CTET Paper 2 Maths & Science 11th Jan 2022 (English-Hindi-Sanskrit) (Previous Year Paper)

Development describes the growth of humans throughout their lifespan, from conception to death. It refers to development as patterns of change over time. It does not just involve the biological and physical aspects of growth, but also the cognitive and social aspects associated with development.

Key Points 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. there are two principles about the development of a child's body. (a) Proximodistal principle (b) Cephalo-caudal Principle.

• Proximodistal sequence:  means that the development proceeds from the central part of the body towards the peripheries. In this sequence, the spinal cord of the individual develops first, and then outward development takes place. 
• For example, babies cut their front teeth before they cut their side ones.
• Thus we can conclude that if Effective use of arms proceeds the ability to use hands means that he follows the Proximodistal principle of development.

Important Points 

• Cephalo-caudal sequence: means that development spreads over the body from head to foot i.e. individual begins to grow from the head region downwards. Sufi first gained control of her head, then she could catch hold of objects, sit, crawl and later she could stand and walk.​

Additional Information Some Principles of development are:

• Principle of Individual Differences: It says that every individual is unique in himself/herself as the heredity and environmental factors make him/her different from others.
• Principle of Generality to Specificity:  The development process starts with general responses shown by the child as s/he passes through the later stages s/ he starts exhibiting specific behaviors.
• Principle of Interrelation: The development of an individual is reflected through the balanced interrelation of all the aspects of life. Development in any aspect affects the other aspect also.
• Principle of Interaction: The principle of interaction suggests that an individual is the product of heredity and environment. In other words, the interaction takes place within and outside forces of the child.

Development describes the growth of humans throughout their lifespan, from conception to death. It refers to development as patterns of change over time. It does not just involve the biological and physical aspects of growth, but also the cognitive and social aspects associated with development.

Key Points  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. there are two principles about the development of a child's body. (a) Proximodistal principle (b) Cephalo-caudal Principle.

Thus by this principle, we can conclude that developmental changes occur in an orderly and sequential manner.

Important Points

• Proximodistal sequence: means that the development proceeds from the central part of the body towards the peripheries. In this sequence, the spinal cord of the individual develops first, and then outward development takes place. 
• For example, babies cut their front teeth before they cut their side ones.
• Cephalo-caudal sequence: means that development spreads over the body from head to foot i.e. individual begins to grow from the head region downwards. Sufi first gained control of her head, then she could catch hold of objects, sit, crawl and later she could stand and walk.

Hint

• Development of the child occurs in a spiral manner, it does not follow the linear pattern in the child's development.
• Development occurs fast in infancy but the growth of the child occurs till adolescence and the development is a continuous process, it is done throughout life.
• The development of the child is a continuous process it does not reverse back.

Development describes the growth of humans throughout their lifespan, from conception to death. It refers to development as patterns of change over time. It does not just involve the biological and physical aspects of growth, but also the cognitive and social aspects associated with development.

Key Points Characteristics of development are:

• Development is a continuous process, it occurs throughout life, and the pace of development may be varying at different ages.
• Development is sometimes predictable as it follows a similar pattern of development as Cephelocaudal and Proximodistal.
• Developments depended on both heredity and environment, according to Woodworth development is a product of heredity and environment.
• Example: Color of eyes, hairs of the child is same as their parents because of inheritance.
• Children can learn much from their environment as such, from school culture, their society, their peer groups, etc.
• Development is not linear in shape it is spiral and it can be back and forth throughout life.

Thus by all these references, we can consider that heredity and environment can result in the physical, cognitive, and social development of the children.

Important Points  Development is of basically six types and these are:

• Physical development: Physical development is the development that covers the growth and development of the personal body of the children.
• Social development: Social development is related to the contexts which explain behaviors, relations, bonding, etc.
• Emotional development: Emotional development is the development of the child which expresses the feelings of the child, such as happiness, sadness, etc.
• Language development: This is a development in which a child can learn how to read, write, speak, etc.
• Moral development: Children are able to decide, about their rights and wrong.
• Cognitive development: Development of child intellect, thinking process, imaginations, etc.

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  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 behaviour patterns of school may be called secondary socialization.
• Example: Church, School, Media, etc.
• So by all these references, we can conclude that Media is an agency of secondary socialization.

Important Points   Some important characteristics of socialization:

• It is a lifelong process.
• The roles a person enacts are the expressions of his social nature.
• The nature of what one communicates in society is determined by the influence of one's interaction with society.

Additional Information There are many sources of socialization such as School, College, Friends, Society, Neighbourhood, Religion, Caste, Media, newspapers, Meetings, Events, etc.

• Media: Media is the source in which observational skills are considered, media such as Television, magazines, Mobile phone, reality shows, newspapers, etc.
• Educational institutions: In educational institutions students socialized by learning various subjects,  interacting in different activities, Peer groups, teachers, textbooks, TLMs, etc.
• Neighbourhood: Children learn many skills by interacting with their neighbourhood, Neighbours play an important role in the socialization of the child.
• Religion: Religion makes child socially active, it gives them knowledge about religions, and Gods, and make them familiar with them.

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 7 years)
• Concrete operational stage (7 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, centration, language development, Egocentrism, and animism.
• During this period, children are thinking at a symbolic level but are not yet using cognitive operations.
• At this stage, the child focuses on one situation or condition at a time and neglects the other possibilities related to the problem, and this condition is known as centration.
• So we can conclude that centration is the tendency to focus attention on only one characteristic of an object at a time.

Important Points

• Egocentrism: It is an inability of a child to see the situation with the perceptions of others.
• Reversibility is the understanding that a child develops to know that things that have been changed can be returned to their original state.
• Animism is the ability which the child thinks that inanimate or non-living objects(such as toys, dolls, and teddy bears) have life and feelings and intentions like a person.

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 7 years)
• Concrete operational stage (7 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, perceptual centration, language development, Egocentrism, and animism.

• Animism is the ability which the child thinks that inanimate or non-living objects(such as toys, dolls, and teddy bears) have life and feelings and intentions like a person.

Thus by all these references, we can consider that animism is the ability that comes in the child at the pre-operational stage of Jean Piaget.

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 cognitive development of the child. According to him, there are three main needs for the cognitive development of the child and these are- Social interaction, Culture, and Language.

Key Points  Cultural tools:

• Lev Vygotsky's social-cultural perspective of learning emphasizes the importance of cultural tools in the process of cognitive development.
• Cultural tools are the main determinant of cognitive development and learning. They play a significant role in human intellectual development and how humans perceive the world.
• Learning takes place through the interaction between the child and the culture. Different cultures play a vital role in shaping the abilities and behaviors of a child and work as a tool of intellectual adaptation.​  
• Example: Maps, Language, computers, traditions, calculators, books, and media, are the basic source of cultural tools.

Thus by all these references, we can conclude that Maps and calculators are the tools that help in the cognitive development of the child.

Important Points Vygotsky also proposed three basic needs of students during learning, these are: ZPD (zone of proximal development), Scaffolding, MKO (more knowledgeable others)

• 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).
• 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.

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. Lev Vygotsky also proposes three types of speech in the development of children as social speech, private speech, and silent speech.

Key Points 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.

Private Speech:

• It refers to the speech produced aloud by young children which seems to be addressed either to the self or to others, which sometimes cannot be easily conceived by a listener.
• It has a major role in the augmentation of the self and self-consciousness. It is the main aspect of the development of self and subjectivity.
• It is important in the cognitive development of the child and gradually enables her to regulate oneself, monitor oneself, plan and solve problems.
• With age, however, private speech disappears or is transformed into silent inner speech or verbal thought but in few cases, it proceeds to the end of adolescence and even later.

Thus by all these references, we can consider that In Lev Vygotsky's view, private speech serves an important social function.

Important Points

• 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.
• 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.

A progressive classroom is a part of progressive education that believes in the capability and potential of every child. It emphasizes enhancing the skills and understanding of the learners by engaging with the contents and experiences. It promotes 'learning by doing to make children self-reliant and productive to use their knowledge and talents effectively. 

Key Points  Characteristics of Progressive education:

• Progressive education emphasizes enhancing the skills and understanding of the learners by engaging with the content and experiences.
• Range of activities and tasks.
• Education for society and democracy.
• It emphasizes Collaborative and cooperative learning.
• Learning as opposed to rote knowledge.
• Learning should be done as per the needs of the students, children either can work in an individual manner or in group learning.
• Importance of inquiry, observation, and investigation so that learners can learn meaningfully.
• De-emphasize textbooks, and emphasize multiple resources.
• In a progressive classroom, a teacher facilitates the children to work in groups to achieve a common learning task.
• Provides opportunities to the learners for the construction of knowledge
• Progressive education is based on learning by doing. Everything learned by the children should be related to their curriculum and activities.
• Emphasis on problem-solving and critical thinking.
• Flexible timetable and seating arrangement.Emphasis on lifelong learning and social skills.
• Integrated curriculum focused on thematic units.
• Availability of a variety of materials

Thus by all these references, we can consider that the Availability of a variety of materials and the Range of activities and tasks mentioned in the questions are correct in the context of progressive education.

Hint

• Progressive education neither follows direct instruction-based learning in the classrooms, the learning should be based on the interest and the needs of the learners.
• Rote leaning or learning through memorization is not promoted in the progressive way of learning, learning should be meaningful and conceptual in the progressive classrooms.

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

• 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.
• Good boy /Good girl morality.
• In this stage, the child avoids disapproval or dislike from others, so this stage refers to a golden rule.
• The child wants to capture the attention of everyone towards himself.
• Ideal reciprocity is one of the major characteristics of this stage.
• The child wants to show that he is the best and he did not have any shortage.

Thus by all these references, we can consider that "Good-boy - Good-girl orientation - ideal reciprocity"  is a correctly matched pair of Kohlberg's stages with their underlying principles.

Important Points Other Stages of Kohlberg's moral development theory:

• Stage-1: 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.
• Stage-4 Law and order orientation: There is an orientation towards authority, fixed rules, and 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.
• 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.
• 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.

Intelligence refers to the capacity to acquire and apply knowledge. It is the ability to solve problems, learn from experiences, and apply knowledge to deal with new situations.

Key Points Characteristics of intelligence:

• It is the ability to acquire new skills and use the existing knowledge to complete a task or deal with a situation.
• Intelligence refers to the capacity to acquire and apply knowledge.
• It is the ability to solve problems, learn from experiences, and apply knowledge to deal with new situations.
• Intelligence includes the capacity to understand novel stimuli, learn a language, and communicate with others, be aware of the environment, have the ability to reason, plan, and solve problems creatively.

Thus by all these references, we can conclude that a set of capabilities refers the intelligence.

Additional Information  Some theories related to Intelligence- 

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.

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 challenged by:

• Promoting flexibility in the classroom.
• Presenting Non-stereotypical sex roles, such as a girl riding the bike, or a boy cooking in a kitchen.
• Treating the girls and the boys equally.
• Teachers should discuss the depiction of men and women in non - conformist gender roles to challenge Gender Stereotyping.
• Discussions refer to the relatively fixed and overgeneralized attitudes and behaviors that are considered normal and appropriate for a person in a particular culture based on his or her biological sex.
• Gave the same and equal opportunity to all the students without making any difference between them.
• Discussion on gender as a social construct reduces children's thoughts towards gender stereotypes, It helps them to build the understanding that there is no difference in boys and girls for any work.
• Engagement of every student in all the activities without distinguishing them according to their sex.
• The sitting arrangement of all the boys and girls should not be separated.

Thus by all these references, we can consider that the teachers should discuss the depiction of men and women in non-conformist gender roles to Challenge gender stereotyping.

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.

Collaborative learning is a method of teaching and learning in which students team together to explore a significant question or create a meaningful project.

• A group of students discussing a lecture or students from different schools working together over the Internet on a shared assignment are both examples of collaborative learning.

Key Points Characteristics of the collaborative learning approach:

• It emphasizes direct or face-to-face coordination.
• The teacher encourages collaborative learning which refers to a situation in which two or more people learn or attempt to learn together in a group.
• Positive interdependence.
• There are many varieties of learning in collaborative learning such as activities, teamwork, group discussions, etc.
• It is an effective opportunity for diverse learners, diverse learners can learn through collaboration in different types with their peers and their curriculum.
• Individual and group accountability.
• Adolescents provide many opportunities in the classroom to share their views and have much involvement in group discussions.
• A heterogeneous group of mixed abilities.
• in collaborative learning, a Group-oriented reward system should be implemented.
• Group learning to master academic materials.

Thus by all these references, we can consider that collaborative learning is emphasized by the teachers so that the learner can learn through cooperation, also this type of learning method helps the diverse learners to learn the concept in a meaningful way. Hence both (A) and (R) are false.

Assessment is a systematic way of collecting information to make a judgment about student learning. It is integral to the teaching-learning process which helps in facilitating student learning and improving instruction. 

Key Points Characteristics of assessment for learning:

• Assessment for learning takes place before, during, and after the teaching-learning process. It is also known as formative assessment.
• It helps teachers to identify problem-facing areas and to understand the learning needs of students to ensure their academic growth.
• Assessment for learning focuses upon a formative type of assessment.
• The process of assessment should be dynamic. It should focus on a variety of methods to assess learner performance.
• This is feedback on the learning of the students, there is no judgemental decision taken after formative assessment.
• It is considered a formal and Informal Method of assessment as it can be conducted at any time or during teaching also.

Thus by all these references, we can consider that Assessment should not focus on the use of standardized assessment tools, this is a dynamic process.

Important Points Assessment of Learning: 

• It is used for labeling children and reporting it to their guardians, which makes the process tiresome for teachers and students.
• Its emphasis is entirely on data compilation, calculation of marks/ grades, and cumulative achievement.

 Assessment as Learning:​

• Assessment as learning builds the capacity of students to absorb new ideas and place them in larger contexts, evaluate their own and their peers’ work against well-defined criteria or learning goals.
• Out of the three purposes of assessment, ‘Assessment as Learning’, helps imbibe skills of learning to learn and lifelong learning among children and, therefore, is the most crucial component of assessment under CCE.

Thinking is the basis of all cognitive activities or processes and is unique to human beings. It involves the manipulation and analysis of information received from the environment. There are different kinds of thinking styles which include creative, critical, logical, concrete thinking, etc.

Key Points Critical thinking means one looks at the available evidence and evaluates it. It is not possible to find an answer to a question just on the basis of the opinions of one’s friends and family which may be quite misleading. Instead, it is important to consider all possible evidence: data gathered through primary research, information available in existing research, and perspectives of different experts and stakeholders.

• For example, if the government has to consider how to prepare for an epidemic.

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. 

• It improves the analysis and observational skills of the learners.
• The path of conceptual learning is from simple to complex, first students have to learn simple concepts, and then they have to learn complex concepts on the basis of simple concepts.
• Conceptual learners always think divergently, they cover all the possible ways to solve the problem,

Thus by all these references, it is clear that conceptual understanding and critical thinking both promote the divergent type of thinking so "What measures should be taken to make society inclusive?" is the conceptual understanding and critical thinking type question.

Inclusive Education means meeting individual differences in the general classroom as It refers to the inclusion of all children in the education system, regardless of their differences and disabilities.

Key Points Characteristics of inclusive education:

• The main objective of inclusive education is to educate and help them in learning every child not label them by different names on their performance.
• accepting all learners without imposing normative standards.
• Equitable education for all, including challenging, backward, disabled children.
• The curriculum of inclusive classrooms is flexible and easy to access.
• using diverse pedagogical strategies and respecting individual students’ pace of learning.
• All the students of different abilities, differences, and disabilities are treated equally.
• have building, campus, and various facilities accessible
• Inclusive education provides barrier-free access for all students.
• Creating an environment in which the child can learn with diversity, not creating a special environment for learning.
• Emphasis on their learning to read instead of emphasizing teaching.
• providing choice and options for learners amidst an array of activities and experiences.

Thus by all these references, we can conclude that the buildings are accessible and a flexible curriculum promotes inclusive education.

Hint 

• The child should not be segregated, make curriculum flexible for all so that they can learn by collaboration and can promote inclusive education.
• The pedagogy used in the classrooms should be child-centered, it does not teacher-centered or competition centered to promote the learning of the students.

Important Points  Principles of Inclusive Education:

• Well constructed educational plan.
• Use of multilingualism as a resource.
• Equity and equal opportunities for all.
• Use of specific pedagogical strategies.
• Sensitization towards individual differences.

The term "Disability" is, generally speaking, a kind of absence or lack of one or more capacities that the majority of human beings possess and without which our physical or mental activities are restricted partially or totally. 

Key Points Autism refers to a neurodevelopment disorder that is characterized by difficulties with social communication and social interaction and restricted and repetitive patterns in behaviors, interests, and activities.

Characteristics of autism include:

• Autism is a “spectrum condition” that affects people differently and to varying degrees.
• It is an early-onset disorder that is present from birth and can be diagnosed as early as 2 years of age in the developmental stage.
• Severe impairment in basic social skills.
• Presence of repetitive patterns of behavior.
• Problems or delays in the development of communication skills.

Thus by all these references, we can conclude that repetitive and ritualistic behavior is the characteristic of Autism.

Important Points

• Dyslexia: It is a Reading disability, which is not due to mental retardation, brain damage, or a lack of intelligence. It is caused by an impairment in the brain’s ability to translate images received from the eyes or ears into understandable language.
• The term 'visual impairment' is used to refer to not only those who are blind but also those who have low vision.
• Dyscalculia is a mathematical disability. In this disability, the learner has difficulty in learning or comprehending mathematics.

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.

Attention deficit hyperactivity disorder(ADHD) is a brain disorder that affects how you pay attention, sit, still, and control your behaviour. 

Key PointsTeaching strategies used for children who have a disability such as ADHD:

• Concepts use actual objects and progress from the concrete to the abstract.
• Breaking the task into small chunks so that disabled learners can do it very well.
• Seating positions facilitate the use of prompts, cues, or other strategies during learning and teaching.
• Make a flexible curriculum also the timeline should be flexible.
• Using various strategies and teaching-learning methods for the students so that the learner can learn the concept meaningfully.
• Establish a baseline for measuring progress and evaluating treatment outcomes.
• Providing regular feedback and reducing the gap between the learning of the learner.
• Learning disabilities can be seen to change over time and with treatment.

Thus we can conclude that ADHD can be cured by breaking the task into small chunks so that they can learn by achieving chunks.

Hint

• ​Giving long and repetitive assignments makes disabled students irritating and makes a negative impact on their learning.
• The classroom should be in disciplined way, and distractions in the classroom should impact negatively the learning of the student who is disabled.
• The teacher should have to provide multiple and various ways to all the learners so that they can improve their divergent thinking while is beneficial for their learning.

Inclusive education goes beyond children with disabilities and refers to an education system that accommodates all children regardless of their physical, intellectual, social, emotional, linguistic, or other conditions.

Key Points

The main objective of inclusive education are:

• accepting all learners such as students with disability, and students from economically weaker sections, without imposing normative standards.
• Equitable education for all, including challenging, backward, disabled children.
• using diverse pedagogical strategies and respecting individual students’ pace of learning.
• The teacher should respect and consider the backgrounds of the learners such as cultural background, economic background, etc.
• All the students of different abilities, differences, and disabilities are treated equally.
• Inclusive education provides barrier-free access for all students.
• Creating an environment in which the child can learn with diversity, not creating a special environment for learning.
• Emphasis on their learning to read instead of emphasizing teaching.
• providing choice and options for learners amidst an array of activities and experiences.

Thus by all these references, we can conclude that teachers should respect and consider their socioeconomic background for the successful inclusion of the students from economically weaker sections.

Hint

• A teacher should not segregate students, all the students have equal write to study in the same classroom.
• A teacher should not correlate learning abilities with the other students, because all the learners are different and have different abilities of learning.
• A teacher should have to use different examples while teaching so that examples are good for all type of learners and they can understand the concept meaningfully.

Learning styles define the way how people learn and how they approach information. VARK is an acronym that refers to the four types of learning styles: Visual, Auditory, Reading/Writing Preference, and Kinesthetic.

Key Points

• Kinesthetic learners best understand information through the tactile representation of information. They learn best by figuring things out by hand.
• Auditory learners best understand new content through listening and speaking in situations such as lectures and group discussions.
• Learners with a strong reading/writing preference learn best through words. These learners are able to translate abstract concepts into words and essays.
• Visual learners prefer the use of images, maps, and graphic organizers to access and understand new information.

Thus by all these references, we can conclude that "Visual: Use maps and flows charts to organize materials" is a correctly matched pair.

Hint

• Tactile material (globe): These globes have convex and concave features on the surface denoting coastlines and country borders which will useful for visually impaired students.

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.

A teacher can improve learning by:

• Making the environment of the classroom according to the needs, abilities, and capacities of the learners.
• Teaching should not be instruction based, it should be done through different activities, experiments, and group discussions, that's why learners can enjoy their learning.
• Learning should be related to the real world and the surroundings of the students, which makes students familiar with the new concepts.
• Learning can be improved when the teacher starts linking the new concepts with the previous knowledge/experiences of the students, which helps the student to get the logic of the new concepts.
• Learning is more interesting by using TLMs for the students.

Thus by all these references, we can conclude that (A) is true but (R) is false.

Important Points

• 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.

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.
• The 360-degree holistic report reflects in great detail the progress as well as the uniqueness of each learner in the cognitive, affective, and psychomotor domains.
• 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.
• Learning how to learn:- The main goal of the school education regulatory system must be to improve educational outcomes so that children can implement the acquired knowledge and skills in real life.
• 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.
• Learning should be done in various methods, and teachers should focus on conceptual learning in a meaningful way.
• 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, a 360-degree holistic progress report card, and learning how to learn are the key features of the NEP 2020.

Hint

• Course content should not increases according to the NEP 2020, the learning of the lessons are done in different methods such as hands-on activities, and experimental way of learning.
• The curriculum should be flexible did not standardized.

Thinking is the basis of all cognitive activities or processes and is unique to human beings. It involves the manipulation and analysis of information received from the environment. There are different kinds of thinking styles which include creative, logical, concrete thinking, etc.

Key Points  A learner can gain thinking capacities by:

• Having engagement in various and different tasks.
• Giving activities based on the transfer of learning
• Engaging himself in problem-solving activities.
• Providing opportunities for self-regulation and being reflective.
• Creative work such as model making improves thinking power and also makes the learners think divergent.
• Relating new information to prior knowledge
• Talking aloud to himself also helps children to think and recall the learned concept.
• Group discussion, Peer discussion, teamwork, and interaction with society make children's thoughts divergent.

Thus by all these references, we can conclude that Aiming toward memorization rather than understanding can not promote the thinking of the learners.

Hint

• Rote memorization is defined as memorization by repetition, often without an understanding of the reasoning or relationships involved in the material that is learned.

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 A teacher can improve learning by:

• Making the environment of the classroom according to the needs, abilities, and capacities of the learners.
• Teaching should not be instruction based, it should be done through different activities, experiments, and group discussions, that's why learners can enjoy their learning.
• Learning should be related to the real world and the surroundings of the students, which makes students familiar with the new concepts.
• Learning can be improved when the teacher starts linking the new concepts with the previous knowledge/experiences of the students, which helps the student to get the logic of the new concepts.
• The atmosphere of the classrooms should be collaborative and cooperative so that the learner can learn through interaction with others.
• Learning is more interesting by using TLMs for the students.

Thus by all these references, we can conclude that a collaborative and cooperative atmosphere is an essential part of learning at school.

Hint

• The atmosphere of the classroom should not be challenging and competitive, because a challenging and competitive environment can make a negative impact on the learning of the students.
• The learning of the students should be done in the interest of the learners, they should not get bored while learning in the classroom.

Concepts are defined as polished ideas created through in-depth Research. Every teacher uses general rules or formulas and applies them while presenting the concepts to make teaching-learning simple and accessible to children. 

Key PointsTeaching strategies-

• From simple to complex- To instill confidence in the student's ability to learn, the teacher should first introduce them to simple concepts. Gradually, using effective teaching strategies, the students should be introduced to more complex concepts.
• From concrete to abstract- The concepts should be taught in a way that concrete (tangible objects) concepts should be taught first and then the teacher should move to abstract concepts. It encourages discovery and stimulates thinking.
• Lower order to higher-order- The teacher should teach lower order concepts first to develop the understanding of the concept and then move towards higher-order thinking which involves the application of the knowledge.
• Understanding based to application-based- The teacher should first prepare the ground for the basic understanding of the concept and then introduce the concepts based on application.

Hence, we conclude that the sequence of presentation of concept should be from simple to complex.

Problem-solving skills help students determine the source of a problem and find an effective solution. These are skills that help students identify and solve problems effectively and efficiently. Problem-solving is a process of overcoming difficulties that appear to interfere with the attainment of a goal.

Key Points  Some basic characteristics of problem-solving skills are-

• These skills don't have rigidity.
• Learners practices different activities, teamwork, and group discussions to improve their skills.
• The curriculum should be regulated as per the needs and the requirement of the students.
• Learners use different ways to gain problem-solving skills, their thoughts are divergent.
• The learner uses their analogical thoughts to solve a single problem in multiple ways.
• Different methods/functions are used by the teachers as well as learners, there is no fixedness in these skills.

Thus by all these references, we can conclude that analogical thoughts facilitate the problem-solving skill of the students.

Hint

• Functional fixedness is a characteristic where a person has a fixed mindset and is unable to visualize different functionalities of a particular object. It is not desirable for a problem solver.
• In the context of problem-solving, getting stuck on one way of representing a problem is called a response set.

Important Points  These are the steps to solve the problem:

• Identification of problem -We have to identify the problem before solving it.
• Analyzing the problem-  After the identification of the problem, we have to analyze the problem, so that we can figure out which, methods and steps we have to use to solve it.
• Evaluating-  After analyzing the problem, the evaluation of the correct step is required.
• Implementation- Once the Evaluation is completed execute the steps if the result doesn't come, again start by analyzing the problem.
• It is important to the identification of the problem and ideas which we are going to follow to solve our problems rather than find the solution in the whole problem-solving technique.

Errors are the window of a child's thinking, the error they make represent the way they are thinking.  Errors are not just careless answers but sometimes they are intelligent generalizations made by students with their previous experience.

Key Points Some important points which are helpful for the students to reduce their errors:

• Errors analysis help teachers to understand the weak lesson of the students so that they can improve them by applying different teaching-learning methods.
• Errors can be removed by conceptual learning, meaningful learning, learning by doing, etc.
• Errors of the learners can be improved by providing them clues and hints related to the concept so they can learn by interlinking their knowledge and correcting their concepts.
• Errors can also be reduced by asking the students or engaging them in the process of problem-solving methods of errors.
• Errors are part of the teaching-learning process teacher should respect students and errors and explain the logic behind the errors in a polite way.
• Errors can also be removed by engaging students in different types of activities related to concepts so that students can learn from these activities.
• Teachers should have to provide opportunities to all these students to find errors in their learning by themselves,
• Errors facilitate the teaching-learning process in which a teacher gets to the point where a student makes faulty so that he focuses more on that type of conceptual point.

Thus by all these references, we can consider that if the teacher Gives cues & hints to the learners so it helps students in identifying their own errors.

Hint

• Reducing marks for making errors de-motivate learners so they can not learn in an effective way through these types of activities by the teachers.
• Teachers should not ignore the errors of the students, they should help them in finding their error points and provide them help to cure them.
• Punishment is an irrelevant way to reduce the errors of the student in the teaching-learning process.

Stereotypes are anything that categorizes a large group of people into having one or many characteristics that may or may not actually be representative of who they are. It is a “quick and easy way of labeling or categorizing the world around us and making it understandable.

Key Points Effective of overcoming the impact of stereotypes thoughts:

• Emphasis on learning of the students, because all the learners are treated in the equal ways and have equal opportunities.
• Makes the thoughts of the person divergent, so that they can think out of the stereotype thoughts.
• Did not segregate the boys and the girls on the basis of work.
• Collaboration between all types of people increases.

Thus by all these references, we can say that if teachers can overcome the impact of these negative stereotypes by emphasizing that learning significantly depends on effort.

Additional Information  Gender stereotypes can be reduced in the classroom by the following:

• Making the environment of the classroom flexible for all, all as treated as students instead of girls or a boy.
• In a classroom, teachers should have to treat boys and girls equally.
• Teachers should provide equal opportunities to both girls and boys.
• 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.

Achievement goal theory proposes that individuals hold a set of beliefs, emotions, perceptions, and attributions that informs the way they approach achievement activities. Goal orientation is defined as the reasons individuals engage in achievement-related activities.

• Goal orientation theory is a social-cognitive theory that tries to find the correlation between goals and goal motivation.

Key PointsPerformance goals: Individuals who are performance-oriented are interested in competition. They use other students as comparing points. The main focus is on outperforming others.

• Students with Avoidance-oriented performance goals are concerned with avoiding failure in front of others. They are extrinsically motivated by a fear of poor performance.
• Example: Taking extra classes for a subject to achieve the first rank in class, working hard to not get outperformed by others.

Thus by all these references, we can conclude that Avoidance-oriented performance goals are an example of a student is studying to avoid the last rank in the exams.

Hint

• Approach-oriented mastery goals are defined as a focus on mastering new skills, trying to gain increased understanding, and improving competence. Students adopting mastery goals define success in terms of improvement and learning.
• Example: Doing a worksheet to improve one's competence in the domain of particular interest.
• Performance-approach goals show mixed patterns across studies. The performance approach goal has been found to correlate with positive factors such as high performance.
• Example: Preparing for a test to win the cash prize.

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 Points Teaching-learning process of the students can be emphasized by:

• Makes students active learners in the classroom, they take part in all the activities, programs, etc.
• Linking of the concepts and learning of the learners with the school, society, and community, because the community provides various ways to solve a single problem.
• improving the environment of the classroom according to the needs and interests of the students,
• Classrooms should be 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.

Thus by all these references, we can consider that the teaching-learning process is much more effective when the linking of the concepts with the society, community, schools etc so that the learner can learn through interaction.

Given:

There is a total of four options in the question to find the wrong Roman Numeral.

Calculation:

We know,

LXIX = 69

XL = 40

XC = 90

But the 'XVV' is not a Roman Numeral.

∴ The XVV is not written correctly in the given Roman Numerals.

Given:

There are three numbers given 40, 50, and 60.

Calculation:

Prime factors of 40 = 2 × 2 × 2 × 5

Prime factors of 50 = 2 × 5 × 5

Prime factors of 60 = 2 × 2 × 3 × 5

∴ LCM of 40, 50, and 60 = 2 × 2 × 2 × 3 × 5 × 5 = 600

∴ HCF of 40, 50, and 60 = 2 × 5 = 10

(LCM of 40, 50, and 60)/(HCF of 40, 50, and 60) = 600/10 = 60

∴ The (LCM of 40, 50, and 60)/(HCF of 40, 50, and 60) is equal to 60.

Given:

(ABA) × 5 = 44B0; where A and B are digits.

Calculation:

Here at 1's place, A × 5 = 0

The unit digit of the resulting number will be 0. There are ten cases such as 0, 10, 20, 30, 40, 50, 60, 70, 80, 90

If we take A = 8, then 8 × 5 = 40

The '0' is the 1's place and the '4' will be carried to the next place.

At 10's place, (B × 5) + 4 = B

Therefore, B will be the number that will be at the unit digit of the resultant number.

If B = 9 then (9 × 5) + 4 = 49

The '9' is the 10's place and the '4' will be carried to the next place.

At 100's place, (A × 5) + 4 = 4

We got, A = 8 and this will satisfy 100's place.

Therefore, (8 × 5) + 4 = 44

The '4' is the 100's place, the '4' will be carried to the 1000's place and will be the resultant number at the place.

Hence, A = 8 and B = 9

∴ The values of A and B are 8 and 9 respectively.

Given:

The given two rational numbers are -7/10 and -1/4

Calculation:

Two rational numbers are,

-7/10 = -0.7

-1/4 = -0.25

Therefore the numbers will be between -0.7 and -0.25.

Let,s justify all the options to find the correct answer.

In option 1, there are three numbers -5/8, 2/3, and -3/5

-5/8 = -0.625; 2/3 = 0.666...; -3/5 = -0.6

Therefore 2/3 does not lie between the given rational numbers.

In option 2, there are three numbers -2/3, -3/5, and -3/4

-2/3 = -0.666...; -3/5 = -0.6; -3/4 = -0.75

Therefore -3/4 does not lie between the given rational numbers.

In option 3, there are three numbers -5/8, -2/3, and -3/5

-5/8 = -0.625; -2/3 = -0.666...; -3/5 = -0.6

Therefore, all the numbers lie between the given rational numbers.

In option 4, there are three numbers -3/5, 0, -1/5

-3/5 = -0.6; -1/5 = -0.2

There is also the number '0'.

Then, the 0 does not lie between the given rational numbers.

Therefore, -5/8, -2/3, and -3/5 lie between the rational numbers -7/10 and -1/4. Hence, option 3 is the correct answer.

Given:

The given number = 3850

Calculation:

We have, 3850 = 62² + 6

Therefore, by subtracting 6 from 3850 we will get a perfect square.

The least number is 6 which must be subtracted from 3850 to make it a perfect square.

Given:

The given equation is 2xm - 3 + 3y2n - 2 = 7

Concept used:

According to the given equation in the question, there are two variables x and y. But we have to convert this to a linear equation in one variable.

Formula used:

The form of a linear equation in one variable = ax + b = 0

Calculation:

The given equation is 2xm - 3 + 3y2n - 2 = 7

There will be one variable. Then the power of either x or y will be 0.

We will calculate the values of m and n for two cases.

If we take the only variable x,

Then, m-3 = 1 ⇒ m = 4

and 2n - 2 = 0 ⇒ n = 2/2 = 1

The values of m and n will be 4 and 1 respectively but these values are not in the given options.

Let's justify another case for only variable y,

Then, m - 3 = 0 ⇒ m = 3

and, 2n - 2 = 1 ⇒ n = (1 + 2)/2

⇒ n = 3/2 = 1.5

The values of m and n will be 3 and 1.5 respectively and these values are available in the given options.

∴​ The values of m and n, m = 3, n = 1.5

Given:

x is increased by 20%, it is equal to y

y is decreased by 50%, it is equal to z

Calculation:

x is increased by 20% = x + (x × 20%)

= x + (x × 20/100)

= x + x/5

= 6x/5

Therefore, 6x/5 = y   .....(1)

y is decreased by 50% = y - (y × 50%)

= y - (y × 50/100)

= y - y/2

= y/2

Therefore, y/2 = z ⇒ y = 2z   .....(2)

Putting y = 2z in the equation (1),

6x/5 = 2z

⇒ z/x = 6/5 × 2

⇒ z/x = 6/10

⇒ z/x = (6/10 × 100)% = 60%

∴​ The 60% of x is equal to z.

Given:

The given value = 196 × 206

The given equation = 2002 + 200p – 24

Calculation:

Here, 196 × 206 = 40376

Therefore, 2002 + 200p – 24 = 40376

⇒ 40000 + 200p - 24 = 40376

⇒ 200p = 40376 - 40000 + 24

⇒ 200p = 400

⇒ p = 400/200 = 2

Then, 3p3 – 28 = 3 × 2³ - 28

= 24 - 28

= -4

∴​ The value of 3p3 – 28 is -4.

Given:

The given expression = (x + 1)(2x + 1) + (x + 2)(x – 1)

Coefficient of x = k

Concept used:

A coefficient is a number that place with a variable.

Calculation:

(x + 1)(2x + 1) + (x + 2)(x – 1)

= (2x² + 2x + x + 1) + (x² + 2x - x - 2)

= 2x2 + 2x + x + 1 + x2 + 2x - x - 2

= 3x² + 4x - 1

Here, coefficient of x = 4

According to the question, coefficient of x = k

Therefore, k = 4

Now, 2k – 9 = 2 × 4 - 9

= 8 - 9

= -1

∴ The value of 2k – 9 is -1.

Given:

The given expression = $\frac{5pq(p^2-q^2)(p-1)}{(5p^2-25p+20){2p(p+q)}}$

Calculation:

$\frac{5pq(p^2-q^2)(p-1)}{(5p^2-25p+20){2p(p+q)}}$

= $\frac{5pq(p+q)(p-q)(p-1)}{(5p^2-20p-5p+20){2p(p+q)}}$

= $\frac{5pq(p+q)(p-q)(p-1)}{{5p(p-4)-5(p-4)}{2p(p+q)}}$

= $\frac{5pq(p+q)(p-q)(p-1)}{2p(5p-5)(p-4)(p+q)}$

= $\frac{5pq(p+q)(p-q)(p-1)}{10p(p-1)(p-4)(p+q)}$

= q(p - q)/2(p - 4)

Hence, option 1 is the correct answer.

Given:

x is the supplement of an angle of 87°.

Concept used:

Two angles are called supplementary when the sum of their measures is up to 180°.

Calculation:

x is the supplement of an angle of 87°

Therefore, x + 87° = 180°

⇒ x = 180° - 87° = 93°

Now, (3x - 100°) = 3 × 93° - 100°

= 279° - 100°

= 179°

∴ The value of 3x – 100° is equal to 179°.

Given:

In △ ABC,

AB = 5 cm, AC = 7 cm, ∠A = 90º

In △ DEF,

FD = 5 cm, EF = 7 cm and ∠F = 90°

Concept used:

The Side-Angle-Side theorem of congruency asserts that two triangles are congruent if two sides and the angle created by these two sides are equivalent to two sides and the included angle of another triangle.

Calculation:

In △ ABC and △ DEF,

AB = FD = 5 cm

AC = EF = 7 cm

∠A = ∠F = 90°

ΔABC $\cong$ΔFDE  [S-A-S rule]

The two triangles ΔABC $\cong$ΔFDE by SAS congruence rule.

Mistake PointsHowever, the hypotenuses of the two triangles are not equal. The hypotenuse of ΔABC is BC, while the hypotenuse of ΔDEF is DE.

Hence, the Given Triangles Donot Follow the RHS criteria

Given:

In △ABC,

D is a point on the side BC.

∠B = 20° and AB = AD

Concept used:

Linear pair: The sum of all angles on a straight line is 180°

Calculation:

In △ABD, ∠B = 20°

AB = AD

Therefore, ∠B = ∠ADB = 20º

Now, ∠ADB + ∠ADC = 180º  [Linear pair]

⇒ 20º + ∠ADC = 180º

⇒ ∠ADC = 180º - 20º = 160º

Then, ∠ADC : ∠ADB

= 160º : 20º

= 8 : 1

∴​ The value of ∠ADC : ∠ADB is 8 : 1

Given:

In parallelogram PQRS,

∠P = 7x – 6°

∠R = 5x + 18°

Formula used:

The opposite angles of a parallelogram are equal.

In a parallelogram, any consecutive angles are supplementary.

Calculation:

In parallelogram PQRS, ∠P = 7x – 6° and ∠R = 5x + 18°

We know that the opposite angles of a parallelogram are equal.

∠P = ∠R

Therefore, 7x – 6° = 5x + 18°

⇒ 7x - 5x = 18° + 6°

⇒ 2x = 24°

⇒ x = 24°/2 = 12°

∴ ∠P = 7 × 12° - 6° = 78°

∴ ∠R = 5 × 12° + 18° = 78°

We know that any consecutive angles are supplementary in a parallelogram.

Hence, ∠P + ∠S = 180°   .....(1)

and, ∠Q + ∠R = 180°   .....(2)

Putting ∠P = 78° in the equation 1,

78° + ∠S = 180°

⇒ ∠S = 180° - 78° = 102°

Then, ∠Q = 102°

∴ The angles of the parallelogram are 78°, 102°, 78°, 102°.

Given:

Number of faces of a polyhedron = 7

Number of edges of a polyhedron = 15

Number of vertices of a polyhedron = x

Formula used:

Euler's formula for a polyhedron: V - E + F = 2

Where, V = Number of vertices of a polyhedron

E = Number of edges of a polyhedron

F = Number of faces of a polyhedron

Calculation:

By Euler's formula for the given polyhedron,

x - 15 + 7 = 2

⇒ x = 2 + 15 - 7 = 10

Now, 3x + 6 = 3 × 10 + 6 = 36

∴ The value of 3x + 6 is equal to 36.

Given:

The three sides of the triangle are 30 cm, 34 cm, and 16 cm.

The altitude corresponding to the longest side of the triangle = x

Formula used:

The area of a triangle using Heron's formula = $\sqrt {s(s-a)(s-b)(s-c)}$

Where, a, b, and c are the three sides of the triangle.

S = Semiperimeter of the triangle

S = (a + b + c)/2

The altitude corresponding to a side of a triangle = (Area of triangle × 2)/Side

Calculation:

Here, the three sides of the triangle are 30 cm, 34 cm, and 16 cm.

Semiperimeter of the triangle = (30 + 34 + 16)/2 = 80/2 = 40 cm

The area of a triangle = $\sqrt {40(40-30)(40-34)(40-16)}$

= $\sqrt {40 × 10 × 6 × 24}$

= √57600

= 240 cm²

The longest side of the triangle = 34 cm

Therefore, x = (240 × 2)/34

⇒ x = 480/34 cm

Now, (2x + 5) = 2 × (480/34) + 5

= 480/17 + 5

= 565/17

∴​ The value of (2x + 5)(in cm) is 565/17.

Given:

Diameter of a circular table = 1.6 m

Formula used:

The radius of a circle = Diameter/2

Area of a circle = πr²

Where, r = Radius of the circle.

Calculation:

Diameter of a circular table = 1.6 m

Therefore, Radius of the table = 1.6/2 = 0.8 m

The area of the circular table = π × (0.8)2

= 3.14 × 0.64

= 2.0096 m²

The cost of polishing = Rs. 30/m2

Total cost to polish the table = 30 × 2.0096 = 60.288 ≈ Rs. 60.30

∴​ The cost of polishing the circular table is Rs. 60.30

Given:

The total surface area of a right circular cylinder = 748 cm2

The circumference of the right circular cylinder = 44 cm

Formula used:

The total surface area of right circular cylinder = 2πr (r + h)

The volume of right circular cylinder = πr²h

The total circumference of right circular cylinder = 2πr

Where, r = Radius of the base of right circular cylinder

h = Height of the right circular cylinder

Calculation:

Suppose, Radius of the right circular cylinder = r

Height of the right circular cylinder = h

The circumference of the right circular cylinder = 44 cm

Therefore, 2 × 22/7 × r = 44

⇒ r = 7 cm

∴ The radius of the right circular cylinder = 7 cm

The total surface area of a right circular cylinder = 748 cm2

Therefore, 2 × 22/7 × 7(7 + h) = 748

⇒ 7 + h = 748 × 1/2 × 7/22 × 1/7

⇒ 7 + h = 17

⇒ h = 17 - 7 = 10 cm

∴ The height of the right circular cylinder = 10 cm

Now, Volume of the cylinder = 22/7 × 7² × 10 = 1540 cm3

∴ The volume of the cylinder is 1540 cm3

Given:

The set of numbers = 27, 28, 29, ___ 76, 77, 78 and 79

Formula used:

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

Calculation:

The list of numbers is 27, 28, 29, ___ 76, 77, 78 and 79.

Total numbers = 53

Total number of outcomes = 53

Numbers are selected that are divisible by both 2 and 3.

That means the number will be divisible by (2 × 3) = 6

The numbers are in the list divisible by 6 are 30, 36, 42, 48, 54, 60, 66, 72, and 78.

Total numbers that are divisible by 6 = 9

Total number of favorable outcomes = 9

The probability that the selected number is divisible by both 2 and 3 = 9/53

∴​ The probability that the selected number is divisible by both 2 and 3 is 9/53.

Given:

The given observations 37, 43, 35, 45, 50, 43, 38, 30, 43, 40, 36, 38, 43, 47 and 38.

Concept used:

Mode: In a data set, the mode is the value that appears most of the time.

Median: The median is the point in a data set where half of the data points are less and half are greater than the median. You have to arrange the data in ascending order from smallest to greatest. The median is the middle data point in the list if the number of data points is odd.

Calculation:

Let's arrange the observations in ascending order,

30, 35, 36, 37, 38, 38, 38, 40, 43, 43, 43, 43, 45, 47, and 50

Here, the value 43 appears the most number of times in the given data.

Mode of the data set = 43

Median of the data set = 40

Mean of median and mode = (43 + 40)/2 = 83/2 = 41.5

∴ The mean of median and mode of the observations is 41.5

Geometry is defined as a branch of mathematics that studies the sizes, shapes, positions angles, and dimensions of things.

• When a teacher presents the subject content in different ways by involving a multi-sensory approach and also taking care of their interest and motivation; it helps all types of learners including children with special needs in the classroom resulting in the most effective teaching.

Key Points

• Multisensory approach: In this type of approach the teachers help the children to use their multiple senses e.g. visual, touch, auditory, etc depending upon the nature of the subject material and its learning objective e.g. to provide wholesome languages experiences, a multisensory approach is also known as  VAKT i.e. Visual Auditory Kinesthetic and Tactile has been devised.
• Teaching Aids is a device by which the teacher helps the students to clarify, establish, and correlate accurate concepts, inspections, and appreciation through the utilization of more than one sensory channel. It means all the materials used to facilitate the understanding of written or spoken words.
• In the teaching of Geometry teaching aids are the objects (such as models, pictures, or maps) or devices (such as a DVD or computer) used by a teacher to enhance classroom instruction.
• They could be audiovisual teaching aids such as videos and guest lectures or tactile like 3D models, Tangram. In today's era, traditional classroom teaching is shifted to online teaching, and therefore, digital tools are used as teaching aids.
• An online whiteboard is a learning space where both teachers and students can write and interact with students in real-time via the internet. LearnCube and Geogebra are some examples of online platforms.

Thus, when a student finds difficulty in applying geometrical theorems to solve a given problem in geometry, then the teacher should adapt to use multisensory models and teaching aids to help the student understand various theorems and their applications.

An 'Error' is referred to as a deviation from accuracy or correctness. A 'mistake' refers to an error caused by a fault: the fault being misjudgment, carelessness, or forgetfulness.

• Errors are accepted as an essential part of the mathematics learning process. The child, freed from the fear of criticism, will more readily experiment.
• All learners make mistakes. As someone has said: "You can't learn without goofing".

Key PointsErrors Are Useful and are parts of learning-

• If the learner was using her/his mind to process the language being learned, errors could not be viewed as 'bad' or as failure to learn.
• Errors had to be looked at as positive signs of mental activity on the part of the learner, as well as, clues to the direction of the learner's thinking.
• The teacher should look at errors as 'attempts at learning' rather than as 'failure to learn'.
• Children's errors must be analyzed and utilized for teaching them.
• They are a rich source of information for improving mathematics teaching.
• Errors can guide the teacher in planning her class lessons.
• Errors never tell about students' low IQ.

Thus, it can be concluded that according to the contemporary view about students' errors in mathematics, the statement that errors tell about students' low IQ.  is no longer valid.

 Additional Information Errors Are Useful While teaching children, Children's errors are a natural and inevitable part of their process of learning.

• In the process of grasping new concepts, children apply their existing understanding, which may not match the method and content of formal instruction.
• Children's errors are also reflections of how children think and learn. They are often a window into the child's world. For example, writing 51 for 15 tells us that the child has not grasped the concept of place value as yet, and needs a lot more practice with grouping.
• This kind of analysis of a child's error can play a highly constructive role in helping the teacher to guide the learner to develop mathematical thinking.
• Making errors, and learning from them, is part of the process of developing a sound understanding.
• This is more important than producing the right answer. Unfortunately, the traditional teacher still tends to view learning as having occurred only when correct responses are given.

Mathematics is a science that deals with logical reasoning, quantitative calculation, practices of counting describing shapes, abstraction of subject matter, etc. Mathematics plays a vital role in daily life.

• The National Council for Educational Research and Training (NCERT) published a document called the National Curriculum Framework (NCF). NCF 2005 has been translated into 22 languages and influenced the syllabi in 17 states. According to NCF 2005.

Key PointsThe National Curriculum Framework, 2000 was initiated specifically to address the problem of curriculum load on children. A committee appointed by the Ministry of Human Resource Development in the early 1990s had analyzed this problem, tracing its roots to the system’s tendency to treat information as knowledge.

• In its report, Learning Without Burden, the committee pointed out that learning at school cannot become a joyful experience unless we change our perception of the child as a receiver of knowledge and move beyond the convention of using textbooks as the basis for examination.

To make mathematics learning more joyful and interesting puzzles, stories, and mathematical tricks in everyday lessons must be included in the math curriculum.

• Benefits of solving mathematical puzzles-
• It enhances divergent thinking.
• As children love to play games and solve puzzles, these things make their brains strong and quick.
• boosts our cognitive skills and we start thinking differently with unique ideas.
• It enhances our logical thinking. Hence, increases our decision-making skills.
• It enhances our problem-solving ability and makes us more creative.
• Games can allow children to operate at different levels of thinking.
• The games help in utilization understanding.
• In a group of children playing a game, one child might be encountering a concept for the first time, another may be developing his/her understanding of the concept, and a third consolidates previously learned concepts. So they are utilizing their understanding while playing games and solving puzzles.
• Stories are for contextualization of math with daily life experiences. It enhances imagination skills and makes learning interesting.

Thus, Including puzzles, stories, and mathematical tricks in everyday lessons is considered to make mathematics learning more joyful and interesting.

​Mathematical modelling is an attempt to study some part (or form) of a real-life problem in mathematical terms. Conversion of the physical situation into mathematics with some suitable conditions is known as mathematical modelling. Mathematical modelling is nothing but a technique and pedagogy taken from fine arts and not from the basic sciences.

Key PointsThe use of Mathematics in solving real-world problems has become widespread especially due to the increasing computational power of digital computers and computing methods, both of which have facilitated the handling of lengthy and complicated problems. The process of translation of a real-life problem into a mathematical form can give a better representation and solution of certain problems. The process of translation is called Mathematical Modelling. 

Mathematical models are used to solve many real-life situations like:

• Launching a satellite,
• Predicting the arrival of the monsoon,
• Controlling pollution due to vehicles,
• Reducing traffic jams in big cities.
• Proper flow of blood is essential to transmit oxygen and other nutrients to various parts of the body in human beings as well as in all other animals. Any constriction in the blood vessel or any change in the characteristics of blood vessels can change the flow and cause damages ranging from minor discomfort to sudden death. The problem is to find the relationship between blood flow and the physiological characteristics of the blood vessel.
• In cricket a third umpire takes a decision of an LBW by looking at the trajectory of a ball, simulated, assuming that the batsman is not there. Mathematical equations are arrived at, based on the known paths of balls before it hits the batsman’s leg. This simulated model is used to decide LBW.
• The meteorology department makes weather predictions based on mathematical models. Some of the parameters which affect change in weather conditions are temperature, air pressure, humidity, wind speed, etc. The instruments are used to measure these parameters which include thermometers to measure temperature, barometers to measure air pressure, hygrometers to measure humidity, and anemometers to measure wind speed. Once data are received from many stations around the country and fed into computers for further analysis and interpretation.
• Department of Agriculture wants to estimate the yield of rice in India from the standing crops. Scientists identify areas of rice cultivation and find the average yield per acre by cutting and weighing crops from some representative fields. Based on some statistical techniques decisions are made on the average yield of rice.

Therefore, Using a model of the solid cube to explain its faces and edges involves no future prediction and hence it is not an appropriate example of Mathematical modelling.

Information and Communication Technology (ICT) is defined as a diverse set of technological tools and resources used to communicate, create, disseminate, store, and manage information.

• This definition of ICT includes such technologies as radio, television, video, DVD, telephone (both fixed-line and mobile phones), satellite systems, computer and network hardware and software as well as the equipment and services associated with these technologies, such as video conferencing and electronic mail.

Key PointsICTs comprise the following three components:

• Information and Communication Infrastructure (ICI) which includes physical telecommunications systems, networks (cellular, broadcast, cable, satellite, postal), and the services that utilize those (Internet, voice, mail, radio, and television)
• Information Technology (IT) refers to the hardware and software of information collection, storage, processing, and presentation (World Bank 2002)
• Communication Technology (CT) like telephones, e-mail, chatting, etc. helps to disseminate information and facilitate interaction among students and teachers irrespective of the distance, time, and situations.

Important PointsICT can play a major role in promoting pedagogy for the facilitation of effective and efficient learning. GeoGebra is defined as a mathematics software system that serves as a tool for inquiry-based learning.

• GeoGebra is an interactive geometry software that offers algebraic possibilities like entering equations directly.
• It is a useful software for students and teachers.

Therefore, Using mathematics-specific computer applications like Geogebra and other simulation tools as teaching resources is the best way of incorporating ICT (Information and Communication Technology) in mathematics teaching.

Mathematics is a science that deals with logical reasoning, quantitative calculation, practices of counting describing shapes, abstraction of subject matter, etc. Mathematics plays a vital role in daily life.

• It enhances divergent thinking.
• Solving math makes our brains strong and quick.
• It boosts our cognitive skills and we start thinking differently with unique ideas.
• It enhances our logical thinking. Hence, increases our decision-making skills.
• It enhances our problem-solving ability and makes us more creative.

Key Points One of the aims of teaching and learning mathematics is to encourage and enable learners to become confident in using mathematics to analyze and solve practical problems in real-life situations.

• However, while a few students prosper in learning mathematics, many students find it difficult and ultimately fail the subject.
• This study analyses students’ mathematics performance data and examines the perception of teachers on the causes of poor academic performance in mathematics among students.
• Researchers, government, and non-governmental organizations have tried to identify factors behind students’ poor performance in mathematics at all levels of education.

Many emphasize that high failure rates have been attributed to, amongst other factors-

• The absence of competent teachers;
• inadequate teaching/learning resources such as books
• Teaching aids;
• Higher failure rates are also associated with a low level of motivation among teachers, teachers’ attitudes towards students and mathematics, poor instructional strategies,
• Teachers’ weak content knowledge ), teachers' emotions in the classroom
• Other factors include poor preparation of teachers in the implementation of the curriculum and ability grouping

Gender stereotypes like in elementary school boys identified with math more strongly than did girls or girls do not have mathematical abilities therefore maximum girls fail in mathematics is not correct. Both boys and girls have equal abilities to learn.

Therefore, Various studies in India show that there is a high failure rate of students in mathematics is correct while girls do not have mathematical abilities therefore the maximum number of girls fail in mathematics is not correct.

Fractions are defined as the numerical values that are a part of the whole.

Key Points Division model - An equal sharing of division where the number of objects is represented by the dividend and the divisor represents the number of parts (or groups) that the objects will be distributed among.

• For example, in the problem 18÷3, the 18 stands for the number of objects, and the 3 stands for the number of groups. The quotient is 6, which tells us the number of objects that will be placed into each group. For example, if you have 18 cookies divided into 6 equal parts, there will be 3 cookies in each part.
• Since there is no wastage, Keshav has $4\frac{1}{2}$ meters of cloth. He needs $1\frac{1}{2}$ meters to make one shirt. How many shirts can be made in the given length of cloth, he will divide $4\frac{1}{2}$ meter by  $1\frac{1}{2}$ and gets the value 3.

Thus, Keshav has $4\frac{1}{2}$ meters of cloth. He needs $1\frac{1}{2}$ meters to make one shirt. How many shirts can be made in the given length of cloth, assuming there is no wastage is an example of division of fractions.

Plane shapes have two measurements like length and breadth and therefore they are called two-dimensional shapes. circle, square, rectangle, triangle, etc are examples.

• The area is defined as the quantity that expresses the extent of a region on the plane or a curved surface.

Key Points

• A triangle is a 2D shape with three sides and three vertices (corners). A triangle is determined by any three noncollinear points and consists of three line segments that join them.
• A rectangle refers to a two-dimensional shape (2D shape) in which the opposite sides are parallel and equal to each other and all four angles are right angles
• A parallelogram is a quadrilateral in which both pairs of opposite sides are parallel. Twice the area of triangular cutting derives from the area of a parallelogram.
• A quadrilateral that has exactly one pair of parallel sides is called a trapezium. Using two triangular and a rectangular cuttings derive the area formula of the trapezium.
• “Polygons are many-sided two - dimensional figures, with sides that are line segments. A regular hexagon has six equal sides. The combination of six triangular cutting gives the formula for the area of a regular hexagon.

Important PointsA quadrilateral is a closed, two-dimensional shape that has four straight sides. or A quadrilateral is defined as the figure formed by four line segments that join four coplanar points, no three of which are collinear and each line segment intersects exactly two others, one at each endpoint.

• The formula of Area cannot be arrived at using any combination of triangular and rectangular paper cuttings.

Therefore, out of the above options, the Formula of Area of quadrilateral cannot be arrived at using any combination of triangular and rectangular paper cuttings

Central tendency refers to the central value of a set of grouped or ungrouped data. 

• The tendency of data to cluster towards the central location or value is called central tendency.
• There are a number of measures of central tendencies, such as the mean, median, and mode.

Key PointsSome aspects of the data can be described quantitatively to represent certain features of the data. An average is one of such representative measures. As average is a number indicating the representative or central value of the data, it lies somewhere in between the two extremes. For this reason, the average is called a measure of central tendency.

• After the data have been collected, organized, and presented they need to be analyzed. Analysis of data is a technique through which significant facts from the numerical data are extracted. One of the most important objects of statistical analysis is to get one single value that describes the characteristics of the whole data.
• Raw data are first edited and then converted into a frequency distribution. One of the basic purposes of descriptive statistics is to find out the most representative value or figure from the data. This representative figure is called average or mean.

The purpose of computing an average value for a set of data is to obtain a single value that is representative of all the items and that the mind can grasp simply and quickly. The single value is the point around which the individual items cluster.

• When a student Classifies the marks obtained by 50 students on a 100 marks exam and grouping in the interval of 10, then data that have been collected, organized and presented need to be analyzed. Raw data are first edited and then converted into frequency distribution then to get one single value that describes the characteristics of the whole data.

Therefore, Classifying the marks obtained by 50 students on a 100 marks exam and grouping in the interval of 10 can help students develop the idea of the central tendencies of a given numerical data.

If we put the whole numbers(0,1,2,3....)  and the negative numbers together, the new collection of numbers will look like 0, 1, 2, 3, 4, 5,..., –1, – 2, – 3, –4, –5, ... and this collection of numbers is known as Integers.

• In this collection, 1, 2, 3, ... are said to be positive integers, and – 1, – 2, – 3,.... are said to be negative integers.
• Integers are numbers that can be positive, negative, or zero, but cannot be a fraction.

Important PointsNumbers are an essential element of our everyday thought and language. In present-day life, every activity requires the use of numbers. Prices and weights of commodities, measurement, scores of games, travel timetables, etc., are all expressed in numbers. Man owes much of his success or progress to the art of computing with numbers.

Following are examples of integers-

• An airplane is flying at a height of two thousand meters above the ground.
• A submarine is moving at a depth, of eight hundred meters below sea level.
• A deposit of rupees two hundred or a Withdrawal of rupees seven hundred.
• Temperature going below and above 0°C.

In the case of using various blood groups like A+, AB+, O- etc. as an example. There is no involvement of numbers in blood groups. Plus and minus are just the symbolic representation not represent quantity. Therefore, using various blood groups like A+, AB+, O-** etc. as an example cannot be helpful to explain the concept of integers.

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

 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:

Law of Floatation:

• When an object is placed on liquid, an upthrust acts on it.
• This upthrust is more than weight when the density of the object is less than weight. The object floats in this case.
• If the density of the object is more, the object will sink as the weight will be more than upthrust.
• 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.
• Considering, the question statement:
• ρ_R > ρ_X > ρ_P

So, from the above relation options A, B, and D are the correct ones.

The correct answer is Vitamin A.

Explanation:

• Vitamins are organic substances that are needed in sufficient quantities to maintain good health.
• Natural sources of vitamins are fruits and vegetables.
• Vitamins are divided into two groups:
• Water-soluble vitamins -> Vitamins of B group and Vitamin C
• Fat-soluble vitamins -> Vitamins A, D, E, and K
• Each vitamin has a specific function and its deficiency leads to a particular deficiency disease.
• Out of fat soluble vitamins -> Vitamin A is the correct answer.
• Vitamin A is an antioxidant that protects the skin and eyes. Thus, vitamin A is necessary for good skin.

List of Vitamins and their functions:

Explanation:-

Sedimentation:

• It is the process of substances settling down.
• It allows particles in a given suspension under the effect of gravity to settle at the bottom.
• For example, a mixture of sand and water where sand is settled at the bottom.

Additional Information

• Loading:-  Loading is the process that is used for the sedimentation of impurity with the help of alum.​

• Condensation:- It is the change in the state of matter from the gaseous phase to the liquid phase.

​

• Distillation:- The process of separating the components or substances by selective boiling and condensation.

​

Explanation:- 

Physical changes:

• The changes that occur in a compound without changing its chemical composition is called physical changes.
• Physical changes can be reversed.
• They occur by the change of state of matter.
• Some of the physical changes occur by heating or cooling the substance.
• No new product is formed in physical changes.

Chemical changes:

• The changes in a substance or compound which brings changes in the chemical composition is called chemical changes.
• Chemical changes cannot be reversed.
• New substances are formed in chemical changes.
• Chemical changes can be endothermic or exothermic.
• Chemical changes either absorb energy or release energy.

Additional InformationReversible changes:-

• The changes that can be reversed are called reversible changes.
• They are represented by forwarding and backward reactions.
• Example -  A + B ⇔ C + D

Irreversible changes:-

• The changes that can not be reversed are called irreversible changes.
• They are only forward reactions.
• Example- A + B  → C + D

Explanation:-

Hydrophytes:-

• Hydrophytes are plants that are found in water.
• They have open stomata.
• They have thin cuticles.
• They have large flat leaves on surface plants for floatation.
• They have large air sacks for floatation.
• Leaves have a waxy coating.
• The roots of these plants are feathery to hold up the plant.
• Hydrophytes have modified roots to pick up oxygen.
• They have finger-like leaves and stems.
• They have a reduction in roots.

Examples:-  Nelumbo Nucifera, Marsilea, etc.

Confusion Points

• Please note that all the given characters might be adaptations of hydrophytes, but all of them do NOT help the plant to stay afloat.
• For example, the waxy coating just prevents wetting and clogging of the stomata on the upper leaf surface.
• Similarly, finger-like and ribbon-like leaves and stems are commonly found in submerged plants to help them sway with the water current.

Hence, statements B and D do not help hydrophytes to stay afloat in water.

Additional Information

• Mesophytes:-  Mesophytes are plants that are found in natural environments. Example - Tulip, Maple trees, etc.
• Xerophytes:- They are plants that live in dry habitats. They easily adapt the environmental changes.

Concept:

Magnet:

• A magnet is an object that has a magnetic field.
• A magnet attracts or repels other items.
• The magnetic field strength of any bar magnet is maximum at the poles.
• The field strength of a bar magnet is shown in the figure.

Explanation:

Magnets should be stored as mentioned below:

• Magnets should be kept in pairs with their unlike poles on the same side.
• They must be separated by a piece of wood while two pieces of soft iron should be placed across their ends.
• For a horseshoe magnet, one should keep a piece of iron across the poles.

​​

So, comparing the above all it is clear that A pair of bar magnets should be separated by a wooden piece.

Additional Information Precautions with Magnets:

• Magnets lose magnetism when they are heated, hammered, or dropped from some height.
• Magnets become weak if they are not stored properly.

The correct answer is Liver, Bile Juice, Gall's bladder.

Explanation:

• Liver is the largest gland of the body.
• It is an exocrine gland (i.e., glands possessing ducts).
• In adults, it weighs about 1.5-1.5 kg and lies in the abdominal cavity below the diaphragm and has two lobes, i.e., left and right lobes.
• Liver is a double membranous structure.
• Interiorly, it is divided into many small units called hepatic or liver lobules (structural and functional units of liver).
• It consists of many hepatic cells (hepatocytes) that are arranged in the form of cords.
• Hepatic cells of liver secrete the bile juice, which passes through the hepatic duct into the gall bladder.
• Functions of liver:
• It helps in producing Red blood cells in embryos.
• Bile secreted by the liver helps in the emulsification of fats, i.e., breaking down of fats into very small micelles.
• Bile also activates lipases.
• It also produces heparin, which is used to prevent blood clotting within blood vessels.

Thus, liver is the largest gland in our body. It secretes bile juice which is stored in gall bladder.

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

Concept:

• Nutrition is the process by which an organism consumes food and uses it.
• The modes of nutrition can be autotrophic or heterotrophic depending on the process of obtaining food.
• Autotrophic nutrition (auto = self; trophos = nourishment):
• It refers to the mode of nutrition in which plants and organisms produce food for themselves from simple substances.
• Heterotrophic nutrition (heteros = other):;
• It refers to the mode of nutrition in which plants and organisms obtain their food from other sources.
• Heterotrophic nutrition can be one of three types – holozoic, saprophytic or parasitic.

Explanation:

Cuscuta: 

• Cuscuta (Amarbel) is an ectoparasite with the parasitic mode of nutrition.
• It takes ready-made food from the plant on which it is climbing. The plant on which it climbs is referred to as the host.
• Cuscuta is known as a parasite because it deprives the host of essential nutrients. Thus, they use the parasitic mode of nutrition.

Mushroom: 

• The mode of nutrition in which organisms take in nutrients from dead and decaying matter is called saprotrophic nutrition.
• Such organisms with saprotrophic mode of nutrition are called saprotrophs.
• Mushroom obtains its food through a saprophytic mode of nutrition.

Algae:

• Algae are autotrophic as they contain photosynthesis pigment.
• The mode of nutrition in Algae is known as autotrophic nutrition.
• Algae are self-feeders. Photosynthesis is used by algae to prepare their food. Their primary requirement is sunlight, which allows the algae to produce food.

Amoeba:

• Amoeba is a single-celled microscopic organism found in pond water.
• The mode of nutrition in amoeba is known as holozoic nutrition.
• Amoeba lacks a specialised nutrition organ.
• Its entire process of obtaining food is carried out on the body's surface with the help of pseudopodia.

CONCEPT:

Nature of Reactants and Products in a Chemical Reaction

• A chemical reaction involves transformation of substances into new substance(s).
• Reactants (A and B) can be elements or compounds.
• The product formed (C) is always a pure substance, not a mixture.
• In a reaction of the type A + B → C (single product formation), it represents a combination reaction.
• In such reactions, the product formed is always a compound.

EXPLANATION:

• Given reaction:

A + B → C

• About A and B:
• They can be elements (e.g., H₂ + O₂)
• They can be compounds (e.g., CaO + H₂O)
• They can also be a combination of element and compound
• About product C:
• Only one product is formed
• This indicates formation of a single new substance
• A mixture cannot be represented by a single chemical formula
• Hence, C must be a compound

Therefore, A and B may be elements or compounds, but C is definitely a compound.

Explanation:-

Mirror:

• Spherical mirrors are polished surfaces that act as reflecting materials.
• They are of two kinds convex and concave.
• The concave mirror is converging in nature.
• The convex mirror is diverging in nature.

Lenses:

• Lenses act as both the reflecting surface and a medium of refraction.
• There are two kinds of lenses- concave and convex.
• The concave lens is diverging in nature.
• The convex lens is converging in nature.

Reflection: The phenomenon of bouncing back of visible light when it strikes a plane surface is called reflection.

**Laws of reflection:**​

• The incident ray, the reflected ray and the normal at the point of the incident all lie in the same plane.
• The angle of incident is equal to the angle of reflection.

Refraction: The bending of the light rays when it enters from a denser to rarer or rarer to denser medium is called refraction.

Laws of refraction:

• The incident ray, the refracted ray and the normal at the point of the incident all lie in the same plane.
• The sine of the angle of incident is equal to the sine of the angle of refraction. (snell's law)

Shadow:- It is the area where the light can't reach is called shadow

Explanation:-

Acid:

• The substances which have a sour taste are called acids.
• They turn blue litmus red.
• They easily give away H⁺ ions.
• Examples - HCl, H₂SO₄.

Base:

• The substances which have a bitter taste are called bases.
• They turn red litmus blue.
• They easily give away 0H^- ions.
• Examples - NH₄OH, NaOH.

Salt:

• The substances are formed by the reaction of acids and bases.
• They show no change in the litmus paper test.
• They easily give away H+ ions and OH^- ions.
• Examples - NaCl.

Acid-Base Indicators: The chemicals that are used to determine whether a given sample of element or compound is acidic, basic or neutral are called Acid-Base indicators.

Some natural indicators are -

Household Indicators-

Universal indicators:- Universal indicators are pH indicators that are usually made of different compound solutions which helps to determine the colour and hence gives details about the acidity or basicity of the sample.

Important Points

• Turmeric:- It contains a chemical called curcumin which remains yellow in an acidic or neutral medium and turns red in a basic medium.
• Litmus:-  It is a water-soluble mixture of lichen plants extracts. It is of two types blue litmus paper and red litmus paper.
• China rose:- It is a natural indicator that turns dark pink in acidic solutions.
• Phenolphthalein:- It is an organic compound that acts as an acid-base indicator. It is colourless in weak acids and turns pink in basic solutions.

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.

Example- 2K + CuSO₄  → K₂SO₄ + Cu

Additional Information

Metal reactivity series:

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

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

Example- NaOH + HCl → NaCl + H₂O

Concept:

Spherical mirror:

• A spherical mirror is a mirror whose reflecting surface is part of a hollow sphere of glass.
• It is also called a curved mirror.
• It can converge and diverge the parallel rays of light that fall on them
• A spherical mirror is a part of a hollow sphere in which one plane is raised and the other plane is suppressed.
• There are two types

               i)      Concave mirror 

               ii)      Convex mirror

Concave mirror 

• A concave mirror is called a mirror in which the central part of the reflecting surface is inwards.
• It is also called a converging mirror.
• Rays of light coming parallel to the principal axis of a concave mirror, after reflection meets at a common point on the principal axis. This point is called Focus.
• The focus of the concave mirror is real.

Convex Mirror

• A convex mirror is called that in which the central part of the reflecting surface is outwards.
• It is also called a diverging mirror.
• Rays of light come parallel to the principal axis of a convex mirror, after, diverging. The divergent rays being produced backward meet at a common point on the principal axis.
• The focus of the convex mirror is imaginary.
• Concave and Convex Mirror - Definition, Properties, & Image Formation.

Explanation:

• Focal Length is the distance between the pole and the principal focus.
• So, the focal length of a spherical mirror that is the convex and concave mirror is equal to half of the radius of curvature of the spherical mirror. Thus, the focal length of both the mirror remains the same.
• Therefore, from the above explanation; we can say that the correct answer is both have the same focal length.

Concept:

Sound: 

• It is a form of energy produced by vibration or disturbance that propagates in a medium.

• ​A sound is a form of energy that produces the sensation of hearing in our ears.

• Sound in the air: In gas-like air, the particles are generally far apart so they travel further before they bump into one another.

• There is not much resistance to movement so it doesn’t take much to start a wave, but it won’t travel as fast.

• Sound in water: In water, the particles are much closer together, and they can quickly transmit vibrational energy from one particle to the next.

• This means that the sound wave travels over four times faster than it would in the air, but it takes a lot of energy to start the vibration.

• Sound in solids: In a solid, the particles are closer together so the wave travels faster than it does in either liquid or air.

EXPLANATION:

• When a source of sound vibrates, it creates a disturbance in the medium.
• The particles of the medium vibrate in their mean position to transfer this disturbance.
• So, the particles move forward and backward about their mean position, creating regions of compression and rarefaction.
• Hence, a sound wave travels in a series of compression and rarefactions.
• Due to the nature of the transfer of sound energy, sound always requires a medium to propagate.
• 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 the light is an example of transverse waves.
• The audible range of sound for a human is 20Hz to 20000Hz.
• Speed of sound in Solid > Liquid > Gas

Confusion Points

• The pitch of a sound depends on the frequency while the loudness of a sound depends on the amplitude of sound waves.

Concept :

• The Moon is the only satellite of our planet with a size nearly greater than our planet.
• It is a dry celestial body that has no atmosphere.
• So there is no air, and hence no wind on the Moon.
• We can see only one side of the moon from the Earth as the Moon's rotation is equal to its revolution.

Explanation :

• The moon is the earth's only natural satellite and the fifth largest moon in the solar system.
• When the moon appears as a full disc, the whole side facing us gets lit up and is called Full Moon.
• When the Moon is on the opposite side of the Earth from the Sun, the bright side of the Moon is facing towards the Earth, and this is known as full moon day.
• The full moon is the lunar phase when the moon appears fully illuminated from the earth's surface.
• This occurs when the earth is located between the sun and the moon.

Additional Information

• The moon's distance from earth is about 240,000 miles ( 385,000 Km).
• The moon has a very thin atmosphere called an exosphere.
• Its surface is crated and pitted from a comet and has asteroid impressions.
• NASA currently has three robotic spacecraft exploring the moon.

        1) Lunar Reconnaissance orbiter

        2) ARTEMIS

        3) New ARTEMIS 

• It has no rings
• It is the only celestial body beyond earth so far visited by human beings.

Concept:-

Electrical circuits:  It is a network of interconnections of electrical components like a bulb, wire, switch, etc.

Short circuit:  It is a disturbance in the electric appliance which causes a fire, breakdown or crash of the circuit. A fuse is a device that can be used to avoid short circuits.

Properties of water:

• Water is a universal solvent.
• It shows solubility with most of the substances.
• Pure water is a bad conductor of electricity.
• Saline water is a good conductor of electricity.
• Water contains charged ions and impurities in it makes it a good conductor.

Explanation:

• As domestic water is a good conductor of electricity, so water can not be used to extinguish fire caused by short circuit of an electrical appliance.
• Because there is a chance of electrical shock.
• In case of fires that involve electrical equipment and inflammable materials, carbon dioxide (CO₂) is used as an extinguisher.
• Water is used to lower the burning point of the materials.

So, Assertion (A) is false and Reason (R) is correct.

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:

Statement S1 is true.

• A soil with high percolation rate has low water holding capacity. (True)
• The particles of sand are quite large. Because they cannot fit close together, there are large gaps between them. These areas are surrounded by air. The sand is said to be well aerated. Water can quickly drain through the gaps between the sand particles. Hence, sandy soils are light, well-aerated, and relatively dry.

Statement S2 is false.

• A soil with high percolation rate has low aeration. (False)
• Clay particles are much smaller, they pack together tightly, leaving little space for air.
• Water can be held in the tiny gaps between the particles of clay, unlike sandy soil.
• Clay has the ability to hold both nutrients and water that plants can use.
• It results in very small pore spaces, which results in poor aeration and water drainage.
• Hence, clayey soils have less air. They are heavier than sandy soils because they hold more water.