the standard of living.
– Helps in policy making and economic planning.
– Influences investment decisions.
### 9. Civics
**Question:**
What are the fundamental rights provided by the Indian Constitution?
**Answer:**
The fundamental rights provided by the Indian Constitution include:
– **Right to Equality:** Equal treatment before the law.
– **Right to Freedom:** Freedom of speech, assembly, movement, etc.
– **Right against Exploitation:** Prohibition of human trafficking and forced labor.
– **Right to Freedom of Religion:** Freedom to practice and propagate religion.
– **Cultural and Educational Rights:** Rights of minorities to preserve their culture.
– **Right to Constitutional Remedies:** Right to approach the courts for enforcement of rights.
### 10. Computer Science
**Question:**
What is a computer network, and what are its types?
**Answer:**
A computer network is a group of interconnected computers that communicate and share resources. Types of networks include:
– **LAN (Local Area Network):** Covers a small geographical area, like an office.
– **WAN (Wide Area Network):** Covers large geographical areas, such as a country or the globe.
– **MAN (Metropolitan Area Network):** Covers a city or a large campus.
– **PAN (Personal Area Network):** Used for communication among personal devices within a short range.
These questions and answers cover a broad range of subjects and key concepts, providing a comprehensive review for Class 10th students.