CTET Paper 2 Maths & Science 29th Dec 2021 (English-Hindi-Sanskrit) (Previous Year Paper)

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

Basically, the development of a child is considered in five stages-

• Pre-natal period (conception period)
• Infancy period (0 to 2 years)
• Early childhood period (2 to 6 years)
• Later childhood (7 to 11 years)
• Adolescence ( 12 to 19 years)

Key Points Early childhood period: The period from birth to six years is a time for rapid development. In this stage, the absence of experience and deprivation can be detrimental to growth. Care and stimulation are critical during early childhood or the first three years.

The characteristics of the early childhood are:

• Children become more self-sufficient, and independent, and develop self-esteem.
• It is a toy age because most of the time children are engaged with their toys. These toys are also helpful to educate the children. Toys are an important element of their play activities.
• A lot of opportunities are provided to children to learn during early childhood with love and care so that they can grow in a positive environment.
• Children are able to form relationships through the consistent and continuous presence of caregivers who talk, feed, play, and tend to give love and care.
• This is a period when a child is considered physically and mentally independent. This is also a school-going age.
• Develop physical, cognitive, emotional, and social development.
• Learning outcomes gained by the learning during early childhood will not be easily modified in the later period, it is modified by the hard work of that learning.
• So, we can consider that **(A) is true but (R) is false.**​

Important Points

• Infancy period: During this stage, adjusting to the new non-uterine environment becomes the major goal or focus in the life of the neonate. Adjusting to room temperature. Breathing independently, sucking and swallowing the milk, eliminating body, and waste are prime areas that the newborn needs to master.
• Later childhood: During this stage children develop marked negativism and because of their desire for independence seldom obey their parents. The child begins going to school and learns the rudiments of knowledge essential for successful adult life. The peer group assumes great significance and children of this age 'crowd together, thus earning the name gang age'.
• Adolescence: It is the threshold to adulthood. There are rapid physical changes taking place including sexual maturity which is attained during adolescence. Consequently, there are also psychological and social changes. Adolescence is a crucial stage for the person.

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

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

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

Key Points Jean Piaget’s theory is critiqued for proposing four stages of cognitive development. It falls under the continuity/discontinuity debate of child development.

• The discontinuity approach considers development as occurring in distinct and abrupt changes, with an emphasis on qualitative experiences that are different at each stage.
• "Discontinuity" in the developmental process refers to new ways of understanding the world that emerge during the process of development.
• The discontinuity approach gives rise to “stage theories”, where development is illustrated with a metaphor of "climbing the stairs", with each step signifying an advanced way of functioning than the previous step.
• And Jean Piaget considers that development is continuous and attained step by step, that's why this type of critique comes.
• Hence we can say that **Jean Piaget’s theory is critiqued for proposing four stages of cognitive development. Which debate of child development does this fall under continuity / discontinuity.**​

Hint

• Inclusion: Inclusion entails remodeling and enriching the general education system, making it more comprehensive, supportive, and responsive to the needs of all children.
• Sensitive periods: a stage in development when an organism can most rapidly acquire a particular skill or characteristic.
• For example, in humans, the 1st year of life is considered significant for the development of a secure attachment bond.
• The nature-nurture debate is concerned with the relative contribution that both influences make to human behavior, such as personality, cognitive traits, temperament, and psychopathology.

Learning can be defined as the process by which any relatively permanent change in behavior occurs as a result of practice and /or experience. Changes that occur due to growth, maturation, fatigue, or injury are not included in learning. Thus learning brings about improvement in performance.

Social learning - learning that is facilitated through social interactions with other individuals. Certain social responses are reinforced by society if they are acceptable as per the norms of the society.

Key Points In addition to other mechanisms social learning involves ‘imitation’ of the role models which is a process by which individuals learn new behavior by observing others, also called modeling or observational learning. 

• Imitation can be defined as the copying of behavior. To a biologist, interest in imitation is focused on its adaptive value for the survival of the organism. Imitations are sometimes referred to as opaque imitations because they are difficult to account for without positing cognitive mechanisms, such as perspective-taking, that most animals have not been acknowledged to have.
• So we can consider that learning through imitation of others is called Social learning.

Important Points

• Behavioristic learning: Behavioristic theories or Behaviorism constitute the traditional theories of Learning. These theories were propounded by Ivan Pavlov and John B. Watson. The behaviorists attribute learning to the association between stimulus and response. Behavioristic theories are also called the connectionist theories of learning because of their emphasis on the connection between the stimulus and the response. They mainly deal with the role played by conditioning in the process of learning.
• Discovery learning: Discovery learning is the type of learning in which students can learn by finding the correct approach for the problem through their cognition.
• Humanistic learning: This is a learning in which learning totally depends on the interest, needs, and abilities of the child, it is also called student-centered learning. Students are encouraged to learn in this type of learning.

According to Piaget, cognitive development takes place at different rates at different stages of development. At the elementary level, there is not only an increase in children's capacity to learn but also a qualitative change in their thinking process.

Piaget talks about cognition, he means the mental process which can Systematize, organize and utilize knowledge. This capacity develops in the learners through the interaction of innate power (heredity), environment, and maturation. Individuals make continuous efforts to adapt to the environment. Through this process of adaptation, cognitive development takes place.

Piaget has classified the whole continuum into four stages to elaborate on the process of cognitive development.

• Sensory Motor Period (0-2 years)
• Pre-operational period (2-7 years)
• (a) pre-conceptual phase (2-4 years)
• ((b) Intuitive phase (4-7 years)
• Concrete operation period (7- 1 1 years)
• Formal operational period (1 1-15 years)

Key Points The Formal Operational Period: Formal operational period is the fourth stage of Piaget's classification which starts at about the age of 11 years and continues till about the age of 15 years. At the stage of concrete operation (7-11 years), the child requires mainly four important cognitive processes: Mental representation, Conservation, Class inclusion, and Multiple classifications.  

 Characteristics of formal operational period:

• A stage of thinking about the thinking process rather than merely thinking about the context of thought.
• A stage of applying different and flexible ways to think about ideas.
• A stage of real versus possible. Children do not think only about concrete things but start thinking about imaginary things and possible occurrences.
• When children start thinking systematically and methodically.
• At when elementary level children can use deductive logic, while at the primary level children prefer inductive logic.
• So by all these references, we can say that in the formal operational stage of cognitive development the ability for abstract thinking and scientific reasoning develops.

Additional Information

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)
• Formal Operational stage (11+ years to adolescence).

Key Points According to Jean Piaget:

• Children develop an understanding of interaction with the surrounding environment. Piaget identifies four factors namely biological maturation, active exploration, social experiences, and equilibration that interact to influence thinking.
• The information does not simply enter children's minds from the environment, it should ensure the learning of children.
• Hence by all these references, we can say that **Active exploration of the surrounding is essential for cognitive development.**​

Important Points

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

Additional Information

• According to Jean Piaget, Development in a child is only based on two factors, which are- 
• ​Physical Environment.
• Biological abilities.
• ​But in reference to Language development, he only recognizes cognition, According to him language is developed in a child only by his cognition, there is no interference from the environmental factor during language development.

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.

Vygotsky also said that for intellectual development, social and practical activities are required. Cognitive development is the product of the dynamic relations between the individual and society. There is a mutual relation between individual and society and it has its impact on both individual and society. Social interaction influences cognitive development by creating cognitive structures and thinking processes.

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

• ​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.
• As per the question, Sumit assists his friends in solving each question, this is an example of scaffolding.

Important Points

• Zone of Proximal Development (ZPD): The concept of MKO is closely related to ZPD. According to Vygotsky, ZPD is the difference between the present level of development attained without anyone’s assistance and the potential level of development that can be attained under the guidance of MKO.
• MKO (more knowledgeable others): Vygotsky defined the “More Knowledgeable Other” (MKO) as anyone who has a better understanding or a higher ability level than the learner, particularly in regards to a specific task, concept, or process. MKO could be teachers, parents, tutors, and even peers.

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

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

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

Key Points Vygotsky proposed three basic needs of students during learning, these are Zone of proximal development, Scaffolding, MKO (more knowledgeable others).

• Zone of Proximal Development: The concept of MKO is closely related to ZPD. According to Vygotsky, ZPD is the difference between the present level of development attained without anyone’s assistance and the potential level of development that can be attained under the guidance of MKO.
• Zone of proximal development (ZPD) drawing upon dynamic systems theory. The principal thesis maintains that ZDP is an emergent and dynamic system that is engendered by a dialectical concatenation of psychogenic and sociogenic facets of human development over time.
• ZPD is a gap between the learning of a child by self and the learning of a child with the help of others(society, culture, etc).
• So by all these references, we can consider that these gaps are comes again and again in different aspects of learning throughout life. Hence ZPD is a dynamic space.

Important Points

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

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.

 Carol Gilligan was one of Kohlberg's research assistants. She believed that Kohlberg's theory was inherently biased against women. Gilligan suggests that the biggest reason that there is a gender bias in Kohlberg's theory is that males tend to focus on logic and rules.

Key PointsGilligan felt that women went through the same three stages (Pre-conventional, Conventional, Post Conventional) of development developed by Kohlberg, but that women reasoned differently than men on moral issues due to having different perspectives on moral issues.

• According to Gilligan, Kohlberg has based his study primarily on a male sample and underestimates the moral reasoning of the females.
• Gilligan’s work on moral development focuses on how women’s morality is influenced by social interactions and relationships.
• She emphasizes that women's ways of thinking are often undervalued compared to men.
• Hence by all these references, we can say that the moral reasoning of the girls is underestimated in Kohlberg's moral development theory.

Important Points  Three levels of moral development by Kohlberg are Pre- Conventional, Conventional, Post conventional.

• Pre- Conventional Level: At this level, the child is not responsive to cultural rules and labels of good and bad, right or wrong but interprets these labels in terms of physical or hedonistic consequences of actions or in terms of physical powers of those who communicate the rules and labels. This level is further sub-divided into two stages.
• Conventional Level: At this level maintaining the expectations of the individual, family, group, or nation is perceived as of value in its own right regardless of the immediate and obvious consequences. The attitude is not only of personal expectations and social order but of loyalty to it of actively maintaining, supporting, and justifying the order, and identifying oneself with persons or groups involved in it.
• Post conventional level: At this level, there is a clear effort to define moral values and principles that have validity and application apart from the authority of the groups or persons.

The learner-centered approach to teaching puts learners in the center and gives primacy to children's experiences and needs. It strongly believes that when children are given the freedom to work at their own pace, they develop the ability to assimilate the concepts efficiently.

Key Points Characteristics of child-centered pedagogy for the classroom:

• In this approach, students are invited to participate actively in the learning process and prepared for self-help to shape their own experiences.
• In Child centered pedagogical methods children are the center of the classroom, and the environment of the classroom is fully free and democratic according to the needs and interests of the students.
• Students work in flexible, cooperative groupings to solve problems to demonstrate an understanding of the task that ensures their holistic development such as Phycological development, Cognitive development, etc.
• Students take leadership in the classroom, present their work, and facilitate groups.
• Different methods of teaching are used in child-centered education as per the needs, capacities, capabilities, and interests of the individuals in the classrooms.
• Hence by all these references, we can conclude that option (4) is the correct answer.

Hint

• Teachers are the passive participants in the child-centered classroom, Everything is decided as per the student's needs, such as environment, curriculum, ways of teaching, etc. ​​

Important Points  The environment of the classroom according to the child-centered approach:

• The child and not the teacher is the focus of the entire process of teaching-learning.
• The child is not a passive but an active participant in the classroom process.
• Has a democratic climate so that the child gets maximum opportunities for interaction with other children in the class, with the teacher, and with a variety of teaching-learning material.
• Teacher adopts a variety of teaching-learning strategies to address the needs of all children at the same time.
• The curriculum and the instructional materials serve as a means to foster the child’s all-around development and are not ends in themselves.
• Evaluation of the child’s attainment is done to ensure the child’s progress and not as a means of passing judgment on the child’s abilities and achievement. it is diagnostic as well as remedial.

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 Bias: Gender bias results when one gender is treated less favorably than the other, often referred to as sexism and it has a range of consequences including being Scientifically misleading. Upholding stereotypical assumptions. Validating sex discrimination.

Key Points

The environment of the classroom as per gender-biased:

• Not equal opportunities are provided to all in gender-biased culture.
• Deciding the work on the respect of sex promotes gender biases.
• Making seating arrangements different for girls and boys shows the gender-biased culture in the classroom.
• Gender-biased classrooms deemphasis the abilities of the students by segregating their work.
• So we can say that separate sitting arrangement promotes gender bias in the classroom.

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 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.​​

Additional Information

 Gender biased culture can be reduced by-

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

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

• “IQ” stands for “intelligence quotient.” A person's IQ is a score derived from standardized tests that were designed to measure human intelligence and intellectual potential. IQ tests include a variety of questions that measure reasoning and problem-solving skills

Key Points The IQ test as a measure of intelligence is a-

• Intelligence tests, paying specific attention to interpretations of and explanations for the comparatively low performance of racially and culturally diverse students on cognitive ability tests.
• Most of the research has targeted Black students' test performance and Black-White IQ differences.
• Intelligence tests contain cultural bias—they contain a strong bias that is in favor of White, middle-class groups; for example:
• (a) the tests measure knowledge and content that are more familiar to White, middle class 6 students than to diverse students.
• (b) the language on these tests is more familiar to White, middle-class students and
• (c) the examples used in the questions are more familiar to White, middle-class students.
• So by all these references, we can consider that the IQ test is a measure of intelligence that has been critiqued since many tests are culturally biased.​

Important Points

• An intelligence quotient (IQ) is a total score derived from a set of standardized tests or subtests designed to assess human intelligence.
• The intelligence quotient is a measure of a person's reasoning ability. In short, it is supposed to gauge how well someone can use information and logic to answer questions or make predictions. IQ tests begin to assess this by measuring short- and long-term memory.
• ${\bf{Intelligence}};{\bf{Quotient}};\left( {{\bf{IQ}}} \right) = \frac{{{\bf{Mental}};{\bf{Age}};\left( {{\bf{MA}}} \right);}}{{{\bf{Chronological}};{\bf{Age}};\left( {{\bf{CA}}} \right)}} × 100$
• Where Mental Age is based on intellectual development.
• Chronological Age is the number of years a person has lived.

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

National Education Policy 2020-

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

Key PointsSome important fundamental principles of the NEP 2020 are- 

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

So by **all these references, we can conclude that NEP 2020 includes assessment of the learner in all three aspects as Cognitive domain, affective domain, and psychomotor domain.**​

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.

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

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

Key Points Characteristics of critical thinking:

• Critical thinking develops the logic to solve the problem so that a student can learn conceptually by critical thinking.
• Direct involvement of the students in the problem related to critical problems.
• It encourages divergent thinking among the students, student covers all the possible aspects related to solving the problem.
• The learner reaches the solution by involvement in different aspects, such as searching, finding, etc.
• Solutions for the problem are taken out by a complete analysis of its pros and cons.
• So by all these references, we can say that the example in option (1) is not an example of critical thinking.

Hint

• Find the value of x if the equation 2x = 12, is related to the knowledge of basic mathematical operations, students should not have to think more critically in this type of thinking.

Individual differences refer to how individuals differ from each other. Different people have different interests; and their behavior is influenced by these interests, likings, dislikings, values, beliefs, etc. Even if we are of the same age group or gender, we are aware of how we differ from others and, others are also aware of these differences.

• For example, you may like dancing and gossiping with friends, but your friend may not like these.

Key Points In a classroom a teacher should treat individual differences:

• Teachers should not have to try to reduce or ignore individual differences because it makes the classroom interesting and also opposes the concept of inclusive education.
• Promotes learners to engage in activities and gives them equal opportunities to share their experiences.
• Students of different languages and cultures are admitted into the classroom, which affects the knowledge of all the students, so teachers should have to promote this diversity.
• Labeling should not be done in diverse cultural classrooms.
• The teacher should respect the values, knowledge, and culture of every student.
• So by all these references, we can conclude that providing equal **opportunities to the learners to share their experiences in the class and value them is the main characteristic of individual differences.**​

Important Points Effective ways for Educators to deal with Individual Differences:

• Knowledge of Individual Personality.
• Adjustment in Curriculum.
• Adjustment of Method of TeachingSpecial Program or Individualizing Instruction.
• Grouping of Learners.

Additional Information The individual difference depends on many factors such as -

• Genetic - This is a factor by which there are many types of individual differences are formed such as eye color, hair color, body shape, muscle growth, skin color, etc.
• Environmental factor- Environmental factor makes much impact on the child, such as their developmental pace, their thought power, etc.
• Cognitive ability- Every child's cognition is different, and their learning power is also different, so it also makes the individual difference between the students.
• Physical disability- If the child has some physical disability such as tilted bone, a fractured hand, dyslexia, dysgraphia, etc. these types of things make individual differences.

The disadvantaged child is one who is from a socially and economically backward section of the community, who cannot profit from school because of deprivation of one sort or another. Such children show cumulative academic deficits, a high dropout rate, and a progressive decline in intellectual functioning. 

Key Points To make improvements in the teaching-learning process of disadvantaged section learners: 

• The teacher is a key figure in the school to ensure inclusion. But his/her role in this process has been largely neglected so far.
• A teacher should adapt different pedagogy as per the needs of every child in the classroom.
• They should be encouraged to talk about and write about their own lives and experiences and these should be treated with respect in the classroom.
• The learners can be given a choice of choosing subjects for writing and books for reading.
• Sensitization of teachers from the stage of pre-service training onwards, developing special modules for use in teacher education and training programs.
• They should be allowed to work on collaborative projects and allowed to make decisions about the choice of topic, method, or group members.
• Co-curricular activities, such as sports, music, and drama which tend to break social barriers among children need to be encouraged.
• So that by all these references a teacher can promote the backward children.

Important Points Characteristics of Underprivileged Learners:

• Low cognitive abilities
• Poor linguistic ability
• Low self-esteem
• Involvement Gap
• Poor ability to read or write
• Their strengths: The higher sense of responsibility and emotional maturity.

Gifted learners: Gifted learners are those who display evidence of high-performance capabilities, in areas such as intellectual, creative, artistic, or leadership quality, or specific academic subjects, in comparison to others of the same age.

Key Points Characteristics of Gifted and talented students:

• They cover all the possible aspects of the problem.
• They are fully active and took part in the competitive environment.
• These children have divergent thinking and are very curious and inquisitive about nature.
• Gifted students learn things conceptually, they want to know the roots of the concepts.
• Gifted learners enjoy their work, and they never thought it was a boring task.
• Talented and Gifted students are ready to take on challenges.
• They always find multiple ways to solve the same problem.
• They connect their thoughts with the real world.
• They have originality in their thought process.
• So that by all these references we can consider that a gifted child is active, curious, and always ready to take on challenges.

Important Points Other Characteristics of Gifted Learner :

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

Learning Difficulties: When a person is facing difficulty in learning it may be due to physical limitations/disabilities such as - impairment in hearing, visual, low intellectual functioning, and inappropriate motor coordination. These physical disabilities will stand as obstacles in the path of learning. They limit the participation of the individual in the learning process. 

Key Points Learning difficulties can be cured by:

• Providing equal opportunities for either normal students or students with disabilities.
• According to the concept of inclusive education, All students should be learned under the same roof so that they can learn by interacting with each other.
• There is no restrictive environment in the classroom, the environment of the classroom is free for the students.
• The curriculum and activities should be based on the needs and interests of the students.
• So we can say that separation of the student for special education is a not desirable method to cure their learning difficulties.

Important Points  Characteristics of Learning Difficulties:

• Reverses letters or symbols too frequently while reading.
• Write letters or words either too close or too far (spacing problems).
• Poor in mathematical calculations.
• Reverses numbers too frequently while reading.
• General difficulty in memorizing things.

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

Attention deficit hyperactivity disorder(ADHD) is a brain disorder that affects how you pay attention, sit, still, and control your behavior. It happens in children and teens and can continue into adulthood. Children with ADHD may have trouble paying attention and controlling impulsive behaviors. ADHD is the most commonly diagnosed mental disorder in children.

Key Points  The main symptoms of ADHD include the following:

• Physical movement: Lack of muscle coordination, so a person who is ADHD disabled can not move easily.
• ​Inattention: Short attention span for age (difficulty sustaining attention) Difficulty listening to others.
• Impulsivity: Has difficulty waiting for his or her turn in school and/or social games, Takes frequent risks, and often without thinking before acting.
• Hyperactivity: Has difficulty remaining in his/her seat even when it is expected, Fidgets with hands or squirms when in his or her seat; fidgets excessively.
• So, Physical movement, Impulsivity, low attention span, fidgeting, and inability are primary characteristics of Attention Deficit Hyperactivity Disorder.​

Additional Information Some Other Common Learning Disabilities in Children:

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

Key Points  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. 

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

Important Points  Basic Principles of Inclusive Education:

• It promotes Multiple ways of representation of content.
• Students can engage in the learning process in multiple ways.
• The classroom is diverse and students, as well as teachers, can express their opinions in Multiple ways.
• It respects multiple languages and cultures.
• Use of specific pedagogical strategies.
• Sensitization towards individual differences.

Impairment or Disability in terms of blindness, low vision, leprosy-cured, hearing impairment, locomotor disability, mental retardation, and mental illness. According to the Persons with Disabilities Act, "person with a disability/impairment" means a person suffering from not less than forty percent of any disability as certified by a medical authority. 

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

Key Points There are many methods to teach visually challenged students such as:

• Teaching by explaining the concept in a loud way with clarity.
• The way of teaching is as so the students can form an image of the concept in their mind to learn it.
• Some materials used for the teaching of visually disabled students:
• Braille: Braille printed books, which have both braille and printed text on each page so that sighted students and adults can read along with students who have visual impairments.
• Tactile globe:  These globes have convex and concave features on the surface denoting coastlines and country borders which will useful for visually impaired students.
• Audio cassettes can also be used for teaching purposes. The audio materials should also have audio so that those without sight can understand their learning effectively.
• Screen reading software: Screen readers are software programs that allow blind or visually impaired users to read the text that is displayed on the computer screen with a speech synthesizer or braille display.
• So, by all these references we can conclude that a colorful worksheet is not an essential material for the learning of visual impairment students.

Hint

• The use of colorful worksheets is an irrelevant method of teaching for the visually challenged students, because they can not see anything properly.

Important Points  Ways that can help in the learning of visual impairment- 

• Use textbooks with big letters, so that they can read them easily.
• Make optimum distance which is required to see clearly.
• The use of dark material for learning can help them,
• They should be seated in the first row of the classroom.

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

Key Points Characteristics of Socio-constructivist classroom:

• 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.
• Encourage students to take responsibility for their own learning, and this includes reflecting on their own thinking and learning processes
• It views learners as makers of meaning and creators of knowledge through social interaction.
• Connect learning with everyday contexts. Where possible, organize courses around problems, of local interest and impact, which have been identified by students.
• Elicit students’ existing ideas, including any alternative conceptions.
• It emphasizes collaboration with others for learning, work, performance, problem-solving, etc.
• It allows learners to foster their own strategy of learning to perform an activity.
• The classroom should be child-centered, not teacher-centered so that students are allowed to ask questions freely
• So by all these references, we can consider that learning in groups, and problem-solving in a group encourages the socio-constructivist classroom.​

Hint

• Fixed sitting arrangement is the emphasis on the feelings of the students as to why they always sit at the corner? and why do they always sit at the last bench? so that fixed sitting arrangement is not a characteristic of socio-constructivism classroom, because here is a collaboration in all the aspects in the classroom.
• Students or learners should be active participants in the classroom, they do not engage in instructional-based learning.
• In a socio-constructivist classroom, Conceptual teaching is preferable, it opposes rote memorization.

Performance of the students depends on many factors such as the development of the students, nutrition, cognition, abilities, disabilities, environment, family backgrounds, Friends, Teaching methods, the environment of the classroom, behavior of the teacher, etc. So that we can say that performance of a child varies from each other.

Key Points When students are not good performers a teacher:

• Using different methods of teaching to know about all the aspects/skills of the students.
• Performance should be maintained by analyzing the system of the teaching-learning process from time to time.
• Make the classroom free for students so that they can engage in the learning process easier.
• Teachers should have to cover all the needs of the students which can motivate them to maintain their performance.
• Learning should be done in a collaborative manner.
• Never leveling the students on behalf of their performance, marks, and score.
• Always use a diagonestic type test to assess students.
• So by all these aspects, we can conclude that the performance of the student can be understood by the teacher by analyzing the system.

Hint

• Blaming the parents for the low performance of the student is irrelevant, teachers, schools, and teaching methods are also part of the performance of the students.
• Shaming students discourages students, which makes an negative impact on the learning process of the learners.
• Referring the students to special schools is not the best way to enhance their performance, although it opposes the concept of inclusive education so it is an irrelevant option.

Learned helplessness underlies psychological cases of depression. It has been found that continuous failure in a set of tasks shows the occurrence of learned helplessness. 

Key Points Learned helplessness is often measured in terms of the subject’s ability and persistence before they give up the task.

• It is acquired behavior that will not succeed and Continuous failure which leads to little persistence and poor performance. This shows helplessness. A child acquires the behavior that he will not succeed in his tasks.
• It also accentuates some of the negative conditions such as depression, disease susceptibility
• The loss of self-esteem may also occur if the individual believes that he/she is personally accountable for the situation.
• So we can consider that the **Internalization of continuous experiences of ‘not understanding’ and blaming the self for the inability to learn and perform in the classroom can potentially result in learned helplessness.**​

Additional Information

• ​The concept of learned helplessness was discovered by psychologists Martin Seligman and Steven F. Maier. They had initially observed helpless behavior in dogs that were classically conditioned to expect an electric shock after hearing a tone.
• Experiment: The dogs were placed in a shuttle box that contained two chambers separated by a low barrier. The floor was electrified on one side, and not on the other. The dogs previously subjected to classical conditioning made no attempts to escape, even though avoiding the shock simply involved jumping over a small barrier.

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

Key Points Some important objectives of learning in the classroom:

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

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

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

Key Points Characteristics of Meaningful Learning:

• It stresses the ability of the learner to apply what is learned because of the involvement of the learners.
• Meaningful learning is possible only when learners make a deliberate effort to relate new knowledge to the relevant concept they already know.
• The main focus of a meaningful learning system is to motivate students for gaining knowledge, not for performance
• It is the active creation of knowledge structures from personal experience.
• .It should be done by the collaboration of the student with the environment which helps them to engage in meaningful learning and learns conceptually.
• Meaningful learning is possible when the learner's thoughts are divergent and they are able to collect knowledge, i.e. discovery learning.
• So that we can consider that **Meaningful learning takes place through active interactions of students with the environment.**​

Hint

• The shape of meaningful learning is spiral not learner, students can learn as a concept by interacting with their previous knowledge.
• In meaningful learning, a teacher should respect the needs, interests, and emotions of all the students, so that they can learn free in their environment.
• Meaningful learning is not instructional-based learning, students can learn conceptually by constructing knowledge from different sources.

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 Motivation can help the students in learning as:

• 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 motivate their students so that they can be fully mastery and goal-oriented.
• Motivation helps students to gain capacities for learning, by focusing on the approach to learning.
• Motivation is the panacea for demotivated students or those who have capabilities but don't perform well.
• So we can consider that Approach focused, mastery goals should be promoted among students for motivating them to learn.​

Hint

• 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.
• Performance goals are short-term objectives that an employee is expected to achieve within a set period of time. These goals are usually attached to specific job positions and are determined after considering the tasks and duties an employee is required to perform in that position.

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

Key Points Characteristics of Metacognition:

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

Important Points

• Intuitive theory: an intuitive theory of psychology features observable concepts, such as actions, and unobservables, such as mental states.
• Accommodation refers to the part of the adaptation process. The process of accommodation involves altering one's existing schemas, or ideas, as a result of new information or new experiences.
• Visual Hierarchy is used to rank design elements and influence in the order you want your users to view them. By using principles like contrast, scale, balance, and, more, you can help establish each element in its rightful place and help the most important elements stand ou

Effective teaching is a term used to describe the knowledge, strategies, and conduct of a successful Teacher. It's the ability to make a positive impact on a student's life and academic career, including the capacity to teach important skills, introduce new concepts and manage any classroom concerns.

Key Points  Characteristics of effective learning:

• ​It makes the thought process of the students conceptually.
• In this type of teaching, the teacher should value the emotional needs of the students..
• It should be done after a complete analysis of the curriculum, facts, concepts, perspectives, environment, and interest in learning of the students.
• It considers the prior knowledge of the students and tries to link the concept from the previous knowledge and experiences of the students.
• No rigidity in the classroom.
• Teaching-learning leads toward the holistic development of the students.
• By all these references we can consider that effective learning is based on a complete analysis of all facts and concepts also it is connected with previous experiences by the teachers.

Hint 

• In an effective teaching method, the teaching of the student doesn't depend on textbooks, it is dependent on various and different methods of teaching.
• The effective teaching-learning process never promotes rote memorization, student learns conceptually by using different methods of learning.

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

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

Key Points

 ​Characteristics of Conceptual learning:

• Conceptual learning makes learners thought processes divergent, by which students can think about all the possible positive and negative aspects related to the problem.
• It opposes rote memorization.
• It establishes the inter-relation between the previous knowledge of the students and the concepts.
• Conceptual learning can be best understood by the learners by giving examples and non-examples to them.
• It improves the analysis and observational skills of the learners.
• Concept understanding is done by creativity, analogies, critical thinking, etc.
• The path of conceptual learning is from simple to complex, first students have to learn simple concepts, and then they have to learn complex concepts on the basis of simple concepts.
• Conceptual learners always think divergently, they cover all the possible ways to solve the problem.
• So by all these references, we can consider that mere reproduction of information is not a part of conceptual understanding.

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

• Example: A parent might display emotions of happiness as their child receives a gold medal.

Key Points There are many emotions while dealing with different persons and objects in the environment. They can be negative emotions like fear and anxiety or positive emotions like pleasure, pride, and love.

• Pride: Pride is an emotional response or attitude to something with an intimate connection to oneself, due to its perceived value.
• It is an emotion that encourages students to put effort into learning.
• This emotion necessarily requires a sense of self and the ability to reflect on one’s actions.
• So **we can conclude that pride is an emotion that would encourage students to put the effort into learning.**​

Important Points Some of the other emotions which are seen in daily life are:

• Hope: Hope is an emotion characterized by positive feelings about the immediate or long-term future. Often hope is coupled with high motivation, optimism, and a generally elevated mood.
• Frustration: Frustration is a common emotional response to opposition, related to anger, annoyance, and disappointment. Frustration arises from the perceived resistance to the fulfillment of an individual's will or goal and is likely to increase when a will or goal is denied or blocked.
• Pleasure: Pleasure or happiness is a positive emotion that gives satisfaction to the person who experiences it. Pleasure is the reaction to the satisfaction of a need or the attainment of a goal. When we are happy we smile and laugh and there is a clear expression of satisfaction on our faces.
• 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.
• Enjoyment: A feeling of taking pleasure in what is going on around you, especially in situations like a leisure activity or social gathering.
• Boredom: ​The state of feeling disinterested in one's surroundings, having nothing to do, or feeling that life is dull.
• ​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.
• Affection: It is a pleasant emotional reaction directed towards a person, an animal, or an object. It is built up as a result of the pleasant experience. The most primitive basis of affection is associated with the warmth of the mother’s body, and being fondled and cuddled.

Calculation:

 $(\frac{2}{3} \space of \space 3\frac{1}{4} ) - (\frac{3}{4}\times (2\frac{1}{4}-1\frac{2}{3}))$

⇒ \()\((\frac{2}{3} \times \frac{13}{4} ) - (\frac{3}{4}\times (\frac{9}{4}-\frac{5}{3}))\)

⇒ $( \frac{13}{6} ) - (\frac{3}{4}\times \frac{7}{12})$

⇒ $\frac{13}{6} - \frac{7}{16}$ 

⇒ $\frac{83}{48}$

Given:

Number 5432x7 is divisible by 9.

Concept:

A number is divisible by 9 if the sum of its digits is divisible by 9 

Calculation:

Sum of digits = 5 + 4 + 3 + 2 + x + 7

⇒ 21 + x

⇒ x = 6

21 + 6 = 27 is divisible by 9.

Given:

 4003250 = 4 × 10x + 3 × 10y + 2 × 10z + 5 × 10w

Calculation:

4003250 = 40 lakhs 3 thousands 2 hundreds fifty

So, 40 lakhs = 4 × 10⁶

3 thousands = 3 × 10³

2 hundreds = 2 × 10²

Fifty = 5 × 10¹

⇒ 4003250 = 4 × 10⁶ + 3 × 10³ + 2 × 10² + 5 × 10¹

On comparing  x = 6, y = 3, z = 2, w = 1

∴  x + y + z + w = 12

Concept:

$\sqrt{a^m}$ = $a^{(m/2)}$

Calculation:

4096 = 2¹²

⇒$\sqrt{4096} =$ 2⁶ 

⇒ 64

∴  $\sqrt{0.004096}$ = $\sqrt{0.000001} × \sqrt{4096}$

⇒ 0.001 × 64

⇒ 0.064

Calculation:

Fraction which is less than $\frac{7}{8}$ and greater than $\frac{1}{3}$

∴ The fraction will be lies between 1/3 and 7/8.

⇒ 1/3 = 0.33 and 7/8 = 0.875

⇒ Option 1: 1/4 = 0.25 ; not lies between 1/3 and 7/8.

Option 2: 23/24 = 0.95 ; not lies between 1/3 and 7/8.

Option 3: 11/12 = 0.91 ; not lies between 1/3 and 7/8.

Option 4: 17/24 = 0.70 ; It lies between 1/3 and 7/8.                    Hence, 17/24 is less than 7/8 and greater than 1/3

Given:

In ΔABC and ΔADB,

∠C = ∠D = 90° 

BC = AD

and ΔABD ≅ ΔBAC

Concept:

RHS rule: If in two right-angled triangles the hypotenuse and one side of a triangle is equal to the hypotenuse and the corresponding side of another triangle then the triangles are said to be congruent by RHS rule. 

Calculation:

In ΔABC and ΔADB,

BC = AD (given)

∠C = ∠D = 90° (given)

AB (hypotenuse of both the triangles) is common

Hence ΔABD and ΔBAC are congruent by RHS rule.

Given:

AC = AE and ∠EAB = 32° and ∠ACD = 125°

Concept:

In an isosceles triangle angles opposite equal sides are equal.

Sum of interior opposite angles is equal to exterior angle.

Calculation:

 ∠ACE + ∠ACD = 180^∘ 

⇒ ∠ACE = 55^∘ 

Also, ΔAEC is isosceles with AE=AC 

∴ ∠AEC = ∠ACE

⇒ ∠AEC = 55∘ 

Now,

 ∠EAB + ∠ABC =  ∠AEC

⇒ ∠ABC = 55∘ - 32°

⇒ ∠ABC = 23^∘ 

Given:

BO is the bisector of ∠DBC and CO is the bisector of ∠ECB

Also, ∠BOC =85^∘ 

Concept:

The intersection point of external bisectors is excentre ,∴ O is the excentre 

Formula:

∠BOC = 90^∘ -  $\frac{∠BAC}{2}$

Calculation:

85^∘ = 90^∘ -  $\frac{∠BAC}{2}$

⇒ ∠BAC = 10^∘ 

Given:

Measure of angle is twice the measure of its supplementary angle.

Concept:

Sum of supplementary angles = 180^∘ 

Calculation:

Let required angle be x

∴ Its supplementary angle = 180^∘ - x

According to question, x = 2(180^∘ - x)

⇒ 3x = 360^∘ 

⇒ x = 120∘

Given:

Vertices of polyhedron = 12

Faces of polyhedron = 8

Formula:

By Euler's Formula,

F + V = E + 2

Calculation:

8 + 12 = E + 2

⇒ E = 18

Shortcut Trick

Area = Total Cost ÷ Rate per m²

⇒ Area = 4000 ÷ 125 = 32 m²

Breadth = Area ÷ Length

⇒ Breadth = 32 ÷ 8 = 4 m

∴ The correct answer is 4 m.

Alternate Method

Given:

Total Cost of tiling = ₹ 4000

Rate of tiling = ₹ 125 per m²

Length (L) of the floor = 8 m

Formula Used:

Area of Rectangle = Length × Breadth

Area = Total Cost ÷ Rate

Calculations:

⇒ Area = 4000 ÷ 125

⇒ Area = 32 m²

⇒ Length × Breadth = 32

⇒ 8 × Breadth = 32

⇒ Breadth = 32 ÷ 8

⇒ Breadth = 4 m

∴ The correct answer is 4 m.

Additional Information

Perimeter of Rectangle

The total boundary length of a rectangle is given by 2 × (Length + Breadth).

Diagonal of Rectangle

The distance between opposite corners is calculated using Pythagoras theorem: √(Length² + Breadth²).

Cost of Fencing

Unlike tiling (Area), fencing cost is calculated on the Perimeter: Total Cost = Perimeter × Rate per meter.

Given:

The inner and outer radii of circular track are 21 m and 28 m respectively.

Cost of levelling the track at Rs. 5 per m2. 

Formula:

Area of track = $\pi$(R₂² -R₁²) 

Total cost = Total area × Cost per unit area 

Calculation:

Area = (22/7) × (28² - 21²)

⇒ 1078 m²

∴ Cost = 1078 × 5 

⇒ Rs. 5390

Given:

Dimensions of each small box are length 0.2 m,  breadth 0.4 m and height 0.5 m.

Dimensions of bigger box are  length 2 m, breadth 1 m and height 0.5 m.

Formula:

Number of boxes = Volume of bigger box / Volume of each small box

Calculation:

Volume of bigger box = 2 × 1 × 0.5

⇒ 1 m³

Volume of each smaller box = 0.2 × 0.4 × 0.5

⇒ 0.04 m3

∴ No. of boxes = 1/(0.04)

⇒ 100/4

⇒ 25

Given:

Numbers from 1 to 50

Concept:

A Prime number is a number that has exactly two factors(1 and the number itself)

Probability = number of favorable outcomes / total outcomes

Calculation:

Prime numbers from 1 to 50 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47

⇒Total prime numbers from 1 to 50 are 15

∴ Probability = 15/50

⇒ 3/10

⇒ 0.3

Shortcut Trick

Sort the data: 1, 1, 2, 2, 2, 2, 3, 3, 4, 5, 5, 6, 6, 6.

Median (average of 7^th and 8^th terms) = (3 + 3) ÷ 2 = 3.

Mode (most frequent value) = 2 (appears 4 times).

Range (Max − Min) = 6 − 1 = 5.

Mean = (3 + 2 + 5) ÷ 3 = 10/3.

∴ The correct answer is 10/3.

Alternate Method

Given Data: 1, 2, 3, 3, 2, 5, 6, 2, 2, 1, 4, 6, 6, 5

Formula Used:

Median = Average of middle terms (for even n); Mode = Value with highest frequency; Range = Maximum − Minimum; Mean = Sum of observations ÷ Number of observations.

1 2 3 4 5 6

Given:

$(\frac{3}{4} x - \frac{5}{6}y) ^2 = \frac{9}{16}x^2 + Ay^2 + Bxy$ 

Formula:

(a - b)² = a² - 2ab + b2

Calculation:

$(\frac{3}{4} x - \frac{5}{6}y) ^2 = \frac{9}{16}x^2 + \frac{25}{36}y^2 -\frac{5}{4}xy$

On comparing , we get A = $\frac{25}{36}$  and B = $(-\frac{5}{4})$

⇒ A - B = $\frac{25}{36} - (-\frac{5}{4})$

⇒ $\frac{35}{18}$

Given:

50% of (x - y) = 30% of (x + y)

Concept:

For same base we can add or subtract percentages

Calculation:

50% of (x - y) = 30% of (x + y)

⇒  50% of x -  50% of y =  30% of x +  30% of y

⇒  (50% - 30%) of x = (50% + 30%) of y

⇒  20% of x = 80% of y

⇒ x = 4y

∴  (y/x) × 100 = 25%

Given:

A = -3x3y2 + 2x2y3, B = -3x2y3 - 5y4 and

C = x4 + 2x3y2 + 3x2y3 + y4

Concept:

When LHS = RHS , we can compare coefficients.

Calculation:

C - (A + B)

⇒ (x4 + 2x3y2 + 3x2y3 + y4) - (( -3x3y2 + 2x2y3) + (-3x2y3 - 5y4))

⇒ x⁴ + 5x3y2 + 4x2y3 + 6y⁴

On comparing coefficients with x4 + mx3y2 + nx2y3 + 6y4

⇒ m = 5 , n = 4

∴ m + n =9

Shortcut Trick

Identify the product xy using 2xy = (x + y)² − (x² + y²).

2xy = 1² − 41 = −40 ⇒ xy = −20.

The expression 1/x + 1/y simplifies to (x + y) / xy.

Substituting the values: 1 / (−20) = −1/20.

∴ The correct answer is − 1/20.

Alternate Method

Given:

Sum of terms: x + y = 1

Sum of squares: x² + y² = 41

Formula Used:

Algebraic Identity: (x + y)² = x² + y² + 2xy

Reciprocal sum: 1/x + 1/y = (x + y) / xy

Calculations:

⇒ (1)² = 41 + 2xy

⇒ 1 = 41 + 2xy

⇒ 2xy = 1 − 41

⇒ 2xy = −40

⇒ xy = −20

Now, evaluate the required expression:

⇒ 1/x + 1/y = (x + y) / xy

⇒ 1/x + 1/y = 1 / (−20)

⇒ 1/x + 1/y = −1/20

∴ The correct answer is − 1/20.

Additional Information

Algebraic Identities

Standard square identity: (a + b)² = a² + b² + 2ab and (a − b)² = a² + b² − 2ab.

Reciprocal Sum Property

For any non-zero variables x and y, the sum of their reciprocals 1/x + 1/y is always equal to their sum divided by their product: (x + y) / xy.

Sum of Cubes Identity

The identity for cubes is x³ + y³ = (x + y)(x² − xy + y²), which can be solved if the sum and product are known.

Given:

10(x + 6) + 8(x - 3) = 5(5x - 4)

Calculation:

 10(x + 6) + 8(x - 3) = 5(5x - 4)

⇒ 10x + 60 + 8x - 24 = 25x - 20

⇒ -7x = -56

∴ x = 8

∴ $\frac{5x + 2}{6}$  = 7

It is echoed in the National Curriculum Framework 2005, “Developing children’s abilities for

mathematization is the main goal of mathematics education.”

Key Points

Desirable Skills to be developed in children as a part of mathematization:

• Problem-solving is an important life skill that suggests a shift from memorization to the understanding of concepts and the ability to apply those in both familiar and unfamiliar situations, whether in daily life problems or problems given in the textbooks.
• Estimating quantities and approximating solutions when exact ones are not available are considered essential skills required for scientific investigations.
• If children are made to identify regularities in events, shapes, designs, and sets of numbers they will realize that regularity is the essence of mathematics. It provides the basis for inductive learning too.
• The process of reasoning and proof is important in mathematics. So school mathematics should encourage proof as a systematic way of argumentation.
• The aim should be to develop arguments, evaluate arguments, make and investigate conjectures, and understand that there are various methods of reasoning.

​Hence A & B are the correct options.

 Additional Information 

• ​On the other hand, Children recalling the formulae and using them to find out a single solution encourages rote memorization and a restricted environment to find a single answer which is not a part of mathematization.

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

Key Points

• According to Polya, the sequence of all the four steps in problem-solving is as:
• Understand the problem
• Devise a plan
• Carry out the plan
• Look back

Additional Information 

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

Hence, we can conclude that 'Revise a plan' is not the correct option.

Important PointsA fraction represents the distribution of a whole into many parts, it has two parts numerator and a denominator the parts selected are denoted in the numerator and the whole parts in the denominator. Fraction is a kind of topic that occurs often in real life also so they should be introduced in a situation based manner like :

• Birthday situations of students can be utilized to take the cake as a whole and distribute the pieces and teach.
• By distributing objects among the students which are part of teaching-learning material and teaching.
• The classroom can be taken as an example and the fraction where boys are seated can be divided and taught.
• Real-life examples like a father distributing his property to his children can be taken and fractions can be introduced in the form of role-playing.
• The whole school can be taken and in each classroom as a part, fractions can be introduced.

Additional InformationOn the other hand First writing the topic on the blackboard then teaching the concept, introducing the numerator and denominator in different types of fractions, and writing the fraction on the blackboard in the form of where y ≠ 0, then teaching the fraction will not be so effective in introducing fractions because here the students remain passive most of the time.

Misconceptions are also a part of learning where the children learn the concept but they learn wrong. These misconceptions need to be cleared by the teacher and addressed to the students at a very earlier stage only or else children apply this false knowledge as they progress further.

 Key Points

To clear the misconceptions of students a teacher should:

• Deliver the content to them in a clear manner without giving scope to any ambiguity.
• Give a chance for the students to ask questions in between also because if they are not answered misconceptions will develop.
• Observe students' work and talk to them to assess their understanding of a concept and clear if they have developed any wrong concept.
• Assess students at regular intervals so that their conceptual understanding of them can be checked.
• Should not hesitate to clear the same doubt asked by the child again and again.

Hence By observing students' work and talking to them to assess their understanding of a concept a teacher help his/her students with their misconceptions in mathematics.

Area and perimeter are one of the important topics of mathematics which also is applied in real life, so this should be taught through real-life situations only like in the above example.

Key Points

• Area:- Here the teacher gives 15 tiles to the students and asks them to arrange them in all possible rectangular ways here the concept of the area can be taught, for example, if the students arrange 5 tiles in three rows then the length becomes 5 and breadth becomes 3 so area = length * breadth = 5*3 =15
• Perimeter is the addition of all sides of a figure so if the students arrange all 15 tiles in a single row here length becomes 15 and breadth becomes 1 so perimeter = 15+1+15+1 = 32
• Factors:- Here everything is about distributing 15 into its factors so that different lengths and breadths are found like 151, 53, 35, 115, etc.

Hence Area, factors, and perimeter can be taught through the above example.

 Additional InformationMoreover, a tile is a 2D object. A 2D shape is a figure that has only length and height as its dimensions. Because 2D shapes lie on a flat surface, they are also known as plane figures or plane shapes. While they have areas, 2D shapes have no volume. Apart from length and height, a 3D shape also has width or depth as its third dimension.

According to National Curriculum Framework 2005, “Developing children’s abilities for

mathematization is the main goal of mathematics education.”

Key Points

• Developing the ability of mathematization which is regarded as constituting the higher aims of mathematics, includes developing such abilities as problem-solving, spatial reasoning, use of heuristics, estimation and approximation, optimization, and use of patterns. visualization, representation, reasoning, proof, making connections, and mathematical communication.
• Spatial reasoning is a category of reasoning skills that refers to the capacity to think about objects in three dimensions and to draw conclusions about those objects from limited information. By doing all the activities mentioned above with the concrete materials given by the teacher children develop the ability to use spatial reasoning.
• The prediction and visualization technique helps in recall and comprehension of the data, children visualize all the concrete materials provided by the teacher and predict different types of arrangements of the shapes without overlap.

​Hence the teacher can use this activity to identify individual differences among her learners in their ability to use spatial reasoning, prediction, and visualization in problem-solving situations.

Data handling is one of the important topics in mathematics that deals with collecting, organizing, and analyzing data. In the above example teacher gave the activity  ‘Survey of socio-economic status of the families of a nearby village.’. The purpose of this activity is 

Key Points

• To introduce data handling to students in an activity method.
• To make students apply the knowledge they have learned in real-life situations.
• To connect the classroom experience with the real world outside the classroom where the application of knowledge happens. which indicates meaningful learning.
• To enhance the student's social and analytical skills.
• To provide an opportunity for students to collect information from the field to understand the area where data handling is applied.

​Hence A & C are the correct options.

 Additional Information​On the other hand, observing different shapes in the surroundings is not a purpose of this activity and survey since it is related to shapes and geometry, not data handling

Error analysis is a method commonly used to identify the cause of student errors when they make consistent mistakes. It is a process of reviewing a student’s work and then looking for patterns of misunderstanding. Errors in mathematics can be factual, procedural, or conceptual, and may occur for several reasons. 

Important Points

Conceptual errors occur when students have misconceptions and poor understanding of mathematics concepts, procedures, and applications. 

• This occurs due to a lack of understanding of the concept.
• In the above example, the child applied the normal addition concept of numbers for the variables also.
• In conceptual error learners, children not only get the wrong answer but they follow the wrong method also due to misconception.
• Conceptual errors may look like procedural errors, but they occur because the student does not fully understand a specific math concept, such as place value. To determine if an error is conceptual, teachers should check by asking the student to represent the problem with concrete objects or show and explain the steps used to solve the problem.

​Hence the above error is a conceptual error.

Additional Information

Starting with his definitions, Euclid assumed certain properties, which were not to be proved. These assumptions are actually ‘obvious universal truths’.

He divided them into two types: axioms and postulates.

• He used the term ‘postulate’ for the assumptions that were specific to geometry. Common notions (often called axioms), on the other hand, were assumptions used throughout mathematics and not specifically linked to geometry.

 Key Points

Euclid’s five postulates:

• A straight line may be drawn from anyone point to any other point.
• A terminated line can be produced indefinitely.
• A circle can be drawn with any center and any radius.
• All right angles are equal to one another.
• If a straight line falling on two straight lines makes the interior
  

angles on the same side of it taken together less than two right angles, then the two straight lines, if produced indefinitely, meet on that side on which the sum of angles is less than two right angles.

​​Hence "A circle can be drawn with any center and any radius". According to Euclid, this statement is a postulate.

 Additional Information

Mathematics anxiety is a feeling of fear or tension which occurs in a student while he/she is dealing with maths problems and also a fear that the final answer may be wrong. 

Key Points

Mathematics Anxiety goes unnoticed among high achievers because

• teachers always have special attention to high achievers.
• they always look at their work, and their way of solving problems and try to facilitate them if they get stuck at any point.
• these students perform well on tests hence teachers and parents only look at their performance and not emotional factors.
• parents also without being emotional just concentrate on their performance and what more they can do to improve it.

​Hence mathematics anxiety goes unnoticed among such students because these students perform well on tests hence teachers and parents only look at their performance and not emotional factors.

The correct answer is Convection and Radiation.

Concept: 

Conduction

• The process by which heat is transferred from the hotter end to the colder end of an object is known as conduction.  In solids, generally, the heat is transferred by the process of conduction
• For example, The heat from the metal handle utensils when put on the gas stove and heated.

Convection

• When water is heated the water near the flame gets hot. Hot water rises up. The cold water from the sides moves down towards the source of heat. This water also gets hot and rises and water from the sides move down. This process continues till the whole water gets heated. This mode of heat transfer is known as convection.

Radiation

• In solids, generally, the heat is transferred by conduction.
• In liquids and gases the heat is transferred by convection. No medium is required for transfer of heat by radiation.
• From the sun the heat comes to us by another process known as radiation.
• The transfer of heat by radiation does not require any medium. It can take place whether a medium is present or not.
• When we sit in front of a room heater, we get heat by this process.
• A hot utensil kept away from the flame cools down as it transfers heat to the surroundings by radiation.

Explanation:

Here, The heat from the burning of wood in a room spreads to corner of the room, the methods of spreading heat in the room is through -

• Radiation - Heat is transferred on the other side of the room through radiation (without touching)
• Convection - The air near the burning wood is heated and goes above while the nearby cold air comes in and the cycle continues. This is a way of convection method of heating in the room.

So the correct answer is Convection and Radiation.

The correct answer is Amplitude of vibration of the roar of a lion is larger as compared to the bird's sound.

Concept:

• Amplitude (A): The maximum amount of displacement of the medium particles from their mean position is called the amplitude of the wave.

• Frequency is the number of oscillations per second and is expressed in hertz.
• The amplitude of vibration is measured by displacement from the mean position.

Explanation:

• The amplitude of a sound determines its loudness.
• When the amplitude of vibration is large, the sound produced is loud.
• When the amplitude is small, the sound produced is feeble.

Therefore, the roar of a lion is loud and the sound of the bird is feeble. 

Additional Information

• The frequency determines the shrillness or pitch of a sound.
• If the frequency of vibration is higher, the sound is shrill and has a higher pitch.
• If the frequency of vibration is lower, the sound has a lower pitch.
• For example, A bird makes a high-pitched sound whereas a lion makes a low-pitched roar. However, the roar of a lion is very loud while the sound of the bird is quite feeble.

The correct answer is A, C, D.

Explanation:

• In low-pressure areas, cyclones are wind storms accompanied by heavy rainfall.
• The centre of a cyclone is a calm area. It is called the eye of the storm. A large cyclone is a violently rotating mass of air in the atmosphere, 10 to 15 km high.
• The diameter of the eye varies from 10 to 30 km. It is a region free of clouds and has light winds.
• Around this calm and clear eye , there is a cloud region of about 150 km in size. In this region there are high-speed winds (150–250 km/h) and thick clouds with heavy rain.
• Away from this region the wind speed gradually decreases. The formation of a cyclone is a very complex process.
• Factors like wind speed, wind direction, temperature and humidity contribute to the development of cyclones.
• A tornado may form within a cyclone. The effect of low pressure in a cyclone's eye causes a tornado to form.
• A tornado is a dark funnel-shaped cloud that reaches from the sky to the ground.
• The chain of events ends with the formation of a very low-pressure system with very high-speed winds revolving around it.

Concept:

Motion:

• A body is said to be in motion if its position changes continuously with respect to its surroundings with time.
• 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.

Non-uniform Motion:

• It is a motion in which the velocity varies with time. Here acceleration of the motion will not be 0.
• The variation of the distance h with the time t for the uniform acceleration f and constant initial speed u can be explained by,

h = ut + 0.5ft2

• The above is representing the parabolic variation of distance h with the time t.

Uniform Motion:

• It is a motion in which a material point moves in a straight line and covers equal distance in equal intervals of time.

If f = 0 (uniform speed u) 

• h = ut →  The distance-time graph of an object is a straight line for the constant initial speed u.

Explanation:

• If u = constant and f = 0 then the above variation of h with t is valid which is fulfilling the conditions for the above case.

⇒ It is moving with uniform speed.

• If u = 0 and f = 0 then also the above variation of h with t is valid (As f  = 0  for u = 0 which is fulfilling the conditions for the above case)

⇒ It is at rest.

• The change in the position of an object with time can be represented on the distance-time graph.
• When an object travels equal distances in equal intervals of time, then it  moves with uniform speed.
• This shows that the distance travelled by the object is directly proportional to the time taken.
• Thus, for uniform speed, a graph of distance travelled against time is a straight line.
• Therefore it can be concluded that the object is in uniform motion or is at rest.

Therefore, from the above discussion, we can conclude that statements A and B can be possible from this graph. Hence option B is the correct answer.

The correct answer is  c → a → d → b → e.

Explanation:

• Wool and silk fibres are obtained from animals.
• Wool is obtained from the fleece (hair) of sheep.

• Sequence of steps in processing of the hair of sheep to wool are:
• Shearing:
• It is the first step of processing of wool.
• The fleece of the sheep along with a thin layer of skin is removed from its body. This process is called shearing.
• Usually, hair are removed during the hot weather. This enables sheep to survive without their protective coat of hair. The hair provide woollen fibres.
• Scouring:
• It is the second step of processing of wool.
• The sheared skin with hair is thoroughly washed in tanks to remove grease, dust and dirt. This is called scouring. Nowadays scouring is done by machines.
• Sorting:
• It is the third step of processing of wool.
• After scouring, sorting is done.
• The hairy skin is sent to a factory where hair of different textures are separated or sorted.
• Carding: 
• It is the fourth step of processing of wool.
• The small fluffy fibres, called burrs, are picked out from the hair. These are the same burrs which sometimes appear on your sweaters. The fibres are scoured again and dried. This is the wool ready to be drawn into fibres.
• Weaving and dying: 
• It is the last step of processing of wool.
• The fibres are straightened, combed and rolled into yarn. The longer fibres are made into wool for sweaters and the shorter fibres are spun and woven into woollen cloth.
• The fibres can be dyed in various colours, as the natural fleece of sheep and goats is black, brown or white.

a) Shearing a sheep (cutting the hair of sheep along with a thin layer of skin in one piece)

b) Scouring in tanks

c) Scouring by machines processing fibres into wool.

d) Rolling into yarn.

The correct answer is Iodine.

Key Points

• Antiseptics are chemicals that either kill or prevent the growth of microorganisms in or on living tissue.
• Antiseptics are applied to living tissues such as wounds, cuts, ulcers, and diseased skin surfaces.
• Iodine, chlorhexidine, alcohol, acetate, hydrogen peroxide, boric acid, silver nitrate, silver sulfadiazine, and sodium hypochlorite are among the most commonly used wound treatments today.
• Iodine is a powerful antiseptic. Its 2-3 percent solution in the alcohol-water mixture is known as a tincture of iodine. It is applied to wounds

Thus, iodine can be put on wounds as an antiseptic.

The correct answer is A = Magnesium oxide, B = Basic.

Explanation:

• When magnesium ribbon is burned, it reacts with the oxygen in the air to produce magnesium oxide.
• The following reaction takes place:

2Mg (s)+O₂ (g) → 2MgO (g)

• When magnesium oxide is dissolved in water magnesium hydroxide is formed. It is a chemical change. As a result of the reaction between magnesium oxide and water, a new substance (magnesium hydroxide) is formed.
• The following reaction takes place:

Magnesium oxide (MgO) + Water (H₂O) → Magnesium hydroxide [Mg(OH)₂]

• Magnesium hydroxide is a base.
• Milk of magnesia (Magnesium hydroxide) is commonly used as an antacid to neutralise stomach acid and relieve indigestion and heartburn.

The correct answer is Mercury.

Explanation:

• Metals are lustrous, malleable, ductile, and are good conductors of heat and electricity.
• Examples of metals are iron, copper, aluminum, calcium, magnesium, mercury, etc.
• All metals are solids at room temperature, except mercury which is a liquid at room temperature.
• Mercury, also known as quicksilver, has a melting point of 38.83 degrees Celsius.
• Mercury (Hg) is a liquid at room temperature because of the behavior of the valence electrons, mercury has a low melting point, is a poor electrical and thermal conductor, and does not form diatomic mercury molecules in the gas phase.

Key Points

• Mercury constitutes a mercury mixture when it is mixed with metal.
• It alloys with copper, tin, and zinc to form amalgams or liquid alloys.
• An amalgam with silver is used as a filling in dentistry.
• Mercury does not wet glass or cling to it, and this property, coupled with its rapid and uniform volume expansion throughout its liquid range, makes it useful in thermometers

The correct answer is Sulphurous acid.

Explanation:

When sulphur dioxide is dissolved in water it forms Sulphurous acid. The chemical formula of sulphur dioxide is SO₂.

The chemical equation is shown below. 

• SO₂ +H₂O ⟶ H₂SO₃
• Metallic oxides are formed when metals react with oxygen. Because they react with water to form bases, these metallic oxides are basic in nature.
• Non-metals, on the other hand, react with oxygen to form non-metallic oxides, which differ from metallic oxides in that they are acidic. Non-metallic oxides also form acids when they react with water.
• Sulphur is a non-metallic element, and sulphur dioxide (SO₂) is acidic. As a result, it reacts with water to produce sulphurous acid (H₂SO₃)
• Properties of Sulphurous acid:
• Sulphurous acid is a colourless liquid.
• Sulphurous acid is a good reducing agent.
• It is used as a mild bleaching agent for applications.
• Sulphurous acid is unstable and has never been isolated in it its pure states.

Additional Information

• Sulphur Trioxide
• It reacts violently with water to form sulfuric acid with the release of heat.
• Sulphur Pentaoxide
• No direct reaction.
• Sulphuric Acid
• Water is less dense than sulfuric acid and will tend to float above the acid.
• The reaction is best thought of as forming hydronium ions.

Mistake Points

• Sulfur dioxide dissolves in water to give solutions that contain sulfurous acid H₂SO₃
• 2 SO₂ (aq) + 2 H₂O (l) + O₂ (g) → 2 H₂SO₄(aq)  formation of the sulphuric acid from the sulphur dioxide.

The correct answer is veins, thin, pulmonary vein.

Concept:

• Blood is the fluid that flows in blood vessels.
• It transports substances like digested food from the small intestine to the other parts of the body.
• It carries oxygen from the lungs to the cells of the body. It also transports waste for removal from the body.

Explanation:

• Two types of blood vessels, arteries, and veins are present in the human body.
• Veins are blood vessels that carry deoxygenated blood from various parts of the body to the heart.
• Veins are thin and elastic, and they are found closer to the skin's surface.
• Pulmonary veins are the vessels that carry carbon dioxide-rich blood from all parts of the body back to the heart.
• There are valves present in pulmonary veins that allow blood to flow only toward the heart.

Hence, In the human circulatory system, arteries are blood vessels that carry oxygenated blood and have thick walls. The pulmonary vein carries blood from the lungs to the heart.

Additional InformationArteries are blood vessels that carry oxygenated blood from the heart to different parts of the body. They are thick, elastic and are divided into a network of small blood vessels known as capillaries.

The correct answer is Bone.

Note According, to the official answer key option 3 is correct, but according to the solution given in this question, option 2 is correct, as the brain is covered and protected with the bone.

Explanation:

• The skeleton is made up of many bones that are connected by various types of joints to form a structural framework for the body, giving it its proper shape and structure.
• Bones protect very delicate organs like the brain, heart, etc.
• The brain is protected by the skull. The skull is a bony structure that makes up the skeleton's head. It provides a protective cavity for the brain and supports the facial structures.
• Any harm coming at the delicate organs passes through the bones first, and the bones act as a shield, protecting our soft internal organs.
• The rigid organ that makes up the skeleton, and bone, has its own nerves and blood vessels to help it stay alive.
• The skeletal system has six major functions, which are as follows:
• Support
• Protection
• Movement
• Storage of minerals
• Production of blood cells
• Endocrine regulation

Additional Information

• The bone of the forelimb (hand) are the followings-
• Arm bone- Humerus, Forearm- Radius, and Ulna, Wrist bones- Carpels, Palm- Metacarpals, Digits- Phalanges.
• The two hands together have 60 bones.

The number of bones in the thumb of the hand is 2.

The correct answer is Both (A) and (R) are true but (R) is not correct explanation of (A).

Explanation:

• Fusion of the egg and the sperm is called fertilization.
• Fertilization which takes place inside the female body is called internal fertilization.
• Internal fertilization occurs in many animals including humans, cows, dogs, and hens.
• Soon after fertilization, the zygote divides repeatedly and travels down the oviduct. As it travels down, many protective layers are formed around it. The hard shell that you see in a hen’s egg is one such protective layer.
• After the hard shell is formed around the developing embryo, the hen finally lays the egg.
• The embryo takes about 3 weeks to develop into a chick.
• After the chick is completely developed it bursts open the egg shell.
• Internal Fertilization takes place in hens is not the correct explanation of assertion because internal fertilization is not related to the hatching process of hens.

Additional InformationFertilization that takes place outside the female body is called external fertilization.

External fertilization occurs in many animals including frogs, fish, starfish, etc.

The correct answer is Vitamin D.

Explanation:

• Vitamins help in protecting our bodies against diseases. Vitamins also help in keeping our eyes, bones, teeth, and gums healthy.
• Our body needs all types of vitamins in small quantities.
• Vitamins help in protecting our bodies against diseases.
• Long-term deficiency of one or more nutrients in our diet may result in certain diseases or disorders.
• Vitamin D helps our body to use calcium for bones and teeth.
• Vitamin D is required for calcium absorption.  Sunlight is the best source of vitamin D.
• When you don't get enough vitamin D, your body's calcium absorption lowers. This usually occurs if you are malnourished or do not get enough sun exposure.
• Our body also prepares Vitamin D in the presence of sunlight. Nowadays, insufficient exposure to sunlight is causing Vitamin D deficiency in many people.

Additional Information

Key Points

• Vitamins were first discovered by FG Hopkins.
• The term Vitamin was coined by C Funk.
• There are two types of Vitamins:
• Fat-Soluble- Vitamin A, D, E, and K.
• Water-Soluble - Vitamin B and C.
• Natural sources of Vitamin D are - Sunlight, fish, eggs, and mushrooms.

The correct answer is Aquatic submerged plants.

Concept:

• Transpiration is the phenomenon of the loss of water in the form of vapor from the living tissues of aerial parts of the plant.
• Water lost is pure water solutes.
• The process of transpiration is carried out by the special structures found in the leaves of plants called stomata. It occurs mainly through stomata.
• It is both a physical and physiological process.

Explanation:

• Aquatic submerged plants do not show transpiration because they do not require a stoma pore for gaseous exchange, they lack stomata on the leaf surface.
• Instead, the gaseous exchange can be accomplished through diffusion through the leaf surface.
• As a result, submerged aquatic plants lack a cuticle structure.
• The cuticle's main function is to prevent excess water through transpiration, and since there are no stomata or transpiration, the cuticle layer is also absent.

Additional Information

Transpiration is of 3 types:

• Stomatal transpiration: Occurs through stomata, about 80-90% of transpiration occurs by stomata.
• Cuticular transpiration: loss of water through the cuticle of herbaceous stems and leaves. The cuticle is the waxy layer present on the epidermis. About 9% of transpiration occurs through it.
• Lenticular transpiration: Occurs through lenticels(minute pores on stem and epidermis of woody plants). The least amount of about 0.1 to 1% transpiration occurs through it.

Important Points 

• Minimum transpiration is found in succulent xerophytes.
• Maximum transpiration occurs in mesophytes.

The correct answer is (A) - (iii), (B) - (v), (C) - (ii), (D) - (i).

Explanation:

Mitochondria:

• Mitochondria are membrane-bound cell organelles, essential for aerobic respiration of eukaryotic cells.
• These are also known as powerhouse of the cell. Thus, they produces cellular energy in the form of ATP.
• Mitochondria are present in all living cells except, prokaryotic cell and certain specialized eukaryotic cells such as anaerobic cells and mature red blood cells.

Vacoule: 

• Vacuoles are large, membranous sacs found in the cytoplasm.
• Vacuoles are known as Store house of cell because they store substances that are not essentially useful for the cell (like water, sap, excretory product, and other minerals).
• Plant vacuoles contain not only water, sugars, and salt, but also contain pigments and toxic molecules and also occupy upto 90% of the volume of the cell.

Cell membrane:

• Every living cell is covered by a thin, elastic, transparent semipermeable and regenerative membrane called the cell membrane, also called plasma membrane.
• The plasma membrane separates the internal environment of the cell from the external environment.
• Cell membrane is the Gate keeper of cell because this membrane help in regulating the entrance and exit of molecules into and out of the cell.

Nucleus:

• It is a specialized and principal organelle of the cell, which contains all the genetic information for controlling all essential processes related to metabolic and hereditary transmission.
• A nucleus is known to be present in all eukaryotic cells except a few cell types such as red blood cells of humans, sieve cells of vascular plants, etc. Thus it is known as the information centre of cell.

The correct answer is Drip irrigation.

Explanation:

Irrigation is the process of supplying water to crops at regular intervals.

• Drip irrigation: 
• The most suitable method of irrigation for areas having low rainfall and very strong winds is drip irrigation, as water will be suitably used in drip irrigation.
• Drip irrigation, also known as 'trickle irrigation system'.
• Waterfalls drop by drop directly near the roots through small openings called drippers or emitters at regular intervals in this system. As a result, it is known as drip irrigation.
• It is the most effective method for watering fruit trees, gardens, and other plants. Water is not wasted at all.
• It is a boon in areas where there is a scarcity of water.

Additional InformationSprinkle irrigation: 

• A sprinkler irrigation system utilises a pump to apply water under high pressure.
• Sprinkler irrigation is a method of applying water in a rain-like pattern through pipes using a small diameter nozzle.

Furrow irrigation: 

• If the slope of the land is 0.4–8 percent, then the furrow irrigation method of irrigation is suitable.
• In this method of surface irrigation, water is applied to the field through furrows, which are small canals having continuous or nearly uniform slopes in the direction of water flow.

Contour irrigation:

• In the Contour, irrigation method water is carried across a sloping field rather than down in the slope.

Concept:

Multiple Reflection:

• Multiple reflections are the phenomenon in which the reflected ray of light reflects again by another reflecting surface.
• Multiple images can be formed by the combination of two or more plane mirrors by multiple reflections of light.

Explanation:

• A kaleidoscope is an optical instrument with two or more reflecting surfaces inclined to each other at an angle so that one or more objects on one end of the mirrors are seen as a regular symmetrical pattern when viewed from the other end due to repeated reflection.
• It was invented by Sir David Brewster in 1816.
• It works on the principle of multiple reflections. When the white light hits the surface of the mirror, it gets reflected at an angle such that the angle of incidence is equal to the angle of reflection. Due to these multiple reflections of light, there is a creation of beautiful patterns.

Thus, from the above discussion, it is clear that Kaleidoscope is based on the principle of multiple reflections from three inclined plane mirrors.

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.

Earth Magnetic Field:

• It is also known as a geomagnetic field.
• The earth's magnetic field resembles that of a bar magnet.
• The field lines emerge from the south pole of the earth and re-enter the north pole.

Explanation:

• A freely suspended magnet always rests in the north-south direction because of the presence of Earth's magnetic field.
• When a magnet is suspended freely, the north pole of the magnet gets attracted toward the geographical north and the south pole of the magnet gets attracted toward the geographical south.

Thus, the correct answer is freely suspending the magnet from the middle.

Concept:

Resistance:

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

Ohm's Law:

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

Explanation:

• A rheostat is used to change the current in the circuit without the change in the voltage because a rheostat is a variable resistor used to control the electric current by increasing or decreasing the resistance manually.

Thus, from the above discussion, we can say that the correct answer is By connecting the rheostat.

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

Concept:

• Whight is absorbed and the rest is radiated in all directions except the incident direction. This isen light strikes particles in the air, some of the l referred to as the "scattering of light".
• The wavelength of the light and the size of the particle that scattered it help to determine the strength of the scattering.

Explanation:

• A daytime sky is blue because molecules in the air scatter more blue light from the sun than red light.
• When we look at the sun at sunset, we see red and orange colours because blue light has been scattered out and away from our line of sight.
• Before reaching our eyes, light from the sun near the horizon travels a greater distance through the earth's atmosphere.
• As a result, the particles scatter the majority of the blue light and shorter wavelengths. As a result, the light that reaches our eyes has longer wavelengths. This causes the reddish appearance.
• During the day, however, shorter wavelengths are scattered more by air molecules, and scattered blue light enters our eyes.
• This is because of the scattering of light.
• Hence, the sky appears blue during the day and red during sunrise and sunset.

Reddening of the sun at sunrise and sunset

Scientific inquiry is a holistic process. All processes in science are done with a specific purpose, evidence is collected with reliable and valid methods, and they are examined critically by controlling different variables.

 Key Points

Some of the processes involved in science as inquiry:

• Observing (patterns), wondering about objects, events, phenomena, experiencing & sensing discrepancies & dissonance, becoming curious & uncomfortable.
• Reflecting on various decisions & processes, aiming for better & contextually appropriate solutions, doing thought experiments, and assessing personal development.
• Deciding purpose, asking answerable questions, refining questions, hypothesizing, predicting.
• Planning, visualizing & designing collecting evidence testing evidence, considering variables, defining ideas, and measuring.

Since many processes listed above like doing experiments, testing evidence, and drawing conclusions are done in options B & D, hence B & D are correct options.

There are many processing skills which are ought to be developed in students so that they can learn the concepts with meaning-making instead of rote memorization. 

Key Points

• Classification is the skill of sorting or grouping items by similar characteristics, such as colors, shapes, or sizes so according to the above question students can classify how many seeds of each kind are growing.
• Observation skills refer to the ability to use all five of our senses to recognize, analyze and recall our surroundings. According to the above example, students can use their sense organ eye to determine which plant is sturdier: the one left in the sun or the one left in the shade which is an observation.
• In the scientific method, a hypothesis is usually tentative; it's an assumption or suggestion made strictly for the objective of being tested According to the above example the students can assume the reasons why some seeds are growing, this is nothing but a hypothesis.

​Hence option 1 is the correct one.

Questions are an aid in the learning process and hence questioning skills is one of the important teaching skills required to be developed to conduct a successful classroom session by the teacher. Effective teachers use productive questions to help students advance in their thinking and to construct their understandings.

Important PointsQuestions can be classified into:

Open-ended questions are the ones that don't have one specific answer or one specific way to answer a question. 

• Features of open-ended questions
• Encourage divergent thinking.
• Avoid rote memorization.
• Give freedom to the student to think in multiple ways to find a solution for a problem.
• Take more time than close-ended ones.
• The above question " How do you use electricity?" is open-ended because we use electricity in many ways like lighting, heating, cooling, and refrigeration and for operating appliances, computers, electronics, machinery, and public transportation systems. This question has many answers so it is open-ended.​

​Close-ended questions have only one specific method to find the answer or one specific answer. 

• Features of close-ended questions
• Give less freedom to the student to find the answer.
• Have one specific answer.
• Consume less time as compared to open-ended ones.
• In the above example the question "Why is copper used for making wire for carrying electricity?" is close-ended because it has only a single answer since copper is a metal and it is a good conductor of electricity.

​Hence A - Open-ended, and B - Closed-ended is the correct option.

Key PointsScience is a subject that involves a lot of inquiry and investigation where the students will have various options among them, they have to investigate and find out the correct one. This will succeed only if the teachers :

• Allows students to think beyond the textbook.
• Makes sure the students get curious about the concept and as a result, they start investigating.
• Allowing students to discuss the possible sources of error among themselves as each student gives a possibility, each possibility will be discussed and the correct one is found.
• Provide students the required freedom and also resources for investigation.
• Do not restrict the student to a single thought or single type of thought.

Additional InformationOn the other hand insisting on the demonstration of correct results by students, assigning tasks that require sophisticated gadgets, and rigidly following the textbook in terms of the prescribed steps and material required doesn't increase the curiosity in children, as a result investigating the environment doesn't form in the classroom.

Hence, we can conclude that option 3 is correct.

Anecdotal records are short narrations or factual descriptions of certain incidents and events that a teacher observes in the context of her research interest. Each incident is written shortly after it takes place.

 Key Points

Thus as given in the above question a teacher can observe and make a note of 

• Who is switching the fan off when not in use?
• Who is switching the light in the daytime when sunlight is there?
• Who is turning off the taps when they finish using them?
• Who is not doing the above and wasting energy sources?

​Hence Observing students and maintaining anecdotal records would be the most appropriate strategy to assess the students’ energy-conserving behavior.​

Additional Information

All the above-mentioned three tools are not appropriate to assess the students’ energy-conserving behavior because her teacher can't observe a student doing energy-saving activities.

Important PointsAccording to the National Curriculum Framework 2005, the science curriculum should aim at :

• addressing the development of process skills like observation, classification, measurement, communication, etc.
• encouraging inventiveness as the children are considered to be young explorers.
• acquisition and understanding of knowledge, development of problem-solving skills, the skill of investigation, and the ability to think logically and to draw conclusions based on experiments.
• development of the ability to reach generalizations and to apply them to solving everyday problems.
• achieving equity.
• development of understanding of inter-relationships of science and society. to foster creativity in people, enabling them to carry out innovations in science.
• encouraging reforms in the examination system as there is a need for a shift from teacher-centered to student-centered curriculum and from rote memorization to a meaning-making process.

​Hence According to the National Curriculum Framework 2005, the science curriculum should aim at addressing all of the following, except improving students’ scores in exams because this may restrict the students to only study for the marks not for gaining knowledge.

Language plays a very important role in the acquisition of scientific concepts it should not be ignored by the teachers because some words which are used in everyday language have specific meanings in science.

Important Points

​Examples of words that are used in everyday language have specific meanings in science.

Hence "Some words which are used in everyday language have specific meaning in science" conveys our understanding of the role of language in the acquisition of scientific concepts.

Archimedes' principle states that the upward buoyant force that is exerted on a body immersed in a fluid, whether fully or partially, is equal to the weight of the fluid that the body displaces. 

Important Points

Here Engaging the students in floating and sinking activities with carefully selected materials will be the best because here students

• get an opportunity to compare various objects' densities by involving in the sinking and floating activities.
• get the same feeling that Archimedes got while he formulated the principle.
• comprehend the concept clearly and remember for a long time because learning by doing happens here.
• clear all the doubts they get because they are not passive, they are involved in the activity.
• develop into young explorers and think innovatively.

Hence option 2 is the correct one.

Key Points Constructing a graph to describe the relationship between the angle of incidence and the angle of reflection is an example of communicating because here -

• the students can easily make a relation between the angle of incidence and the angle of reflection through a graph that they find difficult to explain theoretically.
• students' attention is held towards graphs as it clearly represents the relation in the form of a diagram.
• constructing a graph will solve all the doubts of students and helps them to connect with the concept.

​​Hence constructing a graph to describe the relationship between the angle of incidence and the angle of reflection is an example of communicating.

Important Points

• Interpreting is nothing but understanding something in a detailed way without any confusion or doubt.

Sound is one of the important topics in science that the student needs to learn from basics so that he/she will be able to apply that knowledge in the real-life also. 

Key Points

• Assertion (A): "The teacher should expose the students to various kinds of vibrating bodies" is true because students to become familiar with the sound produced by different objects or vibrating bodies should be exposed to those objects. Here learning by doing happens as students get the real experience.
• Reasoning (R): "Observation is an important process skill in teaching-learning of science" is a correct explanation of A because students when students are exposed to various kinds of vibrating bodies, they observe the sound with the help of their ears and organize the sounds and the objects into their minds accordingly.

Hence both (A) and (R) are true and (R) is the correct explanation of (A).

The correct answer is 'was a hard working farmer'.

 

Key Points

• By referring to the line of the passage: "Of Mortimer she saw very little. Farm and woods and trout streams seemed to swallow him up from dawn till dusk".
• It can be concluded that Sylvia saw very little of Mortimer as he was a hard working farmer.

 

Hence, the correct answer is option 2.

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

 

Key Points

• By referring to the lines of the passage:
• "Of  Mortimer she saw very little. Farm and woods and trout streams seemed to swallow him up from dawn till dusk".
• "Once, following the direction she had seen him take in the morning, she came to an open space among nut bushes, which were further shut in by huge yew trees, in the centre of which stood a stone pedestal surmounted by a small bronze figure of a youthful Pan (Greek god of shepherds)".
• It can be concluded that  Sylvia wanted to know where Mortimer spent his time and thus she followed the path taken by him one day.
• Hence, statement (A) and statement (B) both are true.

Hence, the correct answer is option 3.

The correct answer is 'the statue of Pan in an open space'.

 

Key Points

• By referring to the line of the passage: "Once, following the direction she had seen him take in the morning, she came to an open space among nut bushes, which were further shut in by huge yew trees, in the centre of which stood a stone pedestal surmounted by a small bronze figure of a youthful Pan (Greek god of shepherds)".
• It can be concluded that after leaving home, Sylvia was surprised to reach the statue of Pan in an open space.

 

Hence, the correct answer is option 3.

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

 

Key Points

• By referring to the lines of the passage:
• "Once, following the direction she had seen him take in the morning, she came to an open space among nut bushes, which were further shut in by huge yew trees, in the centre of which stood a stone pedestal surmounted by a small bronze figure of a youthful Pan (Greek god of shepherds)".
• "Her attention was, however, held by the fact that a newly cut branch of grapes had been placed as an offering at its feet".
• "Grapes were none too plentiful at her home."
• Thus, nut growing bushes were surrounded by yew trees.
• It can be concluded that statement (B) and statement (C) both are true but statement (A) is false.

 

Hence, according to the given options the correct answer is option 2.

The correct answer is 'Surprise, Shock, Anger, Fear'.

 

Key Points

• By referring to the lines of the passage:
• "Once, following the direction she had seen him take in the morning, she came to an open space among nut bushes, which were further shut in by huge yew trees, in the centre of which stood a stone pedestal surmounted by a small bronze figure of a youthful Pan (Greek god of shepherds)".
• "Her attention was, however, held by the fact that a newly cut branch of grapes had been placed as an offering at its feet".
• "Sylvia snatched the bunch angrily from the pedestal".
• "She was filled with annoyance as she strolled slowly homeward, and then gave way to a sharp feeling of something that was near fright; from a thick tangle of bushes a boy’s face was scowling at her, brown and beautiful, with unutterably evil eyes".
• It can be concluded that the order in which Sylvia experienced various emotions, while in the forest was surprise, shock, anger, fear.

 

Hence, the correct answer is option 1.

The correct answer is 'Alliteration'.

Key Points

• Alliteration is the figure of speech used in the above expression: 'streams seemed to swallow him up' i.e a word which means the occurrence of the same letter or sound at the beginning of adjacent or closely connected words.
• For example:-All Adam ate in August was apples and almonds.
• Simile is a figure of speech involving the comparison of one thing with another thing of a different kind, used to make a description more emphatic or vivid (e.g. as brave as a lion ).
• Metaphor is a figure of speech in which a word or phrase denoting one kind of object or action is used in place of another to suggest a likeness or analogy between them.
• Irony means the humorous or mildly sarcastic use of words to imply the opposite of what they normally mean.

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Hence, the correct answer is option 2.

The correct answer is 'Adverb'.

Key Points

• Here the underlined word 'further' is an adverb i.e a word or phrase that modifies or qualifies an adjective, verb, or other adverb or a word group, expressing a relation of place, time, circumstance, manner, cause, degree, etc. (e.g., gently, quite, then, there ).
• Further means to a greater degree or extent
• For example:- Read a little further and it will begin to make sense.
• Noun is a word (other than a pronoun) used to identify any of a class of people, places, or things ( common noun ), or to name a particular one of these ( proper noun .
• Verb is a word used to describe an action, state, or occurrence, and forming the main part of the predicate of a sentence, such as hear, become, happen.
• Adjective is a word naming an attribute of a noun, such as sweet, red, or technical.

 

Hence, the correct answer is option 4.

The correct answer is 'hid'.

Key Points

• Discovered means find unexpectedly or during a search.
• For example:- America was discovered by Columbus in 1492.
• Hid means put or keep out of sight.
• For example:- She hid the dagger in a pocket and watched.

 

Hence, hid is opposite in meaning to the word discovered.

  

Additional Information

• The meaning of the other given words are as follows:-
• Recovered- return to a normal state of health, mind, or strength.
• Closed- not open.
• Revealed- make (previously unknown or secret information) known to others.

The correct answer is 'grabbed'.

Key Points

• Snatched means quickly seize (something) in a rude or eager way.
• For example:-She snatched the envelope from his hand.
• Grabbed means grasp or seize suddenly and roughly..
• For example:- She grabbed her tablet and several pencils.

 

Hence, grabbed is similar in meaning to the word snatched.

  

Additional Information 

• The meaning of the other given words are as follows:-
• Picked- detach and remove (a flower, fruit, or vegetable) from where it is growing.
• Pulled- exert force on (someone or something) so as to cause movement towards oneself.
• Threw- propel (something) with force through the air by a movement of the arm and hand.

The correct answer is 'both 1 and 3'.

Key Points 

• An oak tree known for its huge size and its long life as can be seen in the line: Or standing long an oak, three hundred year.
• Look at these lines too:
• Although it fall and die that night -

It was the plant and flower of Light.

• At the end is just a piece of wood; dry, sapless and leafless.
• In these lines we can see an oak tree which lives for 300 years and long in size.
• Here, the oak represents a person who feels it's sufficient to simply exist. Such a person is content to merely be born, live a long time, and die.

Therefore, the correct answer is option 4.

The correct answer is 'size does not matter in life'.

Key Points

• An oak tree teaches us that size does not matter in life.
• The huge, strong and aged oak will soon become a lifeless, ‘dry’ and withered piece of log.
• So too will be the fate of a man who is only blessed with long life and physical and material well being.
• The oak tree teaches us that having a short but beautiful life is much better than a long but ugly life.

 

Therefore, the correct answer is option 3.

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

Key Points

• Statement 'a' is wrong. Here the poet compares the qualities of man with two things 'Oak tree' and 'Lily'.
• It is up to man whether he wants to live his life like Oak tree or Lily.
• A oak tree that old literally just exists motionless from day to day. A tree takes no conscious part in its own existence, similar to a person who is unmotivated and apathetic.
• Growing physically like a bulky tree or living long like a sturdy oak does not make a man a noble being
• Statement 'b' is wrong. A meaningful life like the lily flower, though short, is what makes a man noble and even though a man’s life is short it can be a perfect life.

 

Therefore, the correct answer is option 4.

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

Key Points

• tatement 'c' is right 'Even a young person can be noble', as we see in the poem.
• Long life and big size is not a sign of excellence. Even a short life can be perfect. Long life is not perfect if it is not eventful.
• On the other hand, a short life is perfect if it is filled with beauty it makes a man noble and even though a man’s life is short it can be a perfect life.
• Statement 'a' is wrong, we can say that small life and things are beautiful if is perfect and filled with beauty.
• Statement 'b' is wrong, the lily plant has a short life. It blooms in May and is very beautiful.

 

Therefore, the correct answer is option 3.

The correct answer is 'simile'.

Key Points

• Simile is used in this line.
• Simile: A simile is a figure of speech involving the comparison of one thing with another thing of a different kind, used to make a description more emphatic using the words 'like' or 'as'.
• Ex: It is not growing like a tree.
• In the line, It is not growing like a tree, the poet tells us that a huge and heavy oak tree that lives for more than 300 years but is never of use to others and aged oak will soon become a lifeless, ‘dry’ and withered piece of log.

 

Therefore, the correct answer is option 1.

Additional Information 

• Metaphor: An expression, often found in literature, that describes a person or object by referring to something that is considered to have similar characteristics to that person or object.
• Ex: Life is a highway.
• Personification: When human qualities are shown in non-living things or in abstract, it is called a personification.​​
• Ex: The wind howled in the night.
• Irony: a way of speaking that shows you are joking or that you mean the opposite of what you say.
• Ex: The police station gets robbed.

The correct answer is spreads beauty and fragrance.

Key Points

• Lily has been called ‘flower of light’.
• Long life is not perfect if it is not eventful. On the other hand a short life is perfect if it is filled with beauty.
• A meaningful life like the lily flower, though short, is what makes a man noble and even though a man’s life is short it can be a perfect life.

 

Therefore, the correct answer is option 4.

Grammar is the backbone of any language. It is the womb that gives birth to sentences. These sentences are fertilized using grammar to form correct and appropriate speech.

• Grammar is defined as a theory of language. We consider language as rule-governed behavior, relating to sounds, word formation, and structure. Here grammar constitutes a subset of rules relating to morphology and syntax.

Key Points

• Learners construct the grammar of a language when they are provided with comprehensible inputs in an anxiety-free environment.
• Comprehensible input refers to the input slightly above the learner's current level of mastery. ​An anxiety-free positive learning environment increases student achievement.
• It helps learners in language learning by making them able to communicate efficiently, acquire language naturally and understand the text effectively.
• Language is acquired not when the input is repeated several times, but when that input is understood, when the learner understands what it means and can make use of it. ​

Hence, it is clear that learners construct the grammar of a language when they are provided with comprehensible inputs in an anxiety-free environment.

Language is neither static nor homogeneous. All languages show variation along different dimensions. When one talks about "the English language" or any other language, or when one reads a grammatical description of one language or the other, the impression one gets is that language is a monolithic, homogeneous entity.

Key Points

• Language varies according to the context in which it is used. This variation of language according to its function is called registral variation and such varieties are known as registers.
• In any given language community, the members use language in a variety of situations, for a large variety of purposes, and to perform a wide variety of functions. This phenomenon is known as ‘language register’.
• For example, if one talks to one’s colleagues about their work, the language is likely to be rather different than one will use at home with one’s family.
• The language will depend on the relationship between the participants engaged in the act of communication. With one’s family, one is likely to be informal, with one’s colleagues would be more formal, and with the boss the most formal.

Thus, it is concluded that ‘language register’ denotes the variation in language according to the context in which it is used.

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

Key Points

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

• This approach focuses on developing learners’ proficiency with lexis, or word and word combinations. Lexis includes not only single words but also the word combinations that people store in their mental lexicons.
• This approach believes that ‘language consists not of traditional grammar and vocabulary but often of multi-word prefabricated chunks’ as this approach is a widespread occurrence of multi-word units or lexical chunks in native speakers’ languages.
• Lexical phrases in any language offer more communicative and expressive power than grammatical structures. This approach gives special attention to collocations which helps the individuals to communicate effectively in a particular context.

Hence, it is clear that the Lexical approach to language teaching believes, ‘language consists not of traditional grammar and vocabulary but often of multi-word prefabricated chunks’.

Additional Information 

• Grammar translation is a traditional method through which language is taught with a detailed study of grammar. Thus, learners apply the rule of grammar in translating sentences from their mother tongue to the target language.
• Communicative approach is a method of language teaching which makes learners confident to communicate effectively by involving them in real communication. It highlights the importance of real communication.