Central Teacher Eligibility Test (CTET) · Topic Collection

Mathematics and Science PYQs

Elementary mathematics and science content with the pedagogical issues of teaching both subjects, as asked in upper-primary teacher papers.

3840 Total Questions64 Official PapersYears: 2012–2026Search in Mathematics and Science
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CTET (Maths & Science) Official Paper-II (Held On: 07 Feb, 2026 Shift 1) (Previous Year Paper)·Mathematics and Science
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Question 101

Central Teacher Eligibility Test (CTET) 2026• Mathematics and Science• Mathematics and Science

Fill in the blanks with the correct answer:

    A      pushes the blood into pulmonary artery.    B    take deoxygenated blood from the

heart to the lungs.   C     return oxygenated blood from the lungs to the heart. From the left atrium, blood flows to the   D   .          E    receives blood from different parts of the body.

  1. AOption (a)

    A-Left ventricle; B-Pulmonary arteries; C-Pulmonary veins; E-Right ventricle

    D-right auricle;

  2. BOption (b)

    A-Right ventricle; B-Pulmonary arteries; C-Pulmonary veins; E-Right auricle

    D-left ventricle;

  3. COption (c)

    A-Right ventricle; B-Pulmonary veins; C-Pulmonary arteries; D-left ventricle; E-Right auricle

  4. DOption (d)

     A-Left ventricle; B-Pulmonary veins; C-Pulmonary arteries; D-right auricle; E-Right ventricle

View answer & explanation

Correct answer

Answer: (b)B.

A-Right ventricle; B-Pulmonary arteries; C-Pulmonary veins; E-Right auricle

D-left ventricle;

Why this answer is correct

The correct answer is Option 2.

Key Points

  • A - Right ventricle: The right ventricle is responsible for pushing deoxygenated blood into the pulmonary arteries, which transport the blood to the lungs for oxygenation. Hence, statement A is correct.
  • B - Pulmonary arteries: These arteries carry deoxygenated blood from the heart (right ventricle) to the lungs for oxygenation. Unlike most arteries, they transport deoxygenated blood. Hence, statement B is correct.
  • C - Pulmonary veins: These veins return oxygenated blood from the lungs to the left atrium of the heart. Unlike most veins, they carry oxygenated blood. Hence, statement C is correct.
  • D - Left ventricle: From the left atrium, oxygenated blood flows into the left ventricle, which then pumps it to the rest of the body through the aorta. Hence, statement D is correct.
  • E - Right auricle: The right auricle (or atrium) receives deoxygenated blood from the body through the superior and inferior vena cava and directs it to the right ventricle. Hence, statement E is correct.

Additional Information

  • Heart chambers and their functions:
  • The heart has four chambers: two atria (right and left) and two ventricles (right and left).
  • The right atrium receives deoxygenated blood from the body and sends it to the right ventricle.
  • The right ventricle pumps deoxygenated blood to the lungs via the pulmonary arteries.
  • The left atrium receives oxygenated blood from the lungs via the pulmonary veins.
  • The left ventricle pumps oxygenated blood to the entire body through the aorta.
  • Circulatory pathways:
  • The pulmonary circulation involves the right side of the heart, pulmonary arteries, lungs, and pulmonary veins. It is responsible for oxygenating the blood.
  • The systemic circulation involves the left side of the heart, aorta, and systemic arteries and veins. It supplies oxygenated blood to the body and returns deoxygenated blood to the heart.
  • Pulmonary arteries and veins:
  • Pulmonary arteries are the only arteries in the human body that carry deoxygenated blood.
  • Pulmonary veins are the only veins that carry oxygenated blood.
  • Heart valves:
  • The heart has four valves: tricuspid, pulmonary, mitral, and aortic.
  • The tricuspid valve controls blood flow from the right atrium to the right ventricle.
  • The pulmonary valve controls blood flow from the right ventricle to the pulmonary arteries.
  • The mitral valve controls blood flow from the left atrium to the left ventricle.
  • The aortic valve controls blood flow from the left ventricle to the aorta.

Important Points

  • The circulatory system is divided into two main circuits: pulmonary (lungs) and systemic (body).
  • The heart ensures unidirectional blood flow with the help of its valves, preventing backflow.
  • The oxygenation of blood occurs in the lungs, where carbon dioxide is exchanged for oxygen.
  • Blood circulation is essential for transporting oxygen, nutrients, hormones, and waste products throughout the body.
  • The average adult heart beats approximately 60-100 times per minute, pumping about 5 liters of blood every minute.
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Question 102

Central Teacher Eligibility Test (CTET) 2026• Mathematics and Science• Mathematics and Science

Read the following

Statements:

Assertion (A) : Hypotheses become theories which in turn become laws.

Reason (R) : Scientific laws such as law of gravitation are absolute.

Choose the correct option.

  1. AOption (a)

    Both A and R are true but R is not the correct reason for A 

  2. BOption (b)

    A is true but R is false 

  3. COption (c)

    Both A and R are false.ral

  4. DOption (d)

    Both A and R are true and R is the correct reason for A 

View answer & explanation

Correct answer

Answer: (c)C.

Both A and R are false.ral

Why this answer is correct

The correct answer is Option 3: Both A and R are false.

Key Points

  • Assertion (A): Hypotheses become theories which in turn become laws.
  • This statement is false.
  • Scientific hypotheses, theories, and laws are distinct concepts and do not evolve from one into another.
  • Hypothesis: A tentative explanation or prediction that can be tested through experiments or observations.
  • Theory: A well-substantiated explanation of some aspect of the natural world, based on a body of evidence. It explains how or why phenomena occur.
  • Law: A descriptive statement or equation that predicts a specific outcome under given conditions, often without explaining the underlying reasons.
  • For example, the Law of Gravity describes the attraction between masses, while the Theory of General Relativity explains how gravity works.
  • Reason (R): Scientific laws such as the law of gravitation are absolute.
  • This statement is false.
  • Scientific laws are not absolute; they are dependent on the conditions under which they are applied.
  • For example, Newton's Law of Gravitation works well in many scenarios but is superseded by Einstein's Theory of General Relativity in extreme conditions, such as near black holes.
  • Scientific laws are subject to revision if new evidence or theories emerge.
  • Correct Option: Since both Assertion (A) and Reason (R) are false, the correct answer is Option 3.

Additional Information

  • Differences between Hypotheses, Theories, and Laws:
  • Hypothesis: A proposed explanation made on the basis of limited evidence as a starting point for further investigation. Example: "Plants grow faster under red light."
  • Theory: A comprehensive explanation supported by extensive evidence. Example: Darwin's Theory of Evolution.
  • Law: A concise statement that predicts a specific phenomenon under certain conditions. Example: Boyle's Law in physics, which relates pressure and volume of a gas at constant temperature.
  • Characteristics of Scientific Laws:
  • They are descriptive, not explanatory.
  • They predict outcomes but do not explain the "why" or "how."
  • They are based on empirical evidence gathered through observation and experimentation.
  • They are valid only within the scope of specific conditions, e.g., Newton's laws are applicable at non-relativistic speeds.
  • Examples of Scientific Theories and Laws:
  • Theory: Quantum Mechanics explains the behavior of particles on a microscopic scale.
  • Law: Kepler's Laws of Planetary Motion describe the orbits of planets around the sun.
  • Importance of Revising Scientific Knowledge:
  • Scientific knowledge evolves as new discoveries are made and old concepts are refined or replaced.
  • For instance, the transition from Newtonian mechanics to Einstein's relativity shows how science adapts to new evidence.

Important Points

  • Scientific Method: The progression of scientific understanding often follows the scientific method: observation, hypothesis, experimentation, and refinement.
  • Empirical Nature: Both theories and laws rely on empirical evidence, but theories delve into mechanisms while laws focus on predictions.
  • Flexibility: Science is not static. Laws and theories are open to change when new evidence contradicts existing models.
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Question 103

Central Teacher Eligibility Test (CTET) 2026• Mathematics and Science• Mathematics and Science

Sheena writes the following statements in her notebook:

A1: Cactus is a desert plant.

A2: A desert plant has very small-sized leaves.

A3: Small-sized leaves help in reducing loss of water.

Which of the following is true about A1, A2, and A3 respectively?

  1. AOption (a)

    Inference, Inference, Inference

  2. BOption (b)

    Observation, Hypothesis, Inference

  3. COption (c)

    Observation, Observation, Inference

  4. DOption (d)

    Inference, Observation, Hypothesis 

View answer & explanation

Correct answer

Answer: (a)A.

Inference, Inference, Inference

Why this answer is correct

CONCEPT:

Observation and Inference

  • An observation is something that is directly seen or noticed using senses.
  • An inference is a conclusion or interpretation drawn from observations and prior knowledge.
  • Statements that involve classification, explanation, or reasoning are generally considered inferences.

EXPLANATION:

  • A1: "Cactus is a desert plant"
  • This statement classifies cactus as a desert plant using prior knowledge.
  • Hence, it is an Inference.
  • A2: "A desert plant has very small-sized leaves"
  • This statement gives a generalized characteristic of desert plants.
  • Therefore, it is also an Inference.
  • A3: "Small-sized leaves help in reducing loss of water"
  • This statement explains the function of small leaves.
  • It is a conclusion based on reasoning, so it is an Inference.

Therefore, all the three statements are Inferences.

CTET (Maths & Science) Official Paper-II (Held On: 07 Feb, 2026 Shift 1) (Previous Year Paper)·Mathematics and Science
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Question 104

Central Teacher Eligibility Test (CTET) 2026• Mathematics and Science• Mathematics and Science

Which of the following cannot be regarded as a 'testable question'? 

  1. AOption (a)

    How does flu effect human immune system?

  2. BOption (b)

    When will fossil fuels run out? 

  3. COption (c)

    What does an earthworm eat?

  4. DOption (d)

    What is the effect of cigarette smoke on lungs?

View answer & explanation

Correct answer

Answer: (b)B.

When will fossil fuels run out? 

Why this answer is correct

The correct answer is When will fossil fuels run out?.

Key Points

  • A testable question should be specific, measurable, and based on observations, experiments, or data collection. It should enable clear validation through scientific methods.
  • The question "When will fossil fuels run out?" is based on predictions rather than direct experimentation or observation, making it speculative. Hence, it cannot be classified as a testable question.
  • Other options such as "How does flu affect the human immune system" and "What does an earthworm eat" can be tested through controlled experiments, observations, or data analysis. These are testable questions.
  • "What is the effect of cigarette smoke on lungs" can be studied scientifically, using tools like medical trials, population studies, or controlled laboratory experiments, making it a testable question.
  • Testable questions focus on cause-effect relationships, measurable factors, or specific phenomena, while speculative questions like the depletion of fossil fuels involve assumptions and projections.

Additional Information

  • Characteristics of Testable Questions:
  • They are specific and measurable.
  • They rely on scientific methods such as observation, experimentation, or data analysis.
  • They seek to explore relationships or phenomena that can be validated empirically.
  • Examples: "What factors affect plant growth?", "How does temperature affect water evaporation?"
  • Why Fossil Fuel Depletion Is Not Testable:
  • The timeline for the depletion of fossil fuels depends on various factors such as consumption rates, technological advancements, and resource discoveries.
  • It involves projections based on current data and trends rather than direct scientific testing.
  • Such questions fall into the domain of predictive modeling and policy analysis.
  • Examples of Testable vs Non-Testable Questions:
  • Testable: "What is the effect of sunlight on plant growth?", "How does salt concentration affect water boiling point?"
  • Non-Testable: "What is the best way to achieve world peace?", "How long will the Sun continue to burn?"
  • Scientific Inquiry Process:
  • Formulate a hypothesis based on a specific question.
  • Design experiments or observations to test the hypothesis.
  • Analyze results and draw conclusions.
  • Ensure reproducibility and peer-review for validation.

Important Points

  • Scientific Methodology:
  • All testable questions rely on the scientific method, which includes observation, hypothesis formulation, experimentation, and analysis.
  • The goal is to establish cause-effect relationships and validate findings through reproducible methods.
  • Fossil Fuel Depletion:
  • Global institutions like the International Energy Agency (IEA) and BP Statistical Review of World Energy provide periodic reports on fossil fuel reserves.
  • They estimate depletion timelines based on current consumption trends and advancements in energy technologies.
  • Such predictions are speculative and cannot be tested through direct scientific experimentation.
  • Examples of Scientific Questions:
  • Questions related to environmental science, biology, chemistry, or physics often lend themselves to experimental validation.
  • Example: "What is the impact of pollution on aquatic ecosystems?"
CTET (Maths & Science) Official Paper-II (Held On: 07 Feb, 2026 Shift 1) (Previous Year Paper)·Mathematics and Science
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Question 105

Central Teacher Eligibility Test (CTET) 2026• Mathematics and Science• Mathematics and Science

Read the excerpt given below:

A teacher arranged a fun trip to Qutub Minar for her learners. The learners saw the in pillar in the Qutub complex. The teacher asked the learners to note down the detail displayed about the pillar that is 1600 years old and rust-resistant. She also asked ther to write those iron items in their house, which are being used regularly and are ruste and think of causes of rusting and ways to prevent rusting.

Which of the following process skills are being developed through the above-mentione activity?

  1. AOption (a)

    Classification, observation, measurement 

  2. BOption (b)

    Inference, classification, observation

  3. COption (c)

    Classification, observation, hypothesis

  4. DOption (d)

    Measurement, classification, inference 

View answer & explanation

Correct answer

Answer: (c)C.

Classification, observation, hypothesis

Why this answer is correct

CONCEPT:

Science Process Skills

  • Observation involves carefully noticing and recording details using senses.
  • Classification means grouping or identifying objects based on common characteristics.
  • Hypothesis is a possible explanation or prediction based on observations.

EXPLANATION:

  • The learners observed the iron pillar and noted down its features such as being 1600 years old and rust-resistant.
  • This develops the skill of Observation.
  • The learners were asked to identify and list iron objects in their homes that have rusted.
  • This involves identifying objects on the basis of their properties, which develops Classification.
  • The learners were also asked to think about the causes of rusting and methods to prevent it.
  • This encourages them to form possible explanations, which develops the skill of Hypothesis.

Therefore, the process skills developed are Classification, Observation, and Hypothesis.

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Question 106

Central Teacher Eligibility Test (CTET) 2026• Mathematics and Science• Mathematics and Science

Which of the following does not satisfy 'process validity' of science curriculum as recommended by the National Curriculum Framework, 2005? 

  1. AOption (a)

    Students discussing the possible outcomes of connecting a piece of rubber, hairpin and lead to two open ends of an electric circuit

  2. BOption (b)

    Students involved in developing hypothesis for germination of seeds kept in a dry cotton cloth and moist cotton

  3. COption (c)

    Students involved in making a list of elements given in the periodic table

  4. DOption (d)

    Students investigating the acidity and, basicity of different household items

View answer & explanation

Correct answer

Answer: (c)C.

Students involved in making a list of elements given in the periodic table

Why this answer is correct

The correct answer is Students involved in making a list of elements given in the periodic table.

Key Points

  • Process validity in the science curriculum refers to engaging students in activities that involve scientific inquiry, exploration, and reasoning rather than rote memorization or mechanical tasks.
  • Option 1: Students discussing the possible outcomes of connecting a piece of rubber, hairpin, and lead to two open ends of an electric circuit encourages scientific inquiry and reasoning. Students predict and test hypotheses, which aligns with process validity. Hence, this option satisfies process validity.
  • Option 2: Students involved in developing hypotheses for germination of seeds fosters critical thinking and hypothesis formulation, key components of the scientific process. Hence, this option satisfies process validity.
  • Option 3: Students involved in making a list of elements given in the periodic table is a mechanical task that emphasizes memorization rather than inquiry or reasoning. This does not align with process validity. Hence, this option does not satisfy process validity.
  • Option 4: Students investigating the acidity and basicity of different household items involves experimentation and reasoning, a vital part of scientific inquiry. Hence, this option satisfies process validity.

Additional Information

  • National Curriculum Framework 2005 (NCF 2005):
  • The NCF 2005 emphasizes process validity, which encourages students to learn by doing, exploring, and questioning.
  • It prioritizes activities that promote critical thinking, scientific inquiry, and reasoning skills.
  • Memorization-based tasks are discouraged as they do not contribute to the development of higher-order thinking skills.
  • Key Components of Process Validity:
  • Formulation and testing of hypotheses.
  • Engaging in experiments and observations.
  • Analyzing and interpreting data.
  • Drawing conclusions based on evidence.
  • Examples of Activities Supporting Process Validity:
  • Designing and conducting experiments.
  • Investigating real-world phenomena (e.g., environmental studies).
  • Solving scientific problems using reasoning and evidence.
  • Collaborative discussions and debates about scientific concepts.
  • Periodic Table Memorization:
  • While understanding the periodic table is important, simple memorization does not foster scientific inquiry or reasoning.
  • Interactive and inquiry-based approaches, such as exploring trends in the periodic table or conducting experiments related to elements, are preferred.

Important Points

  • Focus on Inquiry: The NCF 2005 emphasizes the importance of engaging students in inquiry-based activities to develop their understanding and curiosity.
  • Role of Teachers: Teachers are encouraged to create a classroom environment that supports exploration, questioning, and evidence-based learning rather than rote memorization.
  • Skill Development: Process validity supports the development of critical thinking, analytical skills, and problem-solving abilities, which are essential for scientific understanding.
  • Assessment: Assessments should focus on evaluating students' ability to think critically, reason scientifically, and apply their knowledge in real-world situations.
CTET (Maths & Science) Official Paper-II (Held On: 07 Feb, 2026 Shift 1) (Previous Year Paper)·Mathematics and Science
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Question 107

Central Teacher Eligibility Test (CTET) 2026• Mathematics and Science• Mathematics and Science

The science textbooks often include interesting anecdotes from the past. One such story is that of accidental discovery of silk in China and the role of travellers and traders in introducing silk to the rest of the world through the 'Silk Route'.

What objectives of science teaching-learning are being fulfilled by including the above in the textbook?

A. To develop an understanding of nature of science

B. To develop a historical perspective

C. To develop an appreciation of how science is socially and culturally embedded

D. To reduce the burden of science content by including fun stories

Choose the correct option.

  1. AOption (a)

     B, C and D

  2. BOption (b)

    A, B and C

  3. COption (c)

    A, B and D 

  4. DOption (d)

    A, C and D 

View answer & explanation

Correct answer

Answer: (b)B.

A, B and C

Why this answer is correct

The correct answer is 2) A, B and C.

Key Points

  • To develop an understanding of the nature of science: Including stories like the accidental discovery of silk and the role of the 'Silk Route' helps students realize that science is not just a collection of facts but a dynamic, evolving field influenced by chance discoveries and human endeavors. This aligns with the objective of understanding the nature of science.
  • To develop a historical perspective: The anecdote provides a glimpse into history, showing how scientific discoveries and materials like silk influenced trade, culture, and societies over centuries. It fosters a historical perspective among students.
  • To develop an appreciation of how science is socially and culturally embedded: The story highlights how science and discoveries are interconnected with societal and cultural contexts. It shows how a scientific material like silk shaped economies, trade routes, and cultural exchanges globally.
  • To reduce the burden of science content by including fun stories: This option is incorrect. Although such anecdotes make learning engaging, the primary intent is not to reduce content but to enhance understanding and appreciation of science in a broader context.

Additional Information

  • The Nature of Science:
  • Science is not static; it evolves over time with new discoveries and technologies.
  • Historical anecdotes in science education provide insight into how scientific knowledge is built, including through accidents or unexpected findings.
  • Example: The discovery of penicillin by Alexander Fleming in 1928 was an accidental yet groundbreaking advancement in medicine.
  • Historical Perspective in Science:
  • A historical perspective helps students understand the progression of scientific ideas over time.
  • It fosters critical thinking by showing how discoveries are influenced by historical, social, and cultural contexts.
  • Example: The Silk Route not only facilitated the exchange of goods like silk but also ideas, technologies, and cultures between East and West.
  • Social and Cultural Embedding of Science:
  • Scientific discoveries often arise in response to societal needs or cultural practices.
  • For example, the demand for silk in Europe during ancient times influenced the development of trade routes and economic systems.
  • Such stories in textbooks highlight how science is deeply intertwined with human history and society.
  • Role of Anecdotes in Science Education:
  • Anecdotes make learning more engaging and relatable for students.
  • They help in connecting abstract scientific concepts to real-world scenarios and historical events.
  • While they make learning enjoyable, their inclusion aims at deeper educational objectives, not just reducing content burden.

Important Points

  • Silk and the Silk Route:
  • The Silk Route was an ancient network of trade routes connecting China with Europe and the Middle East.
  • Silk, discovered in China around 3000 BCE, became a highly sought-after material and a symbol of wealth and luxury.
  • The route facilitated not just trade but also the exchange of ideas, religions, and technologies across continents.
  • Accidental Discoveries in Science:
  • Accidental discoveries like silk, penicillin, and X-rays have significantly shaped human progress.
  • These stories emphasize the role of curiosity, observation, and open-mindedness in scientific discovery.
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Question 108

Central Teacher Eligibility Test (CTET) 2026• Mathematics and Science• Mathematics and Science

Which of the following tasks would not contribute to developing scientific temper among students? 

  1. AOption (a)

    Emphasizing the historical aspects of the development of scientific concepts

  2. BOption (b)

    Reading out the tenets of nature of science

  3. COption (c)

    Encouraging the students to ask questions

  4. DOption (d)

    Providing hands-on experiences to students 

View answer & explanation

Correct answer

Answer: (b)B.

Reading out the tenets of nature of science

Why this answer is correct

Scientific temper refers to a way of thinking that involves curiosity, reasoning, open-mindedness, and a reliance on evidence to form conclusions. Developing scientific temper among students is essential for fostering critical thinking, problem-solving skills, and an appreciation for the scientific method. It helps students approach problems logically and make informed decisions based on evidence rather than biases or preconceived notions.

Key Points

  • Reading out the tenets of the nature of science does not actively engage students in the process of scientific inquiry. While the tenets of science are important, merely reading them is a passive activity that does not encourage critical thinking or experiential learning. Scientific temper is better developed through active participation, questioning, and hands-on experiences.
  • Emphasizing the historical aspects of the development of scientific concepts helps students understand the evolution of ideas, the challenges faced by scientists, and the evidence-based nature of science. This fosters an appreciation for the scientific process and its relevance in shaping modern knowledge.
  • Encouraging students to ask questions nurtures curiosity and critical thinking. Questioning is a fundamental aspect of scientific inquiry, as it drives exploration and investigation, leading to deeper understanding and discovery.
  • Providing hands-on experiences engages students in practical activities, experiments, and observations, allowing them to directly apply concepts and learn through exploration. This approach makes learning active and enhances their understanding of scientific principles.

Hint

  • Activities that promote active engagement, critical thinking, and inquiry are vital for developing scientific temper. Passive activities, such as reading out information without encouraging interaction or application, fail to achieve this goal.
  • Scientific temper thrives on participation, reasoning, and hands-on exploration rather than rote memorization or passive reception of information.

Hence, the correct answer is 'Reading out the tenets of nature of science'.

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Question 109

Central Teacher Eligibility Test (CTET) 2026• Mathematics and Science• Mathematics and Science

Which of the following is the most appropriate strategy to introduce physical properties metals and non-metals to Grade VII learners as per the inquiry-based approach? 

  1. AOption (a)

    Initiate a discussion on students' everyday experiences of using metallic and non-metall substances

  2. BOption (b)

    Define the terms 'sonorous', 'boiling point' and 'melting point'

  3. COption (c)

    Give a set of materials to students and ask them to deduce the properties of metals an non-metals

  4. DOption (d)

    List the differences between the physical properties of metals and non-metals on thi blackboard

View answer & explanation

Correct answer

Answer: (c)C.

Give a set of materials to students and ask them to deduce the properties of metals an non-metals

Why this answer is correct

The correct answer is Give a set of materials to students and ask them to deduce the properties of metals and non-metals.

Key Points

  • An inquiry-based approach is centered around fostering curiosity, exploration, and active participation among students. It encourages them to investigate and deduce concepts independently.
  • Providing a set of materials to students allows them to physically interact, observe, and test the properties of the items. This hands-on activity enhances experiential learning.
  • By engaging students in deducing the physical properties of metals and non-metals, such as malleability, ductility, conductivity, and sonority, they develop a deeper understanding through direct observation and experimentation.
  • This method aligns with the constructivist learning theory, which emphasizes learning through exploration and deriving conclusions based on evidence.
  • Inquiry-based learning promotes critical thinking and problem-solving skills, making it an effective strategy for teaching scientific concepts like the properties of metals and non-metals.

Additional Information

  • Physical Properties of Metals:
  • Malleability: Metals can be hammered into thin sheets (e.g., gold and silver).
  • Ductility: Metals can be drawn into wires (e.g., copper and aluminum).
  • Conductivity: Metals are good conductors of heat and electricity.
  • Sonority: Metals produce a ringing sound when struck.
  • Luster: Metals have a shiny appearance.
  • Physical Properties of Non-Metals:
  • Brittleness: Non-metals break easily and cannot be hammered into sheets.
  • Poor conductivity: Non-metals are poor conductors of heat and electricity.
  • Dullness: Non-metals generally lack luster, except for diamond.
  • Low density: Non-metals are usually lighter compared to metals.
  • Inquiry-Based Learning:
  • This approach emphasizes asking questions, exploring, and experimenting to understand concepts.
  • Students learn through active participation rather than passive listening.
  • It fosters curiosity, independence, and critical thinking in learners.
  • Role of Teachers:
  • Facilitate the activity by providing materials and guiding observations.
  • Encourage students to share their findings and discuss conclusions.
  • Promote collaboration among students during the exploration process.

Important Points

  • Option 1: Initiating a discussion on students' everyday experiences is a valid approach but does not directly involve hands-on exploration. Hence, this is not the most appropriate strategy.
  • Option 2: Defining terms like 'sonorous,' 'boiling point,' and 'melting point' is informative but does not engage students in active learning or inquiry.
  • Option 4: Listing differences on the blackboard is a traditional method and does not align with the inquiry-based approach.
  • Option 5: No specific strategy is mentioned, making it irrelevant in this context.
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Question 110

Central Teacher Eligibility Test (CTET) 2026• Mathematics and Science• Mathematics and Science

Read the following

Statements:

S₁ Systematic experimentation needs to be introduced in upper primary stage to verify theoretical principles.

S2: Activities and experimental evidence play an important role in understanding nature of science.

S3: Most concepts should be arrived at by an inductive approach at upper primary level.

Choose the correct option.

  1. AOption (a)

    Both S₁ and S3 are true and S3 is the correct reason for S₁

  2. BOption (b)

    Both S2 and S3 are true but Sy is false

  3. COption (c)

    Both Si and S3 are true but S2 is false

  4. DOption (d)

    Both S₁ and S2 are true and S2 is the correct reason for S₁

View answer & explanation

Correct answer

Answer: (b)B.

Both S2 and S3 are true but Sy is false

Why this answer is correct

The correct answer is Option 2.

Key Points

  • Statement S₁: "Systematic experimentation needs to be introduced in upper primary stage to verify theoretical principles." - While systematic experimentation is essential in science education, it is not the focus at the upper primary stage. Instead, this stage emphasizes conceptual understanding and activity-based learning rather than complex verification of theoretical principles. - Hence, this statement is incorrect.
  • Statement S₂: "Activities and experimental evidence play an important role in understanding nature of science." - This statement is valid as hands-on activities and experiments foster inquiry-based learning, which is central to understanding scientific concepts and processes. - Hence, this statement is correct.
  • Statement S₃: "Most concepts should be arrived at by an inductive approach at upper primary level." - This statement is true because the inductive method (moving from specific observations to broader generalizations) aligns with the developmental level of upper primary students. It encourages exploration and discovery, which is vital at this stage. - Hence, this statement is correct.
  • Based on the analysis of the statements, S₂ and S₃ are true, but S₁ is false. Therefore, the correct answer is Option 2.

Additional Information

  • Activity-based Learning: - Activity-based learning focuses on engaging students in hands-on tasks to encourage exploration and critical thinking. - It is widely used at the upper primary stage to help students understand abstract concepts through concrete experiences. - Examples include science experiments, model-making, and interactive group discussions.
  • Inductive Approach: - The inductive approach involves observing specific instances and deriving general principles or rules. - This method is particularly effective for upper primary students as it aligns with their cognitive development stage, fostering curiosity and reasoning skills. - For example, observing the behavior of magnets and then concluding the properties of magnetism.
  • Role of Experimentation in Science Education: - Experimentation is vital for developing critical thinking and problem-solving skills in students. - While it plays a significant role, the complexity of systematic experimentation is better suited for higher secondary education rather than the upper primary stage. - At the upper primary level, simple experiments and activities help students relate scientific concepts to real-world phenomena.
  • Cognitive Development at Upper Primary Stage: - Students at this stage (approximately aged 10–12) are transitioning from concrete operational to formal operational thinking (based on Piaget's theory). - Learning methods should emphasize observation, exploration, and reasoning rather than abstract theoretical verification.

Important Points

  • Systematic Experimentation: - It involves detailed procedures and verification of theoretical principles and is typically introduced at higher grades (secondary level). - For example, verifying laws like Newton's laws of motion or chemical equations requires deeper understanding and maturity, which upper primary students may not yet possess.
  • Activities vs. Verification: - Activities help upper primary students engage with science concepts through observation and exploration. - Verification of theoretical principles is a more advanced process that requires prior understanding of the concepts.
  • National Education Policies: - The National Education Policy (NEP) 2020 emphasizes experiential and activity-based learning at foundational and middle stages to build a strong base for critical thinking. - It recommends the use of inductive and inquiry-based learning approaches to foster curiosity and innovation among students.
CTET (Maths & Science) Official Paper-II (Held On: 07 Feb, 2026 Shift 1) (Previous Year Paper)·Mathematics and Science
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Question 111

Central Teacher Eligibility Test (CTET) 2026• Mathematics and Science• Mathematics and Science

Before beginning to formally teach a chapter on 'force' in Class VI, a teacher holds a discussion in which she asks children to imagine what would they do if they wish to keep a ball rolling on the ground for very long distances. How can she most suitably use the children's responses?

A. To evaluate students

B. To assess students' preconceptions

C. To determine the pedagogical strategy to be adopted to teach the concept

D. To enable students to define force 

Choose the correct option.

  1. AOption (a)

    B and C 

  2. BOption (b)

    C and D

  3. COption (c)

     A and C

  4. DOption (d)

    A and B

View answer & explanation

Correct answer

Answer: (a)A.

B and C 

Why this answer is correct

The correct answer is B and C.

Key Points

  • Evaluating students (Option A) refers to assessing their performance or understanding after teaching. However, the question focuses on pre-teaching discussion, so this option is not applicable.
  • The teacher's discussion with students before teaching the chapter is aimed at assessing students' preconceptions (Option B). This helps in identifying what students already know or believe about the concept of "force."
  • Based on the students' responses, the teacher can determine the pedagogical strategy (Option C) to make the teaching effective. For example, if students have misconceptions, the teacher can address them directly in the lesson plan.
  • Enabling students to define force (Option D) is a part of the formal teaching process, which comes later. Hence, it is not the primary purpose of the discussion.
  • Combining Options B and C is the most appropriate choice as the teacher uses the discussion to both understand students' preconceptions and decide the teaching strategy accordingly.

Additional Information

  • Importance of assessing preconceptions:
  • Preconceptions are the ideas or beliefs that students hold before learning about a concept. These may not always align with scientific principles.
  • Understanding preconceptions helps teachers address misconceptions and tailor the teaching process effectively.
  • For example, students might believe that "force" is only applied when something moves, which is a partial understanding of the concept.
  • Pedagogical strategies for teaching force:
  • Based on student responses, teachers can decide whether to use hands-on experiments, visual aids, or real-life examples to teach the concept of force.
  • Interactive methods, such as group discussions or demonstrations, help in clarifying misconceptions.
  • Practical activities like rolling a ball and observing its motion can help students understand the relationship between force and distance.
  • Examples of misconceptions related to force:
  • Misconception: A force is always needed to keep an object in motion.

Correction: According to Newton's First Law of Motion, an object in motion remains in motion unless acted upon by an external force, like friction.

  • Misconception: Heavier objects fall faster than lighter objects.

Correction: In the absence of air resistance, objects fall at the same rate regardless of their mass.

  • Role of discussions in teaching science:
  • Discussions encourage students to think critically and articulate their ideas.
  • They help teachers gauge the level of understanding and engagement among students.
  • This approach fosters a collaborative learning environment where students feel comfortable sharing their thoughts.

Important Points

  • Force: Force is a physical quantity that can cause an object to accelerate, change its direction, or deform. It is measured in Newtons (N).
  • Types of forces: Forces can be categorized as contact forces (e.g., friction, tension) and non-contact forces (e.g., gravitational, magnetic).
  • Newton's Laws of Motion: These laws form the foundation of classical mechanics and explain the relationship between force and motion.
  • Role of friction: Friction is a force that opposes motion and plays a crucial role in everyday activities, such as walking or driving.
  • Application in real life: Understanding force is essential for designing machines, vehicles, and structures, as well as for solving practical problems in engineering and physics.
CTET (Maths & Science) Official Paper-II (Held On: 07 Feb, 2026 Shift 1) (Previous Year Paper)·Mathematics and Science
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Question 112

Central Teacher Eligibility Test (CTET) 2026• Mathematics and Science• Mathematics and Science

Fill in the blanks with the correct answer: At the onset of puberty, the size of ovaries in females A and produce B. In male C is produced by testes. The production of these hormones is controlled by D.

  1. AOption (a)

    A—enlarges; B—thyroxine; C—testosterone; D—thyroid gland 

  2. BOption (b)

    A—reduces; B—estrogen; C—testosterone; D—pituitary gland 

  3. COption (c)

    A—enlarges; B—estrogen; C—testosterone; D—pituitary gland 

  4. DOption (d)

    A—reduces; B—estrogen; C—sex hormone; D—adrenal glan

View answer & explanation

Correct answer

Answer: (c)C.

A—enlarges; B—estrogen; C—testosterone; D—pituitary gland 

Why this answer is correct

The correct answer is Option 3.

Key Points

  • At the onset of puberty, the size of ovaries in females enlarges and begins to produce estrogen. This statement is correct.
  • Estrogen is a primary female sex hormone responsible for the development of secondary sexual characteristics such as the growth of breasts, widening of hips, and regulation of the menstrual cycle.
  • In males, the testes produce the hormone testosterone, which is responsible for male secondary sexual characteristics like facial hair growth, deepening of the voice, and increased muscle mass. This statement is correct.
  • The production of these hormones (estrogen in females and testosterone in males) is controlled by the pituitary gland, which secretes gonadotropins such as luteinizing hormone (LH) and follicle-stimulating hormone (FSH). This statement is correct.
  • Option 3 correctly identifies that at puberty, the ovaries enlarge, produce estrogen, and the testes produce testosterone, all under the regulation of the pituitary gland.

Additional Information

  • Puberty:
  • Puberty is the biological process through which a child's body matures into an adult body capable of reproduction.
  • In females, puberty typically begins between the ages of 8 and 13, while in males, it starts between 9 and 14 years.
  • It is characterized by the activation of the hypothalamic-pituitary-gonadal (HPG) axis, leading to the secretion of sex hormones.
  • Estrogen:
  • Estrogen is a group of steroid hormones that play a key role in the regulation of the female reproductive system and secondary sexual characteristics.
  • It is produced mainly by the ovaries, but smaller amounts are also produced by the adrenal glands and fat tissues.
  • Estrogen levels fluctuate during the menstrual cycle, peaking during ovulation.
  • Testosterone:
  • Testosterone is the primary male sex hormone and an anabolic steroid.
  • It is produced in the testes in males and in small amounts by the ovaries in females.
  • It plays a crucial role in the development of male reproductive tissues like the testes and prostate, as well as promoting secondary sexual characteristics.
  • Pituitary Gland:
  • The pituitary gland is a pea-shaped endocrine gland located at the base of the brain.
  • It is often referred to as the "master gland" because it regulates the activity of most other endocrine glands.
  • It secretes hormones such as LH and FSH, which stimulate the production of sex hormones in the ovaries and testes.

Important Points

  • Hormonal Regulation:
  • The hypothalamus releases gonadotropin-releasing hormone (GnRH), which stimulates the pituitary gland to release LH and FSH.
  • LH and FSH act on the gonads (ovaries in females, testes in males) to stimulate the production of sex hormones (estrogen and testosterone).
  • Role of Hormones:
  • Estrogen: Regulates the menstrual cycle, supports pregnancy, and promotes the development of female secondary sexual characteristics.
  • Testosterone: Promotes sperm production, enhances libido, and develops male secondary sexual characteristics.
  • Age of Onset:
  • Puberty typically begins earlier in females (8-13 years) compared to males (9-14 years).
  • These hormonal changes mark the transition from childhood to adulthood.
CTET (Maths & Science) Official Paper-II (Held On: 07 Feb, 2026 Shift 1) (Previous Year Paper)·Mathematics and Science
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Question 113

Central Teacher Eligibility Test (CTET) 2026• Mathematics and Science• Mathematics and Science

A circuit comprising three identical bulbs and a switch is connected in differe arrangements as given below. In which arrangement will the bulbs glow the brightest? 

  1. AOption (a)

    Arrangement B-All bulbs in parallel

  2. BOption (b)

    Arrangement C-Two bulbs in parallel connected in series with the third bulb

  3. COption (c)

    Arrangement D-Two bulbs in series connected in parallel with the third bulb

  4. DOption (d)

    Arrangement A-All bulbs in series

View answer & explanation

Correct answer

Answer: (a)A.

Arrangement B-All bulbs in parallel

Why this answer is correct

The correct answer is Arrangement B - All bulbs in parallel.

Key Points

  • Arrangement B ensures that all three bulbs are connected in parallel. In a parallel arrangement, each bulb receives the full voltage of the power supply, which allows the bulbs to glow at maximum brightness. Hence, this arrangement is correct.
  • In a parallel circuit, the current divides across each branch, but the voltage across each bulb remains constant and equal to the source voltage. This ensures that the bulbs are brighter compared to other arrangements.
  • Other arrangements such as Arrangement A (series connection) result in reduced brightness because the voltage is shared among the bulbs. This reduces the voltage across each bulb and consequently diminishes their brightness. Hence, this statement is incorrect.
  • In Arrangement C, two bulbs are connected in parallel and then connected in series with the third bulb. While this improves brightness compared to a complete series connection, the third bulb still receives reduced voltage, and the overall brightness is lower than a fully parallel configuration. Hence, this statement is incorrect.
  • In Arrangement D, two bulbs are in series and connected in parallel with the third bulb. This results in an uneven distribution of brightness, as the two series-connected bulbs share the voltage of one branch. This configuration is also less efficient compared to a fully parallel setup. Hence, this statement is incorrect.

Additional Information

  • Parallel Circuit Characteristics:
  • In a parallel circuit, the total resistance decreases as more branches are added. The formula for total resistance in a parallel circuit is 1/Rtotal = 1/R1 + 1/R2 + ....
  • Each component in a parallel circuit has the same voltage across it, equal to the source voltage.
  • The brightness of bulbs in a parallel circuit remains consistent, as each branch functions independently.
  • Series Circuit Characteristics:
  • In a series circuit, the total resistance increases as more components are added. The formula for total resistance is Rtotal = R1 + R2 + ....
  • The current remains the same throughout the circuit, but the voltage is divided across each component.
  • The bulbs in a series circuit generally appear dimmer because the voltage is shared among all the bulbs.
  • Comparison of Arrangements:
  • Arrangement A (Series): All bulbs are dim due to shared voltage.
  • Arrangement B (Parallel): All bulbs glow at maximum brightness as each receives full voltage.
  • Arrangement C (Mixed - 2 Parallel + 1 Series): Uneven brightness; series bulb glows dimmer than parallel ones.
  • Arrangement D (Mixed - 2 Series + 1 Parallel): Uneven brightness due to different voltage distribution.
  • Applications of Parallel Circuits:
  • Used in household wiring systems to ensure consistent voltage across all appliances.
  • Provides safety and reliability as a failure in one branch does not affect others.

Important Points

  • Power Distribution: In a parallel circuit, the total power consumed is the sum of the power consumed by each branch. This is why all bulbs glow at full brightness in Arrangement B.
  • Energy Efficiency: Parallel circuits are energy efficient for devices requiring consistent voltage, such as bulbs.
  • Real-World Example: In modern homes, electrical outlets are wired in parallel to ensure appliances operate at full capacity without voltage drop.
  • Ohm’s Law: The relationship between voltage, current, and resistance can be used to analyze each arrangement. In parallel circuits, the current through each branch is determined by its resistance.
CTET (Maths & Science) Official Paper-II (Held On: 07 Feb, 2026 Shift 1) (Previous Year Paper)·Mathematics and Science
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Question 114

Central Teacher Eligibility Test (CTET) 2026• Mathematics and Science• Mathematics and Science

Read the following

Statements:

Assertion (A): Anodizing is a method to prevent metal from corrosion.

Reason (R) : Anodizing is a process of coating iron with a layer of zinc.

Choose the correct option.

  1. AOption (a)

    Both A and R are true but R is not the correct reason for A

  2. BOption (b)

    A is true but R is false

  3. COption (c)

    Both A and R are false

  4. DOption (d)

    Both A and R are true and R is the correct reason for A

View answer & explanation

Correct answer

Answer: (b)B.

A is true but R is false

Why this answer is correct

The correct answer is A is true but R is false.

Key Points

  • Assertion (A): Anodizing is a method to prevent metal from corrosion.
  • Anodizing is a process used to increase the thickness of the natural oxide layer on the surface of metal parts, primarily aluminum.
  • The oxide layer formed during anodizing acts as a protective barrier, preventing the underlying metal from corroding.
  • This process also enhances the aesthetic appearance of the metal and can be dyed to achieve different colors.
  • Hence, Assertion (A) is correct.
  • Reason (R): Anodizing is a process of coating iron with a layer of zinc.
  • This statement is incorrect because anodizing is not related to zinc or iron.
  • The process of coating iron with a layer of zinc is called galvanization, not anodizing.
  • Anodizing is specifically used for metals like aluminum, titanium, and magnesium, and does not involve zinc or iron.
  • Hence, Reason (R) is false.
  • Since the assertion (A) is true but the reason (R) is false, the correct option is "A is true but R is false".

Additional Information

  • Anodizing Process:
  • During anodizing, the metal is immersed in an electrolyte solution, and an electric current is passed through it.
  • The process transforms the metal surface into a durable, corrosion-resistant, anodic oxide finish.
  • It is widely used in industries like aerospace, automotive, and construction for improving durability and appearance.
  • Galvanization:
  • Galvanization involves applying a protective zinc coating to steel or iron to prevent rusting.
  • The most common method of galvanization is hot-dip galvanizing, where the metal is submerged in molten zinc.
  • This zinc layer acts as a sacrificial anode, protecting the underlying iron or steel from corrosion.
  • Differences Between Anodizing and Galvanization:
  • Anodizing: Used for aluminum and its alloys; improves corrosion resistance and aesthetic appeal.
  • Galvanization: Used for iron and steel; prevents rusting through a zinc coating.
  • Anodizing involves oxidation, while galvanization involves adding a protective layer of another metal (zinc).
  • Applications:
  • Anodizing: Used for architectural components, consumer electronics, and automotive parts.
  • Galvanization: Used for pipelines, structural steel, and outdoor metal structures.

Important Points

  • Aluminum Oxide Layer in Anodizing:
  • The aluminum oxide layer is non-conductive, making it ideal for electrical insulation in certain applications.
  • This layer also has high hardness and can withstand wear and tear, enhancing the metal’s longevity.
  • Galvanization and Corrosion Protection:
  • In galvanization, even if the zinc layer is scratched, it provides cathodic protection to the underlying iron or steel.
  • Galvanization is an economical method for protecting steel structures, especially in marine and industrial environments.
CTET (Maths & Science) Official Paper-II (Held On: 07 Feb, 2026 Shift 1) (Previous Year Paper)·Mathematics and Science
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Question 115

Central Teacher Eligibility Test (CTET) 2026• Mathematics and Science• Mathematics and Science

Why do silver articles turn black when kept in the open for a few days? 

  1. AOption (a)

    Due to reaction with hydrogen sulphide present in air

  2. BOption (b)

    Due to reaction with nitrogen oxides present in air

  3. COption (c)

    Due to reaction with carbon monoxide present in air

  4. DOption (d)

     Due to reaction with oxygen in air

View answer & explanation

Correct answer

Answer: (a)A.

Due to reaction with hydrogen sulphide present in air

Why this answer is correct

The correct answer is Due to reaction with hydrogen sulphide present in air.

Key Points

  • Silver articles turn black when exposed to air because they react with hydrogen sulphide (H₂S), which is present in trace amounts in the atmosphere.
  • This reaction forms a layer of silver sulphide (Ag₂S), which is black in color, on the surface of the silver articles.
  • Hydrogen sulphide (H₂S) is a gas released from sources like decaying organic matter, sewage, and industrial emissions, contributing to this tarnishing effect.
  • The chemical reaction can be represented as: 4Ag + 2H₂S + O₂ → 2Ag₂S + 2H₂O.
  • Silver sulphide is insoluble in water, which is why the black tarnish cannot be easily washed off with water alone.

Additional Information

  • Other Causes of Tarnishing:
  • Silver can also tarnish due to reactions with sulphur compounds found in food items like eggs, onions, and mustard.
  • Exposure to high levels of pollutants, such as sulphur dioxide (SO₂) and hydrogen sulphide (H₂S), accelerates tarnishing.
  • Prevention of Tarnishing:
  • Store silver articles in airtight containers or use anti-tarnish strips to reduce exposure to air.
  • Regular cleaning with a silver polish or mild detergent can help remove tarnish.
  • Applying a thin layer of lacquer or coating can protect silver from environmental damage.
  • Properties of Silver:
  • Silver is a transition metal with the atomic number 47.
  • It is highly malleable, ductile, and an excellent conductor of electricity and heat.
  • Due to its high reactivity with sulphur compounds, it tarnishes more easily compared to other metals like gold or platinum.
  • Applications of Silver:
  • Silver is widely used in jewelry, cutlery, coins, and as a component in electrical circuits.
  • Its antimicrobial properties make it useful in medical instruments and wound dressings.
  • Silver is also used in photography and as a catalyst in chemical reactions.
  • Other Options Explained:
  • Option 2: Reaction with nitrogen oxides (NOₓ) does not cause tarnishing of silver.
  • Option 3: Carbon monoxide (CO) is not reactive with silver under normal conditions.
  • Option 4: Silver reacts with oxygen very slowly and does not form a black tarnish layer.
CTET (Maths & Science) Official Paper-II (Held On: 07 Feb, 2026 Shift 1) (Previous Year Paper)·Mathematics and Science
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Question 116

Central Teacher Eligibility Test (CTET) 2026• Mathematics and Science• Mathematics and Science

Identify A, B, C and D in the following table:

Name of the saltSalt obtained from AcidSalt obtained from Base
Ammonium chlorideHClA
Sodium nitrateHNO3B
Sodium chlorideCD
  1. AOption (a)

    A—NH4; B—NaOH; C—HCl; D—NaOH

  2. BOption (b)

    A—NH3; B—NaOH; C—HCl; D—NaOH

  3. COption (c)

    A—NH4OH; B—NaO; C—HCl; D—NaHCO3

  4. DOption (d)

    A—NH4OH; B—Na(OH)2; C—HClO2; D—NaH

View answer & explanation

Correct answer

Answer: (b)B.

A—NH3; B—NaOH; C—HCl; D—NaOH

Why this answer is correct

The correct answer is Option 2: A—NH3; B—NaOH; C—HCl; D—NaOH.

Key Points

  • Ammonium chloride (NH4Cl):
  • It is obtained from the reaction of hydrochloric acid (HCl) and ammonia (NH3).
  • Ammonia acts as the base in this reaction.
  • The reaction is: HCl + NH3 → NH4Cl.
  • Sodium nitrate (NaNO3):
  • It is formed from the reaction between nitric acid (HNO3) and sodium hydroxide (NaOH).
  • Sodium hydroxide acts as the base here.
  • The reaction is: HNO3 + NaOH → NaNO3 + H2O.
  • Sodium chloride (NaCl):
  • It is obtained by the reaction of hydrochloric acid (HCl) with sodium hydroxide (NaOH).
  • The reaction is a classic acid-base neutralization: HCl + NaOH → NaCl + H2O.
  • Correct identification:
  • A = NH3 (Ammonia as the base for ammonium chloride).
  • B = NaOH (Sodium hydroxide as the base for sodium nitrate).
  • C = HCl (Hydrochloric acid as the acid for sodium chloride).
  • D = NaOH (Sodium hydroxide as the base for sodium chloride).

Additional Information

  • Salt Formation in Chemistry:
  • Salts are ionic compounds formed by the neutralization reaction between an acid and a base.
  • They typically consist of a positive ion (cation) from the base and a negative ion (anion) from the acid.
  • Example: NaCl (Sodium chloride) is formed from Na+ (from NaOH) and Cl− (from HCl).
  • Types of Salts:
  • Normal salts: Formed when all the hydrogen ions of an acid are replaced by metal or ammonium ions. Example: NaCl.
  • Acidic salts: Formed when not all hydrogen ions are replaced. Example: NaHSO4.
  • Basic salts: Formed when not all hydroxide ions of a base are replaced. Example: Ca(OH)Cl.
  • Neutralization Reaction:
  • It is a chemical reaction between an acid and a base to produce a salt and water.
  • Example: HCl + NaOH → NaCl + H2O.
  • Examples of Acid-Base Pairs:
  • HCl (acid) + NH3 (base): Produces NH4Cl.
  • HNO3 (acid) + NaOH (base): Produces NaNO3.
  • HCl (acid) + NaOH (base): Produces NaCl.
  • Applications of Salts:
  • Ammonium chloride: Used in fertilizers and as a flux in metalwork.
  • Sodium nitrate: Used in food preservation and fertilizers.
  • Sodium chloride: Commonly known as table salt, used in cooking and food preservation.
CTET (Maths & Science) Official Paper-II (Held On: 07 Feb, 2026 Shift 1) (Previous Year Paper)·Mathematics and Science
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Question 117

Central Teacher Eligibility Test (CTET) 2026• Mathematics and Science• Mathematics and Science

Read the following

Statements:

Step 1: A few spoons of sugar are dissolved in water to prepare a concentrated sugar syrup.

Step 2: The sugar syrup is heated on low flame till it caramelizes.

Choose the correct option.

  1. AOption (a)

    Step 1 is a chemical change and Step 2 is a physical change

  2. BOption (b)

    Both Step 1 and Step 2 are physical changes 

  3. COption (c)

    Both Step 1 and Step 2 are chemical changes

  4. DOption (d)

    Step 1 is a physical change and Step 2 is a chemical change 

View answer & explanation

Correct answer

Answer: (d)D.

Step 1 is a physical change and Step 2 is a chemical change 

Why this answer is correct

The correct answer is Step 1 is a physical change and Step 2 is a chemical change.

Key Points

  • Step 1: Dissolving sugar in water:
  • This is a physical change because the sugar molecules disperse in water but retain their chemical structure.
  • The process is reversible by evaporation. The water can be evaporated to retrieve the sugar.
  • No new substance is formed during this process. Hence, Step 1 is a physical change.
  • Step 2: Heating sugar syrup to caramelize:
  • This is a chemical change because heating sugar breaks it down into new compounds like caramel, carbon, and water vapor.
  • The process is irreversible under normal conditions. The original sugar cannot be retrieved after caramelization.
  • New properties such as color, taste, and texture appear, confirming the formation of a new substance. Hence, Step 2 is a chemical change.
  • Physical vs. Chemical Change:
  • A physical change does not alter the chemical composition of a substance, while a chemical change results in the formation of one or more new substances.
  • Step 1 meets the criteria of a physical change, and Step 2 meets the criteria of a chemical change.
  • Correct Option: The correct answer is Step 1 is a physical change and Step 2 is a chemical change.

Additional Information

  • Definition of Physical Change:
  • A physical change involves a change in physical properties such as shape, size, or state, without altering the chemical composition.
  • Examples: Melting of ice, boiling of water, dissolving salt or sugar in water.
  • Definition of Chemical Change:
  • A chemical change involves a transformation at the molecular level, producing new substances with different properties.
  • Examples: Rusting of iron, burning of wood, caramelization of sugar.
  • Caramelization Process:
  • Caramelization occurs when sugar is heated to temperatures of around 170°C (338°F).
  • It involves the breakdown of sugar molecules, releasing water and forming compounds like caramelan, caramelene, and caramelin that give caramel its distinct color and flavor.
  • Reversibility:
  • Physical changes are generally reversible, while chemical changes are typically irreversible under normal conditions.
  • Examples of Similar Processes:
  • Physical changes: Dissolving salt in water, freezing water into ice.
  • Chemical changes: Burning of paper, cooking of food.

Important Points

  • Physical and Chemical Changes in Daily Life:
  • Physical: Cutting paper, melting wax, boiling water.
  • Chemical: Baking a cake, fermenting grapes to make wine, photosynthesis in plants.
  • Indicators of a Chemical Change:
  • Change in color or odor.
  • Release of gas or formation of precipitate.
  • Change in temperature or emission of light.
CTET (Maths & Science) Official Paper-II (Held On: 07 Feb, 2026 Shift 1) (Previous Year Paper)·Mathematics and Science
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Question 118

Central Teacher Eligibility Test (CTET) 2026• Mathematics and Science• Mathematics and Science

The ion of an element has two positive charges. The mass number of the atom is 27 and the number of neutrons is 14. What is the number of electrons in the ion? 

  1. AOption (a)

    10

  2. BOption (b)

    11

  3. COption (c)

    15

  4. DOption (d)

    13

View answer & explanation

Correct answer

Answer: (b)B.

11

Why this answer is correct

The correct answer is Option 2 (11).

Key Points

  • The atom has a mass number of 27, which is the sum of its protons and neutrons.
  • The number of neutrons is 14. Therefore, the number of protons in the atom can be calculated as:
  • Protons = Mass number - Neutrons = 27 - 14 = 13.
  • An atom's atomic number equals the number of protons, which is 13. This is the element aluminum (Al).
  • In its neutral state, the number of electrons equals the number of protons, i.e., 13 electrons.
  • The ion has two positive charges, meaning it has lost 2 electrons. Therefore, the number of electrons in the ion is:
  • Electrons = 13 - 2 = 11.

Additional Information

  • Atomic Number and Mass Number:
  • The atomic number of an element is the number of protons in its nucleus and determines the chemical identity of the element.
  • The mass number is the sum of protons and neutrons in the nucleus.
  • Neutral Atom vs. Ion:
  • In a neutral atom, the number of electrons equals the number of protons.
  • An ion forms when an atom gains or loses electrons. A positive ion (cation) results from the loss of electrons, while a negative ion (anion) results from gaining electrons.
  • Aluminum (Al):
  • Aluminum has an atomic number of 13 and is represented by the symbol Al.
  • It is a metal and is commonly used in manufacturing, construction, and packaging industries.
  • Charge of an Ion:
  • The charge of an ion is determined by the difference between the number of protons and electrons.
  • In this question, the ion has a +2 charge, which indicates the loss of 2 electrons.

Important Points

  • Calculation Summary:
  • Mass number = Protons + Neutrons = 27.
  • Protons = 27 - 14 = 13.
  • Neutral atom electrons = Protons = 13.
  • Ion electrons = Neutral atom electrons - Charge = 13 - 2 = 11.
  • Real-World Application:
  • Understanding ions is crucial in fields like chemistry, biology, and materials science.
  • Aluminum ions (Al3+) are used in water purification and as a catalyst in various chemical reactions.
CTET (Maths & Science) Official Paper-II (Held On: 07 Feb, 2026 Shift 1) (Previous Year Paper)·Mathematics and Science
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Question 119

Central Teacher Eligibility Test (CTET) 2026• Mathematics and Science• Mathematics and Science

A ray of light travels from air into three media A, B and C with different optical densities. Refer to the table given below and identify X, Y, Z and W:

Change in speed of lightChange in frequency of lightChange in wavelength of light
Air to medium AXYDecreases
Air to medium BIncreasesNo changeZ
Air to medium CRemains sameWNo change
  1. AOption (a)

    X—Increases; Y—Increases; Z—Increases; W—Increases 

  2. BOption (b)

    X—Decreases; Y—Remains unchanged; Z—Increases; W—Remains unchanged

  3. COption (c)

    X—Decreases; Y—Decreases; Z—Increases; W—Remains unchanged

  4. DOption (d)

    X—Increases; Y—Decreases; Z—Decreases; W—Increases

View answer & explanation

Correct answer

Answer: (b)B.

X—Decreases; Y—Remains unchanged; Z—Increases; W—Remains unchanged

Why this answer is correct

The correct answer is Option 2: X—Decreases; Y—Remains unchanged; Z—Increases; W—Remains unchanged.

Key Points

  • Change in speed of light (X): When light enters a denser medium (like medium A) from a rarer medium (like air), its speed decreases. This is due to the higher refractive index of the denser medium.
  • Change in frequency of light (Y): The frequency of light remains unchanged when it moves from one medium to another, as it depends only on the source of the light.
  • Change in wavelength of light (Z): The wavelength of light in a denser medium (like medium B) increases if the speed of light increases (as wavelength is directly proportional to speed).
  • Behavior of light in medium C (W): If the speed of light remains the same, the wavelength will also remain unchanged. This occurs when the optical density of medium C is the same as that of air.
  • Correct alignment: The given conditions match Option 2: X—Decreases; Y—Remains unchanged; Z—Increases; W—Remains unchanged.

Additional Information

  • Refractive Index:
  • The refractive index (n) of a medium measures how much the speed of light decreases in that medium compared to air/vacuum.
  • It is calculated using the formula: n = c/v, where c is the speed of light in vacuum, and v is the speed of light in the medium.
  • Higher refractive index means lower speed of light in the medium.
  • Frequency and Wavelength Relationship:
  • The relationship between speed, frequency, and wavelength is given by: v = f × λ, where v is the speed of light, f is the frequency, and λ is the wavelength.
  • If the speed decreases when entering a denser medium, the wavelength decreases proportionally (since frequency remains constant).
  • Optical Density and Speed of Light:
  • When light travels from a rarer medium (air) to a denser medium, its speed reduces due to the higher optical density.
  • Conversely, when light moves from a denser medium to a rarer medium, its speed increases.
  • Behavior of Light in Mediums:
  • Medium A: Light slows down, and its wavelength decreases due to higher optical density.
  • Medium B: Light speeds up, and its wavelength increases due to lower optical density.
  • Medium C: The speed and wavelength of light remain unchanged, indicating that the optical density of medium C is the same as air.

Important Points

  • Frequency of Light: The frequency of light is determined by the source and does not change when light moves between mediums.
  • Snell's Law: The relationship between the angle of incidence and refraction is governed by Snell’s law: n₁ sin θ₁ = n₂ sin θ₂.
  • Applications of Refraction: Refraction explains phenomena such as the bending of light in lenses, mirages, and the dispersion of light in prisms.
  • Critical Angle and Total Internal Reflection: When light moves from a denser to a rarer medium and exceeds the critical angle, total internal reflection occurs.
CTET (Maths & Science) Official Paper-II (Held On: 07 Feb, 2026 Shift 1) (Previous Year Paper)·Mathematics and Science
View full paper

Question 120

Central Teacher Eligibility Test (CTET) 2026• Mathematics and Science• Mathematics and Science

Read the following

Statements:

Situation A : Growth and branching of roots in the A-horizon and B-horizon is advantageous for absorption of water and minerals.

Situation B : C-horizon is rich in humus which makes soil soft and porous. Situation B

Choose the correct option.

  1. AOption (a)

    Only Situation B is true

  2. BOption (b)

    Both Situations A and B are true 

  3. COption (c)

    Both Situations A and B are false

  4. DOption (d)

    Only Situation A is true

View answer & explanation

Correct answer

Answer: (d)D.

Only Situation A is true

Why this answer is correct

The correct answer is Only Situation A is true.

Key Points

  • Situation A: Growth and branching of roots in the A-horizon and B-horizon is advantageous for absorption of water and minerals.
  • The A-horizon, also known as the topsoil, is rich in organic material and nutrients. It is the most fertile layer of soil, allowing roots to absorb essential minerals.
  • The B-horizon, or subsoil, contains minerals leached from the A-horizon and provides additional nutrients for deeper roots. This allows plants to access water and nutrients from deeper soil layers.
  • Roots in these horizons ensure efficient plant growth and survival. Hence, Situation A is correct.
  • Situation B: C-horizon is rich in humus which makes soil soft and porous.
  • This statement is incorrect as the C-horizon, also known as the parent material, primarily consists of partially weathered rocks and mineral fragments. It is not rich in humus.
  • Humus is concentrated in the A-horizon (topsoil), not the C-horizon. The C-horizon lacks significant organic matter and is generally compact and less porous.
  • Hence, Situation B is false.

Additional Information

  • Soil Horizons:
  • A-Horizon: Known as the topsoil, it is rich in organic matter, microorganisms, and nutrients, making it fertile and suitable for plant growth.
  • B-Horizon: Also known as the subsoil, it accumulates minerals like iron, aluminum, and clay leached from the A-horizon. It provides support and additional nutrients for plant roots.
  • C-Horizon: Composed of weathered parent rock material, this layer has minimal organic content and provides raw material for soil formation.
  • Humus:
  • Humus is a dark organic material formed from the decomposition of plant and animal matter.
  • It is primarily found in the A-horizon, where it enhances soil fertility, water retention, and porosity.
  • Importance of Root Growth in Soil Layers:
  • Roots in the A-horizon absorb nutrients and water essential for plant growth.
  • Roots in the B-horizon access deeper water reserves during drought conditions and stabilize the plant.

Important Points

  • Soil Layers and Plant Growth:
  • The A-horizon is crucial for agricultural activities due to its high nutrient content.
  • The B-horizon supports deeper-rooted plants and contributes to the overall stability of vegetation.
  • The C-horizon serves as a reservoir for raw minerals but is not fertile or humus-rich.
  • Soil Composition:
  • Soil is a mixture of minerals, organic matter, air, and water.
  • The distribution of these components varies across different horizons, influencing soil fertility and plant growth.
  • Environmental Impact on Soil:
  • Soil erosion, deforestation, and overgrazing can degrade the A-horizon, reducing fertility.
  • Sustainable agricultural practices help maintain soil health and enhance its productivity.

How should I prepare for Mathematics and Science in Central Teacher Eligibility Test (CTET)?

Solving previous year questions by topic helps identify recurring concepts, question patterns, and frequently asked sub-topics. Attempt each question, review the step-by-step explanation, and note down key formulas or facts for quick revision before the exam.