CTET Paper 2 Maths & Science 21st Dec 2021 (Eng/Hin/Sans/Ben/Mar/Tel) (Previous Year Paper)

The term 'development' refers to a progressive series of changes that occur in an orderly, predictable pattern as a result of maturation and experience. There is a natural arrangement of changes in the individuals, and each change is dependent upon the preceding ones, and also affects the following ones. The changes within the development are called 'progressive' because they enable an individual to adapt to and adjust to his/her environment - physical, social, emotional, etc.

Key Points Factors affecting the development of the child are:

• Genetically Determined Factors: most of the inherited characteristics are essentially influenced by the environment.
• For example, a child may be endowed with the hereditary potential for physical growth, but his/her potential may be stunted due to various reasons such as lack of nutrition or illness or being forced to do too heavy work for the body.
• Non-genetically Determined Factors: There are many non-genital factors that affect the development of the child these are- 
• Conditions in the Pre-natal Environment
• Maternal nutrition
• Maternal health
• Nutrition
• Physical  effects and illness
• **The Psycho-social Environment of family and Culture, and many more.**​
• Principle of individual variation: Interaction between heredity and environmental influences leads to individual differences in the developmental pattern. These differences are caused by the genes one inherits and environmental conditions like food, medical facilities, psychological conditions, and learning opportunities.
• So by all these, we can conclude that the development of the child is dependent on many factors, which decide the rate of development which is different from individual to individual.
• Hence option (4) is the correct answer.

Important Points

• Development is a continuous process, it goes throughout life.
• The development of the child is spiral in shape it can be back and forth throughout the life.
• Development has uniformity in some cases, such as language development, and physical development, but in another context, it varies from individual to individual.

Additional Information

• Principle of Development Sequences: Every living being followed a pattern of development. A child also develops in an orderly sequence that is almost similar to all children.
• Principle of integration: It can generally be defined as a curriculum approach that purposefully draws together knowledge, skills, attitudes, and values from within or across subject areas to develop a more powerful understanding of key ideas.
• Principle of a common pattern of development: Development follows the common pattern. A child follows first from the sensory-motor stage, then the pre-operational stage, the concrete operational stage, and then the formal operational stage. For example, the child of a poor family learns to walk on his knees before learning to walk and the children of a rich family also learn to walk on their knees first.

The idea that childhood is socially constructed refers to the understanding that childhood is not a natural process. rather it is a society that decides when a child is a child and when a child becomes an adult.

Key Points -

• When sociologists say that ‘childhood is socially constructed’ they mean that the ideas we have about childhood are created by society, rather than being determined by the biological age of a ‘child’.
• There are differences in every culture and society,  which affect childhood.

Some of the aspects of childhood which are influenced by the society include:

• The length of childhood and the moment a child becomes an adult.
• The status of children in society – their rights and responsibilities, what legal protections/ restrictions we place on them.
• The general ideas we have about children – for example, whether we think they are innocent and in need of protection, or resilient and in need of freedom to explore and develop by themselves as far as possible.
• So, It is difficult to make generalized claims about children and childhood because there is so much multiplicity.

​Statement (A) and (R) both are correct and (R) is explaining statement (A). 

Hence, we can conclude that the right answer to this question is Both (A) and (R) are true and (R) is the correct explanation of (A). 

Additional Information

• Lev Vygotsky is a Russian Psychologist who proposed the theory of Socio-cultural development. In this theory, Vygotsky emphasizes the role of society and culture in the development of the child.
• According to Lev Vygotsky, the development of children depends on three factors.
• Social interaction- Society plays an important role in the development and knowledge gained by the child.
• Language- Language development in a child should be done by the environment, engagement in family, etc.
• Culture - culture plays an important role in the development of a child, a child behaves as same as they learn from their culture, society, and environment.

The process of learning to internalize the values and norms into itself or the mode of learning to live in society is called the process of socialization. It may be defined more comprehensively as a life-long process of inculcation whereby an individual learns the principles, values, and symbols of the social system in which he participates and the expression of those values and norms in the roles he enacts.

Key Points

• Social development is a product of heredity and environment, the development of a child neither be done by only heredity nor by the only the environment.
• Heredity and Environment both play an important role in the development of a child, "According to Woodworth, Development is the product of Heredity and environment".
• By heredity, they can acquire mental strength and physical strength, and by the environment, they learn how to revoke strengths.
• So we can say that Children's development is a complex interplay of heredity and environment. 
• Hence option (4) is the correct answer.

Important Points

• Socialization can be classified into two broad groups:
• Primary socialization
• Secondary socialization.
• Primary socialization- Inculcation of norms and values within the family is called primary socialization. Here children want to know themselves and try to find their identity and learn the daily routine tasks of humans.
• Example: Family.
• Secondary socialization- The process of imbibing norms, values, and behavior patterns of school may be called secondary socialization.
• Example: Church, School, Media, etc.

Additional Information

Cognitive development involves areas such as problem-solving, moral understanding, and conceptual understanding; language acquisition; social, personality, and emotional development, and self-concept and identity formation. The risk factors and interventions influencing cognitive development in children can be divided into three domains: nutrition, environment, and maternal-child interactions.

Key PointsJean Piaget studied cognitive development among children of different age groups in different developmental stages. According to him the stages of cognitive development are ( sequentially):

• Sensorimotor stage: (birth to 2 years)
• Pre-operational stage: (2 to 6 years)
• Concrete operational stage: (6 to 11 years)
• Formal operational stage: (11+ to adolescence and adulthood)

Important Points 

• Sensory-motor stage - This is a stage of the child from just after birth to two years. In this stage-
• Senses are teachers.
• Reflex action shows in children.
• Intimate behavior by the child is shown.
• Pre-operational stage - This is a stage of the child from two years to 6 years. In this stage, there are many changes are shown in the child such as-
• ​Language development starts.
• Irreversibility in a child.
• Egocentrism
• Animism​
• Concrete operational stage- There are many changes found in the child during the concrete operation stage (6 to 11 years) such as:
• Reversibility: Reversibility comes in a child, he/she can change their views by thinking diversely.
• Logics mapping: Logical mapping begins in a child so they analyze the problem, then think critically about it then comes to conclusion.
• Formal Operational Stage- According to Jean Piaget, this is a stage for a child who belongs from the age group of 11 years till adolescence. Changes are as-
• Hypothetical-deductive logic begins.
• Divergent/Convergent thinking.
• Creative thinking.

Hence, we can conclude that the correct chronological order of Piaget's stages of development is Sensorimotor, Pre-operational, concrete operational, and formal-operational.

Additional Information

• Jean Piaget is a Psychologist from Switzerland who proposed that development is based on Physical environment and Biological abilities. He ignores the social aspects of development.

Cognitive development involves areas such as problem-solving, moral understanding, and conceptual understanding; language acquisition; social, personality, and emotional development, and self-concept and identity formation. The risk factors and interventions influencing cognitive development in children can be divided into three domains: nutrition, environment, and maternal-child interactions.

Jean Piaget studied cognitive development among children of different age groups in different developmental stages, According to Piaget, development is based on Physical environment and Biological abilities, he ignores social Aspects. he categorized it into different developmental stages. These stages are-

• Sensory-motor stage (0 to 2 years)
• Pre-operational stage (2 to 6 years)
• Concrete operational stage (6 to 11 years)
• Formal Operational stage (11+ years to adolescence).​

Key Points

• Pre-operational stage: According to Jean Piaget this is a stage in a child in which a child gains Irreversibility, language development, Egocentrism, and animism.
• There are many critiques of Piaget's Pre-operational stage, some of these are-
• All children will automatically move to the next stage of development as they mature.
• He may have underestimated a child's capabilities.
• Piaget's theory has some shortcomings, including overestimating the ability of adolescence and underestimating a child's capacity.
• Children in the preoperational stage are able to focus on only one aspect or dimension of problems.
• He proposed the development of the language is only based on cognitive abilities, but language development is done by both cognition and environmental factor.
• So, Option (2) is the correct answer.

Hint

• According to Piaget, development is a continuous process and it goes throughout life.
• Children construct knowledge, stage by stage.

​ 

Additional Information

The gradual formation of an individual's concepts of right and wrong, conscience, ethical and religious values, social attitudes, and behavior is called moral development.​

The theory of a child's moral development is proposed by Lawrence Kohlberg in 1958. he describes the theory on 3 different levels and these 3 levels are further classified into 6 stages.

Key Points Three levels of moral development are Pre- Conventional, Conventional, Post conventional.

• Pre- Conventional Level: At this level, the child is not responsive to cultural rules and labels of good and bad, right or wrong but interprets these labels in terms of physical or hedonistic consequences of actions or in terms of physical powers of those who communicate the rules and labels. This level is further sub-divided into two stages.
• Stage-I: The Punishment and Obedience Orientation: The physical consequences of an action determine whether the action is good or bad regardless of the human value or the meaning of these consequences. Avoidance of punishment and deference to power are valued in their own right, not in terms of respect for the underlying moral order.
• Stage-2: Instrumental Relativist Orientation: Right action consists of that which instrumentally satisfies one's own needs and occasionally the needs of others.
• By all these references, we can conclude that children's moral reasoning is controlled by external rewards or punishments in pre-conventional level.

Important Points

• Conventional Level: At this level maintaining the expectations of the individual, family, group, or nation is perceived as of value in its own right regardless of the immediate and obvious consequences. The attitude is not only of personal expectations and social order but of loyalty to it of actively maintaining, supporting, and justifying the order, and identifying oneself with persons or groups involved in it. This level is further classified into 2 levels-
• Stage 3: Good boy - Nice Girl Orientation: Good behavior is that which pleases or helps others and is approved by them. Behavior at this stage is frequently judged by intentions - "he means well", becomes important for the first time. One earns approval by being good to others.
• Stage 4: The Law and Order Orientation: There is an orientation towards authority, fixed rules, and the maintenance of social order. Right behavior consists of doing one's duty, showing respect for established or lawful authority, and maintaining given social order for its own sake.
• Post conventional level: At this level, there is a clear effort to define moral values and principles that have validity and application apart from the authority of the groups or persons. This level also has two stages.
• Stage 5: The Social Contract, Legalistic Orientation:  in terms of general individual rights and standards that have been critically examined and agreed upon by the whole society. Apart from what is constitutional and democratically agreed upon the right is a matter of personal values. The result is based upon a legal point of view but with a Right to Education emphasis upon the possibility of changing the law in terms of consideration of social utility
• Stage 6: The Universal Ethical Principle Orientation: Right is defined by the decision of the conscience in accordance with self-chosen ethical principles appealing to logical comprehensiveness, universality, and consistency. These are universal principles of justice, reciprocity, quality of human rights, and respect for the dignity of human beings as individual persons.

Jean Piaget made a systematic study of cognitive development among children of different age groups and he categorized it into different developmental stages. He is also known as the father of child Psychology. According to him, development is based on the physical environment or Biological abilities, he ignores social aspects.

According to him stages of the cognitive development are-

• Sensory-motor:(birth to 2 years) - (Adaptation)
• Preoperational: (from age 2 years to 7 years) - (Assimilation)
• Concrete operational:(from 7 years to 11 years) - (Accomodation)
• Formal operational: (from11+ - adolescence and adulthood). - (Equilibrition).

Key Points Sensory-motor stage: In this stage of birth to two years, the changes are seen in a child as Reflex actions, Intimate behavior, Schema formation, and senses are the teacher at this stage.

• Schema: Schema is an already existing mental set up in the mind which is a pattern of repeated behavior that allows children to explore and express developing ideas and thoughts through their play and exploration where the senses are the only teachers of children.
• Human babies are born with these schemas and tried to relate their schemas to real-world situations.

Hint 

• Accommodation: Accommodation: Jean Piaget defined accommodation as the cognitive process of revising existing cognitive schemas, perceptions, and understanding so that new information can be incorporated. This happens when the existing schema (knowledge) does not work and needs to be changed to deal with a new object or situation.
• Mind mapping: Mind mapping is the term, by which a child used their cognition to make the way of solving problems.
• Operations: This is an ability of a child to act on a problem in his mind.

Additional Information

Lev Vygotsky is a Russian Psychologist who proposed the theory of Socio-cultural development. In this theory, Vygotsky emphasizes the role of society and culture in the development of the child. According to him, there are three main needs for the development of the child and these are- Social interaction, Culture, and Language.

Key Points

 Vygotsky also proposed three basic needs of students during learning, these are- Zone of proximal development (ZPD), Scaffolding, and Making knowledgeable others (MKO).

• ZPD (zone of proximal development):  The difference between the learning of a child by self and the learning of a child with the help of others(society, culture, etc).
• Example: A parent teaching a child how to ride a bike.
• So we conclude that the new knowledge is constructed in the zone between What a child knows and is capable of knowing.​

Important Points

• Scaffolding: Scaffolding is the term, given by Vygotsky, in which he proposed that the temporary help given by the teachers, family, friends, etc. to the children in his learning.
• MKO (more knowledgeable others)- Vygotsky defined the “More Knowledgeable Other” (MKO) as anyone who has a better understanding or a higher ability level than the learner, particularly in regards to a specific task, concept, or process. MKO could be teachers, parents, tutors, and even peers.

Additional InformationLev Vygotsky argues that communication is the driving force behind speech in both adults and children. According to Vygotsky, there are mainly three types of speech are there-

• Social Speech: In no way is this speech related to intellect or thinking. In this stage, a child uses speech to control the behavior of others. A child uses speech to express simple thoughts and emotions such as crying, laughter and shouting. This speech begins when a child is about 2 years or above.
• Private Speech: Private speech is speech spoken to oneself for communication, self-guidance, and self-regulation of behavior. It is between the ages of two and seven that children can be observed engaging in private speech. Although it is audible, it is neither intended for nor directed at others.
• Silent/Inner Speech: This is a speech in which the use of words or word images in thinking without audible or visible speaking. The ability of this type of speech comes when a child is about 7 years or above.

Learning may be defined as a relatively durable change in behavior due to experience. Thus, if the change in behavior is temporary, or due to instinct or maturation, it is not learning. The key feature of learning is experience. Any change in behavior in the absence of practice or experience does not qualify as learning.

Key Points There are many types of learning by which a child can learn, one of them is- 

• Observational learning: Observational learning refers to the process of change in the behavior of one person simply by being exposed to another person’s behavior. This second person is known as the model.
• A child learning at home and performing same in the school is also an example of observation learning, a child constructs knowledge at home by interacting with family members and then performs the same in the classroom with his friends.
• For example, the child learns to fold the laundry by watching their parents that how they are folding.

In the given question, a child doing the same as he has seen in his home, which is an example of observational learning.

Important Points 

• Constructivism: Constructivism is the term, which explains the construction of knowledge by relating it with previous knowledge. In this type of learning, previous knowledge and understanding play an important role in learning.
• Humanistic learning: This is a learning in which learning totally depends on the interest, needs, and abilities of the child, it is also called student-centered learning. Students are encouraged to learn in this type of learning.​

Additional InformationFactors affecting observational learning are:

• attention
• retention
• motor reproduction
• motivation

The child-centered approach is a teaching-learning process. In this approach, the ‘learner’ or ‘child’ and not the ‘teacher’ is the main focus of the educational program. It emphasizes ‘learning’ rather than ‘teaching’. The overall goal of education, according to this approach is the all-around development of the child and not only that of acquiring knowledge. Curriculum, according to this approach, should be based upon the needs, interests, aptitudes, and abilities of learners at different levels so that it enables them to acquire the necessary skills, knowledge, attitudes, and values for realizing their full potential.

Key Points

 Characteristics of the child-centered classroom:

• Flexibility in the teaching-learning process.
• Various methods of teaching are used in the classroom as per the requirement of the students.
• Involvement of the students in various activities, hand-on-practices, experimental knowledge, by which they can learn with their interest.
• Textbooks are not only the source of knowledge, knowledge is gained by involvement in activities or extra curriculum activities.
• Evaluation of the students is not marks-based, evaluation of the students should be done by diagnostic assessment.
• The students learn collaboratively and share the information actively.
• The teacher is a friend and a facilitator for the children and allows the center of the action to shift in the classroom from herself/himself to the children.
• So by all these references, we conclude that option (1) is the correct answer.

Howard Gardner proposed a theory of multiple intelligence. Gardner defines intelligence as "a biopsychological potential to process information that can be activated in a cultural setting to solve problems or create products that are of value in a culture.

Key Points According to Howard Gardner, he categorized the theory of multiple intelligence into eight different kinds of intelligence-

• Visual-spatial: Learners think about physical space and their surrounding environments.
• For example puzzles, maps, charts, videos, etc. In this class, students use a graphic organizer to map out the differences between facts and opinions.
• Bodily Kinaesthetic: Learners use the body effectively and have body awareness. In this class, students are using their bodies to spell new words.
• For example movement, role-playing, hands-on learning, and using real objects.
• Musical:  Learners understand and are sensitive to rhythm and sound.
• For example, music, speaking rhythmically, music, instruments, etc.
• Interpersonal Intelligence- In Interpersonal Intelligence, Learners understand people’s moods and intentions.
• Example: interacting with others, group activities, writing, etc.
• Intrapersonal: Learners understand themselves and their own goals.
• For Example independent learning, creative materials, and private time.
• Linguistic: Learners understand words effectively.
• For Example, word games, reading, stories/poetry
• Logic mathematical: Learners understand the reasoning and calculating.
• For Example, logic games and puzzles, mysteries, experiments, etc
• Naturalistic:  Learners can identify plants, animals, etc.
• For example, animals, nature, being outside, gardening, etc.
• All these stages are related to a biological factor that affects these stages in a different context, such as interest, activeness, etc. So we can conclude that Gardner explains intelligence can be divided into several independent intelligences each one of which has a unique biological basis.​

Additional Information

Assessment refers to the collection of data and the gathering of evidence from different sources through different tools, whereas evaluation refers to bringing meaning to the collected data through interpretation, analysis, and reflection. An assessment provides feedback on the performance of the student specifying his/ her strengths and areas for improvement which provides insights for taking appropriate steps for improving the learning. There are mainly three types of assessment in learning, these are-

• Assessment of learning
• Assessment for learning
• Assessment as learning.

Key Points Assessment for learning is, generally, formative in nature and helps teachers to monitor their students’ progress and to modify the instruction accordingly. It also helps students to monitor their own progress as they get feedback from their peers and the teacher and find opportunities to revise and refine their thinking.

The major objectives of Assessment for learning are as follows:

• Formative assessment supplements summative assessment and each type of assessment has its own importance in the learning process.
• To make every child know how he/she is doing, understand what he/she needs to do to improve and how to get there. The child gets the support he/she needs to be motivated to become an active learner to continuously improve his/her learning.
• In the assessment for learning, the analysis of the work of each child and determine the gaps in their learning, so that teachers, as well as parents, can help the students to reduce the gap.
• To make every parent or guardian know how their child is doing, what they need to do to improve, and how they can support the child and their teachers.
• To have in every school structured and systematic assessment systems for making regular, useful, manageable, and accurate assessments of students and for using the results of the assessment in tracking the learning progress of the students.
• So we can conclude that assessment for learning is used to reduce the gap in the learning of the child.

Additional Information

• Assessment of learning is generally summative in nature occurring at the end of a class, course, semester, or academic year and intended to measure learning outcomes and report these outcomes to students, parents, and administrators.
• Assessment as learning is comparatively the most difficult of the three categories of assessment. But yet it is the most important skill for a student to grasp and is crucial for independent progress in learning, assessment as learning is entirely student-controlled. It emphasizes the role of the student as the critical connector between assessment and learning.

Education Policy lays particular emphasis on the development of the creative potential of each individual. It is based on the principle that education must develop not only cognitive capacities - both the ‘foundational capacities ’of literacy and numeracy and ‘higher-order’ cognitive capacities, such as critical thinking and problem solving – but also social, ethical, and emotional capacities and dispositions.

National Education Policy 2020-

According to NEP 2020, A good educational institution is one in which every student feels welcomed and cared for, where a safe and stimulating learning environment exists, where a wide range of learning experiences are offered, and where good physical infrastructure and appropriate resources conducive to learning are available to all students.

Key Points

 Some important fundamental principles of the NEP 2020 are- 

• Full equity and inclusion as the cornerstone of all educational decisions to ensure that all students are able to thrive in the education system.
• It includes the overall development of the leader, it covers all three aspects as Cognitive domain, affective domain, and psychomotor domain.
• Emphasis on conceptual understanding rather than rote learning and learning-for-exams.
• Promoting self-assessment and the peer assessment done by the student in the classroom.
• Respect for diversity and respect for the local context in all curriculum, pedagogy, and policy, always keeping in mind that education is a concurrent subject.
• Establishment of the linkage of the concepts with the environment or we can say that the linkage of the school with the home.
• Promoting multilingualism and the power of language in teaching and learning.
• It emphasizes group work as well as individual work, NEP 2020 links the study to the curriculum.
• So by all these references**, we can conclude that NEP 2020 promotes peer-assessment and self-assessment by which a student can learn the concepts easily.**

Inclusive education ensures that children with special needs are taught in regular schools with their age and grade peers with support services provided within the school system. Thus, it reflects the objective of providing quality education to all children by accommodating their needs and learning styles into the general curriculum.

Key Points

• Inclusive education is a process to bring all students together in one classroom and school, regardless of their strengths or weaknesses in any area, and it seeks to maximize the potential of all students.
• Inclusive education is a process where diversity in a group with respect to any aspect is appreciated and in which everyone is recognized and respected for his/her worth.
• In Inclusive education, the abilities of the learners such as diverse cultures and languages should be improved when they got the appreciation to work on their abilities, use their own languages, etc.
• An inclusive classroom meets the individual learning needs of children using a variety of media and allows equal opportunities to learn and grow by making the school a friendly place for all children.
• Inclusive education is an effort to make sure that diverse learners – those with disabilities, different languages and cultures, different homes and family lives, different interests and ways of learning – are taught using teaching-learning strategies adapted to individual learning needs
• So that by **engagement in different activities of the diverse children under the same roof to perform their abilities is the main feature of inclusive education.**​

Important Points 

 In Inclusive education the main objectives are- 

• flexibility in learning.
• Creating an environment in which the child can learn with diversity, not creating a special environment for learning.
• Equitable education for all, including challenging children.
• Emphasis on their learning to read instead of emphasizing teaching.
• To use different teaching methods according to the needs of each student, so that every child can have access to the knowledge.

Gender refers to the socially constructed differences between men and women. It refers to the masculine and feminine qualities, behavior, roles, and responsibilities that society upholds. Gender can be changed / re-oriented.

A stereotype is a simplified and/or standardized conception or image with specific meaning, often held in common by people about another group. A stereotype can be a conventional and oversimplified conception, opinion, or image, based on the assumption that there are attributes that members of the other group hold in common.

Gender stereotype is an oversimplified and unfair belief or idea that groups of people have particular characteristics or that all people in a group are the same.

Key Points Gender stereotypes can be reduced by-

• Treating the girls and the boys equally.
• Gave the same and equal opportunity to all the students without making any difference between them.
• Promoting flexibility in the classroom.
• Presenting Non-stereotypical sex roles, such as a girl riding the bike, or a boy cooking in a kitchen.
• Engagement of every student in all the activities without distinguishing them.
• The sitting arrangement of all the boys and girls should not be separated.
• So that we can conclude that gender stereotypes can be reduced by using all these references.

Additional Information

• Gender stereotyping can limit the development of the natural talents and abilities of girls and boys, women and men, as well as their educational and professional experiences and life opportunities in general.
• Stereotypes about women result from deeply ingrained attitudes, values, norms, and prejudices against women.
• To avoid the situation of gender stereotype, a family should start involving boys in household chores that were mainly concerned with girls traditionally which gave rise to gender biasing and stereotyping.

First-generation school-goers mean those children who are the first in their generation from a family who are going to school. Their parents have completed formal education till the primary level. They have much belief in school and coaching classes.

Key Points Teachers should have to do of First-generation school goers-

• They have to treat as a family member of the child.
• The teacher should respect the needs and the interest of the students.
• The teacher should respect the culture and environment of the child, and also used different techniques to familiarize the learners with the language and culture of the school.
• Teachers should have to use different methods of teachings such as play way methods, hand-on-activities, etc.
• The environment of the classroom should be according to the children's needs and interests.
• So, we conclude that the learning of first-generation schoolgoers is ensured by familiarizing the learners with the language and culture of the school while respecting their culture.

Hint

• Fear of failure demotivates the students, and also makes a negative impact on their learning.
• Separation of the sections should not be a good idea, it opposes inclusive education,
• Teachers should have to provide education to them in spite of no expectations with the children.

Inclusive education ensures that children with special needs are taught in regular schools with their age and grade peers with support services provided within the school system. Thus, it reflects the objective of providing quality education to all children by accommodating their needs and learning styles into the general curriculum. According to the concept of inclusive education, all the students of different cultures, languages, regions, intelligent students, weak students, students with disability in learning, etc are taught in the same classroom. So when these types of students learn under the same roof, they can also understand one another, the culture of one another,

Key Points Characteristics of Inclusive education-

• Inclusive education is a process where diversity in a group with respect to any aspect is appreciated and in which everyone is recognized and respected for his/her worth.
• An inclusive classroom meets the individual learning needs of children using a variety of media and allows equal opportunities to learn and grow by making the school a friendly place for all children.
• Inclusive education is an effort to make sure that diverse learners – those with disabilities, different languages and cultures, different homes and family lives, different interests and ways of learning – are taught using teaching-learning strategies adapted to individual learning needs
• Inclusive education is a process to bring all students together in one classroom and school, regardless of their strengths or weaknesses in any area, and it seeks to maximize the potential of all students.
• So that we can conclude that **inclusive education is familiar to all type of children not only those who are disabled.**​

Important Points  In Inclusive education the main objectives are- 

• flexibility in learning.
• Creating an environment in which the child can learn with diversity, not creating a special environment for learning.
• Equitable education for all, including challenging children.
• Emphasis on their learning to read instead of emphasizing teaching.
• To use different teaching methods according to the needs of each student, so that every child can have access to the knowledge.

The term 'visual impairment' is used to refer to not only those who are blind but also those who have low vision. In the teaching-learning process,  visually impaired children suffer from an issue with sight or vision but when they are facilitated with the right training and tools, they develop a good literacy ability.

Key Points

 Ideas that can help in the learning of visual impairment- 

• Use textbooks with big letters, so that they can read them easily.
• Make optimum distance which is required to see clearly.
• The use of dark material for learning can help them,
• They should be seated in the first row of the classroom.
• They should have provided verbal cues to help the students to think divergently about the problem, they use their imagination to imagine how are the scenarios of the problem looked like, and then they analyze the problem and tried to solve it.
• Hence we can conclude that verbal cues help students who are visually impaired.

Important Points  Teaching Material for Visual impaired Learners: Using appropriate teaching-learning materials is vital for children with visual impairment. Some of the common teaching-learning materials available in the market for educating children with visual impairment: ​

• Braille: Braille printed books, which have both braille and printed text on each page so that sighted students and adults can read along with students who have visual impairments.
• Tactile globe:  These globes have convex and concave features on the surface denoting coastlines and country borders which will useful for visually impaired students.
• Audio cassettes can also be used for teaching purposes. The audio materials should also have audio so that those without sight can understand their learning effectively.
• Screen reading software: Screen readers are software programs that allow blind or visually impaired users to read the text that is displayed on the computer screen with a speech synthesizer or braille display.

Learning Disability: It is a neurological disorder that prevents a person from learning a skill and using it effectively. Generally, it occurs in childhood and is characterized by difficulty with certain skills such as reading, writing, speaking, etc.

Key Points Learning disabilities of the students can be improved by-

• Using the concept of inclusive education that learning of all the students should be done under the same roof.
• Applying a flexible curriculum for the students.
• Engaging the students in different activities, experiments, hands-on activities, etc.
• Using different pedagogical techniques helps the student in reducing the learning disability.
• Making the environment of the classroom, friendly for all the children.
• So option (2) is the correct answer.

Hint

• The curriculum should be flexible, rigidity harms the learning of the students.
• Standardized assessment of the student should be avoided because it includes all the students in the same assessment test without considering their abilities, disabilities, etc.
• Students can learn from errors and mistakes, so teachers should have to guidthem on making errors.

Additional Information

• Common Learning Disabilities in Children:

Gifted learners are those who demonstrate an advanced ability or potential in one or more specific areas when compared to others of the same age, experience, or environment. 

Key Points Characteristics of gifted learners are-

• They are always active, and ready to take on challenges.
• These children are divergent in thinking, they cover all the possible aspects related to the problem.
• They are mostly self-motivated, they don't need much motivation from external sources.
• They always find multiple ways to solve the same problem.
• They connect their thoughts with the real world.
• They have originality in their thought process.
• Gifted learners enjoy their work, and they never thought it was a boring task.
• So by all these references, we can conclude that option (3) is the correct answer.​

Additional Information  Other Characteristics of Gifted Learner :

• Easy retention of facts.
• High intellectual curiosity.
• Unusual alertness, even in infancy.
• High speed in processing information.
• Early development of a sense of time.
• Advanced logical and creative thinking.
• Excellent memory and novelty in expression.
• Curiosity, creativity, and independence in thought.

The constructivist teaching-learning process is based on the belief that learning occurs as learners are actively involved in a process of meaning and knowledge construction as opposed to passively receiving information.

• Learners are the makers of meaning and knowledge.
• In this process teachers observe students actively, learning the students are assessed in different methods by the teachers, teachers never judge the students as weak, intelligent, etc.​

Key PointsA teacher should behave for the constructive teaching-learning process as-

• Students are active learners in the classroom, they take part in all the activities, programs, etc.
• The environment of the classroom should be based on the needs and interests of the students,
• Classrooms are child-centered instead of teacher-centered.
• Assessment of the student should be done using multiple ways.
• Students are the makers of the knowledge, they connect the concepts with their previous knowledge.
• Teachers should understand the feelings, environment, and culture of the students.
• Never judge the student by their marks, or denote them as weak students, low performers, etc.
• So by all these references***, we can conclude that Given black stars to motivate non performing students is detrimental.***

Intuitive thinking: Teachers should encourage learners to think and guess with the help of some incomplete sentences, tasks, or situations. Guesses of learners may be right or wrong but they should be promoted. Teachers should not discourage wrong guesses, because through guessing only you can develop intuitive thinking among learners.

• Intuitive thinking means going with one's first instinct and reaching decisions quickly based on automatic cognitive processes.
• This type of thinking encourages students to think divergently.
• Intuitive thinking helps the student to make their cognitive approach better by which they can make a sense of the different situations throughout life.

Key Points Cognitive reasoning: Cognitive reasoning refers to the ability to analyze the situation and the way to resolve it by breaking it into small chunks, or by thinking the multiple ways to solve it.

 Role of Intuitive thinking in the classroom-

• Intuitive thinking makes able the student to put the question on the thoughts they get in their cognition about the problem.
• Intuitive thinking makes learning interesting for the students.
• It develops the cognition of the students to think divergently, by which they can cover all the possible aspects related to the problem.
• Teacher should have to respect the thoughts of the children, and encourages them, which motivates students.
• So, we can conclude that intuitive thinking develops the cognitive reasoning ability of the students.

Hint

• Intuitive thinking may be the imagination of the children, and also there is a possibility that it should not relate to the concepts, but it should not be ignored because ignoring them de emphasizes the students which makes a negative impact on their learning of the students.
• Teachers should not have to correct the thoughts of the students immediately, they have to respect the thoughts of the students whether they are right or wrong.
• Intuitive thinking is a part of the scientific thinking process, in which a student covers all the possible aspects as much as he can related to the problem.

Conceptual understanding is the understanding in which learners get the knowledge of the roots of the problem. Conceptual learning is easy to get if a learner has any prior experience in the related problem because experience (old ideas) helps them to get the concept (new ideas) in the best manner. 

Key Points

• In conceptual understanding, knowledge is constructed by the learners on the basis of their prior experiences.
• Learners are active participants in conceptual learning.
• In conceptual understanding, students learn the logic behind the problem.
• Conceptual learning should be done by performing many activities, research, and performances, related to the problem.
• Students tried to build a conceptual understanding through their thoughts, they covers all the possible aspects related to the problem to find out the logic behind it.
• Students are the knowledge makers, they make the knowledge by connecting the concepts from their previous knowledge and experiences.
• So that **we conclude that Both (A) and (R) are true and (R) is the correct explanation of (A).**​

Additional Information

• Progressive education which is given by John Dewey promotes the curriculum towards learning by doing, which helps the students to get the basic knowledge of the concepts because they learn by doing.
• children can get the roots of the concepts by engaging in the concepts to find the solution to the problem.
• Students cover multiple possible ways to learn the concept in progressive education.

Learning is a continuous life-long process that is not inherited but can begin right from birth by providing constant interaction and stimulation received from the physical, social, and cultural environment and it does not stop till the end.

Key Points Spiral way of learning is that type of learning in which a student learns each time about the subject when it is reviewed in the class. We can say that in spiral learning the topic is considered again and again, which enhances the learning of the student.

• Spiral way of learning in which a student covers a topic many times so they get a good command of it.
• Curriculum-based on spiral learning repeat a topic more than a single time.
• Students are actively connected with each topic of their curriculum.
• It increases the performance and the knowledge level of the students.
• So that a  Spiral way of learning is concluded in the curriculum rather than linear learning.

Additional Information

• Linear way of learning;  the learning is going step by step but there is no again encountered is seen towards the taught topic. we can say in other words that no again revision or repetition of the curriculum in a linear way of learning.

Learning is an ongoing process, which is often associated with the school. But it is also a result of the interaction between individuals and the environment in which those operate. Hence, it is a dynamic process, which takes place throughout life.

The environment in which learning takes place may be described as a composite of natural conditions, circumstances, and influences such as emotional, cognitive, physical aspects, and sociocultural contexts in which an individual is situated. Therefore, you can say that the learning environment is the sum total of the surroundings in which individuals interact to enrich experiences and thus leading to learning.

Key Points Characteristics of a positive learning environment:

• There should be flexibility in the classroom as per the needs of the students.
• Students are active participants in the classroom in the learning environment.
• It should be designed on the basis of the needs, feelings, emotional level, and cognition of the students so that students can easily survive in this environment.
• The classroom should be child-centered instead of teacher-centered.
• A positive learning environment enhanced the learning of the students which also changes their cognitive level of the students.
• The curriculum is decided according to the interest of the students.
• So that we can conclude that environment for learning is designed as per the student's needs, interests, emotions, etc. so that it influences the cognitive as well as aspects of the children.

Learning is a continuous life-long process that is not inherited but can begin right from birth by providing constant interaction and stimulation received from the physical, social, and cultural environment and it does not stop till the end.

Meaningful learning: Meaningful learning results when a person consciously and explicitly ties new knowledge to relevant concepts they already possess. When meaningful learning occurs, it produces a series of changes within our entire cognitive structure, modifying existing concepts and forming new linkages between concepts.

Key Points  Characteristics of Meaningful Learning:

• Meaningful learning is possible only when learners make a deliberate effort to relate new knowledge to the relevant concept they already know.
• It stresses the ability of the learner to apply what is learned because of the involvement of the learners.
• It is the active creation of knowledge structures from personal experience.
• To encourage meaningful learning students should be motivated to set learning goals rather than performance goals.
• Meaningful learning is possible when the learner's thoughts are divergent and they are able to collect knowledge, i.e. discovery learning.

 So that we can conclude that to encourage meaningful learning students should be motivated to set learning goals rather than performance goals.

Hint 

• Meaningful learning never promotes rote learning or memorization, it is always based on concepts and logic.
• Making a competitive environment by the teacher makes a negative impact on the learners because not all the students are the same in the classroom as per their performance and cognition.
• The environment of meaningful learning is always child-centred instead of teacher-centred because it focuses on the needs and abilities of the students.

Errors are the faults made by the student during their learning. Errors help students to find out their weak point of view regarding the problem and also make a chance to improve their learning. Errors are made because of the different thought processes of the students regarding the problem.

Key PointsCharacterstics of errors performed by the children:

• Errors are part of the teaching-learning process and make the thoughts of the students divergent.
• Errors remove boundaries created by the fear of failure.
• Errors are made due to different thought processes of the children from the adults, Adults thoughts are more divergent due to experience so the thinking of the adults and the children are different qualitatively.
• Errors build problem-solving and critical thinking skills in the children.
• Errors analysis helps learners to create connections between ideas and concepts.
• Errors help students to find out the gap in their learning.
• So by all these references, we can conclude that option (4) is the correct answer.

Additional Information

• Teachers should not punish the students for making errors, they should have to correct their errors of them, and help them with the concept.
• Teachers should not judge the quality of the knowledge by performing errors by the students.
• Errors analysis help teachers to understand the weak lesson of the students so that they can improve them by applying different teaching-learning methods.

Problem-solving is the act of defining a problem; determining the cause of the problem; identifying, prioritizing, and selecting alternatives for a solution; and implementing a solution. 

• There are many different types of methods to solve the problem, a student can use the suitable method after analyzing the problem.

Key Points -

The use of different problem-solving methods leads the student to think divergently and provide another approach to solve the problem. The main procedure to solve the problem are - 

Algorithm: An algorithm refers to a set of rules that "step-by-step" define how a work is to be executed in order to get the "expected results". 

It can be understood by taking the example of cooking a new recipe.

Heuristic: “Heuristic method” has been given by "Armstrong".  This method refers to finding the best possible solution to a problem quickly, effectively, and efficiently. The heuristic technique is a way of solving the problem that uses a process that isn’t guaranteed to be optimal or perfect but is sufficient to achieve a short-term goal or immediate result. 

Analogy: Problem-solving can be done by referring back to previous successful experiences with similar problems. 

In this method, we solve keeping in mind solutions to problems similar to the problem at hand.

Means-end analysis: In this process dividing a problem into sub-goals and then solving each sub-goal. Means-end heuristics is a problem-solving technique that was introduced by "Newell and Simon". The means-end analysis is a creative problem-solving technique used in Artificial Intelligence applications for a quite long time.

Hence, we can conclude that the right answer to this question is (A) - (ii), (B) - (iv), (C) - (i), (D) - (iii).

Learning is the process of acquiring new understanding, knowledge, behaviours, skills, values, attitudes, and preferences. 

• Learning is a change in behaviour or knowledge that results from experience.

Key Points-

• Learning is influenced by two categories of factors: Personal and Environmental.
• Personal factors are such as motivation, ability, attitude, aptitude and interests, attention and age.
• Environmental factors are societal, economic, and cultural, community, religious, school.

Personal factors that influence learning: 

• Aptitude: Aptitude is the natural ability of a person to do a task. Some children are good at mathematics naturally while some others must put in a lot of hard work to perform well in mathematics. Some children have a natural ability to draw and paint while some others are very good at sports and games.
• Motivation: Motivation is an internal state that arouses and maintains behaviour. There are two types of motivation, Intrinsic and Extrinsic Motivation. Motivating a teenager means trying to encourage a teenager to use/her inner resources, sense of competence, self-esteem, and autonomy.
• Attitudes: One may think that rural India is where you find the true traditional dressing and behaviour. This is a preconceived notion that we have and may be termed an attitude. Attitudes are also born out of socialization. Our attitudes can be positive, negative, or neutral
• Aptitude and attitude both are personal factors.

Additional Information-

Environmental Factors: The social-cultural environment in which the child grows has a high impact on the child’s learning. For easy understanding, we divide the socio-cultural factors into 

(A) Family (B) Neighbourhood and Community (C) Class, caste, religion and ethnicity.

• Family is the first and most fundamental influence in the socialization process of the individual.
• It is through the family that a child undergoes conscious, subconscious and subliminal learning. It is within the family the individual learns behaviour patterns for survival, social skills, attitudes, interpersonal skills, social norms, the do’s and don’ts of his culture, and acquires value orientation.
• Neighbourhood and community: Many attitudes, beliefs, perceptions, habits, and social roles are shaped directly or indirectly by our experiences with the persons in our neighbourhood Similarly, caste and religion also play a role in shaping our identity, attitudes, value orientation and achievement patterns.
• Religion, community and school are environmental factors.

Hence, we can conclude that the right answer to this question is Aptitude and attitude both are personal factors.

Socio-constructivist frame: Students have also to include the social and cultural settings, in which they learn and which also have an impact on students as they change their ideas. From this perspective, sometimes referred to as 'situated cognition, the cultural and the social background of students, use of language, and how meaning is derived from various contexts play a role in the students’ construction of ideas.

Key Points The characteristics of the socio-constructivist frame as-

• Knowledge is not fully known and fixed.
• The learner plays an active role in the personal creation of knowledge through experiences.
• Learning is a social process in which the learner constructs meaning that is influenced by the interaction of prior knowledge and new learning events or with the help of teachers.
• It acknowledges the uniqueness and complexity of the learner.

So option (3) is the correct answer.

Important Points The environment of socio-constructivist as-

• Teachers encourage learners to involve in different types of activities, games, Group discussions, Teamwork, etc.
• Students are free to ask questions and say what they want.
• Learning is not dependent on the same methodologies or same way of teaching, it changes as per the student's needs.
• Students experience the real world.

Given:

The given four-digit number = 4ba5

Concept used:

Divisibility rule of 11: The divisibility by 11 rule asserts that if the difference of sum of the digits at odd and even positions of a number is 0 or divisible by 11, then the number is also divisible by 11.

Divisibility rule of 5: The divisibility rule of 5 asserts that a number is divisible by 5 if the digit on the unit's place, that is, the final digit of the number, is 5 or 0.

Calculation:

The given four-digit number = 4ba5

The four-digit number 4ba5 which is divisible by 55 is also divisible by 11 and 5.

The unit digit of the given number = 5

Then, the four-digit number is also divisible by 5.

Let,s check the divisibility of 11 of the number.

Sum of odd numbers = (b + 5)

Sum of even numbers = (4 + a)

Therefore, (4 + a) - (b + 5) = 0, 11, 22.....

⇒ 4 + a - b - 5 = 0, 11, 22.....

⇒ a - b - 1 = 0 (least value of a - b)

⇒ a - b = 1

∴ The value of (a - b) is 1.

Calculation:

$\frac{2}{3}$ × 3$\frac{1}{3}$ = (2/3) × (10/3)

⇒ 20/9

⇒ 2$\frac{2}{9}$

Calculation:

-45 × 109 = -4905

Checking option 1

(-45) × 9 + (-45) × 100

⇒ (-45)(9 + 100)

⇒ -45 × 109 = -4905

Checking option 2

(-45) × (100 + 9)

⇒ -45 × 109 = -4905

Checking option 3

-45 × 100 + 9

⇒ -4500 + 9 

⇒ -4491

It is not equal as -45 × 109 = -4905

Checking option 4

(-40 - 5) × 109

⇒ -45 × 109 = -4905

∴ -45 × 109 is not the same as -45 × 100 + 9

Given:

There are four statements where HCF and LCM are given.

Concept used:

HCF is always a factor of LCM

Calculation:

Justifying option 1,

LCM = 108 and HCF = 12

Here, 108 is multiplied by 12. Hence, 12 is a factor of 108.

Option 1 is true.

Justifying option 2,

LCM = 180 and HCF = 25

Here, 180 is not multiplied by 25. Hence, 25 is not a factor of 180.

Option 2 is not true.

Justifying option 3,

LCM = 196 and HCF = 28

Here, 196 is multiplied by 28. Hence, 28 is a factor of 196.

Option 3 is true.

Justifying option 4,

LCM = 210 and HCF = 15

Here, 210 is multiplied by 15. Hence, 15 is a factor of 210.

Option 4 is true.

∴ The statement of option 2 is not true.

Shortcut Trick

Look at the units column: 3 + B must give a sum ending in 0.

Since B is a single digit, 3 + B = 10 ⇒ B = 7.

This generates a carry of 1 to the tens column.

Look at the tens column: A + 8 + 1 (carry) = 15 ⇒ A = 6.

Therefore, A − B = 6 − 7 = −1.

∴ The correct answer is −1.

Alternate Method

Given:

A3 + 8B = 150, where A and B are single digits.

Formula Used:

A two-digit number XY can be written as 10X + Y.

Calculations:

⇒ Expand the numbers A3 and 8B using their place values.

⇒ (10 × A + 3) + (10 × 8 + B) = 150

⇒ 10A + 3 + 80 + B = 150

⇒ 10A + B + 83 = 150

⇒ 10A + B = 150 − 83

⇒ 10A + B = 67

Since A and B are single digits, 10A + B represents the two-digit number AB.

⇒ This implies the two-digit number AB is 67.

⇒ By comparing the digits, A = 6 and B = 7.

⇒ We need to find the value of A − B.

⇒ A − B = 6 − 7 = −1.

∴ The correct answer is −1.

Additional Information

Place Value Expansion

A general two-digit number XY is mathematically represented as 10X + Y, where X is the tens digit and Y is the units digit. For a three-digit number XYZ, the expansion is 100X + 10Y + Z.

Cryptarithm Puzzles

These are mathematical puzzles where digits are replaced by letters. The key is to analyze the units column first and account for carries to the next higher place value.

Digit Reversal Rule

When the digits of a two-digit number XY are reversed to form YX, the difference between the two numbers is always a multiple of 9: (10X + Y) − (10Y + X) = 9(X − Y).

Given:

Height of the first cylinder = 30 cm 

The radius of the first cylinder = 6 cm

Height of the second cylinder = 15 cm

The radius of the second cylinder = 12 cm

Formula used:

Volume of a cylinder = πr²h

Where, r = Radius of the cylinder

h = height of the cylinder

Calculation:

Volume of the cylinder : Volume of second cylinder

= π × 6² × 30 : π × 12² × 15

= 36 × 30 : 144 × 15

= 1080 : 2160

= 1 : 2

∴​ The ratio of the volume of the first cylinder to that of the second cylinder is 1 : 2

Given:

The perimeter of a rectangle = 104 cm

Length of the rectangle : Breadth of the rectangle = 8 : 5

Formula used:

Area of a rectangle = l × b

Perimeter of a rectangle = 2 (l + b)

Where, l = length of the rectangle

b = Breadth of the rectangle

Calculation:

Length of the rectangle : Breadth of the rectangle = 8 : 5

Suppose, Length of the rectangle = 8x

Breadth of the rectangle = 5x

Therefore, 2 (8x + 5x) = 104

⇒ 2 × 13x = 104

⇒ 13x = 104/2 = 52

⇒ x = 52/13 = 4

Length of the rectangle = 8 × 4 = 32 cm

Breadth of the rectangle = 5 × 4 = 20 cm

∴ Area of a rectangle = 32 × 20 = 640 cm²

∴​ The area of the rectangle is 640 cm2

Given:

The area of a square is 30 times that of a triangle.

The three sides of the triangle are 20 cm, 48 cm, and 52 cm.

Formula used:

Area of a triangle = ${\sqrt {s(s - a) (s - b) (s -c)}}$

Where, S = Semi perimeter of triangle

Three sides of the triangle are a, b, and c

Also, S = (a + b + c)/2

Area of a square = x²

The perimeter of a square = 4a

Where, x = Each side of the square

Calculation:

The three sides of the triangle are 20 cm, 48 cm, and 52 cm.

Semi perimeter of the triangle (S) = (20 + 48 + 52)/2 = 60

∴ Area of the triangle = ${\sqrt {60(60 - 20) (60 - 48) (60 - 52)}}$

= ${\sqrt {60 × 40 × 12 × 8}}$

= $\sqrt {230400}$ = 480 cm²

According to the question, Area of square = 30 × Area of triangle

⇒ Area of square = 30 × 480

⇒ Area of square = 14400 cm2

Therefore, Each side of the square = $\sqrt {14400}$ = 120 cm

∴ The perimeter of the square = 4 × 120 = 480 cm

∴ The perimeter of the square is 480 cm.

Given:

Total number of cards = 32

Formula used:

Probability of an event = Total number of favorable outcomes/Total number of outcomes

Calculation:

Total number of cards = 32

∴ Total number of outcomes = 32

Prime numbers between 1 to 32 = 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31

∴ Total number of favorable outcomes = 11

The probability that the number card bears a prime number = 11/32

∴ The probability that the number card bears a prime number is 11/32

Concept:

The Line of Symmetry is the imaginary line where you could fold the image and have both halves matching exactly.

Rotational symmetry is when an object is rotated around a center point (turned) by a number of degrees and the object appears the same.

Square, rectangle, and rhombus are the quadrilaterals which have both line and rotational symmetry of order more than 1.

Calculation:

A square has 4 lines of symmetry and rotational symmetry of order 4.

A rectangle has 2 lines of symmetry and rotational symmetry of order 2.

A rhombus has 2 lines of symmetry and rotational symmetry of order 2.

Shortcut Trick

According to geometric properties, any quadrilateral whose diagonals bisect each other must be a parallelogram.

Furthermore, if the diagonals of a parallelogram are equal in length, the geometric shape strictly becomes a rectangle.

Since diagonals PR and QS bisect each other and PR = QS, quadrilateral PQRS completely satisfies the conditions for a rectangle.

∴ The correct answer is Rectangle.

Alternate Method

Given:

⇒ In quadrilateral PQRS, diagonals PR and QS bisect each other at point O.

⇒ Length of diagonal PR = Length of diagonal QS.

P Q R S O

PR = QS and bisect at O → PQRS is a Rectangle

Proof:

⇒ A quadrilateral in which diagonals bisect each other is a parallelogram. Thus, PQRS is a parallelogram.

⇒ In any parallelogram, opposite sides are equal (PS = QR).

⇒ Let us consider ΔPQS and ΔQPR:

⇒ PQ = PQ (Common base)

⇒ PS = QR (Opposite sides of parallelogram PQRS)

⇒ QS = PR (Given, equal diagonals)

⇒ By SSS (Side-Side-Side) congruence criterion, ΔPQS ≅ ΔQPR.

⇒ Therefore, corresponding parts are equal: ∠SPQ = ∠PQR.

⇒ Since adjacent angles in a parallelogram are supplementary, ∠SPQ + ∠PQR = 180°.

⇒ 2 × ∠SPQ = 180° ⇒ ∠SPQ = 90°.

⇒ A parallelogram with a right angle is geometrically defined as a rectangle.

∴ The correct answer is Rectangle.

Additional Information

Parallelogram

A quadrilateral where opposite sides are parallel and equal. Diagonals bisect each other, but are not necessarily equal in length.

Rhombus

A type of parallelogram where all four sides are equal. Diagonals bisect each other at exactly 90°, but are not necessarily equal in length.

Rectangle

A parallelogram with one right angle. Both diagonals are always equal in length and bisect each other.

Square

A regular quadrilateral with all sides equal and all angles measuring 90°. Diagonals are equal and bisect each other at exactly 90°.

Given:

Smple interest (SI) = Rs 2520

Rate of interest (R) = 14%

Time (T) = 2 years 

Concept:

Simple interest = (P × R × T)/ 100

Calculation:

Put the value of SI, R and T in the above formula, we get:

⇒ 2520 = (P × 14 × 2)/100

⇒ 2520 = (P × 28)/100

⇒ 2520 × 100 = (P × 28)

⇒ (2520 × 100)/28 = (P)

⇒ P = Rs 9000

The sum of money is Rs 9000

Given:

8x + 33 = 25 + 17x 

To find = x3 + 2

Calculation:

⇒ 8x + 33 = 25 + 17x 

⇒ 33 - 25 = 17x - 8x

⇒ 8 = 9x

⇒ x = 8/9

⇒ x³ = 8³/9³

⇒ x3 = 512/729

⇒ Now, x3 + 2 = (512/729) + 2

⇒ x3 + 2 = ((512 + (729 × 2))/729

⇒ x3 + 2 = ((512 + (1458))/729

⇒ x3 + 2 = 1970/729

Given:

⇒ x2 - 17x - 38

Calculation:

⇒ The given expression = x2 - 17x - 38

⇒ x2 - 19x + 2x - 38

⇒ x2 + 2x - 19x - 38

Now, x is common in (x2 + 2x)  and 19 is common in (-19x - 38)

⇒ x(x + 2) - 19(x + 2)

∴ (x - 19)(x + 2) are the two factors of expression (x2 - 17x - 38)

Given:

 (2x2 - 5x + 4) and (x2 + 7x - 8)

Concept:

A coefficient is an integer that is written along with a variable or is multiplied by the variable.

Calculation:

⇒ (2x2 - 5x + 4) × (x2 + 7x - 8)

⇒ (2x2(x2 + 7x - 8) - 5x(x2 + 7x - 8) + 4(x2 + 7x - 8))

⇒ 2x⁴ + 14x³ - 16x² -5x³ - 35x² + 40x + 4x² + 28x - 32

⇒ 2x4 + 9x³ - 47x² + 68x - 32

We can clearly see that the coefficient of x² is -47

Given:

15(x2 - x - 12) by 5(x + 3)(x2 - 16)

Calculation:

⇒ 15(x2 - x - 12) = 15x² - 15x - 180

⇒ 15x2 - 15x - 180 = 5(3x2 - 3x - 36)

⇒ 5(3x2 - 3x - 36) = 5(3x2 - 12x + 9x - 36)

⇒ 5(3x2 - 12x + 9x - 36) = 5(3x(x - 4x) + 9(x - 4))

⇒ 5(3x(x - 4x) + 9(x - 4)) = 5((x - 4x) (3x + 9))

⇒ Now Diving 5((x - 4x) (3x + 9)) by 5(x + 3)(x2 - 16)

⇒ We get 5((x - 4) 3(x + 3))/5(x + 3)(x - 4)(x + 4)

⇒  (3/(x+4))

Given:

The ratio of the angles of a triangle is 3 : 2 : 4.

Concept:

The sum of internal angles of a triangle is 180°

Calculation:

The angles of triangle are say 3x, 2x, and 4x

⇒ Now the sum of 3x + 2x + 4x = 180° 

⇒ 9x = 180° 

⇒ x = 20° 

⇒ All the angles of triangle are now

⇒ 3x = 60° 

⇒ 2x = 40° 

⇒ 4x = 80° 

⇒ The difference of the largest and the smallest angles of the triangle = 80° - 40° = 40°

Given:

AB is a line and a point O.

A ray OC is drawn taking a point C not lying on line AB.

Concept:

Linear pair of angles are formed when two lines intersect each other at a single point. The angles are said to be linear if they are adjacent to each other after the intersection of the two lines. The sum of angles of a linear pair is always equal to 180°

Two angles are said to be adjacent angles, if, they share a common vertex, a common side and they do not overlap. Angle 1 and 2 are adjacent because they have a common side BD and a common vertex B.

Calculation:

a) ∠AOC and ∠BOC form a linear pair = true because ∠AOC + ∠BOC = 180° and they are adjacent to each other.

b) ∠AOB and ∠BOC are adjacent angles = False because they don't have a common side OC and a common vertex O.

Hence, options 1 are true.

Given:

One of the angles of triangle = 100° 

To find: ∠BOC

Calculation:

Consider a ΔABC, such that ∠BAC=100° 

and bisectors of ∠B and ∠C meet at O.

To find: ∠BOC

Now, in △ABC,

⇒ ∠BAC + ∠ABC + ∠ACB = 180°

⇒ 100° + ∠ABC + ∠ACB = 180° (Angle sum property)

⇒ ∠ABC + ∠ACB = 80°

⇒ 1/2(∠ABC+∠ACB) = 40°

⇒ ∠OBC + ∠OCB = 40° (OB and OC bisect ∠ABC and ∠ACB)

Now, in △OBC,

⇒ ∠OBC + ∠OCB + ∠BOC = 180°

⇒ 40 + ∠BOC = 180°

⇒ ∠BOC = 140°

Given:

3, 9, 11, 16, 19, 12, 18, 30, 19, 25

Concept:

Mode = Most repeated term of a data

The range of the data is the difference between the largest value and the smallest value.

If the total number of observation(n) is an odd number,

Median = ((n + 1)/2)^th term

If the total number of observations(n) is an even number,

Median = ((n/2)^th term + ((n/2) + 1)^th term)/2

Mean = (Mode+ Range + Median)/3

Calculations:

Arranging the given terms in Ascending order,

3, 9, 11, 12, 16, 18, 19, 19, 25, 30

Most repeated term = 19 (2 times)

⇒ Mode = 19

Number of terms = 10

Median = ((10/2)^th term + ((10/2) + 1)^th term)/2

⇒ Median = (5^th term + 6^th term)/2

⇒ Median = (16 + 18)/2 = 17

⇒ Range = (30 - 3) = 27

⇒ Mean of the mode, median and range = ( 19 + 17 + 27)/3 = 63/3 = 21

Mean of the mode, median and range = 21

The education for the children in the school should be child-centered and the curriculum should be related to children's daily life.

Key Points

• All types of children should be considered as same and equal.
• Education should be child-centered instead of Teacher centered.
• The environment must feel free for the children.
• That's why option (2) is correct.

​  

Additional Information

• Fear and Anxiety can retard the mind of the students, so the environment of the classroom must be fear-free.

A systematic and balanced arrangement of the content by which a teacher can teach and the way by which Children can understand easily, this type of arrangement of the content is called Unit Planning.

Key Points

• Unit Planning helps the teacher to teach concepts one by one
• A unit planning is a balanced and systematic arrangement of the content.
• It helps the teacher more than the children.

Hence, option (4) is correct.

Conceptual errors can be prevented by practicing more problems, living in a rich mathematics environment, and also connecting your daily life with mathematics.

Key Points

• By avoiding rote learning and emphasizing conceptual learning.
• Avoidance the use of a calculator which helps in building concepts and also makes calculations skills better.
• Hands-on activities are much helpful to learn the concept and make the performance better.
• That's why option  (3) is the correct answer.

National Mathematics day is celebrated on 22 December on the birth anniversary of "Srinivasa Ramanujan".CBSE started the celebration of GANIT week in the primary school from 16th Dec. to 22 Dec.

Key Points

• GANIT week:
• This week, Students of different classes (1st to 5th) are engaged in different types of games that can strengthen their logical approach, boost their morale and confidence.
• Example:- Puzzle game, Thinking caps, Just figure out, etc.

Additional Information

• Objectives of GANIT week:
• Learning by doing.
• Encourages Teachers to develop logical thinking, conceptual knowledge among students.
• Emphasis hand on activities among the children.

The NCF (National curriculum framework) 2005 is published by NCERT (National council of educational research and training) which explains the changes and new ways by which teaching and learning can be enhanced.

Key Points

• NCF(2005) focused to connect the curriculum with the daily life experiences of the children.
• NCF(2005) opposes rote or memory-based learning.
• According to NCF(2005), experiences or activities should be based on hands-on activities.
• NCF(2005) supports burden-free learning which is proposed by Dr. Yashpal in 1993.
• The thinking should be divergent to approach the problems of mathematics that's why a student can find different ideas to solve the problems.

So According to National Curriculum Framework 2005, School Mathematics must take place in a situation, where students realize Mathematics as a part of their life experiences.

According to NCF 2005, children can learn through interesting activities, real-life examples, learning by doing, learning through playing etc.

Key Points

• According to the question, when a student tries to measure the length of different objects:
• Children will familiar with different objects in their daily life.
• The thinking power of Children will enhance and divergent.
• They can easily understand the unit of length by practicing on different objects of different lengths.
• That's why option (2) is correct.

Hint

• In option (4), "This type of activity should be given only as a home task so that class time is utilized for solving the questions",​
• Activities should be connected with the life of the children, these are not only in homes but they can also be performed anywhere.

George Polya is known as the father of modern mathematical problem-solving.In 1945, he proposed a book "How to solve it", in which he explains all the four steps.

Key Points

• According to Polya, the sequence of all the four steps in problem-solving is as:
• Understand the problem
• Devise a plan
• Carry out the plan
• Look back
• That's why option (3) is correct.

Additional Information

• Understand the problem:
• Children should put their efforts to understand the problem as to which type of the given problem is.
• Devise a plan:
• Plan a strategy by which the problem gets easily solved.
• Example: Use symmetry, make a list, use the model, etc.
• Carry out the plan:
• Persist with the plan that you have chosen, check each step and if the plan is continuous not working leave the plan and devise another plan.
• Look Back:
• Check the outcome (result) of the problem, look back to see from which steps you get results.

Concept:

The density property of fractions states that between any two fractions there is another fraction. Both the whole numbers and the fractions are infinite but the set of fractions are dense and the whole numbers are not.

Calculation:

The fact that there is a fraction between any two fractions is called the density property of fractions.

Van Hiele's model's theory explains how students learn geometry, This theory is proposed in 1957. The theory is mainly classified into five levels:

• Visualization
• Analysis
• Abstraction
• Deduction
• **Rigor **​

Key Points

• Level 1 (Visualization):
• At this level, students recognize the figure by its physical appearance.
• Example: A closed figure of 4 sides is quadrilateral.
• Level 2 (Analysis):
• Students identify a figure based on its properties not by its physical appearance.
• ​Example: Identify 4 sided figures as square, rectangle, parallelogram, etc
• Level 3 (Abstraction):
• ​The student deduces the figures and starts making the relation between the figures on the basis of their properties.
• ​Level 4 (Deduction):
• ​At this level, learners are able to construct geometric proofs, able to understand theorems.
• ***​So option (4) is correct.*​

Additional Information

• Level 5 (Rigor):
• At this level, Geometry is understood by the learners at the level of mathematicians, and the objectives of thought are deductive in nature.​

Method: method which is used to teach the learners in different ways by using different approaches, try to solve the problem by considering different scenarios so that learner can learn easily.

Key PointsAnalytical Method:

• In this method, we analyze the problem and then break it into a meaningful way to solve the given problem.

so we conclude option(4) as the answer that she used the Analytical method to solve the problem.

Important Points

• Inductive method:
• ​In this type of method, learning should be started with examples and then come to the general principle.
• ​This method is specific to general.
• ​​Deductive method:
• ​In this type of method, learning should be started with Concepts and then come to examples.
• ​This method is general to specific.
• **​Proof by contradiction:**​
• ​In this method, first, we assume the opposite condition of the question asked and prove ourselves wrong.
• ​Example: Prove that 
  

${ \sqrt{2}}$ is irrational.

Concept:

Electric Conductivity

• It is simply a measurement of a material's ability to pass an electric current flow.
• The ability of a liquid to carry electricity is directly proportional to the concentration of ions in the liquid.
• Liquids like lemon juice, vinegar, and salt solution will cause the compass needle to show deflection.

Explanation:

• The sodium atoms and chlorine atoms separate when sodium chloride dissolves in water due to the effect of water molecules.
• They are free to move around as positively and negatively charged ions in the water.
• The solution can conduct electricity because of the charge separation.

Liquids like sugar solution, distilled water, and Kerosene don't have minerals and ions. So, this type of solution will not cause the compass needle to show deflection.

Therefore, the salt solution will show compass needle deflection.

Additional Information Conductor 

• The material which allows an electric current to pass through them easily is called good conductors of electricity. 
• For example, Silver, Gold, Aluminum, Steel, Copper, etc.
• The material which doesn't allow an electric current to pass through them easily is called bad conductors of electricity.
• For example, Zinc, Lead, Wood, etc

Insulator

• An insulator is a substance that does not conduct electricity.
• Because of the absence of free electrons.
• A wire is coated by an insulator.
• Examples of insulators, Plastic, paper, rubber, glass, mica, etc.

Explanation:

Gases:

• Gases have expanding nature and completely fill their containers.
• Gases take the shape of their containers.
• They are compressible by nature.
• Mixtures of gases are always homogeneous.
• They have low density.
• Gases can be mixed easily.
• Most of the oxides are gaseous in nature.
• Hydrogen, carbon. sulphur, nitrogen, phosphorus are found in the gaseous state in nature.

Petrochemicals:

• Petrochemicals are chemical substances that are derived from petroleum and natural gas.
• Example- Propylene, Ethylene, Butadiene, etc.
• They are used for medical, household, clothing and other purposes.
• They are also used in the making of paints and building materials.

Acid Rain:

• It is the process of forming acidic components while the precipitation of rain.
• Sulphuric and nitric acids are commonly found in acid rains.
• Acid rain is also called acid deposition.
• This acidic rain has an acidic pH value (0-7).
• This can take the form of rain, snow, fog, hail, etc.

Concept:

Pressure: 

• The pressure is the physical quantity which is defined as the force acting per unit of area.

P = Force / Area  

where P is pressure, F is force, and A is an area.

• The SI unit of pressure is Pascal.

Pascal's Law:

• Pascal's principle states that pressure applied to fluids is equally transmitted in all directions, to all parts of the fluid, and to all parts of a container.
• The increase in pressure at one point of the enclosed liquid in an equilibrium of rest is transmitted equally to all other points of the liquid and also to the walls of the container, provided the effect of gravity is neglected.

Explanation:

Option 1. Only in a downward direction (False)

• If the liquid has the tendency to exert the pressure only downwards then the holes in the container do not exert the liquid out of the container.
• But it is not happening like this, because the liquid does not exert the pressure downwards only.

Option 2. Only in an upward direction (False)

• Due to the gravitational force, there is no possibility to exert pressure against the gravitational force.
• So the oil never exerts the force upwards.

Option 3. In all directions (True)

• All the liquids have molecules with free-motion pressure.
• That’s why they are free to exert pressure in all directions

Option 4. Only sideway (False)

• If the liquid has the tendency to exert the pressure sideways only then the oil does not fall on the surface.
• The tendency to spill all over the surface and contain the whole surface of the container is occurring only if having the tendency to move freely.

Thus, The pressure exerted by oil will be in all directions.

Explanation:

Refraction of Light:

• When a ray of light propagating in a medium enters the other medium, it deviates from its path.
• This phenomenon of change in the direction of propagation of light at the boundary, when it passes from one medium to another medium, is called the refraction of light.
• When a ray of light enters from a rarer medium to a denser medium from (air to water) it deviates towards the normal drawn on the boundary of two media at the incident point.

​

• The entity that doesn't change is the frequency.
• The entity that changes are wavelength and velocity.
• Refractive index is also equal to the velocity of light c of a given wavelength in empty space divided by its velocity v in a substance,

n = (c/v)

• Thus, Velocity, Wavelength & Refractive index change when light travels from one medium to another but Frequency remains unchanged.
• Similarly, in passing from denser to rarer medium, a ray deviates away from the normal.
• If the light is incident normally on the boundary, i.e. parallel to normal, it enters the second medium undeviated.

Thus, when light travels from air to water Both its wavelength and velocity decrease.

Concept:

Archimedes principle:

• It states that a body, when wholly or partially immersed in liquid, experiences an upward thrust that is equal to the volume of the liquid.
• Archimedes Principle is also known as the physical law of buoyancy.
• When a solid is fully immersed in a liquid, it loses weight, which is equal to the weight of the liquid it displaces.

Apparent weight= actual weight−buoyant force= mg−ρgV

Where m = mass of the object and ρ = density of the fluid

 

Explanation:

• When a body is immersed partially or completely in a fluid (liquid or gas), it experiences an upthrust or buoyant force that is equal to the weight of the fluid displaced by the body.
• So the upthrust on the ball is given as,

⇒ FB = ρVg

⇒ FB ∝ V     -----(1)

Where ρ = density of the liquid, V = volume of liquid displaced = volume of ball, and g = gravitational acceleration

• As in the question, it is mentioned that the same size is inserted in the same liquids, so the volume is the same, which means, (⇒ FB ∝ V) Buoyant Force is also the same for all liquids.

Thus, it is proven that  Buoyant force acting on aluminum = buoyant force acting on lead.

Important Points 

The correct answer is A - Ovary, B - Stamen, C - Pistil.

Concept:

• As a plant's reproductive part, a flower contains a stamen (male flower part) or pistil (female flower part).
• Flowers that contain either only pistils or only stamens are called unisexual flowers. Flowers that contain both stamens and pistil are called bisexual flowers.

Explanation:

• The stamen is the male reproductive unit of plants and consists of the following two parts:
• i) A long and slender stalk called filament which may be joined or free.
• ii) A bilobed terminal structure called (anther).
• The pistil is the female reproductive unit of plants.
• A pistil has the following three major parts:
• Stigma: The stigma is at the top and is connected to the ovary by the style. It receives the pollen grains.
• Style: It is an elongated slender part beneath the stigma, that connects the stigma with ovary.
• Ovary: It is the basal swollen part of the pistil. The ovary is the ductless reproductive gland containing one or more ovules. It is the part of the plant where seed formation occurs.

Explanation:

Cyclone: 

• A cyclone is a large air mass that rotates around a strong centre of low atmospheric pressure.
• Cyclones rotate clockwise in the Southern Hemisphere and anti-clockwise in the Northern Hemisphere.
• Cyclones are rapid inward air circulation around a low-pressure area.
• Factors like wind speed, wind direction, temperature and humidity contribute to the development of cyclones.
• Cyclone/Storm is termed in different names in different continents -

 

1. A cyclone is a chain of events that ends with the formation of a very low-pressure system with very high-speed winds revolving around it.
2. The center of a cyclone is a calm area. It is called the eye of the storm. A large cyclone is a violently rotating mass of air in the atmosphere, 10 to 15 km high.

Additional Information

• A cyclone is known by different names in different parts of the world. It is called a ‘hurricane’ in the American continent.
• In the Philippines and Japan, it is called a ‘typhoon’.

Concept:

Transpiration

• It is a process in which excess water is lost in the form of vapors from the aerial parts of the plant.
• Mainly through the stomatas of leaves.
• Stomatal openings are necessary to admit carbon dioxide to the leaf interior and to allow oxygen to escape during photosynthesis, hence transpiration is generally considered to be merely an unavoidable phenomenon that accompanies the real functions of the stomates.
• It has been proposed that transpiration provides the energy to transport water in the plant and may aid in heat dissipation in direct sunlight (by cooling through the evaporation of water), though these theories have been challenged.
• Excessive transpiration can be extremely injurious to a plant.
• When water loss exceeds water intake, it can retard the plant’s growth and ultimately lead to death by dehydration.
• The stomata present in the leaves are responsible for the uptake of carbon dioxide and limit the loss of water due to evaporation.

 

Explanation:

• There are many factors that affect the rate of transpiration such as light, humidity, and temperature wind.

Amount of sunlight:

• As the Light increases, the rate of transpiration increases.
• This is because with the increase in lights, the rate of water absorption, and the resulting turgidity of the two guard cells increases.
• This forms the boundary of each stoma and brings about the opening of the stomates, which increases the transpiration rate.

Relative humidity:

• As the relative humidity of the air around the plant rises, the transpiration rate falls.
• Water is easily evaporated into dryer air than into more saturated air.
• The atmosphere has more moisture when the relative humidity is high.
• This reduces the driving factor for transpiration.
• Lower levels of relative humidity correspond to less moisture content in the atmosphere and hence higher the driving factor for transpiration.

Temperature:

• Transpiration rates increase with the increase in temperature.
• This happens especially during the growing season when the air is warmer due to stronger sunlight.

From the above explanation, it is clear that the factor which affects the most is  Relative humidity.​

• Relative Humidity can often more immediately dictate the rate of transpiration due to its direct effect on the moisture gradient, affecting transpiration in both low and high temperatures.

Concept:

Temperature:

• The temperature refers to the degree of hotness and coldness which decides the substance will supply or absorb heat from one another.
• SI unit is Kalvin.
• CGS unit is Celsius.

Thermal Conductivity:

• It states that the amount of heat that flows through the face of solid material is directly proportional to the area of the cross-section, the temperature difference, and the period and inversely proportional to its thickness.

Explanation:

• In this case, plastic and glass bottles behave similarly because the lower thermal conductivity of plastic is offset by a thinner wall.

Thus, from the above discussion, we can say that the temperature of the water glass bottle is almost equal to 10^oc.

Concept:

Sound:

• A  sound is a form of energy that produces a sensation of hearing in our ears.
• Vibration is the physical phenomenon responsible for the production of sound.
• Vibration is the rapid to and fro motion of an object.
• Medium is necessary for the propagation of sound.
• The substance through which sound is passed is known as a medium of sound.
• The waves in which particles oscillate up and down and also the oscillation is perpendicular to the direction of propagation are known as transverse waves.
• The waves in which oscillation of particles occurs in direction of propagation that is parallel to the line of propagation are known as longitudinal waves. sound is an example of longitudinal waves while light is an example of transverse waves.
• The audible range of sound for a human is 20Hz to 20000Hz.
• Non-periodic sound waves are term as noise.
• The sound speed is 346 m/s.

Explanation:

• As we know that the intensity of sound is directly proportional to the square of the amplitude of vibration.
• I ∝ A² since, the amplitude of vibration of air molecules (empty vessel) is greater than liquid molecules (filled vessel), therefore empty vessel produces a louder sound than the filled vessel.
• If we consider the liquid (water), then the density of the liquid is more than air, as it is heavier than air, so both A and R are true and R is the correct Explanation for A.

Additional Information

Transverse Wave-

• The waves in which the particles oscillate up and down and also the oscillation is perpendicular to the direction of propagation are known as Transverse Waves.
• Light is an example of transverse waves.

 

Longitudinal Waves-

• The wave in which the oscillation of particle occurs in the direction of propagation i.e. parallel to the line of propagation is known as longitudinal waves.
• Sound is an example of Longitudinal waves.

Concept: 

Mixture:

• The substance which is formed by mixing two or more two substances is called a mixture.

Homogeneous Mixture:

• A mixture whose particles are similar in size and texture is homogeneous in nature.

Heterogeneous Mixture:

• A mixture whose particles are not similar in size and texture is heterogeneous in nature.

Explanation:

Air:

• Air is a mixture of different gases and dust particles.
• Percentages-wise distribution of different gases is: Nitrogen - 78%, Oxygen - 21%, Argon - 0.9%, and the remaining portion is occupied by various other gases like carbon dioxide, neon, helium, sulfur dioxide, etc.
• Air also contains water vapor.

Sugar:

• Sugar is a compound that is formed by a combination of three atoms: carbon, hydrogen, and oxygen.
• Since these three atoms are chemically joined with each other thus they form a compound in nature.

Milk:

• It is a mixture of water, fat, and solids (in the form of milk protein and carbohydrates) that is mixed irrationally.
• Therefore milk is a mixture, not a pure substance.
• The main compounds of milk are lactose and casein.

CO2 :

• Carbon dioxide, CO2, is a chemical compound composed of two oxygen atoms and one carbon atom.

Seawater: 

• It is a mixture of pure water and dissolved ionic substances.
• Water is a very good solvent.
• Solvents are liquids that dissolve other substances.

Soap:

• It is a mixture of sodium salts of various naturally occurring fatty acids.
• Air bubbles added to a molten soap will decrease the density of the soap and thus it will float on water.
• If the fatty acid salt has potassium rather than sodium, a softer lather is the result.

Soil:

• It is a mixture of minerals, dead and living organisms (organic materials), air, and water.

Foam: 

• Colloids are things like this.
• A colloid is a heterogeneous mixture of two different phase substances.
• Shaving cream and other forms are made up of gas that has been dispersed in a liquid.
• Liquid dispersed in solids includes Jello, toothpaste, and other gels.

From the above explanation, it is clear that option 2 is the correct form of a mixture.

Additional Information

Solution:

• A liquid mixture that has solute particles dissolved in a solvent medium.
• The solute is the component that is present in less amount.
• The solvent is the component of the solution which is present in more quantities.

Explanation:-

Chemical reaction: The chemical reaction is said to be the change that brings new products.

Displacement reaction: 

• The reaction in which cation or anion from the reactant side is displaced to the products is called displacement reaction.
• A displacement reaction is also known as a metal displacement reaction.
• Metals of high reactivity displace the metals of low reactivity from their anions.

Double displacement reaction: The reaction in which both cation and anion is displaced to the products is called double displacement reaction.

Properties of Elements:

• Zinc: Zinc is more reactive metal than Iron and copper.
• Iron: Iron is least reactive than zinc but more than copper.
• Copper: Copper is least reactive than zinc and iron.

Metal reactivity series:

The metals are arranged in increasing order of their reactivity which is known as the metal reactivity series. 

Concept:

• A flame is divided into three zones.
• The temperatures in each zone are varied.
• Each zone has a distinctive color, which will aid us in determining the temperatures in each zone.
• The outermost zone
• The color of this zone is blue.
• This is the region where complete combustion is taking place.
• It is the hottest part of the region.
• It is the non-luminous part of the flame.
• The middle zone 
• The color of the flame is yellow.
• This zone is bright and luminous.
• The wax vapors here are burnt partially.
• The partially burnt fuel in this zone releases carbon particles.
• These carbon parties are responsible for the smoke and the soot being released into the air.
• The temperature of this zone is moderate.
• The innermost zone 
• The color of flame here is dark black.
• It basically pertains to the unburnt wax vapors.
• This region is the least hot region.

Explanation:

• Due to complete combustion, the outer zone is blue in color.
• This zone is the hottest in temperature (1400 °C) when compared to the other zones.
• This blue-colored zone is the nonluminous part of the flame.
• The yellow color region which is the bright part of the flame is the middle zone.
• It is moderately hot (1000 °C) and partial combustion of fuel takes place.
• The least hot region (800 °C) of the flame is the innermost zone.
• This inner zone is black in color due to the presence of unburnt wax vapors.

 So, the temperature of the outermost zone of the flame is more than 100° C.

Explanation:-

Temperature: The degree to measure the amount of hotness and coldness.

Boiling Point: The minimum temperature at which a liquid starts boiling is called its boiling point.

Freezing Point: The minimum temperature at which liquid starts getting frozen or solidified is called its freezing point.

Increasing order of melting point:

Mercury < Aluminium < Copper < Iron.

Additional Information

• Mercury: It is a liquid metal. Its melting point is -38.83⁰C.
• Copper: Copper is a noble metal. Its melting point is 10850C.
• Iron: Iron is a highly reactive metal.  Iron has high melting point of 15380C.
• Aluminium: The melting point of aluminium is 660.30C.

Explanation:-

Acid: The substances which can turn blue litmus paper red. Acids are donors which give away hydrogen ions easily.

Base: The substances which can turn red litmus paper blue. Bases are received that give away hydroxide ions easily.

Salt: The neutral substances which are neither acidic nor basic in nature. Mostly, they have 7 as their pH value.

Neutralization Reaction: A reaction in which acids and bases react in fixed quantities to neutralize one another.  

Acid + Base → Salt + Water

• Strong acid and a weak base result from a weakly acidic solution.
• Weak acid and a strong base result from a weakly basic solution.

Important Points

• Baking soda is a base that neutralizes the formic acid in the ant sting.
• Quick lime is calcium oxide which is a base.
• Magnesium hydroxide is also called milk of magnesia which is a base used to neutralize the excess hydrochloric acid in the stomach.
• The zinc layer is made over iron articles to prevent corrosion.
• Corrosion is a chemical process of the formation of metal oxide in presence of water or moisture.

The correct answer is cotton.

Concept:

• The amount of water that can pass through the soil is defined as percolation.
• The percolation rate of water is different in different types of soil.
• Percolation is highest in the sandy soil and least in the clayey soil.
• The formula for percolation rate is

$percolation rate (mL/min) = { amount of water (mL)\over percolation time (min)}$

Explanation:

• Soil is of different types: clayey, loamy, and sandy.
• Water percolation rates vary depending on the type of soil. It is highest in sandy soil and lowest in clayey soil.
• A soil with a high percolation rate has low water holding capacity.
• Different types of soils are used to cultivate various crops.
• Wheat, gram, and paddy can be grown in clay and loam soils.
• Cotton grows best in sandy loam soil.

The correct answer is b and c.

Key Points

• The size of the organism is not determined by the size of the cells.
• It is the number of cells that differs and determines the size of various organisms.
• The cell size of a monkey and that of an elephant are nearly identical. Hence, statement b is false.
• A large organism, such as an elephant, has many more cells than a smaller organism, such as a monkey. Hence, statement a is true.
• The cells of an elephant are not larger than those of a rat; only the number of cells differs.
• The shape of the cells of the monkey and the elephant are similar. Hence, statement c is false.

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

Explanation:

• Peels of fruits and vegetables like Apple, tomato, kiwi, cucumber, and peaches are extremely beneficial and should be consumed due to their higher mineral and vitamin content.
• Fruit and vegetable skins and peels contain more antioxidants, vitamins, fibre, and minerals than flesh.
• The skin of a vegetable can contain up to 31% of its total fibre content.
• Furthermore, antioxidant levels in fruit skins may be up to 328 times higher than those found in the flesh.

The correct answer is (a) - (ii), (b) - (iv), (c) - (i), (d) - (iii).

Explanation:

• In plants, the root is the non-green (due to the absence of chlorophyll), cylindrical and descending part that normally grows downwards into the soil.
• It does not bear leaves, buds and is not distinguished into nodes and internodes.

Types of root:

Taproot:

• The taproot develops from the radicle of embryo of a seed.
• The first root formed by the elongation of radicle is called primary root. It continuously grows and produces lateral roots called secondary roots.
• These types of roots are present in dicots, e.g., carrot, pea, gram, groundnut, etc.

Adventitious root:

• The roots developing from any part of the plant other than the radicle are known as adventitious roots.
• These are usually found in monocots, e.g., Sweet potato, wheat, onion, etc.

Prop root:

• The prop roots grow as the horizontal branches of the stem and grow vertically downward.
• They become thick pillar-like and provide mechanical support to the giant trees e.g., banyan tree

Stilt root:

• These are small, thick supporting roots growing obliquely from the basal nodes of the main stem.
• They provide mechanical support, e.g., sugarcane, maize, etc.

Concept:

Acclimatisation and Adaptation:

• The process of changes that can occur in an organism over a short period of time that helps it to adjust to its surroundings is known as acclimatization.
• Acclimatization is irreversible and temporary.
• Adaptation is the changes in an organism over a long period of time, whereas acclimatization is change over a short period of time.

Camouflage:

• It is an adaptation mechanism that allows tuning in with certain aspects of their surrounding environment.
• Camouflage increases the chances of survival of an Organism in a particular habitat. They hide from their predator.
• E.g: Caterpillar larvae, Black moth, African weaver birds, Mice, Stone flounder, a Flatfish

Hibernation: 

• It can be defined as a state of minimal functional activity and reduced metabolism in warm-blooded animals or endotherms.
• Hibernation is most commonly related to a seasonal phenomenon in animals in order to avoid or survive through adverse climatic conditions.
• The process of hibernation is characterized by lowering body temperature, slow breathing process with decreased heart rate, and low metabolic rate​
• Hibernation is often referred to as winter sleep.
• E.g: Skunks, Bees, Snakes, Groundhogs, Bears, Bats etc.

Explanation:

• Acclimatization is the temporary adjustment of the organism to its surroundings - (True)
• Camouflage is a type of adaptation- (True)
• Hibernation is acclimatization -(False as Hibernation reversible and acclimatization is irreversible).
• Long-time adjustment to surroundings leads to adaptations- (True)

Thus, Hibernation is acclimatisation is incorrect.

The NCF (National curriculum framework) 2005 is published by NCERT (National council of educational research and training) which explains the changes and new ways by which teaching and learning can be enhanced.

Key Points

• Science emphasizes social endeavor. social endeavor is that which focuses to build relations.
• ​Example: Scientists working together.
• ​Science is dynamic in nature so that it expands the body of knowledge and covers new areas of experiences.
• According to A.J.  Balfour, Science is an instrument of social change because its object does not change but knowledge may be changed related to the object.
• ***So option (3) is correct.*​

Important Points 

Additional Information

• Objectives of teaching science in schools according to NCF 2005:
• To encourage the student to learn about nature.
• To improve divergent thinking skills.
• To connect the curriculum with the daily routine through hands-on activities.

According to NCF 2005, the learning of the students should be done through different interesting activities, by hands-on experiences. 

Key Points

• Learning of the students should be done by those types of activities in which students can enjoy their curriculum such as: 
• Storytelling method.
• Connect with daily life examples.
• Concepts should also be taught by the play-way method.
• Hands-on activities.
• Experiment-based teaching.
• That's why option (3) is correct.

Additional Information

• Teaching should not be instruction-based and complaint-based, because these activities may increase the fear in the children's minds, which may perform a negative impact on their lives.

Science activities are the activities by which children can learn all the aspects of their curriculum by practicing and experimenting.

Key Points

• Objectives of planning of science activity:
• Should be familiar to all types of students.
• Should be enjoyable for the students and related to their environment, culture, etc.
• By this, students can easily understand the related concept and can be able to apply them.
• Enhance the divergent thinking of the student.
• ***That's why option (2) is the correct answer.*​

Hint  

• Activities should not be based on memorization.

Investigable questions are those types of questions in which students should investigate, analyze the problem given in the question, and tries to solve according to their investigation.

Key Points

• Samples are given of the food items, students should have to investigate which food contains starch.
• ***That's why option (3) is the correct answer.*​

Important Points

• Option(1), Why are lentils high in protein?
• ​This is not an investigatable question, this is a reason-based question, here students have to give only the reason.
• ​Option(2), Why do we grow weak with age?
• ​This is an observation-based question

Hint

• ​​Option(4), Consumption of what kind of food leads to a stress-free life?
• This is basically figuring out based on the question, in which students can figure out the foods which lead stress-free life.

Concept: 

Density:

• It is defined as the mass of a body per unit volume.
• We can also say how much mass it can contain in a specific volume.
• Mathematically it gives a formula Density (ρ) = mass (m) / Volume (V)
• SI Unit is kg/m3.

Flotation:

• It can be defined as the tendency of an object to rise to the upper levels of the fluid or to stay on the surface of the fluid.

Sinking: 

• The opposite of floatation is sinking which can be defined as the tendency of an object to go to the lower levels of the fluid.

 Buoyant force:

• ​When a body is wholly or partially immersed in a fluid at rest, the fluid exerts pressure on the surface of the body in contact with the fluid. The pressure is greater on lower surfaces of the body than on the upper surfaces as the pressure in a fluid increases with depth. The resultant of all the forces is an upward force called buoyant force

Explanation:

• Wood floats on water because it is less dense than water, regardless of how large or little the piece of wood is.
• If you compared the weight of wood to an identical amount (or volume) of water, you'd find that the wood sample weighs less.
• This indicates that wood has a lower density than water.
• The buoyant force on wood will be equal to the weight of the wood piece.
• We can also say that an upthrust force also acts on an object. If the density of the object is less then the upthrust is more and vice versa.
• Upthrust is also known as buoyancy.
• We can also explain this answer in terms of buoyancy force acting upon the object. If the buoyancy force is positive the object floats and if the buoyancy force is negative the object sinks.

So, from the above discussion, it is clear that statement A can be taken as observation and statement B can be taken out as inference, as it is based on the facts based on A.

Teachers can use different teaching methods depending on the needs of their students, their personal preferences, and other factors

Key Points

Thus, the above table shows correct match descriptions for the given teaching methods.

Metals are the type of substance that is hard, solid, sonorous, and can pass electricity through it.

• Example: Sodium, Calcium, magnesium, etc.

Non-metals are those type of substance which is usually in liquid and gas state, non-sonorous, and electricity can not pass through them.

• Example: bromine, chlorine, iodine, etc.

Key Points

• Typical examples of metal:
• metals are generally as common as all metals.
• Example: Calcium, Sodium, potassium, etc.
• Non Typical examples of metal (exceptions):
• Those metals that do not have similar properties to all the metals are called non-typical examples of metals.
• Example: Mercury (liquid at room temperature) - "Thermometer"
• So option (1) is correct.

Additional Information

• malleability:
• ​The quality of being malleable is called malleability.
• Metals are malleable in nature.
• Ductility:
• The quality of changing the metal into the wire is called ductility.

The Food Chain is the chain in which one living organism consumes another one and so on.

• Example: Grass consumed by grasshopper, the grasshopper is consumed by frog, and the frog is consumed by hawks.

The Foodweb is the web in which one living organism is consumed by the different organisms, there is no chain process in the food web.

• Example: Plants are eaten by grasshoppers and squirrels.

Key Points

• Divergent thinking:
• Those types of thought processes in which students can think of many possibilities to solve problems, this type of thinking are called Divergent thinking.
• So option (4) is correct. (Use of different aspects about possible environmental consequences if all deer were to disappear).

​​

Additional Information

• The food chain always starts with the producer because the producer makes food and then it is consumed by another one so that the energy of the food gets transferred.
• Example: grass, grasshopper, frog, and hawk.

Science Testbook is the textbook that contains activities, explanations with storytelling methods, experiments, the best explanation with interesting facts, knowledge related to real-life situations, consists of hands-on activities, etc.

Key Points

• The objectives of the Science textbook:
• Testbook should be children-oriented.
• The colors chosen in the textbook should be attractive for the children.
• The explanation should be in an easy langauage.
• Topics should be directly related to the hands-on activities and daily life of the children.
• Textbooks should be appreciative in nature so that concepts evolve with time.
• ​So option (4) is the correct answer.

In the given situation, the student prepared his report by observing the plants and trees, then Hypothesizing that may be due to the hot summer these plants and trees are without flowers and fruits.

• So option (1) is correct.

​

Important Points  

• Observation:
• Observation is the act of knowing and recording something carefully, especially for learning.
• Estimation:
• ​Estimation is the understanding of something by observation, by which one can make opinions.
• Hypothesis:
• ​A hypothesis is an assumption, an idea that can not be proven but can be suggestible as the best possible explanation.
• ​Prediction:
• ​Prediction is a forecast which can be assumed by overall experiences of one's life.

The correct answer is 'Both (a) and (b) are right'.

Key Points

• As we can see in the first paragraph of the passage, it is clearly mentioned that "It is very clear when a person is being disloyal - when he lets his parents suffer without showing any concern, or fights in any army against his fellow countrymen. Most of us would disapprove of such people".
• Thus, it can concluded that we admire people who are loyal both to their parents and to their country.
• Hence, statement (a) and statement (b) both are true.

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The correct answer is option 3.

The correct answer is 'helps a friend in need'.

Key Points

• As we can see in the first paragraph of the passage, it is clearly mentioned that "We approve of loyalty to our friends and loyalty to our country. Loyalty here means a readiness to help people when they are in difficulty, and a constant interest in their well-being".
• Thus, it can be concluded that a loyal person helps a friend in need.

<br>

Hence, the correct answer is option 1.

The correct answer is 'ignore his parents’ advice to make a career'.

Key Points

• As we can see in the second paragraph of the passage, it is clearly mentioned that "A clever child may resist his parent’s appeals to stop studying and pick up a job in order to help them financially. He may believe that he will be able to help his parents better in the near future if he continues his studies for a few years longer, whereas, if he stops now, his talent will be wasted".
• Thus, it can be concluded that a clever child’s first choice will be to ignore his parents’ advice to make a career.

<br>

Hence, the correct answer is option 3.

The correct answer is 'sacrifice his studies'.

Key Points

• As we can see in the second paragraph of the passage, it is clearly mentioned that "On the other hand, if a boy’s parents are in great poverty, it might be disloyal for him to refuse to help them by going to work. If later in life he is successful, he may regret his disloyalty as a boy".
• Thus, it can be concluded that a loyal child will sacrifice his studies for his very poor parents.

<br>

Hence, the correct answer is option 1.

The correct answer is 'Critics of a government are at once called rebels and traitors'.

Key Points

• As we can see in the third paragraph of the passage, it is clearly mentioned that **"**A group of people who sincerely love their country and are anxious for its prosperity may disagree with their government because they believe that certain policies or Acts (for example Rowlatt Act) of the government are against the interests of the people. This situation was faced by Indians when they were struggling for freedom. We were immediately called rebels and traitors".
• It can be concluded that critics of a government are at once called rebels and traitors.
• Thus, first statement is the only statement which is not false i.e true.

 

Hence, the correct answer is option 1.

The correct answer is 'Determiner'.

Key Points

• Here the underlined word 'their' is a determiner i.e. a word, phrase, or affix that occurs together with a noun or noun phrase and serves to express the reference of that noun or noun phrase in the context.
• Their means belonging to or associated with the people or things previously mentioned or easily identified.
• For example:- (1) Parents are keen to help their children. (2) A double portrait of their Majesties.
• Adjective is a word naming an attribute of a noun, such as sweet, red, or technical.
• Adverb is a word or phrase that modifies or qualifies an adjective, verb, or other adverb or a word group, expressing a relation of place, time, circumstance, manner, cause, degree, etc. (e.g., gently, quite, then, there ).
• Conjunction is a word used to connect clauses or sentences or to coordinate words in the same clause (e.g. and, but, if ).

 

Hence, the correct answer is option 2.

The correct answer is 'Adjective'.

Key Points

• Here the underlined word 'clear' is an adjective i.e a word used to describe an action, state, or occurrence, and forming the main part of the predicate of a sentence, such as hear, become, happen.  
• Clear means easy to perceive, understand, or interpret.
• For example:- (1) He was the clear winner. (2) She has made it abundantly clear that she does not support us.
• Noun is a word (other than a pronoun) used to identify any of a class of people, places, or things ( common noun ), or to name a particular one of these ( proper noun .
• Adverb is a word or phrase that modifies or qualifies an adjective, verb, or other adverb or a word group, expressing a relation of place, time, circumstance, manner, cause, degree, etc. (e.g., gently, quite, then, there ).
• Determiner is a word, phrase, or affix that occurs together with a noun or noun phrase and serves to express the reference of that noun or noun phrase in the context.

 

Hence, the correct answer is option 1.

The correct answer is 'Variable'.

Key Points

• Constant means a situation that does not change.
• For example:- (1) The condition of struggle remained a constant. (2) The fridge keeps food at a constant temperature.
• Variable means not consistent or having a fixed pattern; liable to change.
• For example:- (1) The drill has variable speed. (2) The quality of hospital food is highly variable.

    

Hence, variable is opposite in meaning to the word constant.

<br>

Additional Information

• The meaning of the other given words are as follows:-
• Temporary- lasting for only a limited period of time; not permanent.
• Permanent- lasting or intended to last or remain unchanged indefinitely.
• Weak- lacking the power to perform physically demanding tasks; having little physical strength or energy.

The correct answer is 'oppose'.

Key Points

• Resist means withstand the action or effect of.
• For example:- (1) Antibodies help us to resist infection. (2) Students want to discover the truth themselves, and they resist having conclusions forced upon them.
• Oppose means disagree with and attempt to prevent, especially by argument.
• For example:- (1) A majority of the electorate opposed EC membership. (2) A senator might oppose a bill.

<br>

Hence, oppose is similar in meaning to the word resist.

<br>

Additional Information

• The meaning of the other given words are as follows:-
• Persist- continue in an opinion or course of action in spite of difficulty or opposition.
• Follow- go or come after (a person or thing proceeding ahead); move or travel behind.
• Distinguish- recognize or treat (someone or something) as different.

the correct answer is it is the black part of his body.

Key Points

• These lines are taken from famous chinese poem of children called "A Bird's Desire".
• The bird Magpie has black neck and in this poem poet address to him by stating that he is wearing a black tie in his neck and sings the morning music.

The correct answer is the darkness of night.

Key Points

• These lines are taken from famous Chinese poem of children called "A Bird's Desire".
• In this poem the poet state that the sun has risen and used the word " its dark net" for the "darkness of night".

The correct answer '(a) is wrong and (b) is right.'

Key Points

• These lines are taken from famous chinese poem of children called "A Bird's Desire".
• The bird had many options to eat in breakfast and he had an insect. While eating the insect his wings played the music .

The correct answer is disturb the silence of the butterflies.

Key Points

• These lines are taken from famous chinese poem of children called "A Bird's Desire".
• In these lines the poet suggests that the in morning, the barking of dogs, children's noise and the traffic horns have disturbed the silence of the morning of butterflies.

The correct answer is  Personification. 

 Key Points

• These lines are taken from famous chinese poem of children called "A Bird's Desire".
• Personification is the literary device in which non living things are given the qualities of living things.
• ​The magpie robin is described as wearing a black tie and conducting the morning music, which attributes human-like characteristics to the bird.

Therefore, the correct answer is Option 1. 

Additional Information

• Simile compares two things stating that one thing is like the other by using the word 'like' or 'as' in the sentence. E.g. "Time is like money''.
• Metaphor compares two things stating that one thing is other. E.g. "Time is money"

The correct answer is Metaphor.

Key Points

• These lines are taken from famous Chinese poem of children called "A Bird's Desire".
• A  Metaphor is a figure of speech that compares two unrelated objects with one another. It compares two things that have a little in common.
• A Metaphor states that one thing is other.
• Let's look at Line 4:
• The sun is released from its dark net.
• In this line the poet states that the sun comes out of the dark clouds and used the word "dark net" instead of "the darkness of night".
• Thus, metaphor has been used.

Language teaching refers to a process whereby a child gains communicative comprehension or fluency over a language. It involves practice by learners where facilitation is provided by a teacher. There are several methods of English language teaching and the Lexical Approach is one of them.

Key Points

Lexical Approach: The lexical approach, proposed by Michael Lewis (1993), has emerged as an alternative to grammar-based approaches to second language teaching. It focuses on developing learners’ proficiency.

• This approach gives special attention to collocations which helps the individuals to communicate effectively in a particular context as collocations are words that co-occur naturally in a significant way, for example, sunny occurs with day and disposition. They can be grammatical and lexical collocations.
• This approach focuses on developing learners’ proficiency with lexis, or word and word combinations. Lexis includes not only single words but also the word combinations that people store in their mental lexicons.
• This approach is a widespread occurrence of multi-word units or lexical chunks in native speakers’ languages. Lexical phrases in any language offer more communicative and expressive power than grammatical structures.

Hence, it is clear that the Lexical approach to learners teaching places collocations as one major aspect of language development.

Additional Information

• Structural Approach is a language tool that helps the learner to master the structure or pattern of sentences. It improves the fundamental skill of language learning and corrects learners' speech habits.
• Communicative approach is a method of language teaching which makes learners confident to communicate effectively by involving them in real communication. It highlights the importance of real communication.

The study of linguistics is the formal description of the structure of language, including a description of speech sounds, meanings, and grammar. Language, as studied by linguists, tends to be competency-based, while psychologists generally view language in terms of performance, or how humans use language. The discipline that incorporates both approaches to the study of language is called psycholinguistics.

Key PointsSequential stages of a psycholinguistic model of language production:

• Conceptualization:
• This component is responsible for generating the communicative intention and for encoding it into some kind of coherent conceptual plan. In addition, the conceptualizer monitors what is about to be said as well as what has been said and how. Conceptualizing the message requires attentional control.
• Formulation:
• In the next component in the production system, the formulator, the propositionally organized preverbal plan activates the items in the lexicon that best correspond to the different chunks of the intended message that will, in turn, be responsible for transforming it into a linguistic structure.
• Articulation:
• Articulation is the motor execution of the phonetic plan, and it involves the respiratory, laryngeal, and supralaryngeal systems. Briefly put, as the phonetic plan is being generated, its bits are temporarily stored in an ‘articulatory buffer’. This buffered information will trigger the ‘unpacking’ of motor commands which will finally cause articulation of the message.
• Audition, speech comprehension, and monitoring:
• As previously stated, the conceptualizer is in charge of both generating messages and monitoring the whole process of production. Speakers make use of their speech comprehension system to listen to and process their own speech in exactly the same way they listen to and process the speech of others. Hence, learners monitor both the meaning and the well-formedness of their productions.

Hence, it is clear that Conceptualisation, Formulation, Articulation and Self-monitoring are the sequential stages in a psycholinguistic model of language Production.

Language in education is the basis for the learning and development of children during the formative years of school. It is equally important for learning in general and learning the content subjects in particular in later years.

Key Points

• The three-language formula is an attempt to address the challenges and opportunities of the linguistic situation in India. It is a strategy that serves as a launching pad for learning of 3 languages: Hindi, English, and a regional language.

The Three-Language Formula as stated in the 1968 Policy is: 

• The First language: It has to be studied must be the mother tongue, home language, or the regional language.
• The Second language: In Hindi-speaking States, the second language will be English or some other modern Indian language. In non-Hindi-speaking States, the second language will be Hindi or English.
• The Third language: The third language is taught at a later stage in school, and that too for a shorter time, as it is needed only in a limited context i.e. in a social situation where neither first nor second language could help the child to communicate.

Hence, it could be concluded that India’s language in education policy is known as the three-language formula.

Additional Information

• 'Multilingualism as a policy' means learners begin their schooling with their mother tongue/home language and move on to add more languages in school.