CTET Paper 2 Maths & Science 10th Jan 2022 (English-Hindi) (Previous Year Paper)

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 Points The principle of independence of systems:

• Principle of Differentiation in Rate: Differentiation in the rate indicates that individuals differ in the rate of development. There is a difference in the rate of development in girls and boys like girls grow faster than the boys at the early stage of development.

 Thus we can consider that every individual has a different rate of growth in their body. so that the development follows the principle of independence of system.

Important Points  There are some principles of development, which show the features of development, these are:

• Principle of Continuity: Development follows the principle of continuity which starts with conception and ends with death. It is a never-ending process in life.
• Principle of Individual Differences: It says that every individual is unique in himself/herself as the heredity and environmental factors make him/her different from others.
• Principle of Generality to Specificity:  The development process starts with general responses shown by the child as s/he passes through the later stages s/ he starts exhibiting specific behaviors.
• Principle of Interrelation: The development of an individual is reflected through the balanced interrelation of all the aspects of life. Development in any aspect affects the other aspect also.
• Principle of Interaction: The principle of interaction suggests that an individual is the product of heredity and environment. In other words, the interaction takes place within and outside forces of the child.
• Principle of Integration: The principle of Integration refers to the integration of various aspects of development like physical, mental, emotional, social, and moral.
• Principle of Predictability: Development is predictable i.e. with the help of the uniformity of the pattern and sequence of development, we can predict the behavior to a great extent of a child in one or more aspects in a particular stage of her/his growth and development.
• Principle of Sequentiality: It states that every individual although exhibit difference in change, they follow the same sequence of change.

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 Points Characteristics of development are:

• Development is a continuous process, it occurs throughout life, and the pace of development may be varying at different ages.
• Physical development is sometimes predictable as it follows a similar pattern of development as Cephelocaudal and Proximodistal.
• All domains of development such as the cognitive domain, affective domain, and psychomotor domain are interrelated.
• 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.
• Physical development depends on many factors such as environment, nutrition, physical abilities, disabilities, biological factors, etc, so the pace of development of every individual is different.
• 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 physical development occurs in a sequential manner but the rate of development of individuals is different.

Important Points  There are some principles of development, which show the features of development, these are:

• Principle of Continuity: Development follows the principle of continuity which starts with conception and ends with death. It is a never-ending process in life.
• Principle of Individual Differences: It says that every individual is unique in himself/herself as the heredity and environmental factors make him/her different from others.
• Principle of Generality to Specificity:  The development process starts with general responses shown by the child as s/he passes through the later stages s/ he starts exhibiting specific behaviors.
• Principle of Interrelation: The development of an individual is reflected through the balanced interrelation of all the aspects of life. Development in any aspect affects the other aspect also.
• Principle of Interaction: The principle of interaction suggests that an individual is the product of heredity and environment. In other words, the interaction takes place within and outside forces of the child.
• Principle of Differentiation in Rate: Differentiation in the rate indicates that individuals differ in the rate of development. There is a difference in the rate of development in girls and boys like girls grow faster than the boys at the early stage of development.
• Principle of Integration: The principle of Integration refers to the integration of various aspects of development like physical, mental, emotional, social, and moral.
• Principle of Predictability: Development is predictable i.e. with the help of the uniformity of the pattern and sequence of development, we can predict the behavior to a great extent of a child in one or more aspects in a particular stage of her/his growth and development.
• Principle of Sequentiality: It states that every individual although exhibit difference in change, they follow the same sequence of change.

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 Points Characteristics of development are:

• Development is a continuous process, it occurs throughout life, and the pace of development may be varying at different ages.
• Development is sometimes predictable as it follows a similar pattern of development as Cephelocaudal and Proximodistal.
• All domains of development such as the cognitive, affective, and psychomotor domains are interrelated.
• Development depends on many factors such as environment, nutrition, physical abilities, disabilities, biological factors, etc, so the pace of development of every individual is different.
• Developments depended on both heredity and environment, according to Woodworth development is a product of heredity and environment.
• 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 conclude that the rate of development depends on many factors so the pace of development is different in all individuals.

Important Points There are some principles of development, which show the features of development, these are:

• Principle of Continuity: Development follows the principle of continuity which starts with conception and ends with death. It is a never-ending process in life.
• Principle of Individual Differences: It says that every individual is unique in himself/herself as the heredity and environmental factors make him/her different from others.
• Principle of Generality to Specificity:  The development process starts with general responses shown by the child as s/he passes through the later stages s/ he starts exhibiting specific behaviors.
• Principle of Interrelation: The development of an individual is reflected through the balanced interrelation of all the aspects of life. Development in any aspect affects the other aspect also.
• Principle of Interaction: The principle of interaction suggests that an individual is the product of heredity and environment. In other words, the interaction takes place within and outside forces of the child.
• Principle of Differentiation in Rate: Differentiation in the rate indicates that individuals differ in the rate of development. There is a difference in the rate of development in girls and boys like girls grow faster than the boys at the early stage of development.
• Principle of Integration: The principle of Integration refers to the integration of various aspects of development like physical, mental, emotional, social, and moral.
• Principle of Predictability: Development is predictable i.e. with the help of the uniformity of the pattern and sequence of development, we can predict the behavior to a great extent of a child in one or more aspects in a particular stage of her/his growth and development.
• Principle of Sequentiality: It states that every individual although exhibit difference in change, they follow the same sequence of change.

Socialization is a way of learning in which humans are interacting with friends, family members, teachers, television, smartphone, newspaper, etc. to build their knowledge, learning, and skills. Socialization can be classified into two broad groups:

• Primary socialization
• Secondary socialization.

Key Points 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.

• Schools are one of the major sources of socialization for the learners.
• Learners learn about disciplines, norms, and rules of society, daily life handling, etc, from schools.
• Learners also learn many skills such as vocational, dramatic, and listening from schools.
• Learns are also learn leadership qualities from the school.

Thus we can say that Schools are a secondary source of socialization and learners learns many skills from the school apart from academics.

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.

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.​

Key Points Assimilation: Piaget defined assimilation as the cognitive process of fitting new information into existing cognitive schemas, perceptions, and understanding.

• Example: When a child learns the word for dog, they start to call all four-legged animals dogs.

Thus by the reference to the above-given example, we can conclude that if the child sees a camel for the first time she calls it a 'lumpy horse'. is also an example of Assimilation.

Important Points

• centration is the tendency to focus on one salient aspect of a situation and neglect other, possibly relevant aspects.
• Conservation refers to a logical thinking ability that allows a person to determine that a certain quantity will remain the same despite the adjustment of the container, shape, or apparent size.
• Animism is the ability which the child thinks that inanimate or non-living objects(such as toys, dolls, and teddy bears) have life and feelings and intentions like a person.

Additional Information

• Accommodation: Jean Piaget defined accommodation as the cognitive process of revising existing cognitive schemas, perceptions, and understanding so that new information can be incorporated.
• Object permanence means knowing that an object still exists, even if it is hidden. It requires the ability to form a mental representation of the object.
• Adaptation: Adaptation is one schema that describes how people learn and understand new information.

Cognitive Development Theory- Jean Piaget said that a child's power to reflect and discover the reality of life not only depends on the child's maturity level or on his or her experience but on the interaction of both.

Key Points Jean Piaget made a systematic study of cognitive development among children of different age groups and he categorized it into different developmental stages. These stages are-

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

Formal Operational Stage- According to Jean Piaget, this is a stage for a child who belongs from the age group of 11 years till adolescence. Changes are as-

• Hypothetical- deductive logic begins.
• Divergent/Convergent thinking.
• Creative thinking.

Thus we can conclude that the ability of Hypo-thetico deductive reasoning comes in the formal operational stage of Jean Piaget's cognitive development theory.

Important Point

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 Cultural tools:

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

Thus we can conclude that computers, calculators, and language are called cultural tools according to Lev Vygotsky.

Hint 

• Concepts maps include graphical and diagrammatical representations to illustrate the meaningful relationships of various sub-topics of a concept.

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

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

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.

Thus by all these references, we can say that flexibility and mobility are the main characteristics of the teachers in the classrooms.

Hint

• Didactics is the way of teaching in which a teacher generally gives the information to the child in an organized and systematic manner, controls classroom instruction, and evaluates his performance to give reinforcement.
• Transfer of knowledge from one person to another person to clear the concept and make the learning of the learners a meaningful way.

Additional Information Jean Piaget proposed that humans progress through four developmental stages: the sensorimotor, preoperational, concrete operational, and formal operational periods.

John Dewey, an American philosopher has proposed the concept of 'Progressive Education' which emphasizes that learning takes place only through a 'hands-on' approach so the students must interact with their environment to adapt and learn. 

• A progressive classroom is a part of progressive education that believes in the capability and potential of every child.​

Key Points In Progressive education teachers should:

• Emphasis on learning by doing – hands-on projects, expeditionary learning, experiential learning.
• Provide ample opportunities to the students so that they can understand the concept easily in multiple ways.
• Emphasis Collaborative and cooperative learning.
• De-emphasize textbooks, and emphasize multiple resources.
• Learning as opposed to rote knowledge.
• Give importance to the learner's previous knowledge and experience.
• Make an Integrated curriculum focused on thematic units
• Flexible timetable and seating arrangement.
• Emphasis on lifelong learning and social skills.
• Strong emphasis on problem-solving and critical thinking
• Emphasis on education for social responsibility and democracy.

Thus by all these references, we can conclude that Teachers should provide ample opportunities to the students so that they can learn the lesson conceptually.

Hint

• The curriculum is flexible in Progressive education, so the sitting arrangement is not fixed in the classroom.
• The assessment of the students is done before a, during, and at the end of the year and it is done in a formal way, not to make a judgment by the marks of the students, it is done just to find out the gaps in the learning of the students.
• Material is not only for display it is used to learn concepts by using it to make the understanding.

Lawrence Kohlberg, an American psychologist, has propounded the 'Theory of Moral Development. He has made a systematic study of moral development in his theory that is categorized into 3 levels and 6 stages.

Key Points 

 Stage 3: Good boy - Nice Girl Orientation: Good behavior is that which pleases or helps others and is approved by them. Behavior at this stage is frequently judged by intentions - "he means well", becomes important for the first time. One earns approval by being good to others.

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

Thus by all these references, we can consider that the third stage of moral development theory in which a child maintains the approval of others is also referred as the stage of the golden rule.

Additional Information

• 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 4: The Law and Order Orientation: There is an orientation towards authority, fixed rules, and maintenance of social order. Right behavior consists of doing one's duty, showing respect for established or lawful authority, and maintaining given social order for its own sake.
• Stage 5: The Social Contract, Legalistic Orientation:  in terms of general individual rights and standards that have been critically examined and agreed upon by the whole society. Apart from what is constitutional and democratically agreed upon the right is a matter of personal values. The result is based upon a legal point of view but with a Right to Education emphasis upon the possibility of changing the law in terms of consideration of social utility.
• Stage 6: The Universal Ethical Principle Orientation: Right is defined by the decision of the conscience in accordance with self-chosen ethical principles appealing to logical comprehensiveness, universality, and consistency.

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  Howard Gardner's theory of multiple intelligences proposes that people are not born with all of the intelligence they will ever have. It includes eight types of intelligence.

• Linguistic intelligence
• Logical-Mathematical intelligence
• Musical intelligence
• Bodily-kinaesthetic intelligence
• Interpersonal intelligence
• Intrapersonal intelligence
• Spatial intelligence
• Naturalistic intelligence

Thus, we consider that Howard Gardner argued that several distinct types of intelligence exist. 

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.

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

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

Key Points

• Gender stereotype is the belief that set the limit on the learning of the students and also demotivates them if they are willing to learn some new skills.
• Gender stereotype is a belief of the society that boys have a good command of tools and utensils as compared to the girls, this shows Gender Stereotyping thought.
• It is believed that girls are not much intelligent in mathematics as boys, so boys should have to choose Mathematics and Science as a subject, and girls have to choose languages and arts.

Thus, Gender stereotype is reflected in the perception that girls will do well in languages but will perform poorly in mathematics and science. 

Hint

• Gender equality is when people of all genders have equal rights, responsibilities, and opportunities. Everyone is affected by gender inequality - women, men, trans, and gender diverse people, children, and families.
• Gender equity is the process of being fair to women and men. To ensure fairness, strategies and measures must often be available to compensate for women's historical and social disadvantages that prevent women and men from otherwise operating on a level playing field. Equity leads to equality.

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 According to the concept of inclusive education, diverse learners should provide learning by the teachers by following these ways:

• Teachers should respect their diverse nature, their culture, and their tradition.
• A teacher should encourage diverse learners and promotes unity in diversity in the classroom.
• Teachers should provide ample opportunities to all the students including diverse learners so that they can learn the concepts.
• A teacher should have to use various teacher learning strategies as per the needs of the individuals.
• Teachers should provide the task as per the ability of the diverse learners.

Thus by all these references, we can conclude that understand that all children have the potential to learn and design activities to help them progress at their own pace. 

Important Points Basic Principles of Inclusive Education:

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

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 Characteristics of Assessment:

• It is a narrower concept than evaluation as it is a part of the evaluation.
• It is a process-oriented approach that is used to identify the areas for improvement in the learning process.
• It is used to determine the outcomes (what students have learned), process (the way they learned), and their approach to the learning before, during, or after the program or course.
• It refers to the process of obtaining information about a learner's learning, progress, and achievement.
• It provides feedback on the performances of the students so that they can be improved further.

Hence we can conclude that assessment must be dynamic – to identify the skills that the child possesses and the learning skills that he or she has the potential to achieve.

Additional Information  There are basically three types of assessment:

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

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 Learning can be facilitated by following these methods:

• Teachers should provide ample opportunities to all the students.
• Teachers should make a flexible environment in the classroom.
• Promoting learning by doing  in the classroom
• Makes students feel free so that they can ask questions in the classroom and clear their doubts.
• Organizing different activities related to concepts so that learners can learn through activities.
• Teachers should ask questions during thelearning which captures the attention of the learner also creates cognitive conflicts.
• Promoting Peer learning, discovery learning, and group discussions in the classrooms.

Thus by all these references, we can conclude that Teachers should use questions in the class to create cognitive conflict to facilitate learning.

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 Basic Principles of Inclusive Education:

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

So we can consider that equality is the main characteristic of inclusive education.

Hint

• Stereotyping is a process by which children are socialized into sex roles, and by which adults and children are denied opportunities for more individually varied development.
• Labeling the students and providing them special education is not a perfect way to cure misconceptions, labeling may hurt the feelings of the students, and according to the RTE- 2009,  students of all categories should learn under the same roof, i.e. inclusive education.

Important Points  In Inclusive education the main objectives are- 

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

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

Key Points Cerebral palsy includes a group of disorders that affect a person’s ability to maintain balance and posture It is a motor disability that mainly occurs in childhood.

• Palsy means weakness. CP is caused by abnormal brain development.

Thus we can conclude that cerebral palsy affects an individual's ability to move and maintain balance and posture.

Hint

• 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.
• Dyslexia: It is a Reading disability, which is not due to mental retardation, brain damage, or a lack of intelligence. It is caused by an impairment in the brain’s ability to translate images received from the eyes or ears into understandable language.

Important Points Types of Cerebral Palsy

• Stiff muscles (spasticity)
• Uncontrollable movements (dyskinesia)
• Poor balance and coordination (ataxia)

Causes of Cerebral Palsy

• Brain injury is caused by a lack of oxygen to the brain before, during, or shortly after childbirth
• Brain damage caused by lack of oxygen (hypoxia) can result in motor skills, movement, coordination, muscle tone, and developmental delays.

Learning Disabilities- The disability due to external and internal(Neurological) factors create Physical, Psychological, and Emotional barrier which affects one or more cognitive processes of students while learning

Key Points Teaching Strategies and Intervention for Children with learning disabilities.

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

Thus by all these references, we can conclude that setting a rigid timeline should be avoided by the teacher from the curriculum.

Important Points  Some types of learning disabilities

• Dysgraphia- This is a writing disability, here the child might have problems in his hands where he has difficulties in holding a pen to write, Due to this his handwriting is not good and he is not able to improve it.
• Dyscalculia-  In this case, the learner has the difficulty in solving mathematical equations Here the learner's ability to deal with numbers gets affected.
• Auditory Processing Disorder(ADP)- It is a hearing disability, The learner is not able to process the audio he gets from his ears. They don’t like noises and distinguishing between sound and noise is difficult for them.
• Attention Deficit Hyperactivity Disorder – It is generally called ADHD, Here the learner has a problem paying attention and difficulty controlling the behavior.

The Right to Education Act commonly known as RTE Act 2009 is an act which aims to provide free and compulsory education to all children between the age of 6 to 14 years in India under Article 21A of the Indian Constitution.

Key PointsObjectives of RTE Act 2009:

• Appoint trained teachers for better educational outcomes.
• Improve school infrastructure (if needed) every three years.
• Prohibit private tuition by teachers to equalize educational opportunities to all.
• Reserve 25% seats for children belonging to economically weaker sections in private schools, so that social stratification can be reduced.
• Not to deploy teachers in non-academic work except for census, population elections, and disaster relief duties.
• Establish primary and upper primary schools within the distance of 1km and 3kms respectively from the child's house.

Thus by all these references we can conclude that social stratification can be reduced by the Inclusion of students from economically weaker sections in private schools under the provision of the Right to Education Act (2009).

Gifted Learner, who is naturally blessed with a high degree of general mental ability or talents in a specific sphere of activity and also acquiring knowledge. They can perform at higher levels compared to others of the same age, experience, and environment. Also, they have divergent thinking.

Key PointsCharacteristics of gifted children:- 

• Rapid learners put thoughts together quickly.
• Highly sensitive
• Enjoys solving problems
• Longer attention span
• They work more proficiently by giving them space to work, and  by using their methods.
• Learn all skills quickly
• Excellent memory
• A teacher for gifted children must be flexible.
• Gifted children need recognition.
• The motives of gifted children should be satisfied.

Thus the teacher should have to provide space to gifted learners so they can make their concepts well by using their skills and divergent thoughts.

Hint

• 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.
• ​So by increasing sensory loa,d they face many problems in learning due to disability.
• Dyslexia: It is a Reading disability, which is not due to mental retardation, brain damage, or a lack of intelligence. It is caused by an impairment in the brain’s ability to translate images received from the eyes or ears into understandable language.
• So increasing assignment work makes a negative impact on the learning of the students who face dyslexia.
• Hearing impairment is defined as the inability of an individual to hear sounds appropriately or suitably.
• Learners can not understand anything if movies have no subtitles because they can not hear properly.

Discussions- It is an open-ended, collaborative exchange of ideas between students with the goal of improving their thinking, learning, problem-solving, comprehension, or literary appreciation.

Classroom Discussions play a vital role in shaping or constructing the overall personality of a child. The discussions help the child to not only presents his or her point of view but to get an idea of others' perception as well and this helps in shaping the all-around thinking of a child.

Key Points Teachers should have to follow these ways for having meaningful classroom discussions:

• The environment of the classroom should be flexible.
• All the students and teachers have equal right to deliver their point of view in front of others.
• Rules should be made by the discussion with learners so that rules and norms are flexible for all.
• The classroom environment should be free, there is no rigidity in any context that should be seen in the classroom.
• The topic of the discussion should be changed every time so that learners and teachers develop their skills of thinking in a divergent manner.
• No limitations and prohibitions for the learners while discussing the respected topics.
• No partiality and differences to the learners for giving them the opportunity to take part in the discussion.

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

Important Points Importance of discussion method-

• Students' ability to think and communicate can be developed.
• Leadership quality and ability to articulate oneself can also be improved.
• This method aids in the development of students' creative abilities and attitudes and enthusiasm for learning.
• Classroom conversations can help students achieve higher-level cognitive and affective goals.

Socio-constructivism focuses on the collaborative nature of learning. Knowledge develops from how people interact with each other, their culture, and society at large.

Key Points Characteristics of Socio-constructivist classroom:

• Encourage students to take responsibility for their own learning, and this includes reflecting on their own thinking and learning processes
• Elicit students’ existing ideas, including any alternative conceptions.
• It emphasizes collaboration with others for learning, work, performance, problem-solving, etc.
• students construct knowledge by interacting with each other and the teachers.
• Connect learning with everyday contexts. Where possible, organize courses around problems, of local interest and impact, which have been identified by students.
• It views learners as makers of meaning and creators of knowledge through social interaction.
• The student performs different tasks which helps them to make their thoughts divergent. There is no repetition of the task in socio-constructivist classrooms.
• Rote memorization, learning based on recalling, and repetition are not allowed in a socio-constructivist classroom,
• The classroom should be child-centered, not teacher-centered so that students are allowed to ask questions freely
• It allows learners to foster their own strategy of learning to perform an activity.

Thus we can conclude that the students construct their knowledge by interacting with others and also with society.

Hint

• The learning of the students in socio-constructivist classrooms should be contextualized.
• Learners are the active participants in the classroom, and we can also say that socio-constructivist classrooms are child-centered.
• Assessment in a socio-constructivist classroom is formative and the motive of the assessment to find out the gap in the learning of the learners.

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- 

• Emphasis on conceptual understanding rather than rote learning and learning-for-exams.
• Full equity and inclusion as the cornerstone of all educational decisions to ensure that all students are able to thrive in the education system.
• Classrooms are flexible for learners where learners can decide the path of their learning and also free to choose programs in the classrooms as per their needs and interests.
• Assessment of the students should be done by using different methods, by different activities including role play, portfolios, etc.
• It includes the overall development of the leader, it covers all three aspects as Cognitive domain, affective domain, and psychomotor domain.
• Establishment of the linkage of the concepts with the environment or we can say that the linkage of the school with the home.
• It emphasizes group work as well as individual work, NEP 2020 links the study to the curriculum.
• Promoting multilingualism and the power of language in teaching and learning.
• Creativity and critical thinking encourage logical decision-making and innovation.
• 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.
• Promoting self-assessment and the peer assessment done by the student in the classroom.

Thus we can say that Flexibility should be provided for students to choose their learning trajectories and programs is an important characteristic of NEP 2020.

Hint 

• Using technologies should encourage the learning of the divyang students

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

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

A teacher can improve learning by:

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

Thus by all these references, we can say that new learning should be improved by connecting the concepts with the previous knowledge.

Hint

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

Discussions- It is an open-ended, collaborative exchange of ideas between students with the goal of improving their thinking, learning, problem-solving, comprehension, or literary appreciation.

Classroom Discussions play a vital role in shaping or constructing the overall personality of a child. The discussions help the child to not only presents his or her point of view but to get an idea of others' perception as well and this helps in shaping the all-around thinking of a child.

Key Points Teachers should have to follow these ways to facilitate learning through classroom discussions:

• The environment of the classroom should be flexible.
• All the students and teachers have equal right to deliver their point of view in front of others.
• Rules should be made by the discussion with learners so that rules and norms are flexible for all.
• The classroom environment should be free, there is no rigidity in any context that should be seen in the classroom.
• The teacher should encourage the students to take part in the classroom discussions so that they can learn conceptually.
• The topic of the discussion should be changed every time so that learners and teachers develop their skills of thinking in a divergent manner.
• Classroom discussion and other collaborative activities facilitate the learning of the students, students learn much by interacting with their peers and others.
• No limitations and prohibitions for the learners while discussing the respected topics.
• No partiality and differences to the learners for giving them the opportunity to take part in the discussion.

Thus we can say that a teacher should encourage students to participate in classroom discussions and other collaborative activities. 

Important Points

• The teacher should not discourage the students for learning, they should provide ample opportunities to all the learners so that they can learn conceptually.

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.
• Students can also improve their learning through their own activities by analyzing them also they can learn through social interaction.
• by providing ample opportunities to the students to learn and make thinking divergent.
• By organizing different types of activities, and hands-on activities for the learners, 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.

Thus we can say that students can learn through their own activities in the world including social interactions.

Hint 

• Learners should be the active receiver of the information.
• The learner can not learn in the fearful environment, they should have provide freely environment to expend their 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 conceptions of the learners are based on their experiences gained by the engagement with society and learning through their knowledge.
• The teacher used instructional strategies to be effective in achieving conceptual change and helping students leave their alternative conceptions.

Thus we can say that Children are illogical, unintelligent, and do not possess the capacity for meaning-making is not correct in the context of alternative conceptions of children.

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:

• 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.
• Metacognition makes students' thoughts divergent and gives them control over their own functionalities.
• 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'.
• Metacognitive capabilities are high-order knowledge as a way to access the process and learning. The metacognitive strategies provided teachers with concrete actions and thought processes to reflect upon.
• A teacher should promote the development of the metacognition of the students through different activities, experiments, and hand-on-performances.
• 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.
• It deals with the individual's awareness of the self as a knower and processor of information.

Thus by all these references, we can conclude that Metacognition is the skill in which learner makes their knowledge through their own thinking.

Hint

• Declarative knowledge enables a student to collect facts in memory. It is also called descriptive knowledge which explains the basic knowledge about something.
• Procedural knowledge is the knowledge of how to perform a specific skill or task, it is considered as knowledge related to methods, procedures, or operation of equipment.

Motivation can be defined as the process of activating, maintaining, and directing behavior towards a particular goal. The process is usually terminated once the desired goal is attained by the person. The process of initiating action is technically called ‘motivation’.

Key Points Mastery goals are aimed at attaining a standard of competence defined by self-improvement or skill development. Individuals who hold mastery goals either seek task-related self-improvement or strive to gain task mastery.

 Motivation can help the students in learning:

• With the help of motivation, students have much focus on goals.
• Motivation always supports the students in their learning individually.
• The teacher should have to encourage their students so that they can set their goals fully mastery and goal-oriented and attain adopt the incremental view of ability.
• Motivation helps students to gain capacity for learning, by focusing on the approach to learning.
• Mastery goals are aimed at attaining a standard of competence defined by self-improvement or skill development. Individuals who hold mastery goals either seek task-related self-improvement or strive to gain task mastery.
• Motivation is the panacea for demotivated students or those who have capabilities but don't perform well.

Thus by all these references, we can say that the students should be encouraged by the teachers for setting mastery-oriented goals.

Failure  is the state or condition of not meeting a desirable aim and may be viewed as the opposite of success. There are many cognitive, physical, intellectual, scholastical, emotional, and cultural causes for the failure of students.

Key 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.
• Boredom: ​The state of feeling disinterested in one's surroundings, having nothing to do, or feeling that life is dull.
• Confusions: Confusion disturbs the concepts of the students so they can not relate to the concepts and also do not learn meaningfully.
• Irrelevant curriculum: Irrelevant curriculum also affects the learning of the students, it can not provide much help to the students according to their needs.
• Teachers should adopt contextualized curriculum according to students' needs and use pedagogy centered approach for every group in the classroom. The teacher should motivate the students to set moderately challenging goals and provide appropriate instructional support.

Thus we can consider that all the four factors given in the questions are affecting the learning of the students.

Important Points There are many emotions that affect the learning of the learners, these are -

• ​Happiness
• Anxiety
• Fear
• Boredom
• Hope
• Hopelessness
• Pride
• shame
• fear
• Curiosity
• Enjoyment

Given:

x is the sum of integers between -9 and -1

y is the product of integers between -3 and 5

Calculation:

Integers between -9 and -1 = - 8, - 7, - 6, - 5, - 4, - 3, - 2

So, sum = - 35 i.e x

Integers between -3 and 5 = - 2, - 1, 0, 1, 2, 3, 4

So, product = 0 i.e y

x + y = - 35 + 0

⇒ x + y = - 35

∴ The value of x + y is - 35

Given:

The number is 893308

Calculation:

With the help of the long division method, we can easily find the number

So,

x = 283

As 945² = 893025

So, sum of the digits of x = 2 + 8 + 3

⇒ 13

∴ Required answer is 13

Given:

x = 3127 × 5121 × 716

y = 3128 × 5119 × 721

z = 3126 × 5120 × 719

Concept used:

HCF = the greatest number which divides each of the two or more numbers

Calculation:

x = 3126 × 3 × 5119 × 5² × 716

y = 3126 × 3² × 5119 × 7¹⁶ × 7⁵

z = 3126 × 5119 × 5 × 716 × 7³

So,

HCF = 3126 × 5119 × 716

∴ Required HCF is 3126 × 5119 × 716

Given:

a = $\frac{{\frac{2}{3} \div \frac{{ - 4}}{5} + \frac{7}{{12}} + \frac{{ - 11}}{6}}}{{\frac{1}{9} + \frac{5}{3} \times \frac{{ - 8}}{{15}} + \frac{7}{{27}}}}$

Concept used:

Calculation:

a = $\frac{{\frac{2}{3} \div \frac{{ - 4}}{5} + \frac{7}{{12}} + \frac{{ - 11}}{6}}}{{\frac{1}{9} + \frac{5}{3} \times \frac{{ - 8}}{{15}} + \frac{7}{{27}}}}$

⇒ a = $\frac{{\frac{2}{3} \times \frac{{5}}{-4} + \frac{7}{{12}} + \frac{{ - 11}}{6}}}{{\frac{1}{9} + \frac{5}{3} \times \frac{{ - 8}}{{15}} + \frac{7}{{27}}}}$

⇒ a = $\frac{{\frac{{5}}{-6} + \frac{7}{{12}} + \frac{{ - 11}}{6}}}{{\frac{1}{9} + \frac{{ - 8}}{{9}} + \frac{7}{{27}}}}$

⇒ a = $\frac{{-\frac{{5}}{6} + \frac{7}{{12}} - \frac{{11}}{6}}}{{\frac{1}{9} -\frac{{8}}{{9}} + \frac{7}{{27}}}}$

⇒ a = $\frac{{\frac{{-10 + 7 - 22}}{12}}}{{\frac{3 -24+7}{{27}}}}$

⇒ a = $\frac{{\frac{{-25}}{12}}}{{\frac{-14}{{27}}}}$

⇒ a = ${{\frac{-675}{{-168}}}}$

⇒ a = $\frac{{675}}{{168}}$

∴ The required answer of a is $\frac{{675}}{{168}}$.

Given:

If x = ${\left( {\frac{1}{2}} \right)^{ - 2}} \div {\left( {\frac{2}{3}} \right)^{ - 3}}$, then what is the reciprocal of x

Calculation:

⇒ x = ${\left( {\frac{1}{2}} \right)^{ - 2}} \div {\left( {\frac{2}{3}} \right)^{ - 3}}$

⇒ ${\left( {\frac{2}{1}} \right)^{2}} \div {\left( {\frac{3}{2}} \right)^{3}}$

⇒ 4 ÷ $\frac{27}{8}$ 

⇒ 4 × $\frac{8}{27}$ = $\frac{32}{27}$

Its reciprocal 

⇒  $\frac{27}{32}$

∴ The reciprocal of x is $\frac{27}{32}$.

Given:

A factor common to both

x² - x + 6  and x2 - 5x + 6 Is

Calculation:

Let  A = x² - x - 6  and B = x² - 5x + 6 

A = x² - x - 6 

⇒ A = x² - 3x + 2x - 6 

⇒ x (x - 3) + 2 (x - 3)

⇒ (x - 3) (x + 2)      ----(1)

B = x² - 5x + 6 

⇒ B = x² - 3x -2x + 6 

⇒ x( x - 3) - 2(x - 3)

⇒ (x - 3)(x - 2)      ----(2)

From the equation (1) and (2) common factor (x - 3)

∴ x² - x + 6  and x2 - 5x + 6 Is (x - 3)

Given:

The coefficient of x2 in the product

Calculation:

⇒ ( 2 x²/3  +  5x/4 - 3 ) × ( 3x² + 4x + 1 ) 

⇒ 2x²/3 (3x² + 4x + 1 ) + 5x/4 (3x² + 4x + 1 ) - 3(3x² + 4x + 1)

 ⇒  6x⁴ /3 + 8x³/ 3  +2x²/3  + 15x³/4 + 20x²/4 + 5x /4  - 9x² - 12x - 3

⇒ x² is the coefficient 

⇒ 20 x²/4 + 2x²/3 - 9x² 

⇒ - 40x²/12 = - 10x²/3

∴ The value is -10/3.

Given: 

I$\frac{{2(3y - 4) + 6}}{{3y - (4 + 5y)}} = \frac{3}{5}$,

Calculation:

According to the question

⇒ 6y - 8 + 6/3y - 4 - 5y = 3 / 5 

⇒ 6y - 2 / - 2y -4 = 3 / 5

Doing the cross multiply

⇒ 5 ( 6y - 2 ) = 3 ( - 2y - 4 ) 

⇒ 30y - 10 = - 6y - 12 

⇒ 36y = - 2  

⇒ y = - 1/18 

Put the value of y  (9y + 1) equation 

⇒ 9 × (- 1/18)  + 1 = 1/2

∴ The value of (9y + 1) is 1/2 .

Given:

2x - 3y = 5 and xy = 6

Formula used:

( a - b )² = a² + b² - 2ab

Calculation:

⇒ 2x - 3y = 5 

On squaring both sides,

⇒ ( 2x - 3y )² = ( 5 )²

⇒ 4x² + 9y² - 12xy = 25 

Put the value xy = 6

⇒ 4x² + 9y² - 12 × 6 =25

⇒ 4x² + 9y² = 25 + 72 = 97 

∴ The value of (4x2 + 9y2) is 97.

Given:

Rs. x amounts to Rs. 18422.25 in 2$1 \over 2$ years at 10% p.a

Concept used:

A = P(1 + r/100)^t

A = amount

P = principal

r = rate of interest

t = time

Calculation:

For the last 1/2 year rate of interest = 5%

10% of 12 months

So, 5% for 6 months

According to the question,

18422.25 = x(1 + 10/100)² × (1 + 5/100)

⇒18422.25 = x(1 + 1/10)2 × (1 + 1/20)

⇒18422.25 = x(11/10)2 × (21/20)

⇒18422.25 = x × (121/100) × (21/20)

⇒18422.25 = 2541x/2000

⇒ x = 18422.25 × 2000/2541

⇒ x = 14500

∴ The value of x is 14500

Shortcut Trick

Standard Circle with Radius 7 m has Area 154 m² and Circumference 44 m.

Given Area = 154 × 100 m² ⇒ Radius scale factor = √100 = 10.

Actual Circumference = 44 × 10 = 440 m.

Total Cost = 440 × 12.50 = 440 × (25 ÷ 2) = 220 × 25 = 5500.

∴ The correct answer is Rs. 5500.

Alternate Method

Given: Area of circular field = 15400 m², Rate of fencing = Rs. 12.50 per m.

Formula Used: Area = πr² | Circumference = 2πr | Total Cost = Circumference × Rate.

⇒ πr² = 15400

⇒ (22 ÷ 7) × r² = 15400

⇒ r² = (15400 × 7) ÷ 22

⇒ r² = 700 × 7 = 4900

⇒ r = √4900 = 70 m

⇒ Circumference = 2 × (22 ÷ 7) × 70

⇒ Circumference = 2 × 22 × 10 = 440 m

⇒ Total Cost = 440 × 12.50

⇒ Total Cost = Rs. 5500

∴ The correct answer is Rs. 5500.

Additional Information

Circle Properties

For a circle of radius r, the Diameter d = 2r, Circumference C = 2πr, and Area A = πr².

Fencing vs Leveling

Fencing is always done along the Perimeter (Circumference), while Leveling or Ploughing is done on the Area.

Semicircle Formulas

Perimeter of a semicircle = πr + 2r = r(π + 2). Area of a semicircle = (πr²) ÷ 2.

Shortcut Trick

Volume of a cylinder = (Curved Surface Area × Radius) ÷ 2

⇒ Volume = (2640 × 35) ÷ 2

⇒ Volume = 1320 × 35

⇒ Volume = 46200 cm³

∴ The correct answer is 46200 cm³.

Alternate Method

Given:

Base Radius (r) = 35 cm

Curved Surface Area (CSA) = 2640 cm²

Formula Used:

CSA of cylinder = 2πrh

Volume of cylinder = πr²h

Calculations:

⇒ 2 × (22/7) × 35 × h = 2640

⇒ 2 × 22 × 5 × h = 2640

⇒ 220 × h = 2640

⇒ h = 2640 ÷ 220 = 12 cm

⇒ Volume = (22/7) × 35 × 35 × 12

⇒ Volume = 22 × 5 × 35 × 12

⇒ Volume = 110 × 420

⇒ Volume = 46200 cm³

∴ The correct answer is 46200 cm³.

Additional Information

Total Surface Area of Cylinder

The Total Surface Area (TSA) includes the curved area and the two circular bases: TSA = 2πr(h + r).

Hollow Cylinder Volume

For a hollow cylinder with outer radius R and inner radius r, the volume is V = π(R² − r²)h.

Relation between Volume and CSA

The Volume (V) can be expressed in terms of CSA as V = (CSA × r) ÷ 2, which is a useful time-saving identity.

Given: 

The ratio of adjacent sides of a parallelogram is 2 : 1

Perimeter = 36 cm

The altitude corresponding to the smaller side is 10 cm

Concept used:

Area = Base × Height

Perimeter = 2(a + b)

Here,

a and b are the sides of the parallelogram

Calculation:

Let the lengths of the adjacent side be 2x and x respectively

So,

2(2x + x) = 36 cm

⇒ 6x = 36 cm

⇒ x ​= 6 cm

Thus, the adjacent sides of the parallelogram are 12 cm and 6 cm

So, area = 6 × 10 = 60 cm²

∴ The area of the parallelogram is 60 cm2

Given:

F, E and V are respectively the number of faces, edges and vertices of a square pyramid

Concept used:

A square-based pyramid has 5 faces, 4 equal triangles and a square.

A square-based pyramid has 8 edges.

A square-based pyramid has 5 vertices.

Calculation:

Number of faces = F = 5

Number of edges = E = 8

Number of vertices = V = 5

So, 3F + 2E - 2V

⇒ 3(5) + 2(8) + 2(5)

⇒ 15 + 16 - 10

⇒ 21

∴ Required answer is 3F + 2E - 2V = 21.

Given: 

AB = DE, AC = EF and BC = FD

Concept used:

SSS or Side-Side-Side congruence rule states that if three sides of one triangle are equal to three corresponding sides of another triangle, then the triangles are congruent.

Calculation:

In ΔABC and ΔDEF,

if AB = DE, AC = EF and BC = FD then, ΔDEF ≅ ΔBAC 

∴ Required answer is ΔDEF ≅ ΔBAC

Shortcut Trick

The angle formed by the angle bisectors of two adjacent angles in a quadrilateral is equal to half the sum of the other two angles.

∠APB = (∠C + ∠D) ÷ 2

⇒ ∠APB = (110° + 50°) ÷ 2

⇒ ∠APB = 160° ÷ 2 = 80°

∴ The correct answer is 80°.

Alternate Method

Given: ∠D = 50° and ∠C = 110° in quadrilateral ABCD. AP and BP are angle bisectors of ∠A and ∠B.

Formula Used: Sum of all interior angles of a quadrilateral = 360°. Sum of angles of a triangle = 180°.

In quadrilateral ABCD:

⇒ ∠A + ∠B + ∠C + ∠D = 360°

⇒ ∠A + ∠B + 110° + 50° = 360°

⇒ ∠A + ∠B + 160° = 360°

⇒ ∠A + ∠B = 360° − 160° = 200°

In ▵APB:

⇒ ∠PAB = ∠A ÷ 2 and ∠PBA = ∠B ÷ 2 (Since AP and BP are bisectors)

⇒ ∠PAB + ∠PBA = (∠A + ∠B) ÷ 2

⇒ ∠PAB + ∠PBA = 200° ÷ 2 = 100°

⇒ ∠APB + ∠PAB + ∠PBA = 180°

⇒ ∠APB + 100° = 180°

⇒ ∠APB = 180° − 100° = 80°

∴ The correct answer is 80°.

Additional Information

Adjacent Angle Bisectors Property

In any quadrilateral, the angle between the bisectors of two adjacent angles is half the sum of the remaining two angles: ∠APB = 1/2(∠C + ∠D).

Opposite Angle Bisectors Property

In a quadrilateral, the angle between the bisectors of two opposite angles is half the difference of the other two angles: θ = 1/2|∠B − ∠D|.

Angle Sum Property

For any n-sided polygon, the sum of interior angles is given by (n − 2) × 180°. For a quadrilateral (n=4), it is 360°.

Shortcut Trick

Since RT || QP, corresponding angles ∠TRS = ∠PQR = 35°.

Alternate interior angles ∠QPR = ∠PRT = 68°.

In ΔPQR, ∠QRP = 180° − (35° + 68°) = 77°.

Difference = |∠QRP − ∠TRS| = 77° − 35° = 42°.

∴ The correct answer is 42°.

Alternate Method

Given:

∠PRT = 68°, ∠PQR = 35°, RT || QP, and QR is produced to S.

Calculations:

⇒ RT || QP and QS is the transversal.

⇒ ∠TRS = ∠PQR (Corresponding angles)

⇒ ∠TRS = 35°

⇒ RT || QP and PR is the transversal.

⇒ ∠QPR = ∠PRT (Alternate interior angles)

⇒ ∠QPR = 68°

⇒ In ΔPQR: ∠PQR + ∠QPR + ∠QRP = 180°

⇒ 35° + 68° + ∠QRP = 180°

⇒ 103° + ∠QRP = 180°

⇒ ∠QRP = 180° − 103° = 77°

⇒ Difference = ∠QRP − ∠TRS

⇒ Difference = 77° − 35° = 42°

∴ The correct answer is 42°.

Additional Information

Parallel Lines Properties

When two parallel lines are cut by a transversal, corresponding angles are equal and alternate interior angles are equal.

Exterior Angle Theorem

The exterior angle of a triangle (∠PRS) is equal to the sum of the two opposite interior angles (∠PQR + ∠QPR).

Angle Sum Property

The sum of all interior angles of a triangle is always 180°.

Shortcut Trick

Sum of all interior angles = (n − 2) × 180°

⇒ (n − 2) × 180° = 1080° ⇒ n = 8

Each exterior angle = 360° ÷ n

⇒ 360° ÷ 8 = 45°

∴ The correct answer is 45°.

Alternate Method

Given:

Sum of all interior angles of a regular polygon = 1080°

Formula Used:

Sum of interior angles = (n − 2) × 180°

Each exterior angle = 360° ÷ n

Ext = 45° 135° Regular Octagon Σ Int. Angles = 1080° Sides (n) = 8

Calculations:

⇒ (n − 2) × 180° = 1080°

⇒ n − 2 = 1080° ÷ 180°

⇒ n − 2 = 6

⇒ n = 8 (The polygon has 8 sides)

Now, substitute the value of n into the exterior angle formula:

⇒ Each exterior angle = 360° ÷ 8

⇒ Each exterior angle = 45°

∴ The correct answer is 45°.

Additional Information

Sum of Exterior Angles

The sum of all exterior angles of any convex polygon is always exactly 360°, regardless of the number of sides it possesses.

Each Interior Angle

For a regular polygon with n sides, the measure of each interior angle is calculated as [(n − 2) × 180°] ÷ n.

Number of Diagonals

The total number of unique diagonals that can be drawn in an n-sided polygon is given by the formula [n(n − 3)] ÷ 2.

Linear Pair Relation

The sum of an interior angle and its corresponding exterior angle at the same vertex always equals 180° since they form a straight line.

Given:

Numbers 40, 41, 42, ........, 129, 130 are written on cards, one number on one card, and put in a box.

Concept used:

t_n = a + (n - 1)d

Here,

tn = last term

a = first term

n = no. of terms

d = common difference

P(A) = n(A)/n(S)

P(A) is the probability of an event “A” n(A) is the number of favorable outcomes. n(S) is the total number of events in the sample space.

Calculation:

130 = 40 + (n - 1).1

⇒ 130 = 40 + n - 1

⇒ n = 91

Now,

LCM of 2, 3, 4 = 12

So, numbers which are divisible by 12 between 40 to 130 = 48, 60, 72, 84, 96,

108, 120

So, total of 7 numbers are there

So,

Probability = 7/91 = 1/13

∴ The required probability is 1/13.

Shortcut Trick

Mean (x) → Sum ÷ Count = 108 ÷ 12 = 9

Mode (y) → Most frequent value = 7 (appears 3 times)

Median (z) → Average of 6^th and 7^th terms in sorted data = (8 + 9) ÷ 2 = 8.5

Value → x + y − z = 9 + 7 − 8.5 = 7.5

∴ The correct answer is 7.5.

Alternate Method

Given data: 7, 9, 19, 11, 10, 8, 7, 5, 7, 6, 9, 10

Sorted data: 5, 6, 7, 7, 7, 8, 9, 9, 10, 10, 11, 19

Number of observations (n): 12

1. Calculation of Mean (x):

⇒ x = (5 + 6 + 7 + 7 + 7 + 8 + 9 + 9 + 10 + 10 + 11 + 19) ÷ 12

⇒ x = 108 ÷ 12 = 9

2. Calculation of Mode (y):

⇒ Frequency of 7 is 3 (maximum).

⇒ y = 7

3. Calculation of Median (z):

⇒ Since n = 12 (even), Median = Average of (n/2)^th and (n/2 + 1)^th terms.

⇒ z = (6^th term + 7^th term) ÷ 2 = (8 + 9) ÷ 2 = 8.5

4. Final Calculation:

⇒ (x + y − z) = (9 + 7 − 8.5)

⇒ 16 − 8.5 = 7.5

∴ The correct answer is 7.5.

Additional Information

Empirical Relationship

For a moderately skewed distribution, the relationship between measures of central tendency is: Mode = 3 × Median − 2 × Mean.

Median for Even n

If the number of observations (n) is even, the median is the arithmetic mean of the (n/2)^th and (n/2 + 1)^th observations after sorting the data.

Measures of Central Tendency

Mean provides the average, Median provides the middle value of a sorted list, and Mode provides the most frequently occurring value in the dataset.

The wrong concepts registered in the minds of students regarding various concepts in the curriculum are known as misconceptions. This need to be cleared by the teacher as early as possible to avoid the errors of the students on the same topic in the future. 

Key Points

• The students didn't have a correct understanding of the equal symbol.
• They were just concentrating on the addition and missing the equality symbol in the middle.
• They did not have an idea that the values on both sides of the equivalence symbol should be equal.
• This miscommunication lead them to just stick to the addition concept and ignore the equivalence concept.

Hence it is a misconception that arose because students were not viewing the symbol "=" as a symbol to indicate equivalence. 

Additional Information

On the other hand, all the other options are wrong as they indicate that work of the students is correct or indicate that teacher should directly say the correct answer which may not clear the misconception of the children.

A mathematical statement is a rule or generalization in mathematics that is further used as a starting point for the other concepts related to it. 

Key PointsA number of factors of a given number are always countable is the best example of a precise mathematical statement because:

• Every number in mathematics has a limited number of factors and it can be counted.
• For example, 12 has factors like 2,3,4,12, and 1 which are countable and limited.
• Factors of any number can be found through the factorization method which means dividing the big number till no more division is possible.
• For example if we take 20 we start by diving by 2 and the again by 2 then by 5 now 1 is remaining and we can't divide it further.
• Here we stop and count the factors.

Hence number of factors of a given number is always countable is the best example of a precise mathematical statement.

Additional Information

On the other hand all the other given statements are not precise because they are not exact and totally true to be accepted as a correct mathematical statement.

Newman's error analysis arose from research into language issues in maths in the 1970s. The theory posits that there are five stages that a student goes through to solve a word problem in mathematics. The student reads the problem and decodes words and symbols. The student makes sense of what they have read. 

Key Points

Stages according to Newman:

Hence option 3 is the correct answer.

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. Whenever we're unsure about the outcome of an event, we can talk about the probabilities. 

Key PointsIn the above example the purpose of this activity is to help students arrive at the fact as the number of tosses gets larger, the probability of head or tail gets closer to 0.5 as:

• The teacher first asks the students to toss a fair coin 10 times and record their observations
• Then she keeps on increasing the number of tosses and asks the students to record their observations.
• The students may not arrive to the fact that when a coin is tossed probability of head or tail is closer to 0.5 when they toss the coin only few times.
• This can be proved and taught to the students only a coin is tossed many times where they understand the concept.

​Hence in the above example, the purpose of this activity is to help students arrive at the fact as the number of tosses gets larger, the probability of head or tail getting closer to 0.5.

Additional Information On the other hand introducing the concept of fractions, completing experiments prescribed in textbook and helping students identify the situations in which probability is greater than 1 is not the aim of this activity as students may not arrive at these conclusions after doing the activity.

Problem solving skills are very important in mathematics.The ability to think creatively, critically, and logically, the ability to structure and organize, and the ability to process information are some of the problem-solving skills involved in mathematics. 

Key PointsThe question "Find the value of 3.25 × 6 " does not involve problem solving skills as:

• It is a direct question of multiplication.
• The student may get the answer easily.
• Doesn't require any problem-solving skills like critical thinking and analysis.
• The student is not required to read and understand the problem in order to solve it.
• Doesn't enhance the thinking capacity of the student.

Hence the question "Find the value of 3.25 × 6 " does not involve problem-solving skills.

Additional Information

On the other hand, all the other questions enhance the problem-solving skills of students as there is a scope for the student to read, understand, analyze, think and arrive to the solution.

In mathematics, a ratio is a comparison of two or more numbers that indicates their sizes in relation to each other. A ratio compares two quantities by division, with the dividend or number being divided termed the antecedent and the divisor or number that is dividing termed the consequent. 

Key Points

"How can I compare the length of a toy car with the length of a real car using division?" is the most appropriate strategy for a teacher to use in an introductory class on ratios:

• As the ratio is nothing but comparison the students should get at least two quantities to compare.
• As in the example, the students can compare the length of a toy car with the length of a real car using division.
• The students get to know how many times is the length of a real car greater compared to the length of a toy car.
• When they divide both they get the ratio of both the quantities which may familiarize them the with ratio topic.

​Hence "How can I compare the length of a toy car with the length of a real car using division?" is the most appropriate strategy for a teacher to use in an introductory class on ratio.

Additional Information

On the other hand all the other options are wrong as there is no sign of comparison in that questions which may introduce the topic of ratio to the children.

• A Field Trip is a visit to a place away from their normal place of study. The purpose of this trip is to provide students an experience outside the classrooms or labs to provide hands-on experience to the students.
• A project is a series of tasks that need to be completed to reach a specific outcome. A project can also be defined as a set of inputs and outputs required to achieve a particular goal.

Key PointsField trips and projects can be used to encourage interdisciplinarity in Mathematics assessment as:

• The Interdisciplinary Mathematics curriculum focuses on solving problems and understanding how things connect.
• Interdisciplinary mathematics is a field of mathematics that merges math expertise with proficiency in another discipline, usually science, business, medicine, or engineering.
• In projects and field trips children will not only focus on the mathematics topics but also get to know and explore topics related to other subjects.
• Students connect the concepts of mathematics with other subjects in projects and field trips as they have a lot of scopes to explore and learn.

Hence Field trips and projects can be used to encourage interdisciplinarity in Mathematics assessment.

Additional Information

Dice (singular die or dice) are small, throwable objects with marked sides that can rest in multiple positions. They are used for generating random numbers, commonly as part of tabletop games, including dice games, board games, role-playing games, and games of chance. 

Key Points

• Bar graph concept can be taught using the dice by rolling the dice many times and taking two parameters frequency and results at x and y of the bar graph.
• Euler's formula F + V = E + 2 can be easily taught using the die and also will be understood by the students very well as a die contains faces, vertices and also edges.
• Probability can also be taught using a die as it can be used to calculate the number of outcomes and also see how many times each number occurs in rolling specific times
• Direct proportion can't be taught using the die as it has no relation with the increase and decrease of some quantities in the same proportion and rolling dice 2 times may not increase the chance of getting 2.

Hence direct proportion can't be taught by using a die.

GeoGebra is a computer program to support teaching and learning mathematics subject, especially in geometry, algebra, and statistics. The various facilities provided by GeoGebra software expect that it can be a great medium to help its users visualize abstract geometric objects quickly, accurately, and efficiently. 

Key PointsWith the help of 'GeoGebra software', students can learn geometrical concepts through- an exploratory approach as:

• GeoGebra is the new essential tool that can be used to explore mathematics.
• It is a powerful tool as it makes it easy to link visual geometry with algebraic representations.
• GeoGebra allows students to actively and through the sharing of the work online, socially construct an understanding of geometry.
• This program allows for simple visualizations of possibly complex geometric concepts and helps enhance a student's understanding of those concepts through an exploratory approach.

​Hence With the help of 'GeoGebra software', students can learn geometrical concepts through- an exploratory approach.

Additional Information

Developing logical and problem-solving abilities in children is the main objective of teaching Math, according to NCF 2005 the development of children's abilities for mathematization is the main goal of mathematics education which means the child's thought process should be mathematized. 

Key PointsAccording to the National curriculum Framework 2005, school Mathematics takes place in a situation where

• Students avoid rote memorization and develop concepts with understanding.
• Students are treated as the center of the class and the teaching and learning activities are developed according to their abilities.
• Students see mathematics as a part of their daily life experiences and something to talk and discuss about.
• Students start using the concepts of mathematics they learned in the classroom in their daily life as well.
• Students enjoy solving different types of problems in different methods according to their understanding.

​Hence According to the National Curriculum Framework 2005, school Mathematics takes place in a situation where students see mathematics as a part of their daily life experiences and something to talk about and discuss.

Additional Information ​On the other hand students reciting multiplication tables, teachers becoming active narrators, and students solving higher education-related problems are not given importance by NCF 2005 as these don't allow students to see mathematics as a part of/her daily life experiences.

Concept:

Magnet:

• Magnets refer to an object which is capable of producing a magnetic field. and attracts iron pieces and settles itself along the north-south pole.
• Magnets have 2 poles: a North pole and a South pole.
• Magnetic poles always exist in pairs.
• Like poles of 2 magnets repel each other while unlike poles attract each other.
• The strength of the magnet is highest at the poles and weakest in the middle.

Explanation:

• Each magnet contains a North pole at one end and a South pole at the other end.
• So, when two magnets are brought closer to each other, they will either attract or repel because like poles repel each other whereas unlike poles attract each other.
• If C1 is the north pole then C2 is the south pole, as it is given that A1 repels C2, to repel C2, A1 must have the same pole as C2, so A1 is the south pole.
• Now, as A1 and A2 are south and north pole, it is also given that A1 repels B1, so A1 is south, to repel B1 It must also me South.
• From the above, it is clear that A1 and B1 are the south poles.

Thus, the correct answer is Both B1 and A1 are south poles.

Additional Information Electromagnet:

• A strong magnetic field produced inside a solenoid can be used to magnetize a piece of a magnetic material like soft iron when placed inside the coil. The magnet so formed is called an electromagnet.

Concept:

Motion:

• A body is said to be in motion if its position changes continuously at the same rate with respect to its surroundings.
• The motion of an object could be uniform or non-uniform depending on whether its velocity is constant or changing.
• Uniform and non-uniform motions of objects can be shown through graphs.
• The speed of an object is the distance covered per unit of time.

Uniform Motion:

• It is a motion in which a material point moves in a straight line at a uniform speed.

Non-uniform Motion:

• It is a motion in which the velocity varies with time.

Explanation:

​

Therefore, from the above discussion, the correct answer is A and B

Key Points

• In a distance-time graph, for non-uniform motion, the object's speed keeps changing.

Note:-  According to the question statement the provided answer is best suited.

Concept:

Mixture:

• A mixture contains more than one substance or element or compound mixed in any proportion.
• These mixtures can be separated into pure substances using appropriate methods of separation.

Explanation:

• Sedimentation is the process of allowing solid particles in suspension in water to settle out of the suspension under the effect of gravity.
• The particles which settle down during sedimentation are called sediments.
• This method is used for the separation of insoluble substances which are heavier than liquid or water.
• In this process, heavier components of the mixture settle on the bottom on their own due to gravity.

Thus, the correct answer is heavy and insoluble in water. 

Additional Information Evaporation:

• Evaporation is a technique that is used in separating a mixture usually a solution of a solvent and a soluble solid.
• In this method, the solution is heated until the organic solvent evaporates where it turns into a gas and mostly leaves behind the solid residue.

Decantation:

• Decantation is the process of separation of liquid from solid by removing the liquid layer at the top from the layer of solid or liquid below.

Filtration:

• Filtration is the process of the solid unwanted particles from a given liquid or gaseous mixture through the pores of a membrane called a filter.
• The filter can be paper, cloth, wool, slag, or any porous material.
• The process of filtration cannot be used to separate the soluble component from liquids.
• Example: Tea leaves from tea.

Centrifugation:

• Centrifugation is the process that uses centrifugal force for the separation of two liquids in a mixture.
• Examples: extraction of fat from milk, separation of butter from milk. spin-drying of water etc.

Concept:

• Any fabric made up of yarns arranged together which are further made up of still thinner strands is called Fibers.
• Classification of fibers:
• Natural fiber
• Semi-synthetic fiber
• Synthetic fiber
• Natural fibers are fibers obtained from plants and animals. Examples: Cotton, silk, and jute.
• Semi-synthetic fibers are fibers obtained from naturally occurring fibers by chemical modifications. Examples: cellulose diacetate, etc.
• Synthetic fibers are fibers manufactured by man in laboratories. Examples: Rayon, nylon, polyester, etc.

Explanation:

• Silk is a protein fiber that burns with bright light and greyish black ash is left.
• It smells like burned hair or charred meat.
• Denim is made from cotton fiber using a twill weave that burns by curling and produces dark crisp ash.
• Nylon is made from petroleum.
• So, they quickly burn and also melt on burning.
• They also shrink to flame.
• The beads are hard, grayish, and uncrushable.

Thus, the correct answer is Silk, denim, and nylon.

Additional Information

• Cotton is a cellulose fiber.
• ​ It burns and may flare up when lit.
• ​No melted beads are left.
• After burning it continues to glow.
• It gives a smell like that burning paper.
• Wool is a protein fiber that burns slowly.
• It sizzles, and curls away from the flame.
• It gives dark smoke and moderate fumes.
• Jute is also a cellulose fiber.
• It does not shrink or melt on the flame.
• The ash is gray and the smoke has no fume.
• It smells like burning leaves and woods.
• Rayon is a manufactured cellulose fiber.
• It burns without flames or melting.
• It may flare-up.
• It may glow longer than cotton after burning.
• It smells like burning paper and leaves.

Concept:

• Power in a circuit is a product of the voltage and the current.
• Its SI unit is the watt.
• Mathematically, P= IV

Explanation:

• If the bulb is connected in series circuits, the current will be the same in all the bulbs.
• So, among the above-given options,  a simple circuit with one bulb and two cells provides greater electricity, and thus the circuit having maximum output power will have the bulb which grows the brightest.

Thus, we can say that one bulb with two cells will glow brighter.

Concept:

Thyroid gland

• It is a butterfly-shaped gland.
• It lies in front of the trachea and below the larynx.
• It is a type of endocrine gland.
• Thyroid glands represent 2 main thyroid hormones that are thyroxine (T4)  and triiodothyronine(T3).

Explanation:

• Both these forms are iodinated forms of an amino acid.
• Iodine (in diet) is essential for the normal rate of hormone synthesis in the thyroid.
• Deficiency of iodine in our diet results in hypothyroidism and enlargement of the thyroid gland commonly called goitre.
• In the hilly regions like the Himalayas, the soil lacks iodine as it is far from the sea.
• Thus, the people living in hilly regions get a iodine-deficient diet.
• Hence, goitre becomes an endemic disease (consistent but confined to these regions) in the hilly regions.
• Iodine deficiency may also lead to infant mortality and mental retardation in children.
• Therefore, we can identify the given as follows:
• A - Iodine
• B - Goitre
• C - Hilly
• D - Mental retardation

Hence, the correct answer is option 4.

Additional Information

• People are advised to include iodized salt in their diet, in order to fight this endemic deficiency disorder.
• The iodized salt ensures that our body gets the required amount of iodine, irrespective of the food we eat.

Concept:

• There are 2 eclipses that occurred on our earth are-
• Solar eclipse
• Lunar eclipse

Solar Eclipse:

• A solar eclipse occurs when the moon comes between the Earth and the Sun.
• The moon casts a shadow over Earth.
• A solar eclipse only takes place during the phase of the new moon.

Lunar Eclipse:

• A lunar eclipse occurs when the Earth comes between the Sun and the moon.
• A lunar eclipse occurs only at the full moon.

Explanation:

• When the moon comes in between the earth and the sun. This is known as a solar eclipse.
• As a result, the moon blocks the sunlight from reaching the earth's surface and casts a shadow on the earth.
• This happens in the new moon phase.

Thus, we can say that A is correct and R2 is the correct explanation of A. 

Additional Information Phases of the moon:

• New Moon: On this day, the moon is between the earth and the sun align in a straight line. And the moon becomes invisible.
• Full moon: On this day, a perfect round-shaped moon appears.
• Crescent Moon: The shape of the moon during the phases between the new moon and half-moon is the crescent moon.
• Gibbous Moon: The shape of the moon during the phases between the full moon and half-moon is the gibbous moon.

Explanation:

• A shadow is a black spot that is formed when an opaque object comes into the path of light.
• This happens because the light travels in a straight light and if there is any obstacle in between the light could not pass through it.
• It is formed on the screen. It can be a wall or anything like this.
• The size of the shadow depends upon the distance between opaque objects and the source of light.
• ​This is caused as the path of light is blocked by the object.
• A yellow object is an opaque object hence a black shadow will be formed.
• The size of the shadow will become larger as the distance between the source of light and the object is larger.
• So, the size always depends upon the relative distance between a light source. Hence, statement 3 is incorrect.

Thus, the incorrect statement about shadow formation is that length of the shadow is always same as length of object.

Concept:

Stomata

• Stomata are the small openings found on the leaf epidermis.
• It can be found on stems and other plant parts.
• It can be seen beneath the light microscope.
• Stomata structure:
• Two guard cells surround each stoma.
• The kidney-shaped guards contain chloroplasts.
• In the stoma, there is a respiratory chamber.

Stomatal transpiration:

• It is the evaporation of the water from the plant's stomata.
• The majority of the water from the plants is lost through transpiration.
• When the stomata are open, the water at the surface of the leaves turns into vapor and evaporates.
• Water in liquid form converts to water vapor near the leaf's surface and evaporates from the plant

Explanation:

• Guard cells are bean-shaped cells.
• Guard cell plays an important role in the gaseous exchange of plant leaves by opening and closing the pore through the stomata.
• In succulent plants, stomata open at night and close during the daytime.  through open stomata.
• In succulent plants, CAM (Crassulacean acid metabolism) metabolism is present.
• In desert plants, sunken stomata are present deep in the leaves and stem of a plant which helps these plants to retain their water by reducing the loss of water by transpiration.
• The position of stomata does affect the rate of transpiration.
• Stomata present on the lower surface of the leaf are less exposed to heat and wind and thus, reduce the transpiration rate.
• Some leaves may have stomata only on the lower surface and are called hypostomatous leaves.

Thus, we can say that Both A and R are correct but R not is correct explanation for A.

Concept:

• There are two modes of reproduction in plants;
• Sexual and Asexual
• The sexual mode of reproduction takes place through flowers by transfer of pollen grains.
• The asexual mode of reproduction takes place includes budding, spore formation, fragmentation, etc

Explanation:

Pistils:

• The pistils are the female reproductive organ of the flower.
• They are usually located in the center of the flower.
• It is having 3 parts;
• Stigma- It is the sticky knob at the top of the pistils which is receptive to pollen grains.
• Style- It is a long tube-like structure. Stigma is attached to the style of the pistil. 
• The style leads to the ovary that contains the female egg cells called ovules and fertilization takes place.
• Ovary- It is the enlarged basal portion of the pistil where ovules are produced.

Therefore, the correct answer is X - pistil, Y - stigma, Z - ovules.

Key Points 

Stamens:

• The stamen is the male reproductive organ of the flower.
• It is having 2 parts:
• Anthers - It is a two-lobed structure that contains microsporangia for the production of pollen grains.
• Filaments - It is a long stalk-like structure that connects the base of the flower with an anther.
• Petals are the colored part of the flowers that give them a unique shape.
• Sepals are leaf-like structures attached to the outside of the flower,

Additional InformationPollination refers to the transfer of pollen grains from the anther of a stamen to the stigma of a carpel.

• Pollination is done by insects, wind, water, and birds.
• It occurs in 2 ways:
• Self-pollination
• cross-pollination
• Self-pollination refers to the transfer from the anther of a flower to the stigma of the same or genetically similar flowers on the same plant.
• Examples of self-pollinating plants are peanuts, wheat, rice, tomato, etc.
• Cross-pollination refers to the transfer from the anther of a flower on one plant to the stigma of the flower on another plant.
• Examples of cross-pollinating plants are grass

Explanation:

RBC

• Red blood cell is also known as erythrocytes.
• RBCs are formed in the red bone marrow of adult humans.
• RBC is devoid of a nucleus.

Onion peel

• An onion is multicellular.
• It consists of a cell wall, a large vacuole, nucleus, cytoplasm, and cell membrane.

Cheek cells

• Cheek cells are simple squamous epithelium.
• They are animal cells so they do not have a cell wall.

Guard cell

• Guard cells are bean-shaped cells that stomata.
• Guard cell plays an important in the gaseous exchange of plant leaves by opening and closing the pore through the stomata.
• Guard cell helps in transpiration.
• Stomata helps in opening and closing of guard cell.

Xylem

• Xylem tissues carry water and minerals.
• It also transports nutrients from the roots of the plant to its leaves.
• Xylem are tube-like projections that are open at both ends.
• The process of transpiration helps in the upward movement of water from roots to the leaves through steam.

Thus, we can say that A - RBC, B - Cell on onion peel, C - Cheek cells, D - Guard cell, E - Xylem cells.

Additional Information

• WBC is white blood cell.
• They are colorless due to a lack of hemoglobin.
• They have a nucleus.
• Phloem tissues carry the food prepared by the plants.
• It also carries the hormones made by the plants in their root and shoot tips.
• It is multidirectional.
• The transport of food from leaves to other parts of the plant is called translocation.

Concept:

• The density of a substance is its mass per unit volume.
• Its SI unit is kg per cubic meter.
• Mathematically, density = mass\ volume.
• ​The liquid that is denser will sink into less dense liquids.
• ​The liquid that is less dense will float into less dense liquids.

Calculation:

We know that,

Density = mass\ volume

• ​The density of liquid A = 5.4\5 = 1.08 g\cm3.
• ​The density of liquid B = 4.6\5 =  0.09 g\cm3
• ​The density of liquid C = 130/100 = 1.3 g\cm3.

Explanation:

• ​The density of liquid A is 1.08 g\cm^3.
• The density of water is 1 g/cm3.
• The liquid A is denser than the water, so it will not float over water.
• Hence, option 1 is incorrect.
• ​The density of liquid B is 0.09 g\cm3.
• The density of water is 1 g/cm3.
• The liquid B is less dense than the water, so it will float over water.
• Hence, option 3 is correct.
• ​The density of liquid C is 1.3 g\cm3.
• The density of water is 1 g/cm3.
• The liquid A is denser than the water, so it will not float over water.
• ​The density of liquid A is 1.08 g\cm3.
• The density of water is 1 g/cm3.
• The liquid A is denser than the water, so it will not float over water.
• Hence, option 2 and 3 is incorrect.

Thus, the correct statement is Liquid B will float in water.

Concept:

• A sound is a form of energy that produces the sensation of hearing in our ears.
• Sound is a type of longitudinal wave.
• Sound is measured in Decibels(Db).
• The speed of the sound varies in different mediums.

Explanation:

• Sound from a violin and a flute played at the same time travel at the same speed.
• Both the sounds travel through the same medium which is air.
• Both the sound travel through at the same speed at the same time but the sound we receive are different due to characteristics associated with the sound such as pitch and amplitude.
• Hence, option 1 is correct.
• Two sound waves of the same intensity would not be perceived to have the same loudness because of the human's ear tendency to amplify sounds having frequencies in the range from 2kHz to 4kHz, sounds with these intensities seem louder to the human ear. Hence, option 2 is incorrect.
• Speed of sound in hot air is more than that of the room temperature because heat makes air molecules move around faster. Hence, option 3 is correct.
• The speed of sound depends on the density of the material.
• Tightly packed material molecules transfer the sound at high speed.
• Speed of sound is fastest in Solids, Liquids then Gas.
• Hence, option 4 is correct.

Thus, the incorrect statement is that two sound waves of the same intensity will always have equal loudness. 

Important Points Amplitude:

• Amplitude is the measure of compression or rarefaction of particles of a medium through which sound is traveling.
• The higher the amplitude, the louder the sound.
• The amplitude A is related to loudness as loudness ∝ A2

Frequency:

• Frequency refers to the rate of vibration of sound.
• The pitch of a sound is decided by the measure of frequency.
• The higher the frequency, the shriller the sound.
• Frequency measured in Hertz (Hz).

Additional Information Sound in the air: 

• In a gas-like air, the particles are generally far apart so they travel further before they bump into one another.
• There is not much resistance to movement so it doesn’t take much to start a wave, but it won’t travel as fast.

Sound in water:

• In water, the particles are much closer together, and they can quickly transmit vibrational energy from one particle to the next.
• This means that the sound wave travels over four times faster than it would in the air, but it takes a lot of energy to start the vibration.

Sound in solids: 

• In a solid, the particles are even closer together and linked by chemical bonds so the wave travels even faster than it does in either liquid or air, but you need quite a lot of energy to start the wave at the beginning.

Concept:

• Evaporation is the phenomenon of change in a liquid into vapors at any temperature below its boiling point.
• Rate of evaporation depends upon-
• Surface area
• Temperature
• Humidity
• Wind speed

Explanation:

Surface area:

• If the surface area increases, the rate of evaporation increases, and decreases with a decrease in the surface area.
• This means the surface area is directly proportional to the rate of evaporation.

Temperature:

• With the increase in temperature, more number of particles get enough kinetic energy to go into the vapor state.
• With the increase in temperature, the rate of evaporation increases, and decreases with a decrease in the temperature.
• This means the temperature is directly proportional to the rate of evaporation.

Humidity:

• Humidity is the amount of water vapor present in the air.
• If the amount of water in the air is already high, the rate of evaporation decreases.
• This means the humidity is inversely proportional to the rate of evaporation.

Wind speed:

• If the wind speed increases, the rate of evaporation increases, and decreases with a decrease in the wind speed.
• This means the wind speed is directly proportional to the rate of evaporation.

Thus, the correct answer is humidity.

Key Points

• Evaporation causes cooling.
• Latent heat of vaporization is the heat energy required to change 1kg of a liquid to gas at atmospheric pressure at its boiling point.

Concept:

• Reactivity series is the arrangement of metals with oxygen in a vertical column in order of decreasing reactivities.
• The most reactive metal is placed on the top while the least reactive metal is placed at the bottom.
• If the metal atom can lose electrons easily to form positive ions and it will react rapidly with other substances. Hence, it will be reactive metal.
• If the metal atom loses electrons less readily to form positive ions and it will react slowly with other substances. Hence, it will be a less reactive metal.
• Metals that lose electrons more readily than hydrogen are also said to be more reactive.
• Metals that lose electrons less readily than hydrogen are also said to be less reactive.

Explanation:

• Metal A is able to displace the least reactive metal B from the salt solution because metal A is more reactive than metal B.
• But metal A is not able to displace metal C from the salt solution because metal C is more reactive than metal A.
• Metal B is able to displace the least reactive metal D from the salt solution because metal B is more reactive than metal D.
• So, from the above discussion, we can say that metal C is more reactive followed by metal A, metal B, and metal D.

Thus, the correct answer is C > A > B > D.

Explanation:

Chlorine:

• Chlorine is the non-metal that possesses the quality of killing germs present in the water. Hence, it is used for disinfecting water.

Zinc:

• Zinc is the metal commonly used in electroplating.
• Electroplating is the process of metal coating on another piece of metal through an electrodeposition process.

Carbon:

• Carbon is non-metal that exists in 2 forms and shows allotropism.
• Allotropism is the property of some chemical elements in which the element exists in two different forms in the same physical states and those forms are the allotropes of elements.
• Diamond and graphite are 2 allotropes of carbon.

Bromine:

• Bromine is the only non-metal that is liquid at room temperature.
• It is a thick, reddish-brown liquid that evaporates to an orange vapor at standard temperature & pressure.
• While sulfur and carbon are the non-metals which is solid at room temperature.

Copper:

• Copper is a metal.
• Brass & bronze are copper-based alloys.
• Brass is a metal alloy that is made up of copper and zinc.
• Bronze is a metal alloy that is made up of copper and tin.
• Alloy is a substance that combines more than one metal or mixes metal with other non-metallic elements.

Therefore, the correct answer is (a) - (iii), (b) - (iv), (c) - (v), (d) - (i), (e) - (ii).