CTET Paper 2 Maths & Science 7th Jan 2022 (English-Hindi) (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 the development

Key Points

• The development follows a definite and predictable pattern: It follows a definite and predictable pattern. There are orderly patterns of physical, motor, intellectual and speech development. Development is governed by certain laws: Cephalocaudal Law and Proximodistal Law.
• ​Cephalocaudal: Development of the upper portions of the body precedes the development of the lower portions. The Cephalocaudal tendency exhibits that the development proceeds in the longitudinal direction. This is known as the 'cephalocaudal' or "head to toe" sequence. 
• That is the reason why the child first gains control overhead before she/he starts walking.
• Hence we can say that the cephalocaudal principle suggests that the pattern of the growth begins with heads and upper body parts and then proceeds to the rest of the body.

Important Points

• Proximodistal: The development moves from the centerline of the body outward towards the distant or peripheral parts referred to as 'proximodistal' or 'near to far'.
• The middle part of the body develops quicker than the outer part of the body.​
• Principle of Integration: The principle of Integration refers to the integration of various aspects of development like physical, mental, emotional, social and moral.

Culture: Culture is defined as the "Culture is a set of rules or standards that, when acted upon by the members of a society, produce behavior that falls within a range of variance the members consider proper and acceptable."

Key Points Characteristics and effects of culture:

• Culture differs according to place, time, community, and race and this is natural.
• Everyone's life is influenced by the culture that surrounds them and adopts it as the same it is.
• Culture can never be the result of any single person's initiative or endeavor nor can it be the consequence of any particular incident at any particular time.
• It can be different from place to place, from conditions, language, traditions, etc.
• childhood is the age in which children experience the difference between cultures, and also get how is the diverse culture make their life different from one another.
• Thus by all these references, we can consider that the childhood is the age the at which girls have menarche, and people, community, and areas have different cultures, so it is possible that in childhood when a girl have menarche it can be celebrated or not as per the culture of the society.

Important Points Childhood refers to the period of the human lifespan, ranging from birth to puberty. It consists of many developmental stages. It is from two years to the age of 10 or 12 years. It consists of two stages i.e. Early & Late Childhood.

• Early Childhood:
• 'Early childhood' lies between the age of '2 to 7 years.
• It is also known as the toy age, pre-gang age, curiosity age, exploratory age, etc. It is a very crucial period for the overall development of the child.
• Later childhood: 
• Later childhood is the time period from the age of '7 to 12 years.
• The signs of puberty usually begin to appear in this stage. It is also known as elementary school-age, troublesome age, gang age, play age, etc.

The term ‘development’ refers to qualitative changes in an individual such as changes in personality or other mental and emotional aspects. However, very often growth and development are used interchangeably. The process of development continues even after the individual has attained physical maturity (growth). The individual is continuously changing as he/she interacts with the environment.

Key PointsCharacteristics 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 socio-cultural 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 behavior patterns of school may be called secondary socialization.
• Example: Church, School, Media, books, magazines, etc.

Thus we can say that family is an agency of primary socialization and books is an agent of secondary socialization.

Important Points

• Change in a child by the Primary socialization-
• The identity of the child is formed.
• Primary socialization takes place in infancy and childhood.
• Infancy is the most crucial stage of socialization as the child learns basic behavior patterns at this stage.
• Change in a child by the secondary socialization-
• ​Development of different aspects starts with secondary socialization as Divergent thinking, Creative thinking, etc.
• children learn how to act in a way that is appropriate for the situations they are in.

Additional Information  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.

Jean Piaget was a Swiss psychologist who proposed his theory of cognitive development in 1936. Jean Piaget made a systematic study of cognitive development among children of different age groups and he categorized it into different developmental stages.

Key Points

According to Jean Piaget, the most important characteristics of a teacher are-

• Providing students with appropriate learning experiences and materials that encourage them to think more critically.
• A teacher should be flexible as it enables them to respond to a variety of student abilities, requirements, and interests.
• A teacher should be mobile (walk around) in the classroom as it helps in promoting and maintaining engagement.
• A teacher should act as a facilitator and assess the children's educational preparedness and ensure that he or she is in a setting that meets their needs.

Hence, we conclude that according to Jean Piaget, the most important characteristics of a teacher are flexibility and mobility.

Hint

• As Piaget's theory influences the concept of student-centered learning, the teacher should not be dominant, autocratic, rigid, or authoritative.

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

According to him stages of the cognitive development are-

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

Key PointsConcrete Operational Stage:

• Piaget’s Concrete Operational stage (7–11 years) is when children acquire logical operations that apply to concrete, familiar situations.
• They can perform class-inclusion tasks (understand subsets and supersets) and transitive inferences (if A→B and B→C, then A→C) when the items are tangible or realistic.
• The example uses familiar, concrete categories (toffees, candy, sweetness), so a child in this stage can correctly apply the rule and reach the conclusion.
• The reasoning does not require abstract or hypothetical thinking beyond concrete examples, which is why this stage best fits the skill tested.

Thus, the correct answer is Concrete Operational Stage.

Confusion Points

• Pre-operational stage: Children (2–7 yrs) are good with symbols and language but lack reversible logical operations and struggle with class-inclusion and transitive inference.

Additional Information

• Sensori-motor stage: Infants/toddlers (0–2 yrs) act through sensorimotor exploration and do not perform symbolic logical reasoning.
• Formal operational stage: Adolescents (11+ yrs) can do abstract and hypothetical-deductive reasoning (they can solve this problem), but the task does not require formal-level abstraction — it is already solvable at the concrete operational level.

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

Key Points  According to Vygotsky, there are three main factors that play an important role in the cognitive development of the child and these are- Social interaction, Culture, and Language:

• Social interaction: ​​Children try to interact with people.
• Culture: ​Children adopt the culture by interaction.
• Language: Children can easily intimate their primary language through interaction or communication.

Thus we can consider that cultural tool plays an important role in the cognitive development of the learner.

Hint

• According to Piaget's theory of cognitive development, only physical and biological factors can affect the cognitive development of the child there is no involvement of society and culture in the cognitive development of the child.
• Operant conditioning:- B.F Skinner propounded this theory as a way of learning by means of rewards and punishments.
• Lawrance Kohlberg proposes moral development theory.

Important Points Four Principles of Vygotsky:

• Children construct their own knowledge: It is rightly said that knowledge is not transferred passively, but is personally constructed by the individual. It means that for the transfer of knowledge, some medium is necessary on the basis of which knowledge can be received but every individual has his/her own way of perceiving the things and as per his/her perception or understanding, he/she constructs his/her knowledge
• Acquisition of knowledge cannot take place without social context: It is correct to say that knowledge cannot be acquired without social context as a human being is a social being and he/she lives in society by following certain rules, and norms of the society, and learn or expand his/her knowledge by interacting with the social surroundings.
• Learning is mediated: Mediated learning takes place when there is an interaction between a learner and a person who is more knowledgeable and helps the learners to modify stimuli and change their own cognitive structure. The person can be a parent, adult, grandparent, or peer and is called by Vygotsky a More Knowledgeable Other (MKO).
• Language plays a central role in cognitive development: Language is the means of communication and socialization. With the passage of time, it becomes a tool for cognitive development or thinking.

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

Key Points

• According to Lev Vygotsky, cognitive development is dependent on the social interaction among people.
• The student learns through society, social norms, culture, etc.
• children can improve their cognitions, by engaging in group discussions, team works, activities, etc.
• Vygotsky opposes the ideas of Piaget, according to Piaget cognitive development is only dependent on physical and biological abilities, but Vygotsky opposes it and said that cognitive development is dependent on social factors also.
• Thus according to the socio-cultural theory of Lev Vygotsky, social interaction plays an important role in the learning of the children.

Hint

• Operant conditioning:- B.F Skinner propounded this theory as a way of learning by means of rewards and punishments.
• It is a method of learning that employs rewards and punishments for behavior.
• This type of conditioning holds that certain behavior and a consequence, either a reward or punishment, have a connection that brings about learning.

Important Points Vygotsky also proposed three basic needs of students during learning, these are:

• 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.

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.
• 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.
• 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.
• 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.
• Thus we can say that in the progressive classroom, children should work in both individual and group manner.

Hint

• Learning should not be memorization based, it should always be done in a conceptual manner.
• In progressive education, children should be the center of the classroom, and they should participate in various tasks.
• Assessment of the students is not only done by pen-paper mode, assessment of the students should be formative which can cover the overall abilities and disabilities of the learners.

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.

Key Points Gender role flexibility: The practice of employing behavioral responses based on the requirements of the situation as opposed to what may be considered appropriate for one’s gender identity.

• Gender is not biologically determined at the time of birth, it is developed by society by segregating the works, and cultures, on the basis of the sexes of people.

Gender roles can be flexible among the children if:

• In a classroom, teachers should have to treat boys and girls equally.
• Making the environment of the classroom flexible for all, all as treated as students instead of girls or a boy.
• Teachers should provide equal opportunities to both girls and boys.
• There is no place for particularized activities for girls and some for boys. Everything is for both.
• Thus by all these references, we can consider that (A) is true but (R) is false.

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 5: The Social Contract, Legalistic Orientation:  in terms of general individual rights and standards that have been critically examined and agreed upon by the whole society. Apart from what is constitutional and democratically agreed upon the right is a matter of personal values. The result is based upon a legal point of view but with a Right to Education emphasis upon the possibility of changing the law in terms of consideration of social utility
• In this stage, the laws and rules can be changed.

So by these references, we can consider that social-contract orientation is the stage of Kohlberg's moral development theory in which laws and rules are considered flexible.

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

• Stage-I: The Punishment and Obedience Orientation: The physical consequences of an action determine whether the action is good or bad regardless of the human value or the meaning of these consequences. Avoidance of punishment and deference to power are valued in their own right, not in terms of respect for the underlying moral order.
• Stage-2: Instrumental Relativist Orientation: Right action consists of that which instrumentally satisfies one's own needs and occasionally the needs of others.
• Stage 3: Good boy - Nice Girl Orientation: Good behavior is that which pleases or helps others and is approved by them. Behavior at this stage is frequently judged by intentions - "he means well", becomes important for the first time. One earns approval by being good to others.
• Stage-4 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 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.

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

Key Points

• According to Gardner's theory of multiple intelligence, intelligence is of eight types.
• All the eight types of intelligence belong from different aspects but are interrelated to each other.
• These eight types of intelligence are considered as a set of capabilities that allows individuals to learn in different fields with the help of different intelligence and skill.
• Assessment of the intelligence on the basis of Gardner's theory of multiple intelligence, a teacher should have to use different ways or methods of assessment because all the assessments are related to different fields.
• So we can consider that an individual can learn with the capabilities of different intelligence proposed by Howard Gardner.

Important Points

• Linguistic Intelligence refers to the ability to use language. It is the capacity to use spoken and written words in a skilled way. Individuals with high verbal/linguistic intelligence are very good at using words and language to express themselves, articulate things, and create.
• Logical-mathematical intelligence is the ability to use logical reasoning and mathematical ability. Individuals high in this intelligence have good abstract reasoning, critical thinking, and good in dealing with numbers. This type of intelligence correlates well with the traditional notion of intelligence. Scientists, engineers, physicists, and economists are people with high logical-mathematical intelligence.
• Musical Intelligence is the ability to use rhythms, sounds, and patterns to create, compose and perform music. It involves sensitivity to music, and the ability to recognize and manipulate musical patterns. People with high musical intelligence are likely to be singers.
• Bodily-kinesthetic intelligence is the ability to use and control one’s body movements and actions. Dancers and sports persons are usually high in such intelligence.
• Spatial Intelligence is the capacity to perceive, understand and use spatial and visual information effectively. Such people are good at spatial orientation, forming visual images and patterns.
• Interpersonal Intelligence refers to the ability to understand others and social interactions. They can understand the emotions and the perspectives of others and relate well to others. They can establish good interpersonal relationships with others. They have good and effective communication skills.
• Intrapersonal Intelligence is the ability to understand oneself and know one’s thoughts, emotions, feelings, motives, and desires, and how these influence their behavior.
• Naturalistic Intelligence is the ability to recognize and understand the various patterns in nature. It includes sensitivity to nature with all its features including flora, fauna, and biodiversity. Gardner has added this eighth type of intelligence to his original seven bits of intelligence.

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

National Education Policy 2020-

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

Key Points Some important fundamental principles of the NEP 2020 are- 

• Full equity and inclusion as the cornerstone of all educational decisions to ensure that all students are able to thrive in the education system.
• It includes the overall development of the leader, it covers all three aspects as Cognitive domain, affective domain, and psychomotor domain.
• Emphasis on conceptual understanding rather than rote learning and learning-for-exams.
• Promoting self-assessment and the peer assessment done by the student in the classroom.
• Reduction in curriculum content and learning should be done by direct involvement in the activities of the learners.
• 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 is conceptual which is given by involving the students in experiments, and hands-on activities related to the concept.
• 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.
• Thus we can consider that holistic development, experimental learning, reduction in curriculum content, and multilingualism are the main features of the NEP 2020.

The analysis is the process of breaking down the subject matter into smaller parts to better understand the concept.

Key Points

Hence, we conclude that an example of a question that promotes analysis is what can you infer from the depiction of men and women in media after watching advertisements.

Assessment serves to promote learning by reinforcing the efficacy of teaching-learning when teachers can customize their teaching plans through relevant information on students’ interests, abilities, and learning progress with constant involvement and input from students.

Key Points There are three major purposes of assessment, which include ‘Assessment for Learning’, ‘Assessment as Learning’, and ‘Assessment of Learning’.

 Assessment for Learning:

• It occurs during, and after, the teaching-learning process as it has its primary focus on the ongoing improvement of learning for all students.
• It is also known as Assessment for Learning, used to evaluate student learning progress and achievement.
• It helps teachers to identify problem-facing areas and to understand the learning needs of students to ensure their academic growth.
• It also helps students to actively think about where they are, where they are going, and how to get there.
• 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 conclude that assessment for learning consists of (i) (iii) (iv) points given in the question.

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 a learning provides a variety of opportunities for the student to reflect on his/her learning through the processes of meta-cognition. This can be facilitated through brainstorming, group discussion, collaborative learning situations, and through peer and self-assessment.
• As a teacher, the best thing that you can do is to convince your students for self-assessment and peer assessment which in turn help them to use assessment as learning.

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 Basic Principles of Inclusive Education:

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

Thus by all these references, we can conclude that respect for individual differences is the principle of inclusive education.

Important 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, and disabled children.
• 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.

Learning disabilities, refer to a heterogeneous group of disorders manifested by significant difficulties in the acquisition and use of listening, speaking, reading, writing, reasoning, or mathematical skills. Major learning disabilities are Dyslexia, Dysgraphia, Dyscalculia, and Dysphasia.

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.
• Problems with non-verbal communication such as body language.
• Trouble in developing and maintaining relationships with others
• Avoiding eye contact with others.
• Under or overreaction to one or more of the five senses: sight, touch, taste, smell, or hearing.
• Thus by all these references, we can consider that autism is a disorder in which learners can not make friends and also do not have good communication skills.

Hint 

• Cerebral palsy includes a group of disorders that affect a person’s ability to maintain balance and posture It is a motor disability mainly occurs in childhood. Palsy means weakness. CP is caused by abnormal brain development.
• Dysgraphia is a type of intellectual disability that impacts the writing abilities of learners.
• ‘Locomotor Disability’ refers to a person’s inability to execute distinctive activities associated with the movement of self and manipulation of objects resulting from affliction of the musculoskeletal and/or nervous system.

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

Key Points  Dysgraphia: Dysgraphia is a disability in which student faces difficulties related to writing, they can not write properly. Example: A student writes a number "0' in place of the alphabet "O".​

A teacher should have to follow these objectives for the students who have a learning disability "dysgraphia"--

• Teachers should respect all the students including the disabled.
• For the student who has a problem in writing, the best way to cater to that student is by the Oral way, so they also do not feel bad.
• Increasing the writing amount make disabled student frustrated also they have to face more problem during writing which makes a negative impact on their learning.
• Teachers should have to use different techniques which helps that students tackle disabilities.
• Learning of the disabled child should be done using TLMs, play-way methods, activities, etc.
• Thus by all these references we can consider that compulsory writing work as assignments, hamper the inclusion of the learner facing learning disability "dysgraphia".

Important Points

• Some Other Common Learning Disabilities in Children:

The term 'hearing handicap' refers to the effect of hearing impairment on a person's day-to-day life. In the absence of appropriate and early intervention, hearing impairment often turns into a handicap, negatively affecting a person's development and functioning in day-to-day life.

Key Points The hearing impairment child can be helped by-

• Providing the child with hearing aids to improve the existing hearing capacity.
• Provides the training to develop speech.
• Teachers can learn some of the techniques that help the child in the classroom.
• The use of expression or non-verbal expressions can also help the students to learn the concept.
• The child will have to be taught lip-reading or sign language and finger-spelling instead of sending him to a special school.

Thus we can consider that the use of less verbal or non-verbal expression can facilitate the learning of the hearing impairment child.

Hint

• Providing audio tapes to the students having a hearing impairment is totally irrelevant because they can not hear, so the tape is not relevant for them.
• A teacher should have to encourage sign language because the child having hearing impairment can learn by sign language.

Inclusion in education means education for all children in school 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 or inclusion of the students in education:

• Inclusive education can help break the cycle of poverty and exclusion.
• It makes the curriculum flexible and easy to access the infrastructure for the students.
• It encourages children to stay with their families and communities.
• The school atmosphere can improve to the benefit of all the learners.
• The practice can help overcome discrimination which is widespread in every sphere of society.
• The evaluation of the students is a comprehensive way, not o a particular ability/disability.
• No segregation of children with learning/physical disabilities, children who are socially, economically, culturally, marginalized children, gifted, creative, and linguistically disadvantaged.
• Students actively participate in group activities, tasks, and hands-on experiences, so that they learn the concept conceptually.
• The education system will make suitable modifications to suit the needs of children.
• Students are never made to feel inadequate as curricular and co-curricular activities are modified to the requirement of specific.
• All the required support will be made available to the students in the regular classroom.

Thus by all these references, we can say that actively participating in hands-on activities is the main characteristic of inclusive education.

Hint

• Auditory: Assessment based on written work- Assessment based on writing work, should not be supported by the teacher because it is not an active way of learning.
• Visual: Content delivered mainly through lectures- Teachers should not deliver the lectures, they should teach the concept through hands-on activities, by experiments, etc.
• Kinesthetic: Expect passive listening- Active listening is a part of inclusive education, students should have to learn actively, which helps them to make concepts clearly.

Learning is primarily a social process and participation in the social life of the school is central to the learning process. Social participation is the main activity through which learning occurs. 

• Participation in the social process begins early when parents interact with their children. Through these interactions, children acquire the behaviors that enable them to become effective members of society.​

Key Points The characteristics of the socio-cultural classroom as-

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

Thus the children of fruit and vegetable seller see many times and listen to the addition of numbers orally by their parents in the shop, thus this experience can help them to learn the addition faster than their peers.

Hint

• The curriculum should be contextualized, it gives a proper way to the students to learn the concept.
• The curriculum should not be centralized or standardized, it should be flexible so that a student can learn as per their needs.

Important Points  In a socio-cultural classroom, a teacher should:

• Adopt a culturally-responsive pedagogy in her class giving primacy to children's socio-cultural contexts as it is based on the idea that every student brings unique cultural strengths to the classroom.
• Recognizing and nurturing those strengths not only encourages success but also promotes an open-minded, supportive environment that celebrates cultural differences.
• Consider the needs and interests of all the students individually, so that they can learn by their capabilities and capacities.
• Schools need to follow a flexible curriculum and individual differences should be considered in the classroom. Every individual differs from each other and has a different learning pace so, the curriculum should be organized and made flexible as per the needs and requirements of the individual.

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 Some important objectives of learning in the classroom:

• Learning is a lifelong process so it should be given to the students based on concepts.
• The curriculum should be designed by the teachers as per the needs and interests of the students.
• Students learn by interaction more than by textbooks, so the environment of the classroom should be socially constructivist.
• Students should be the center of the classroom so that everything in the classroom is done with the reference to students' capabilities.
• The nature of the classroom should be child-centered instead of teacher-centered.
• Various methods of teaching should be taken so that students can learn conceptually.
• The teacher should have to respects all the students and also pay attention to the needs of every individual.
• Learning and knowledge are constructed as well as transmitted so that the nature of the classroom should be collaborative. learners can construct their knowledge through reception.
• Learning should be of diverse nature, teachers should promote students of different cultures and environments to learn under the same roof.

Thus by all these references, we can consider that children are the center of the class and they can construct their knowledge through reception, Hence Both (A) and (R) are false.

<br>

Important Points Social-constructivist classroom gives primacy to:

• peer tutoring.
• group activity.
• Challenging environment.
• Emphasis on students to think divergently and critically.
• cooperative learning among the students.

Culture: Culture is defined as the "Culture is a set of rules or standards that, when acted upon by the members of a society, produce behavior that falls within a range of variance the members consider proper and acceptable."

Key Points Benefits of cultural differences of the children in the classroom:

• There is diversity in the classroom by having different cultures, which follow the rule of "Unity in diversity".
• The teacher can give examples of the students who can relate to the same culture and tradition while teaching the concepts.
• Children can gain different types of knowledge, such as different types of clothes, festivals, dances in a different cultures,
• Different cultures can facilitate the concept of multilingualism in the school.

Thus by all these references, we can consider that cultural differences can not impact the learning of the students, they can strengthen their learning.

Hint

• Culture can not make a barrier in the process of learning, it facilitates the learning of the students.
• Cultural differences promote unity in diversity in learning, it is relevant to the process of learning.

Important Points  Characteristics and effects of culture:

• Culture differs according to place, time, community, and race and this is natural.
• Everyone's life is influenced by the culture that surrounds them and adopts it as the same it is.
• Culture can never be the result of any single person's initiative or endeavor nor can it be the consequence of any particular incident at any particular time.
• It can be different from place to place, from conditions, language, traditions, etc.
• childhood is the age in which children experience the difference between cultures, and also get how is the diverse culture make their life different from one another.

Constructivism: Constructivism is centered on the idea that human knowledge and learning are actively constructed by the learner, not passively received from the environment. Constructivist views learning as the result of mental construction. It is created or constructed by the experiencing individual. It is not impersonal or absolute.

Key PointsIn a constructivist classroom, however, the materials would be used by the children as an aid for them to explore the world and discover ideas through contexts that they relate to. This alternative was presented as the constructivist view of learning. Two essentials of this model of learning are the active participation of the child and the role of the teacher as a facilitator and encourager.  

• Learners are active participants in constructivist classrooms.
• A constructivist classroom always promotes group work and collaborative and cooperative learning.
• In the constructivist classroom, learning is done in a meaningful and effective manner, students can learn by making a mental image of the concepts.
• Tasks in the constructivist classroom are moderately difficult, which can be done by the involvement of all the learners.
• It doesn't promote rote learning or memorization.
• Learners in constructivist classrooms, learn by interacting with others.

Thus by all these references, we can conclude that learning is meaningful and effective if the teacher used a constructive approach to the learners.

Important Points

• Behavioristic learning: Behavioristic theories or Behaviorism constitute the traditional theories of Learning. These theories were propounded by Ivan Pavlov and John B. Watson. Behaviorists attribute learning to the association between stimulus and response.
• Decontextualization is the Process of examining or interpreting something that is separate from the context in which it is embedded. "Decontextualization occurs consciously or subconsciously." The content and curriculum should be designed according to the laid principles of inclusive education.

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

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 Student's learning and thinking can be improved by:

• Engaging the students actively in the curriculum.
• Tours and visits should be arranged for the students so that they can learn by observing things.
• The teacher should have to provide ample opportunities to the students to learn and make thinking divergent.
• Teachers should organize different types of activities, and hands-on activities so that students can construct their knowledge, learning, and thinking on their own.
• The teacher should create situations where students are active listeners, and gain knowledge with interests.
• The use of divergent thinking, and delivering thoughts in a classroom should also be encouraged by the teacher.

Hence, by all these references we can conclude that providing hands-on activities promote the learning and thinking of the students.

Hint

• The teacher should encourage the students to think in a different manner.
• Participation of the students in the classroom should be encouraged by the teacher, they should have to provide opportunities to the students to take part in learning.

When teachers provide instruction on concepts in various subjects, they are teaching students who already have some pre-instructional knowledge about the topic. Student knowledge, however, can be erroneous, illogical, or misinformed. These erroneous understandings are termed alternative conceptions or wrong concepts. 

Key Points

Alternative Conceptions:

• These concepts are a normal part of the learning process.
• Through this process, the teacher recognizes that children are capable of thinking and their thinking is different from that of adults.
• They naturally form ideas from our everyday experience, but not all the ideas we develop are correct concerning the most current evidence and scholarship in a given discipline.
• Students have an inherent need for meaning-making, they can develop meaning and concepts through their own experiences whether it is correct or not.
• This helps the students to interpret new experiences through these erroneous understandings for being able to correctly grasp new information.
• The teacher used instructional strategies to be effective in achieving conceptual change and helping students leave their alternative conceptions.

Thus by all these references, we can consider that alternative conceptions of students illustrate that students have an inherent need for meaning-making.

Hint

• Alternative conceptions of the students can be formed of any type either based on social or cultural experiences.
• Alternative conceptions of the students should not be discouraged by the teachers, teacher should have to respect these conceptions.

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 Barriers to problem-solving include: 

• Confirmation Bias- It focuses on when the learner does not follow the problem-solving method. It can result in missing steps or not using them in the correct order. It can also arise when the solver takes the approach to confirming a preconceived solution (perspective and intellectual blocks).
• Mental Set- This comes when the solver relies heavily on the rule of thumb or common sense rather than making efforts to look for the best solution.
• Functional Fixedness – It is about having a narrow mindset. Here the solver assumes the object just has one function and hence doesn’t make use of the object to solve the problem at hand.
• Affective response - It happens when a solver tries to solve a problem at hand by focusing on the previous emotions or take decisions in the heat of the moment.
• Irrelevant information – It happens when a person focuses too much on irrelevant information and hence diverging themselves from the main problem.
• Thus we can say that focusing on functional fixedness can hinder problem-solving techniques in children.

Important Points The teacher promotes problem-solving skills in the student by-

• allowing students to develop and learn at their own pace.
• providing a stress-free stimulating and enabling learning environment.
• promoting articulation of the student's problem-solving methods.
• allowing students to explore, observe and experiment.
• building experiences on students’ previous experiences and learning.

Additional Information 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.

Cognition is the mental processing of information, which is the function of the human mind that allows perceptions to grow into conceptions. When we have control over our own cognitive functions that are termed metacognition.

Key Points Characteristics of Metacognition:

• Metacognition makes students' thoughts divergent and gives them control over their own functionalities.
• A teacher should promote the development of the metacognition of the students through different activities, experiments, and hand-on-performances.
• Metacognitive strategies include Self-correction as it refers to methods used to help students understand the way they learn in other words, it means processes designed for students to 'think' about their 'thinking'.
• It pertains to the student’s capability of setting goals for learning, estimating the success with which the goals are being met, and selecting alternative strategies to meet the goals.
• It deals with the individual's awareness of the self as a knower and processor of information.
• Metacognitive capabilities as a way to access the process and learning. The metacognitive strategies provided teachers with concrete actions and thought processes to reflect upon.
• If a student is able to think about their thinking/way of thinking, it is much more beneficial for their learning, they can improve their learning by changing their thoughts.

Thus we can conclude that metacognition thinking about our own thinking is a key component of our own ability to regulate our own learning processes.

Hint

• Attentional processes: It refers to the process of paying attention to the model to observe to learn.
• Retentional processes: It refers to the process of recalling the learning activities for later use.
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Learning is a continuous life-long process that is not inherited but can begin right from birth by providing constant interaction and stimulation received from the physical, social, and cultural environment and it does not stop till the end.

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

Key Points Characteristics of Meaningful Learning:

• It stresses the ability of the learner to apply what is learned because of the involvement of the learners.
• Meaningful learning is possible only when learners make a deliberate effort to relate new knowledge to the relevant concept they already know.
• It encourages the mastery-oriented goals of the learners so that learner gains mastery of the related concepts.
• It is the active creation of knowledge structures from personal experience.
• This type of learning encourages students to ask questions and the logic behind the concepts.
• It enhances the relationship of the teachers with the students, students and teachers are familiar with each other, and both have equal contributions in the construction of the new concepts.
• Students have been involved directly so meaningful learning is a child-centered method of teaching in which the teacher feels the interest and values of the students.
• Meaningful learning should be enhanced by creating a collaborative learning ethos, by connecting the concepts with the prior knowledge or real-life examples makes the learning effective.
• Meaningful learning is the human mechanism par excellence for acquiring and storing a vast quantity of ideas.

Thus by all these references, we can conclude that Promoting an entity view of ability in students would not be helpful in motivating children for learning meaningfully.

Emotions play an important role in an individual's life. Emotion is a psychological state with four components, a positive or negative subjective experience, bodily arousal, the activation of specific mental processes and stored information, and characteristic overt behavior”.

Key Points Effect of emotions on learning of the students:

• Anxiety is an emotion in which a student suffers problems related to painful discomfort in the mind also retarded the learning of the students, So the curriculum is always designed as per the needs of the students.
• Fear is an emotion that creates high levels of anxiety in a person and causes the loss of courage in a person and makes a negative impact on the learning of the student.
• ​Fear damages the mental and emotional state.
• Fear makes the student's mind mentally retarded, and students' performance slows down by having fear of different types such as fear of failure, etc. So that the parents, as well as teachers, should have to provide teaching as per the interest of the students.
• Sometimes the fear overpowers the students in such a manner that they even commit drastic measures.

Thus by all these references, we can say that fear of failure and anxiety have a negative effect on learning.

Hint

• Anxiety and Fear never facilitate effective learning, it impacts the mind of the students**.**
• Anxiety and fear never motivate students either intrinsically or extrinsically.

Important Points

• ​Fear: Fear is caused by situations that are perceived as physically threatening. The situations that produce fear change with age. During early childhood, we are afraid of strange objects and persons, loss of support, darkness and devils, etc. During adolescence, fears are mostly social in nature.
• Anxiety: Anxiety is a state of painful discomfort in the mind. During anxiety, a vague fear or apprehension occurs. You may feel anxious if you don’t know the exact cause.

Given: 

⇒ $4\frac{3}{8}$+ $\frac{5}{16}$

Concept used: 

LCM : It is the smallest positive integer that is divisible by both a, b.

Calculation: 

⇒ $4\frac{3}{8}$+ $\frac{5}{16}$

⇒ $\frac{35}{8}$ + $\frac{5}{16}$

⇒ ${70 + 5\ \over 16}$

⇒ ${75 \over 16}$

⇒ $4\frac{11}{16}$

∴ $4\frac{11}{16}$ is correct.

Given: 

The given number is 9222 making it a perfect square after subtracting the smallest number.

Concept used: 

Find the perfect square nearest the given number.

Perfect square: It is the product of some integer with itself.

Calculation: 

⇒ Nearest perfect square of 9222 =  9216 = (96)²

The smallest number we subtract to make it a perfect square = 6

⇒ 9222 - 6 = 9216, which is a perfect square of 96.

∴ Option 3 is correct.

Given: 

Numbers are given .

Select the number which is not divisible by 11.

Concept used: 

If the difference of the sum of the digits at odd places and the sum of the digits at even places of the number is 0 or divisible by 11, then the number is divisible by 11.

Calculation: 

Option 1:

⇒ 222222

Sum of the digits at odd places = 2 + 2 + 2 = 6

Sum of the digits at even places = 2 + 2 + 2 = 6

Difference  = 6 - 6 = 0 

∴ The number is divisible by 11. 

Option 2: 

⇒ 333333

⇒ Sum of the digits at odd places = 3 + 3 + 3 = 9

Sum of the digits at even places = 3 + 3 + 3 = 9

Difference  = 9 - 9 = 0 

∴ The number is divisible by 11. 

Option 3: 

⇒ 10111013

Sum of the digits at odd places = 1 + 1 + 1 + 1 = 4

Sum of the digits at even places = 0 + 1 + 0 + 3 = 4

Difference  = 4 - 4 = 0

∴ The number is divisible by 11. 

Option 4: 

⇒ 10011013

Sum of the digits at odd places = 1 + 0 + 1 + 1 = 3

Sum of the digits at even places = 0 + 1 + 0 + 3 = 4

Difference  = 4 - 3 = 1

∴ The number is not divisible by 11. 

∴ Option 4 is correct.

Given:

⇒ $\left( {\frac{{ - 5}}{{55}} \div \frac{2}{{11}}} \right)$

Concept used: 

Reciprocal of a number is defined as the inverse of a value or a number.

Calculation:  

⇒ $\left( {\frac{{ - 5}}{{55}} \div \frac{2}{{11}}} \right)$

⇒ $\left( {\frac{{ - 5}}{{55}} } \right)$ × $\left( {\frac{{ 11}}{{2}} } \right)$

⇒ $\left( {\frac{{ - 1}}{{2}} } \right)$

⇒ Reciprocal of $\left( {\frac{{ - 1}}{{2}} } \right)$ = - 2 

∴ Option 2 is correct.

Given: 

If A, B and C are digits and 

A B

× 3

CAB

Concept used: 

Multiply same place value.

Calculation: 

First we multiply unit place,

B × 3 end with B.

We put different value of B and check which ends with B.

∴ B can be 0 or 5.

For B = 0 

⇒ (A 0) × 3 = C A 0

Here, A × 3 ends with A,

Check for different value of A.

∴ A can be 0 or 5.

For A = 0 and B = 0

⇒ (0 0) × 3 = C 0 0 

∴ This is not possible.

For A = 5 and B = 0 

⇒ (5 0) × 3 = 1 5 0 

This is possible. 

∴ A = 5, B = 0, C = 1 

∴ Option 4 is correct.

Given: 

The value of x is 25 % more than the value of y.

Concept used: 

Change in value % = Change value × 100 / original value 

Calculation: 

Let value of y = 100

Value of x = 125 % of y = 125

Value of y is less than x = 125 - 100 = 25

Value of y less than x in % = 25 × 100 / 125

⇒ 20 % 

∴ Option 1 is correct.

Given: 

⇒ (2 y4 - 15 y2 + y + 15) and (18 y3 + 34 y2 - 50 y + 70)

Concept used: 

Subtract the coefficient of same power variable.

Calculation: 

⇒ (2 y4 - 15 y2 + y + 15) - (18 y3 + 34 y2 - 50 y + 70)

⇒ 2 y ⁴ - 18 y ³ + (-15 - 34) y² + (1 + 50) y + (15 - 70)

⇒ 2 y 4 - 18 y 3+ (- 49) y2 + (51) y + (- 55)

⇒ 2 y 4 - 18 y 3- 49 y2 + 51 y - 55

∴ Option 2 is correct.

Given: 

7x - 1 = 48

Calculation: 

⇒ 7x - 1 = 48

⇒ 7x = 48 + 1

⇒ 7x = 49 

⇒ x = 7 

⇒  2x3 + 3x = 2 (7)³ + 3 (7) 

⇒ 2 (343) + 21

⇒ 686 + 21

⇒ 707

∴ Option 1 is correct.

Given: 

Two algebraic expression are (x - y) and (3x + 5y).

Concept used:

when we multiply the two same variable then power of these two variable will be added .

Calculation: 

⇒ (x - y) and (3x + 5y)

⇒ (x - y) × (3x + 5y) 

⇒ 3x² + 5xy - 3xy - 5y²

⇒ 3x² + 2xy - 5y²

∴ coefficient of x is 2y.

∴ Option 1 is correct.

Given: 

⇒ 15xy - 6x + 5y - 2 

Concept used: 

Taking common.

Calculation: 

⇒ 15xy - 6x + 5y - 2 

⇒ 3x (5y - 2) +1 (5y - 2)

⇒ (5y - 2) (3x + 1)

∴ Option 1 is correct.

Given: 

In a triangle ABC, AB = 12 cm and BC = 15 cm

Concept used: 

When two side are given then third side lies between difference of these two sides and sum of these two sides.

Calculation:

In a triangle ABC, AB = 12 cm and BC = 15 cm

Two side are given, then third side lies between

⇒ 15 - 12 <  AC < 15 + 12

⇒ 3 < AC < 27

∴ Option 1 is correct.

Given: 

Some triangles and quadrilaterals are given.

Find the line of symmetry.

Concept used: 

The line of symmetry can be defined as the axis or imaginary line that passes through the center of the shapes and divide into two identical halves. 

Calculation:

In isosceles triangle,

Only one line of symmetry.

In Kite,

Only one line of symmetry.

In rhombus, 

Two lines of symmetry.

In rectangle, Two line of symmetry.

In scalene triangle,

No any line of symmetry.

In parallelogram,

No any line of symmetry.

∴ Option 4 both have no same line of symmetry.

∴ Option 4 is correct.

Given:

In a triangle PQR,

Side QP is produced to a point S. 

⇒ ∠RPS = 108° and ∠Q = 20°

Concept used:

The sum of angles of a linear pair = 180º

Sum of all angles of triangle = 180º

Calculation: 

In a triangle PQR,

⇒ ∠RPS = 108° and ∠Q = 20°

⇒ ∠RPS + ∠RPQ = 180º ( Linear pair)

⇒ 108º + ∠RPQ = 180º

⇒ ∠RPQ = 72º

⇒ ∠PQR + ∠QRP + ∠RPQ = 180º (angle sum property)

⇒ 20º + ∠QRP + 72º = 180º 

⇒ ∠QRP = 88º

⇒  3∠R + 2∠Q = 3 × 88º + 2 × 20º = 304º

∴ Option 2 is correct.

Given: 

O is a point on a line AB

OC and OD are two rays on the same side of AB such that ray OC lies between rays OA and OD.

⇒ ∠AOC = 3y, ∠COD = 30° and ∠BOD = 5y

Concept used: 

The sum of angles of a linear pair = 180º

Calculation:

⇒ ∠AOC = 3y, ∠COD = 30° and ∠BOD = 5y

⇒ ∠AOC + ∠COD + ∠BOD = 180º ( linear pair)

⇒ 3y + 30º + 5y = 180º

⇒ 8y + 30º = 180º

⇒ 8y = 150º

⇒ 4y = 75º

⇒  4y + 10° = 75º + 10º = 85º

∴ Option 3 is correct.

Given: 

A pentagon prism is given.

Concept used:

Pentagon prism is a prism that has two pentagonal bases like top and bottom and five rectangular sides.

Euler's formula, for any polyhedron,

F + V = E + 2

Calculation: 

In pentagon prism : 

Number of faces = 7 

Number of vertices = 10 

Number of edges = 15 

Option 1: 

F + E - V = 12 

⇒ 7 + 15 - 10 = 12 

Option 1 is correct.

Option 2:

V + E - F = 18 

⇒ 10 + 15 - 7 = 18.

Option 2 is also satisfied.

Option 3: 

⇒ 2V + F - E = 10 

⇒ 20 + 7 - 15 = 12

Which is not satisfied.

Option 3 is false.

Option 4: 

⇒ 2V + 2F - E = 19 

⇒ 20 + 14 - 15 = 19 

Option 4 is correct.

∴ Option 3 is correct.

Given: 

Area of rhombus = 240 cm²

Length of one diagonal = 30 cm

Concept used: 

Area of rhombus = 1 / 2 × P × Q

Where P and Q are diagonals of rhombus.

Diagonals of rhombus are bisect at 90º

Perimeter of rhombus = 4 × side

Calculation: 

Area of rhombus = 240 cm²

⇒ 1 / 2 × P × Q =  240 cm2

⇒  1 / 2 × 30 × Q =  240 cm2

⇒ Q =  16 cm

Side² = (P/2)² + (Q/2)²

Side² = (15)² + (8)²

Side = 17 cm

Perimeter of rhombus = 4 × side

⇒ 4 × 17 cm 

⇒ 68 cm

∴ Option 2 is correct.

Given: 

Length of rectangle = 3 × Breadth

Perimeter of rectangle = 400 m 

Concept used: 

Perimeter of rectangle = 2 × ( L + B)

Calculation: 

Let breadth of rectangle = x 

Length of rectangle = 3x 

Perimeter of rectangle = 400 m 

⇒ 2 × ( L + B) = 400 m

⇒ 2 × ( 3x + x) = 400 m

⇒  2 × (4x) = 400 m

⇒ x = 50 m

Length of rectangle = 3x = 150 m

Breadth of rectangle = 50 m

⇒ (2 × length + 3 × breadth) = (2 × 150 + 3 × 50) 

⇒ 450 m

∴ Option 2 is correct.

Given: 

A cube of side = 8 cm

Small cubes each of side 4 cm are cut.

Concept used: 

Volume of cube = a³

Total surface area of cube = 6 a²

Calculation: 

A cube of side = 8 cm

Small cubes each of side 4 cm are cut.

Volume of 8 cm cube = (8)³ = 512 cm³

Volume of 4 cm cube = (4)³ = 64 cm³

Total number of 4 cm cubes = volume of 8 cm cube / volume of 4 cm cube

⇒ 512 / 64 = 8 cubes

Total surface area of 8 cm cube = 6 (8)² = 384 cm²

Total surface area of 4 cm cube = 6 (4)² = 96 cm²

Total surface area of all small cubes = 8 × 96 cm² = 768 cm²

The difference between the total surface area of all the small cubes and that of the original cube = (768 - 384) cm²

⇒ 384 cm²

∴ Option 2 is correct.

Given: 

The observations are given 15, 21, 6, 18, 25, 13, 20, 9, 12 and 8

Concept used: 

Mean = Sum of all observations / Total number of observations

Median :

Average of n/2^th & n/2 + 1^thterm ; when n is even.

(n + 1)/2^th term  ; when n is odd.

n is number of observations.

Calculation: 

First, arrange the observations in ascending or descending order.

⇒ 6, 8, 9, 12, 13, 15, 18, 20, 21, 25

Here, n is even = 10

Median = (13 + 15)/2 = 14

Mean = (6 + 8 + 9 + 12 + 13 + 15 + 18 + 20 + 21 + 25)/10

Mean = 14.7

Sum of mean and median = 14 + 14.7 = 28.7

Given: 

The letters written on paper slips of the word M A T H E M A T I C S are put in a bag. If one slip is drawn from the bag, without looking at.

Concept used: 

Probability = Number of favorable outcomes / Total outcomes

Calculation: 

The word is, 

M A T H E M A T I C S

Number of outcomes getting a consonant = 7 (M, T, H, M, T, C, S)

Total outcomes = 11

Probability of getting a consonant = 7 / 11

Probability of getting a letter M = 2 / 11

The difference between the probabilities of getting a consonant and a letter M = 7 / 11 - 2 / 11 

⇒ 5 / 11

∴ Option 1 is correct.

The true definition of assessment is not that it only concentrates on giving greats and marks to the students through pen and paper tests but on recognizing the learning difficulties of students and designing the teaching-learning strategies accordingly to help them overcome those learning difficulties and misconceptions. 

Key Points"Assessment techniques in Mathematics is an important factor that contributes to Mathematics anxiety among students" as:

• It is only concentrated on testing and awarding marks to the students accordingly.
• Assessment in Mathematics is done only to test if the student knows or does not know the answer.
• Assessment is done only in the classroom through pen and paper tests.
• Assessment in Mathematics is designed to test the student's capability of arriving at a unique answer using the correct procedures.
• Assessment is focused on testing the memorisation of facts and formulae rather than concept learning.

​Hence,  A, B & D are the correct options.

A mathematical statement is a meaningful composition of words that can be either true or false. Simply, they are known as a statement. A precise mathematical statement is exactly true and correct. 

Key Points"Similar triangles can be formed if two angles are known." is a precise mathematical statement as:

• If two pairs of corresponding angles in a pair of triangles are congruent, then the triangles are similar.
• We know this because if two angle pairs are the same, then the third pair must also be equal.
• When the three angle pairs are all equal, the three pairs of sides must also be in proportion.

Hence "Similar triangles can be formed if two angles are known." is a precise mathematical statement.

 Additional InformationOn the other hand, all the three statements are not precise because:

• The altitude of a triangle is perpendicular to the opposite side. Thus, it forms 90 degrees angle with the opposite side. It can be drawn from any point.
• LCM of two numbers can be calculated by multiplying them only if they are prime numbers.
• Pentagon may also be symmetrical.

The inductive method is one of the teaching methods which is being used for a long time. This method is used in mathematics to form generalizations are rules based on the examples studied before. Here first many examples are studied and all the examples are giving the same result then a generalization or a rule is formed and is followed. 

Key PointsFeatures of the inductive method:

• Hear the approach moves from concrete to abstract.
• The inductive method goes from known to unknown.
• Forming the generalization or formula is the last step in the inductive method.
• The inductive method is more time taking on compared to other methods but once the formula is formed it can be used without any ambiguity.
• In the above example also the teacher insisted the students compare the diameter and radius of various circles and finally form a relation between them.

Hence it is an example of the inductive method. 

Additional Information

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates the impossibility of the event and 1 indicates certainty.

 Key PointsThe statement "I don't know what scores I will get in the exam tomorrow. So probability of my passing the exam is 50%" is showing the MOST conceptual clarity as:

• This statement, although not entirely accurate, demonstrates a basic understanding of probability.
• The student acknowledges the uncertainty of the exam outcome (doesn't know the score) and assigns a middle value (50%) to represent this lack of knowledge.
• While a 50% chance of passing might be an oversimplification, it shows they recognize probability as a tool to express uncertainty.

​Hence the correct statement is "I don't know what scores I will get in the exam tomorrow. So probability of my passing the exam is 50%."

Additional Information

• Statement 1 incorrectly assigns a probability of 0 (certain not to happen) to an uncertain event (rain tomorrow). Probability can range from 0 to 1, with 0 being certain not to happen and 1 being certain to happen.
• Statement 2 completely dismisses the role of probability. While confidence plays a part, there's always some level of uncertainty in any outcome, and probability can help quantify that uncertainty.
• Statement 3 confuses correlation with causation. Just because petrol prices have increased in the past doesn't guarantee a 100% chance of future increases. Probability deals with the likelihood of an event, not a guaranteed outcome.

Fraction is a topic that needs to be explained to the students in their earlier stage of learning mathematics because fractions lay a base for all other topics like ratios and percentages which they are going to study in their higher classes. 

Key PointsThe correct order to be followed by the teacher is:

• First, the teacher has to engage the students with concrete material to represent different fractions because the learning nose from concrete to abstract. When they first realize and familiar is the concept of fractions using concrete objects like cutting a small piece of cake into 4 pieces or cutting fruits into pieces then they can move to an abstract concept.
• After dealing with the concrete objects the next step to be followed by the teacher is representing different fractions using diagrams in various ways for example the teacher can represent a house and in that for rooms and the teacher can pick up to rooms then the fraction can be made like 2/4 which can be relatable to students.
• Symbolically representing fractions on the blackboard should be the last step of the teacher because when the students have familiarized themselves with the concept of fractions they will not have a problem understanding the symbols written on the blackboard.

Hence option one is the correct answer.

According to the National Curriculum Framework (NCF) 2005, the main goal of Mathematics education in schools is the 'mathematization' of a child's thinking. Clarity of thought and pursuing assumptions to logical conclusions are central to the mathematical enterprise. 

Key PointsThe vision of the National Curriculum Framework 2005 for mathematics and its pedagogy:

• Enable students to recognize that mathematics permeates the world around us.
• Make students appreciate the usefulness, power, and beauty of mathematics.
• Make students enjoy mathematics and develop patience and persistence when solving problems.
• NCF considers mathematics as a way of thinking in which students explore various concepts.
• NCF also focuses on engaging every student with a sense of success, while at the same time offering conceptual challenges to the emerging mathematician.

​Hence the statement "Mathematics is a way of thinking" resonates with the vision of the National Curriculum Framework 2005 for mathematics and its pedagogy.

 Additional InformationOn the other hand, computation, creating competition and regular tests can't justify the vision of mathematics pedagogy according to NCF.

Errors committed by the students should be taken as a source of information to identify their misconceptions. Once the student commits an error it is the duty of the teacher to understand the actual misconception of the student and immediately remediate the misconception by developing appropriate teaching strategies. 

Key Points

• In the above example, the student has committed the error as he did not know the actual difference between a variable and a constant.
• Constants are nothing but numbers whose value never changes and variables are the alphabets whose value depends on the constants.
• Here the teacher can explain that 5x is totally different from 5 and addition of constants can be done with constants only.
• So the teacher can explain that first, the student has to add the variables which are 5x and 2x which results in 7x.
• Then the student can add the constants 5 and 6 which results in 11.
• Then the final answer can be obtained as 7x + 11.

Hence explaining the meaning of a variable and how it differs from a constant is the most appropriate step for the teacher to remediate the misconception. 

Additional Information

• On the other hand, revising the terms and putting different values of X doesn't provide perfect remediation to the student to clear his misconception.

A chess board can be used as an important teaching-learning resource for mathematics in various topics because it contains 64 squares of equal dimensions and measurements moreover the colors of the squares will be white and black alternately. 

Key Points

• The concept of fractions can be taught using the chess board because the squares in equal dimensions can be used to explain the concept of numerator and denominator. For example, if 16 squares are taken from the total of 64 squares then the fraction would become 16/64.
• If the chess board is considered to be the whole surface of a square then e square can be taken as 1 cm and by calculating the side of the square the children can get an idea about the area concept.
• Congruence can also be explained using the chess board because all the squares will be congruent to each other just differing in colors. Here the properties of squares can be taken and the theory of congruence can be explained to the students.
• And the other hand the topic of percentage cannot be explained using the chess board because percentage means 100 but the squares on the chess board or less than 100 so children may get confused about the concept.

​Hence Percentage can't be explained using a Chess board.

A geoboard is a mathematical manipulative used to explore basic concepts in plane geometry such as perimeter, area, and the characteristics of triangles and other polygons. It consists of a physical board with a certain number of nails half driven in, around which are wrapped geo bands that are made of rubber. 

Key Points

• A geoboard has many nails attached to apply to the board.
• A rubber band or a thread can be used to build different shapes by rotating the thread or rubber around the nails.
• Many shapes like squares, rectangles, and triangles can be formed by using a geoboard.
• Here the students should themselves be given chance to form the shapes which they know using the geoboard.
• Once they form the shapes they can get familiarized with the various concepts related to the shapes like perimeter and area.
• Hence the concepts of perimeter and area can be taught by using geoboards.

Hence the concepts of area and perimeter can be taught using Geoboards.

​

Additional Information

• On the other hand, the other concepts like volume, tessellations, and symmetry cannot be taught using a geoboard because it is just a plane board with nails attached to it. A container that may be filled with liquid can be a good tool for teaching volume.

The authentic and meaningful tasks should be immediately given after a teacher explains the concepts to the students so that the teacher may get the idea of how far the students have understood the concept and if there is any need to change the teaching strategy used by the teacher currently. 

Key PointsHere the teacher after explaining the concept of the area of a circle can ask the students to buy the right amount of paint for painting a circular table in a school because

• To know the exact amount of paint that will be sufficient for the circular table in the school first students need to calculate the area of the circular table.
• As the top of the table is circular the students first calculate the radius of the circular top.
• Then according to the radius students use the formula for the area of a circle and calculate the area of the circular table in their school.
• Finally, they conclude how much paint can be sufficient to paint the table in a certain area.
• Here application of knowledge in a real situation happens and the children learn through their own experiences.

Hence the teacher asking students to buy the right amount of paint for painting a circular table in the school is an authentic task to assess the students regarding the concept of the area of a circle. 

Additional Information

• On the other hand, directly giving the values to the student and asking them about the area or diameter of a circle or asking them to design a bangle for their sister by using a wire does not access the concept of the area of a circle.

Concept:

Kharif Crops:

• The sowing of Kharif crops takes place at the starting of the southwest monsoon from June to July, and the crop is harvested from September to October.
• Examples- Rice, maize, jawar, pulses, etc.

Explanation:

• Paddy and maize are a set of Kharif crops as these are the crops of the monsoon season.
• In option 1 wheat, and paddy is rabi crops. Hence, option 1 is an incorrect set.
• In option 2 mustard is a rabi crop. Hence, option 3 is an incorrect set.
• In option 4 peas are rabi crops. Hence, option 4 is an incorrect set.

Thus, the correct set of Kharif crops is Paddy, and Maize.

Additional Information Rabi crops: 

• Rabi crops are the crops of the winter season.
• The sowing of rabi crops takes place at the starting of winter, October to December, and the crop is harvested from March to April.
• Examples- Wheat, potato, gram, mustard, barley, etc,

Zaid Crops:

• These crops are sown in the summer season which includes mainly vegetables.
• Examples - watermelon, cucumber, bitter gourd, etc

Concept:

Disease:

• The disease is defined as any condition which impairs health or interferes with the normal functioning of the body.
• It may be caused by some external agencies such as deficiency of nutrients, worms, viruses, bacteria, etc.

Acquired Diseases:

• Acquired diseases are diseases that develop after birth and are known as acquired diseases.
• These are two types-
• Communicable Diseases
• These diseases are caused by any infectious agents such as bacteria, viruses, etc.
• These diseases are infectious or transmissible and can spread from diseased persons to healthy persons using air, water, food, or by physical contact.
• Examples- Tuberculosis, malaria, covid-19, influenza, etc.
• Non- Communicable Diseases​
• These diseases are neither present at birth nor spread from one person to another.
• These diseases are non-infectious or not transmissible.
• They may be caused by improper functioning of organs, hormonal imbalance
• Examples- hypertension, arthritis, diabetes, anemia, goiter, etc.

Explanation:

Typhoid:

• Typhoid is the most common communicable disease.
• It is caused by the bacteria Salmonella typhi.
• This bacteria is commonly found in the intestine of man.
• The bacteria are spread through water, fecal matter by house flies, etc.
• Symptoms are fever, red grains appear on the stomach.

Measles:

• It is a highly infectious disease in children.
• It is caused by the Rubella virus.
• It spreads through indirect contact or through the air.
• Symptoms are sore throat, white spots appearing in the throat and mouth, etc

Dengue:

• It is a dangerous communicable disease.
• It is caused by the dengue virus.
• It is spread by the mosquito Aedes aegypti.
• Two types:
• Dengue fever
• Dengue hemorrhagic
• Symptoms are high fever, headache, convulsion, etc.

Thus, the X, Y, and Z represent Water, Virus, and Virus respectively.

Additional Information

Key Points

• Congenital diseases- Congenital diseases are caused due to defective development of embryos or defective inheritance.
• Ex- Hemophilia, color blindness, etc.
• Acute diseases occur suddenly and last for a shorter period.
• Chronic diseases develop slowly over time in a body and may last for a lifetime.

Concept:

Thermometer: ​

• A device that measures the temperature is called a thermometer.
• A thermometer is based on the principle of thermal expansion.
• Mercury, liquid metal with high density is used.
• More the heat will be the expansion.
• Mercury thermometers are based on the principle that liquids expand when heated and contract when cooled. So, when the temperature increases, the mercury expands and rises up the tube, and when the temperature decreases its contracts and does the opposite.

Explanation:

• Most metals are good conductors of heat and are solid are room temperature.
• But, mercury is only one in liquid form at room temperature.
• It is used in the thermometer because it has a high coefficient of expansion and expands uniformly when heated.
• Hence, the slightest temperature change is notable when it is used in the thermometer.

Thus, the correct answer is that R₁ and R2 is the correct explanation for A.

Additional Information

 

Important Points 

Conductor:

• The materials which allow heat to pass through them easily are conductors of heat.
• Examples: Aluminum, Iron, and Copper

Insulators:

• The materials which do not allow heat to pass through them easily are poor conductors of heat and are known as insulators.
• Examples: Plastic and wood.

Explanation:

Bacteria:

• Bacteria come under the kingdom Monera.
• They are prokaryotic with cell walls.
• They are unicellular because they consist of a single cell and are prokaryotic.
• Mycoplasma is the smallest living organism.
• They are photosynthetic autotrophic or chemosynthesis autotrophic.
• Based on their shape, bacteria are classified into 4 groups: cocci, Bacillus, Vibrio, and spirilla.

Fungi:

• Fungi are non-green and are heterotrophic.
• They are both unicellular and multicellular because they consist of both single & multiple cells.
• They are saprophytes or parasites or a few are symbiotic as in lichen.
• They are eukaryotes with cell walls containing chitin.

Protozoa:

• Protozoa are heterotrophs and live as predators and parasites.
• They are unicellular because they consist of a single cell.
• There are 4 groups of protozoans:
• Amoeboid protozoans: Example: Amoeba
• Flagellated protozoans: Example: Trypanosoma
• Ciliated protozoans: Example: Paramoecium
• Sporozoans : Example: Plasmodium

Thus, the correct statements are A & B.

Given:

Radii of two metallic balls A & B = ratio 3 ∶1 

Their densities = 1: 3

Concept:

The density of a substance is its mass per unit volume.

Its SI unit is kg per cubic meter.

Mathematically, density = mass/volume

Volume of sphere = (4/3) × π × r³

Calculation:

Let volume of 1st and 2nd balls = V₁ and V₂

And Mass be M₁ and M_2.

 Density = D₁ and D₂

According to question,

D₁/D2  = 1/3

D1/D2  = (M1 V2)/(M2V1)

1/3 = (M1 × 1)/(M2 × 27)

M1/M2 = 9/1

∴ The ratio of the mass of balls A and B is 9:1.

Concept:

• The boiling point refers to the temperature at which the vapor pressure of a liquid equals the pressure surrounding the liquid and the liquid changes into a vapor.
• The boiling point of water varies with the air pressure.
• The boiling point of a liquid at high pressure is higher than the boiling point of the same liquid at atmospheric pressure.

Explanation:

• The normal boiling point of water is 100 degrees Celcius.
• The boiling point of the water is affected by its purity.
• So, the impurities in the water increase the boiling point because impurities decrease the water molecules during boiling.
• The temperature at which vapor pressure equals normal sea-level air pressure is known as the normal boiling point.
• The boiling point of water at sea level is 100^oC.
• Water boils at 212^oF at sea level.
• At low pressure and high altitude, the boiling point is low due to the decrease in atmospheric pressure.
• From 100^oC it may decreases to 93^oC to 96^oC.

Thus, the correct answer is only C.

Concept:

• Metals are the elements that conduct electricity and heat and are malleable and ductile.
• But all metals are not malleable and ductile. Exception, mercury is malleable and not ductile.
• The property which allows the metals to be hammered into thin sheets is called malleable.

Explanation:

• Aluminum is malleable, soft and does not react with food items, so it is used to wrap food items.
• Aluminum metals can be beaten with a hammer to form very thin sheets called foils.
• So, aluminum foils are used for packing or wrapping food items like chocolates, biscuits, medicines, cigarettes, etc.

Therefore, the correct answer is that it is highly malleable. 

Key Points

• Silver, gold, and copper are also highly malleable.
• Copper sheets are used to make utensils and other containers.
• Iron is also quite malleable and iron sheets are used to make boxes, buckets, drums, etc.
• The property which allows the metals to be drawn into the thin wires is called ductility.

Concept:

• Nitrogen is very essential for the substance of life. It is present in approximately 78% of the earth’s atmosphere.
• Nitrogen fixation needs a strong reducing agent and energy in the form of ATP.
• N2 fixation is accomplished with the help of nitrogen-fixing microbes mainly Rhizobium.
• The enzyme nitrogenase which plays an important role in biological N₂ fixation is very insensitive.

Explanation:

• Some living organisms (only prokaryotes) can utilize the nitrogen in the form of N2 available abundantly in the air.
• So, the plants cannot use atmospheric nitrogen directly.
• Thus, the reduction of nitrogen into ammonia by a living organism is called biological nitrogen fixation.
• Ammonia produced following N2 fixation is incorporated into amino acids as the amino group.
• After that, ammonia is 1st oxidized to nitrite by the bacteria Nitrosomonas.
• The nitrite is further oxidized to nitrate with the help of the bacteria Nitrobacter.
• The nitrate thus formed is absorbed by the plant.
• But some of the plants in association with N2 fixing bacteria, especially in the roots of legumes can fix this atmospheric nitrogen into biologically usable forms.
• All 3 other options are the steps involved in the process of the nitrogen cycle.

Therefore**, the correct option is the conversion of ammonia into nitrites and then into nitrates.** 

Additional Information

Concept:

Average Speed:

• Average speed refers to the total distance traveled by the object in a particular time interval.
• SI unit is meter per second (m/s).
• Mathematically, Average speed = Total distance covered\ total time taken

Calculation:

Given,

Total distance travelled by car = 6092km - 5812km = 280km

Total time taken =  5 hrs 20 mins = 5 + 20\60 = 5+ 0.33 = 5.33 hrs

We know that,

Average speed = Total distance covered\ total time taken 

Average speed = 280km \ 5.33 hrs

Average speed = 52.5 km/h

Therefore, the average speed is 52.5 km/h.

Explanation:

• The gastric juice contains three substances that are HCl, pepsin, and mucous.
• If an excess of the HCl is secreted in our stomach due to overeating caused acidity.
• So, the milk of magnesia consists of magnesium hydroxide which acts as an antacid.
• This antacid which is the milk of magnesia reacts with excess hydrochloric acid in the stomach and neutralizes it. This is an example of a neutralization reaction.
• This gives relief to the person suffering from acidity.
• The chemical reaction takes place in the stomach
• Mg(OH)₂ + 2 HCl → MgCl₂ +H₂O
• In the above reaction, we can also see that two compounds react by an exchange of ions to form new compounds. Hence, it is also an example of a double displacement reaction.

Thus, the correct answer is both double displacement and neutralization reaction.

Additional Information 

• Mucous is a gel barrier secreted by epithelial cells and glandular cells in the stomach wall.
• Thus, the mucous protects the inner lining of the stomach from hydrochloric acid.
• HCl converts the medium of food from alkali to acidic which also enables pepsin to do its work.
• Pepsin helps in breaking down the digestion of protein in the stomach.

Key Points

Double Displacement Reaction:

• The reaction in which two compounds react by an exchange of ions to form new compounds is called a double displacement reaction.
• Examples: BaCl2 + Na2SO4  →   BaSO4 + 2Nacl

Neutralization Reaction:

• The chemical reaction is in which an acid and a base react together to form salt and water as a product.
• Example: HCl + NaOH  →   NaCl + H2O

Explanation:

• Images are 2 types:
• Real imagesd
• Virtual image
• The image that cannot be obtained on the screen is a virtual image while real images are formed on the screen.
• The virtual image can not be obtained on the screen as the image formed is from the light rays that do not meet but appear to meet when they are produced backward.
• The formed image is always erect.
• When the light rays diverge but project imaginary extensions that converge to a focal length, the image is virtual.

Thus, we can say that R₁ and R2 both are correct but R₁ provide correct explanation for A.

Additional InformationDifferentiate between real and virtual image:

Concept:

• An ideal simple pendulum consists of a heavy point mass body suspended by a weightless, inextensible, and perfectly flexed supportable string from rigid support about which it is free to oscillate.
• Mathematically, the time period of swing of a pendulum,
• ​T = 2π√l\g

Calculation: 

• For a simple pendulum, the time period of the simple pendulum and acceleration depends on the length of the string due to gravity,
• ​T = 2π√l\g
• When its length is increased four times, then the time period of the simple pendulum
• ​​T'= 2π√l\g = 2π√4l\g = 2T

Thus, the time period of a simple pendulum becomes twice. if its length is increased four times.

Concept:

• The fusion of male and female gametes forms a zygote is known as fertilization.
• Humans are viviparous and reproduce sexually.
• Fertilization is internal in humans
• Fertilization takes place in the junction region of the ampulla.
• Male and female gametes are haploid.
• A zygote is a diploid.

Explanation:

• The X and Y are also known as sex chromosomes.
• It determines the biological sex of individuals.
• Female contains XX chromosome while male contain XY chromosome.
• The presence of the X or Y chromosome in the sperm determined the sex of the zygote.
• During fertilization, if the zygote inherits an X chromosome from the father then the zygote will be female.
• If the zygote inherits a Y chromosome from the father, then the zygote will be male.

Therefore, the correct answer is the sperm had one Y chromosome.

Concept:

Respiration:

• Respiration is a biochemical process.
• The process of respiration involves taking oxygen into the cells, using it for releasing energy by burning food, and eliminating the carbon dioxide, and water from the body.
• The process of respiration which releases energy takes place inside the cells of the body. So, it is also called cellular respiration.

Types of respiration:

• Aerobic respiration is the respiration that takes place with oxygen.
• It is a continuous process that takes place within the cells of animals and plants.
• C₆H₁₂O₆ + 6O_{2  →}  6CO₂ + 6H₂O + Energy (ATP)
• Anaerobic respiration is the respiration that takes place without oxygen.
• ​In this respiration, microorganism like yeast breaks down glucose into ethyl alcohol, and carbon dioxide and release energy.
• C₆H₁₂O₆  →  2(C₂H₅OH)   2CO₂ + Energy (ATP)

Explanation:

• Anaerobic respiration takes place in our muscles during physical exercise when oxygen gets used up faster in the muscle cell than can be supplied by the blood.
• When the anaerobic respiration takes place in human muscles or animal muscles, then glucose is converted into lactic acid with the release of a small amount of energy.

Thus, the correct answer is Lactic acid.

Concept:

• Corrosion refers to the eating up of metals by the action of air, moisture, or a chemical on their surface.
• The reaction of iron and oxygen forms an iron oxide which is a reddish-brown oxide.
• This is called Rust or corrosion of iron metal.
• This reaction happens only in presence of oxygen and moisture.
• The presence of impurities like Moisture, Acid, salt, Temperature, Presence of acid, etc. is some factors that affect corrosion.

Explanation:

• When the iron nail gets rusted, the weight of the nail increases.
• It is because the layer of iron oxide is formed on the surface of the iron nail.
• The iron oxide layer is adding oxygen and hydrogen to the nail.
• Here is the chemical reaction of Rust:-
• Fe2+ + 3O2 → 2Fe2O3
• Fe2O3 + xH2O → Fe2O3. xH2O (rust)

Thus, the correct answer is that It increases.

Important Points 

Corrosion can be protected using the following methods-

• Electroplating
• Cathodic Protection
• Galvanization
• Painting and Greasing
• Using corrosion inhibitor

​Different Types of corrosion are-

1. General Corrosion- an overall attack on the surface without distinguishing anodic and cathodic areas.
2. Galvanic Corrosion- When two metals are connected to an electrode, here anodic material will corrode.
3. Pitting Corrosion- is the localized corrosion of a metal surface confined to a point or small area, that takes the form of cavities.
4. Crevice Corrosion- takes place in confined liquid-filled slots.
5. Intergranular Corrosion- occurs between grain boundaries inside a metal.
6. Selective corrosion- occurs when alloying elements are not uniformly distributed.
7. Cavitation Corrosion- occurs when vapor bubbles are formed due to low pressure.

Concept:

Indicators:

• Indicators are chemical or natural substances that are used to test whether a substance is acidic or basic in nature.
• Examples of Indicators of acid and base are:
• Litmus paper
• Methyl orange
• Phenolphthalein.​

Litmus solution:

• Litmus is also a natural acid-base indicator.
• It is obtained from plant lichens.
• Litmus solution is a purple dye.

Explanation:

• Metals react with oxygen to form metallic oxides and these metallic oxides are basic in nature.
• So, when magnesium burns in the air it combines with the oxygen of the air to form magnesium oxide.
• 2Mg + O₂ → 2MgO
• Then, magnesium oxide dissolves in water to form a magnesium hydroxide solution that is alkaline in nature.
• This magnesium hydroxide turns red litmus to blue litmus which shows its alkaline nature.
• While Sulphur and carbon form oxides as SO₂ and CO₂ gas respectively which shows acidic properties. Hence, they will turn blue to red litmus.
• Nitrogen is neutral gas. Hence, it does not show any change with litmus & does not change the color of the litmus.

Thus, the correct answer is magnesium.

Additional Information

Acids and bases: 

Concept:

• In asexual reproduction, a single individual is capable of producing offspring.
• The offspring that are produced are not only identical to one another but the exact copies of their parents.
• Clone is also used which describe morphologically and genetically similar individuals.
• Asexual reproduction takes place by 5 different methods:
• ​Fission
• Budding
• Spore formation
• Regeneration
• Vegetative propagation

Explanation:

• In binary fission, the parent organism splits to form two new organisms.
• It is an asexual method of reproduction.
• When the simple animals like Amoeba and paramecium cells have reached their maximum size of the growth, then first the nucleus of the amoeba & paramecium lengthens and divides into 2 parts.
• ​After that their cytoplasm divides into 2 parts, one part around each nucleus.
• In this way, one parent of amoeba & paramecium divides, and two smaller new organisms (daughter cells)of amoeba & paramecium come into existence.
• Thus, amoeba & paramecium reproduce by binary fission by dividing into 2 parts.

Additional Information

• Hydra and yeast reproduce by the process of budding is an asexual method of reproduction.
• In budding, a small part of the body of the parent organism grows out as a 'bud' which then detaches and becomes an organism.
• Cockroach reproduces sexually which means cockroach relies on eggs from a female and sperm from a male.
• But female cockroaches can also reproduce through the process of parthenogenesis.
• Parthenogenesis is a form of asexual reproduction in which an egg can develop into an embryo without being fertilized by a sperm.

Concept:

• Every day a lot of changes occur in our surroundings.
• Broadly, all the changes occurring around can be classified into 2 categories:
• Physical changes
• Chemical Changes

Explanation:

A. Not all physical changes are reversible. A physical change involves a change in the physical properties of a substance, but its identity remains the same. While many of these changes can be reversed (like freezing and melting water), not all can. For example, when you cut a piece of paper, it's a physical change that can't be reversed back into the original piece of paper.

Example : An example of a non-reversible physical change could be breaking a glass. Even though no new substances are formed in this process and it's a physical change, it can't be reversed to its original state.

B. Not all chemical changes are irreversible either. A chemical change involves a change in the identity of a substance—a new substance with different properties is formed. While many chemical changes are irreversible under normal conditions (like burning a piece of paper), some can be reversed, often with the input of energy (like the electrolysis of water).

Example: An example of a reversible chemical change is the process of photosynthesis in plants. In the presence of sunlight, plants take in carbon dioxide and water to produce glucose and oxygen. At night, the process of respiration reverses this, as glucose and oxygen are used to produce water and carbon dioxide, effectively reversing the chemical change. Another example is the heating and cooling of bi-metal materials - a chemical reaction that can be reversed.

The correct answer is 4) Neither A nor B.

Note: The official answer of this question is option 3 but according to the question statement the answer will be option 4

Concept:

• A pinhole camera is a simple camera that does not have any lens.
• Light is made to pass through a very small pin size hole which is made light roof by proper covering around it.
• A real and inverted image is formed on the screen.
• There is rectilinear propagation of light which means light travel in a straight line.
• The size of the image may change on the distance of the object from the camera.

Explanation:

• The image formed by a pin-hole camera is real because in a pinhole camera light travels in a straight line.
• We can see in giving the following diagram, that the light from the top of the object after passing through the pinhole and reaching the bottom of the camera screen, and light from the bottom of the object will pass through the pinhole and reach the top of the screen. Thus, the light passes straight through the hole and forms images.
• This will cause the inverted image.

Therefore, the correct answer is that light travels in a straight line.

Additional Information

Designing a pinhole camera

• A pinhole camera can be designed in-home.
• Take two boxes of cardboard such that one can slide into another with no gap in between them.
• The opposite side of each box is cut out.
• On the opposite facet of the larger box, we need to make a small hole in the middle In the smaller box, cut out from the middle square with size 5 cm around.
• Cover this open square in the box with some translucent material like tracing paper.
• Slide the smaller box inside the larger one with the hole, in such a way that the side with the tracing paper is inside.

Important Points Real image is formed when the light actually meets. The virtual image is formed when light appears to meet just like an in-plane mirror.

Concept:

Resistance:

• Resistance is the property of the conductor to oppose the flow of electric current.
• SI unit is the ohm.

Law of Resistance:

• It states that when all the external physical conditions are kept constant, the resistance of the conductor is directly proportional to its length and inversely proportional to its cross-section.
• Mathematically, R = ρ ​l \ A
• Where R is resistance, ρ is resistivity (constant), l is length, and A is a cross-section

Explanation:

We know that, Resistance of wire

R = ρ ​l \ A

Given,

l' = 2l and A'= 2A

Therefore, the new resistance of a wire

R' = ρ ​l' \ A'  = ρ ​2l \2 A = R

Thus, the correct answer is resistance will remain unchanged.

Additional Information

Ohm's Law: 

• It states that when all the external conditions are kept constant, the electric current that passes through the conductor is directly proportional to the potential difference applied across it.
• Varying the resistance of R_h (rheostat) then the formula obtained is:​ 
• V = RI where V is voltage, R is resistance and I is electric current.

An activity should be always followed by the theoretical lecture or knowledge given by the teacher to the students. 

Hint

• Deflating an air-filled balloon using a pin is most aligned with the understanding that air is all around us. On the other hand, analyzing the quality of air, lighting a matchstick, drawing a flowchart, and explaining do not achieve the lesson objective because here the students cannot conclude that air is all around us.

Key Points

• First, a balloon will be taken and inflated with a lot of air in that so that the balloon will bulge to a certain size.
• Here the students are already with an idea that the balloon contains some Air that they have just blown into it.
• After that, a pin will be taken and pierced into the balloon and the balloon gets deflated.
• When the balloon gets deflated immediately the air inside it will be vanished within some microseconds.
• Then the teacher can ask the students where the air which was inside the balloon is gone then automatically they can conclude that air is all around them.

​Hence deflating an air-filled balloon using a pin is most aligned with the understanding that air is all around us.

Concepts of the curriculum are arranged in a pre-defined order where the students go from simple to complex. The depth of the concept increases as they get promoted from one grade to the other. If the flow of concepts is not taught in the pre-defined order then the students have to face problems in understanding some concepts.

 Key PointsThe students of grade 7 are likely to master the following topics in the concept of heat and electricity:

• Symbols of electric components.
• The wires used in making electric fuses and the uses of electric fuses.
• The functioning of an electric bell.
• The role of insulators in thermo flasks.
• The effect of current on a compass needle.

​On the other hand, the role of current in inducing chemical changes will not have been mastered by the students as the topic is above the cognitive level of students it will be introduced in the later stages of their learning.

Hence the role of current in inducing chemical changes will not be mastered by the students who have just entered grade 8.​

The water cycle shows the continuous movement of water within the Earth and atmosphere. It is a complex system that includes many different processes. Liquid water evaporates into water vapor, condenses to form clouds, and precipitates back to earth in the form of rain and snow. 

Key PointsCollecting the steam of boiling water on a plate with an ice cube over it will be most suitable  to introduce the 'water cycle' as:

• The water cycle has many processes like evaporation, condensation, and precipitation.
• Students should understand these processes to understand the concept of the water cycle.
• Boiling water produces steam, to collect the steam a plate will be arranged on the top.
• The steam will go and deposit on the plate in the form of small water droplets.
• When they observe this they understand the various processes in the water cycle.

Hence collecting the steam of boiling water on a plate with an ice cube over it will be most suitable to introduce the 'water cycle'.

Additional InformationOn the other hand, all the other activities will be less suitable because in that activities the students can observe the effect but not the process which they observe in the activity involving collecting steam.

Open-ended questions are the ones that don't have a fixed answer or a fixed method to find out the answer. These types of questions give full freedom to the learner to explore and enhance his thinking capacity. 

Key PointsAdvantages of open-ended questions:

• Enhance creativity and promote divergent thinking.
• Avoid rote memorization as this type of question doesn't have a fixed answer.
• The child can answer comfortably as there is no fixed way to answer.
• Meaningful learning takes place as the child thinks, the analysis then concludes with an answer.
• The question "What are the characteristics of a sprouted seed?" is an example of an open-ended question because here the student has the scope and chance to tell any characteristic of the sprouted seed that he/she knows.

​Hence the question "What are the characteristics of a sprouted seed?" is an example of open-ended.

 Additional Information

On the other hand remaining questions are not open-ended because they have a fixed answer or they are yes or no type questions.

In the deductive method first, a generalization or a rule is family arranged to the students then according to the generalization the examples will be taken. An established formula will be followed by solving the problems according to it. 

Key PointsFeatures of the deductive method:

• Hear the flow goes from complex to simple.
• The approach progresses from abstract to concrete.
• The flow of concepts goes from unknown to known.
• For example, first, a generalization will be formed like all birds have wings then examples will be followed like a crow is also a bird, the eagle is also a bird and pigeon is also a bird.
• Similarly in the above example first the teacher explain the features of animal and plant cells to the students then they were asked to identify a given cell as a plant cell or an animal cell.
• As the generalized features were already presented before students and now they are insisted to identify the cells.

Hence the activity in option two is most appropriate to develop deductive reasoning while teaching the concept of different types of cells. 

Additional Information

• On the other hand, remaining all three options are examples of inductive reasoning as they progress from simple to complex and examples to generalization.