CTET Paper 2 Maths & Science 2nd Feb 2023 (English-Hindi) (Previous Year Paper)

Key Points

• Growth refers to the process of physical development and increase in size or dimensions of an organism over time.
• In Sneha's case, her height is increasing, and as a result, her hand can now easily reach the handle of her cupboard.
• This increase in height is a natural part of her biological development as she matures.
• Growth is a common phenomenon in living organisms, including humans, and it encompasses changes in various physical attributes as they age.

Thus, it is concluded that Sneha's height is growing very fast and now her hand can easily reach the handle of her long cupboard from which she can open the cupboard very easily. Sneha's change in height is called growth.

Child development is a complex process influenced by both genetic factors (heredity) and environmental influences. The interaction between a child's genetic makeup and their environment plays a significant role in determining the rate and course of their development.

Key Points

• Genetic factors provide the foundation for a child's development, including aspects like physical growth, cognitive abilities, and certain personality traits.
• However, the environment in which a child grows up, including their family, culture, socioeconomic status, and experiences, also has a profound impact on their development.
• Child development is not solely predetermined at conception, nor is it entirely random.
• It involves a dynamic interplay between genetic factors and environmental influences, and this interaction shapes the trajectory of a child's growth and development.

Thus, it is concluded that the rate of development of each child unfolds in a dynamic manner through the interaction of heredity and environment.

The role of family as an agency for socialization of children remains significant throughout their developmental stages, including middle school.

 Key Points

• As children move into middle school, they start spending more time outside the family environment, interacting with peers and teachers at school.
• The influence of the family on socialization tends to decrease compared to the early childhood years.
• During middle school, children are exposed to a wider social context beyond their immediate family, and they begin to develop social skills and values from various sources, including friends, teachers, and the broader community.
• While the family remains an important influence, its relative significance may decrease during the middle school years.

Therefore, the family's role as an agency for the socialization of children decreases as compared to the early childhood years.

Jean Piaget's theory of cognitive development is one of the most influential theories in developmental psychology. It emphasizes that children are not passive recipients of information; rather, they are active learners who interact with their environment to construct their understanding of the world.

Key Points

• (A) A major criticism of Jean Piaget's theory is the consideration that children are active beings. This statement is false. Jean Piaget's theory actually emphasizes that children are active learners who construct knowledge through their interactions with the environment.
• (R) Children learn through the passive reception of information. This statement is also false. Piaget's theory, in contrast, highlights the active role of children in constructing their understanding of the world through exploration and interaction.

Both statements are inaccurate, and, therefore, option 4 is the correct choice.

Jean Piaget's theory of cognitive development emphasizes the active role of children in constructing their understanding of the world through interactions with their environment.

 Key Points

• One of the central tenets of Piaget's theory is the concept of activity, which refers to the idea that children are active participants in their own learning and development.
• Piaget believed that children are not passive recipients of information; rather, they are actively engaged in exploring and interacting with their environment.
• Through their actions, children encounter new experiences, objects, and situations. These interactions lead to cognitive conflict and disequilibrium, which spur them to adapt and adjust their mental structures.

Thus, it is concluded that Activity factor plays an important role in cognitive development.

Piaget's theory of cognitive development is a comprehensive framework that describes how individuals progress in their cognitive abilities from infancy through adolescence.

Key Points

• Formal operational stage - Abstract thinking:- In Piaget's theory of cognitive development, the formal operational stage (adolescence and beyond) is characterized by the ability to think abstractly and hypothetically.
• This stage involves the capacity to engage in complex reasoning, solve problems with abstract concepts, and think about possibilities and hypothetical situations.

Thus, it is concluded that option 4 is the correct answer.

Kohlberg's theory of moral development is a psychological theory proposed by Lawrence Kohlberg in the 20th century. It outlines stages of moral reasoning that individuals progress through as they develop their understanding of right and wrong and how to make ethical decisions.

Key Points

• In Kohlberg's theory of moral development, post-conventional morality is the highest stage of moral reasoning.
• Individuals at this stage develop their own moral principles and values that may go beyond societal norms and laws.
• They recognize that ethical decisions are not solely determined by rules and authority but are also based on principles of justice, fairness, and individual rights.
• The child's reasoning about changing laws through democratic procedures demonstrates an understanding of higher moral principles and the idea of a social contract, which aligns with post-conventional morality.

Thus, it is concluded that Post-conventional Morality is the correct answer.

Vygotsky's theory emphasizes the importance of social interaction and guidance in the learning process.

 Key Points

• Scaffolding refers to the support and guidance provided by a more knowledgeable individual, such as a teacher, to help a learner develop their cognitive skills and understanding.
• The teacher assists the child in the "zone of proximal development," which is the range of tasks that the child cannot yet do alone but can do with guidance.
• By providing scaffolding, the teacher helps the child progress from their current level of understanding to a more advanced level.
• This approach encourages meaningful learning and ensures that the child is challenged while receiving appropriate support to successfully complete tasks and develop new skills.

Thus, it is concluded that In Lev Vygotsky's theory, the teachers should provide scaffolding  to enable the child to learn meaningfully.

A progressive classroom refers to an educational environment that follows the principles of progressive education. Progressive education is a pedagogical philosophy that emphasizes student-centered, experiential, and holistic learning.

Key Points

• In a progressive classroom, the emphasis is on active and experiential learning.
• Students are encouraged to engage with the subject matter, explore concepts, and construct their understanding through hands-on activities, critical thinking, problem-solving, and collaboration.
• The teacher serves as a facilitator, guiding students in their learning journey and promoting independent thinking and creativity.
• This approach contrasts with passive learning, where students simply receive information without actively engaging with it.

Thus, it is concluded that a key characteristic feature of the progressive classroom is that the learner construct knowledge actively.

​ Key Points

• Assertion (A) - Teachers should use standardized IQ tests to measure children's intelligence: This assertion is not true. While standardized IQ tests are commonly used to assess certain cognitive abilities, their use as the sole measure of a child's intelligence is limited and controversial. Intelligence is a multifaceted trait that encompasses a wide range of cognitive, emotional, and social abilities. IQ tests primarily measure certain cognitive skills such as logical reasoning, mathematical ability, and language skills. However, they may not capture other important aspects of intelligence, such as creativity, emotional intelligence, or practical problem-solving skills.
• Reason (R) - Standardized IQ tests can predict intelligence accurately: This reason is also false. While standardized IQ tests can provide an estimate of a person's cognitive abilities within the scope of the test's content, they do not provide a comprehensive or definitive measure of a person's overall intelligence. No single test, including IQ tests, can accurately predict all dimensions of a person's intelligence.

Thus, both Assertion (A) and Reason (R) are false.

According to Gardner's theory, there are multiple types of intelligences, each representing different ways in which individuals perceive and understand the world.

 Key Points

• Individuals with high musical intelligence possess a heightened sensitivity to musical elements such as rhythm, pitch, meter, tone, and melody.
• This intelligence type, as proposed by Howard Gardner's theory of multiple intelligences, involves the ability to appreciate, create, and understand music in various forms.
• People with musical intelligence often excel in activities such as playing musical instruments, composing music, singing, and recognizing different musical patterns.

Thus, it is concluded that Individuals having high musical intelligence have sensitivity to rhythm, pitch, meter, tone melody.

Hint

• Bodily-Kinesthetic Intelligence: This intelligence involves physical coordination, dexterity, and a sense of body awareness.
• Interpersonal Intelligence: This intelligence involves understanding and interacting effectively with other people.
• Linguistic Intelligence: This intelligence involves sensitivity to spoken and written language.

In socio-constructivism, which is a theory of learning developed by scholars like Lev Vygotsky, language plays a crucial role in cognitive development and learning.

 Key Point

• According to this perspective, language is not only a means of communication but also a tool for thought and learning.
• Language enables individuals to engage in meaningful social interactions, share ideas, negotiate meaning, and co-construct knowledge with others.
• Through language-mediated interactions, learners can internalize and build upon their understanding of concepts, leading to cognitive growth.

Therefore, in socio-constructivist perspective language facilitates learning by provisioning for social interaction.

Gender refers to the roles, behaviors, activities, and expectations that a society considers appropriate for men and women.

Key Points

• The culture of a society is highly influential in the development of gender roles because gender roles are primarily shaped by societal norms, beliefs, and expectations rather than solely by biological factors.
• While biological sex is determined by physical attributes, gender is a complex and multifaceted concept that is largely constructed through social and cultural processes.
• In different societies and cultures, ideas about masculinity and femininity can vary widely, leading to the establishment of distinct gender roles and expectations.
• These roles can influence various aspects of individuals' lives, such as their behaviors, career choices, and social interactions.
• Cultural norms, traditions, media, and social institutions all contribute to the formation of gender roles within a society.

Therefore, understanding gender as a social construct is essential for comprehending how culture influences the development of gender roles.

Assessment in education serves the purpose of evaluating students' learning progress, understanding, and performance.

 Key Point

• Its primary goal is to support and enhance the teaching-learning process.
• Effective assessment provides valuable feedback to both teachers and students, helping them identify strengths and areas for improvement.
• It informs instructional decisions, curriculum design, and teaching strategies.

Thus, it is concluded that Assessment should help to improve the process of teaching-learning.

Continuous and comprehensive evaluation (CCE) is an assessment approach that involves ongoing assessment of a student's progress and understanding throughout the learning process. It encompasses both formative assessment and summative assessment.

 Key Points

• The focus on formative assessment is particularly important to ensure that teachers have a continuous understanding of students' learning needs, strengths, and areas for improvement.
• Formative assessment involves gathering information about students' learning and using it to provide feedback and adapt instruction.
• It helps teachers understand how well students are comprehending concepts, identify any misconceptions, and make instructional decisions accordingly.
• Formative assessment is integral to CCE because it allows for timely adjustments to teaching methods, ensuring that students have the opportunity to achieve learning outcomes.

Thus, it is concluded that in order to ensure continuous and comprehensive evaluation teachers should use formative assessment..

Inclusion aims to provide equal opportunities for all students, including those with disabilities, to fully participate in regular classroom settings and the broader school community. The essence of inclusion is to create an environment where diversity is valued, and all students are supported to reach their full potential.

Key Points

• Option 2 is incorrect because inclusion is not solely focused on adapting the curriculum for a specific group of students who are disabled.
• Inclusion goes beyond disability and encompasses a broader perspective of diversity, including factors such as cultural backgrounds, learning styles, and individual needs.

Thus, it is concluded that Inclusion is focused on adapting the curriculum for a specific group of students who are disabled statement about inclusion is NOT Correct.

Hint

• It regards inclusion and exclusion as connected processes: Inclusion and exclusion are connected processes because by promoting inclusion, schools aim to minimize exclusion and ensure that all students are actively engaged and valued members of the learning community.
• Inclusion benefits all students: Inclusion is not only beneficial for students with disabilities but also benefits all students by promoting diverse interactions, fostering empathy, and creating a more enriching learning environment.
• Inclusion is a process in which a school attempts to respond to all students as individuals: This statement accurately captures the essence of inclusion. Inclusion involves recognizing and responding to the unique strengths and needs of every student, with the goal of creating an inclusive and supportive learning environment.

Key Points

• Assertion (A) states that in a classroom of diverse learners, teachers should give reasonable autonomy and flexibility in curriculum and assessment strategies. This is true because in a diverse classroom, students have varying learning styles, abilities, and needs. Providing autonomy and flexibility allows teachers to tailor their approaches to accommodate different learning preferences and create a more inclusive and effective learning environment.
• Reason (R) explains that children learn better when they take ownership and their learning needs are accommodated. This is also true because when students feel a sense of ownership over their learning and when teaching strategies align with their individual needs, they are more engaged, motivated, and likely to succeed.

Thus, it is concluded that Both (A) and (R) are true and (R) is the correct explanation of (A).

Assistive technology refers to devices, tools, software, or equipment that are designed to help individuals with disabilities or specific challenges to perform tasks, enhance their capabilities, and improve their quality of life.

 Key Points

• Walking sticks, also known as canes, are devices that provide support and stability to individuals with mobility challenges.
• They assist people who have difficulty walking independently by providing an additional point of contact with the ground, helping them maintain balance and reduce the risk of falls.
• Walking sticks come in various designs and styles to suit different needs and preferences.
• They are commonly used by individuals with disabilities or those who have difficulty walking due to age or injury.

Thus, it is concluded that an example of assistive technology to aid mobility is a walking stick.

Creating an inclusive and supportive learning environment is essential for engaging students with visual challenges. Segregation, or isolating students with visual impairments from their peers, goes against the principles of inclusion and may lead to feelings of isolation and exclusion. It is important to promote a sense of belonging and equal participation for all students, regardless of their abilities.

Key Points Effective strategies for engaging students with visual challenges include:

• Provide least restrictive environment in the classroom: This strategy aims to ensure that students with visual challenges have access to the same educational opportunities and resources as their peers. It involves making appropriate accommodations and modifications to support their learning needs.
• Eliminate unnecessary obstacles from the classroom: Creating a safe and accessible physical environment by removing obstacles and clutter can help students with visual challenges navigate the classroom more easily.
• Present the concepts in multiple ways: Offering information through various modalities, such as auditory, tactile, and kinesthetic methods, can enhance understanding and engagement for students with visual impairments.

Thus, it is concluded that Focus on segregation of the students and always make them sit separately is NOT an effective strategy to engage students with visual challenges.

Creativity refers to the ability to generate original and innovative ideas, solutions, or expressions that are novel and valuable.

 Key Points

• It involves thinking outside the box, breaking away from conventional patterns, and bringing together different concepts or elements in new and unique ways.
• Creative individuals are capable of exploring alternative perspectives, embracing uncertainty, and producing outcomes that have not been seen before.
• Creativity is not limited to a single domain but can manifest in various fields, including art, science, technology, literature, problem-solving, and more. It often involves combining existing knowledge, skills, and experiences to generate fresh insights and outcomes.

Thus, it is concluded that  creativity is ability to create or discover something that is novel.

Hint

• Ability to repetitively perform an action without being bored: This refers to perseverance or engagement, rather than creativity.
• Ability to rote memorize sequences of numbers: This is related to memorization, not creativity.
• Ability to do convergent thinking: Convergent thinking is a type of thinking that focuses on finding a single, correct solution to a problem, whereas creativity often involves divergent thinking and generating multiple potential solutions or ideas.

Key Points

• Assertion (A) states that teachers should provide a lot of opportunities to children for discussion and dialogue. This is true because discussions and dialogues in the classroom create an interactive and participatory learning environment. They allow students to actively engage with the content, express their thoughts, ask questions, and learn from one another.
• Reason (R) explains that meaningful learning involves the processes of interaction with others**. This is also true** because meaningful learning goes beyond rote memorization and involves making connections, reflecting, and engaging in dialogue with others. Interacting with peers and teachers helps learners clarify their understanding, gain different perspectives, and construct deeper knowledge.

Thus, Both (A) and (R) are true, and Reason (R) provides a correct explanation for Assertion (A).

Learner-centered approach emphasizes placing the learner at the center of the learning process.

 Key Points

• These approaches focus on actively engaging students, promoting their autonomy, and involving their own initiative and efforts in the learning journey.
• Learner-centered methods encourage students to take responsibility for their learning, set goals, make decisions, and explore topics based on their interests and needs.
• Examples of learner-centered methods include problem-based learning, inquiry-based learning, project-based learning, and collaborative activities.

Thus, it is concluded that Learner-centred approach involves methods where learners' own initiative and efforts are involved in learning.

Teachers play a crucial role in shaping students' beliefs and attitudes towards learning.

 Key PointsAn active process which has a social context accurately reflects a constructivist and sociocultural perspective on learning, which is widely supported by educational research.

In this perspective:

• Learning is viewed as an active process, meaning that students construct their own understanding by actively engaging with new information, connecting it to their prior knowledge, and making sense of it in meaningful ways.
• Learning also has a social context, as interactions with peers, teachers, and the broader community contribute to the learning process. Social interactions help students negotiate meaning, share ideas, and co-construct knowledge.
• Promoting the belief that learning is an active process with a social context encourages students to take ownership of their learning, collaborate with others, and develop a d eeper and more meaningful understanding of the content.

Thus, it is concluded that Teachers should promote the beliefs that learning is an active process which has a social context.

Hint

• An active process but does not have a social context: This option does not acknowledge the importance of social interactions in the learning process.
• A passive process which has a social context: This option contradicts the idea of learning as an active process.
• A passive process which does not have a social context: This option does not reflect the active and social nature of contemporary educational theories.

The sequence of introducing new concepts to children typically follows a progression from simple to complex.

 Key Points

• This approach aligns with the principles of effective pedagogy and cognitive development.
• Starting with simpler concepts before moving to more complex ones allows children to build a solid foundation of understanding and gradually develop higher-order thinking skills.

Here's why the other options are not the primary sequence:

• Unknown to known: While introducing new concepts, it's generally more effective to start with what is already known or familiar to the child and then build upon that knowledge. This is a form of connecting new information to existing cognitive structures.
• Higher order to lower order: This sequence may not be as effective initially, as higher-order concepts often require a foundation of understanding lower-order concepts. Starting with complex ideas without proper foundational knowledge can lead to confusion and hinder comprehension.
• Abstract to concrete: Beginning with abstract concepts might be challenging for young learners. Concrete experiences and examples often serve as tangible entry points for understanding abstract ideas. Gradually moving from concrete to abstract helps children grasp the underlying principles.

Thus, starting with simple concepts and gradually progressing to more complex ones is a widely accepted and effective approach in education.

Contemporary policies of education, including the New Education Policy 2020, emphasize a shift away from traditional methods of learning that are solely recall-based or exam-oriented. Instead, there is a strong focus on experiential learning.

Key Points

• Experiential learning is an approach that encourages students to actively engage with the learning process through hands-on experiences, practical activities, and real-world applications.
• It promotes critical thinking, problem-solving, creativity, and a deeper understanding of concepts. Experiential learning allows students to connect theoretical knowledge to practical situations, making learning more meaningful and relevant.
• While exams and textbooks still play a role in education, the emphasis on experiential learning recognizes the importance of preparing students for the complexities of the modern world, where the ability to apply knowledge in practical situations is highly valued.

Thus, it is concluded that Contemporary policies of education such as New Education Policy 2020 propose that learning should be experiential.

Problem-solving refers to the process of finding solutions to difficult or complex issues or challenges.

Key Points Effective problem-solving strategies include:

• Analogical thinking: This involves finding similarities between the current problem and previously encountered problems. It allows for transferring solutions or approaches from one context to another.
• ​Algorithms: These are step-by-step procedures or formulas for solving problems. They guarantee a correct solution if followed correctly, but they might not be efficient for all types of problems.

Thus, it is concluded that the effective problem-solving strategies  are Analogical thinking and Algorithms.

Hint

• Functional fixedness: This is not an effective problem-solving strategy. It refers to a cognitive bias where a person sees objects as having only their traditional uses and fails to see alternative uses or functions.
• Convergent thinking: This involves narrowing down possible solutions to find the single best solution to a problem. While it is a valid problem-solving approach, it may not be as flexible as divergent thinking.

Key Points

• Encouraging original discovery and thinking in the classroom is a positive approach that fosters critical thinking, creativity, and problem-solving skills among students.
• When students are encouraged to explore and discover knowledge on their own, they become active participants in their learning process.
• This approach helps them develop a deeper understanding of concepts, encourages them to ask questions, analyze information, and find innovative solutions to problems.

Therefore, option 1 accurately reflects the positive impact of encouraging original discovery and thinking in the classroom.

Mastery-oriented learners are individuals who exhibit certain characteristics and behaviors that reflect a positive and growth-oriented approach to learning. 

Key Points Mastery-oriented learners exhibit characteristics:-

• Low fear of failure: Mastery-oriented learners are less afraid of making mistakes or failing because they view challenges as opportunities for learning and growth. They understand that setbacks are a natural part of the learning process.
• Incremental view of ability: Mastery-oriented learners believe that their abilities and intelligence can be developed and improved through effort, practice, and learning. They see challenges as a way to enhance their skills and knowledge.

Thus, it is concluded that Low fear of failure and incremental view of ability characterises mastery-oriented learners.

Intrinsically motivated learners are those who engage in learning for the sheer joy and satisfaction of it, rather than for external rewards or avoidance of punishment. Fostering intrinsic motivation in students is a key goal for educators, as it leads to more meaningful and self-directed learning experiences.

Key Points Here's how teachers can encourage children to become intrinsically motivated learners:

• Create Joyful Learning Environments: Incorporate interactive and hands-on activities, games, storytelling, and multimedia that make learning enjoyable and engaging.
• Provide Meaningful and Relevant Content: Design learning experiences that are relevant to students' lives, interests, and experiences. When students can see the real-world application of what they're learning, it enhances their intrinsic motivation
• Challenge and Curiosity: Present tasks and activities that are challenging yet attainable. Encourage students to ask questions, explore, and seek answers to stimulate their curiosity and desire to learn.
• Encourage Exploration: Create an environment where students can explore their interests and pursue self-directed projects. Encourage them to delve deeper into topics that intrigue them.
• Provide Constructive Feedback: Offer specific and constructive feedback that highlights students' strengths and areas for improvement. This helps them see learning as a journey of growth and development.

Thus, it is concluded that b y creating a joyful and engaging learning environment, teachers can nurture intrinsic motivation and empower students to become enthusiastic and self-driven learners.

Teachers play a significant role in shaping students' mindsets and beliefs about their abilities and potential.

 Key Points

• Conveying the belief that ability is incremental is important for fostering a growth mindset in students.
• A growth mindset is the belief that intelligence and abilities can be developed through effort, learning, and perseverance.

When teachers convey the belief that ability is incremental, they are promoting the idea that:

• Skills, intelligence, and talents can be cultivated and improved over time with dedication and practice.
• Challenges and failures are opportunities for growth and learning.
• Effort and hard work are key factors in achieving success.
• Learning is a dynamic process that involves continuous improvement and development.

Thus, it is concluded that Teachers should convey their beliefs to the students that ability is incremental.

Calculation:

(−3)3 × (0.3)-2 × 0.01

⇒ -27 × $\frac{1}{0.09}$ × 0.01

⇒ -27/9

⇒ - 3

Here, - 3 lies between - 3.5 and - 2.5

∴ The correct answer is option 3

Calculation:

According to the given question,

(A + 7) = 12 (here 1 is at carry), so A must be 5

Now, 3 + carry 1 + B = 6, so B = 6 - 4 = 2

So AB = 52 and twice of AB = 52 × 2 = 104

∴ The correct answer is 104

Calculation:

According to the given options,

In the option 4, factors of 28 = 1, 2, 4, 7, 14 (except the number itself 28)

Now, sum of the factors = (1 + 2 + 4 + 7 + 14) = 28 satisfies

∴ The correct answer is 28

Calculation:

Let's assume a square number divisible by 6 is 36

Here, 36 is divisible by 36 (option 1 satisfies)

square root of that number = √36 = 6 is also divisible by 6 (option 2 satisfies)

square root of that number = √36 = 6 is also divisible by 3 (option 3 satisfies)

But 36 is not divisible by 24 ( Option 4 not always be true)

∴ The correct answer is option 4

Concept used:

• If the sum of all the digits divisible by 3, then the number itself divisible by 3

• If last 2 digit of any number divisible by 4, then the number is also divisible by 4

Calculation:

From the given options,

The number 1716, sum of its digits = (1 + 7 + 1 + 6) = 15 is divisible by 3, so the number 1716 divisible by 3

Again, last 2-digit of the number is 16 which is divisible by 4, so the number 1716 is divisible by 4

∴ The number 1716  is divisible by 3 and 4 both

Calculation:

1.2 kg of gun powder is to be made by mixing Carbon, Sulphur and Potassium Nitrate in the ratio 3 : 2 : 1

So, (3 + 2 + 1) = 6 unit → 1.2 kg

Then sulfur should add 2 unit → 1.2/6 × 2 = 0.4 kg = 400 g

∴ The correct answer is 400 g

Concept used:

4% = 1/25, and 4% decrease means 25 unit becomes 24unit

Calculation:

From 2020 to 2022, for two years price decrease each year at 4%

So, value of 25² = 625 unit becomes after 2 years 24² = 576 unit

Now, according to the question,

625 unit → 500000, then 576 unit → 500000/625 × 576 = 460800

∴ The correct answer is 460800

Calculation:

Initially acid is 60% in that mixture, so, Acid : Water = 3 : 2

After acid added, water becomes 25%, now, Acid : Water = 3 : 1

Here we see, no water is added, we have to do equal water unit in both the ratio,

 

Here, (3 + 2) = 5 unit → 10 litre, then acid added 3 unit → 10/5 × 3 = 6 L

∴ The correct answer is 6 L

Calculation:

 x + $\frac{y}{2}$ = $\frac{1}{4}$ … (i)  y + $\frac{z}{2}$ = $\frac{1}{4}$  … (ii) and z + $\frac{x}{2}$ = $\frac{1}{4}$ … (iii)

Adding all three equations, we get

(x + y + z) + 1/2(x + y + z) = 3/4

⇒ 3/2(x + y + z) = 3/4

⇒ (x + y + z) = 1/2

∴ The correct answer is 1/2

Concept used:

17³ = 4913

Calculation:

Here ab = 4913 = 17³ (as a & b are positive integers), where a = 17 and b = 3 

So, the value of (a + b)^{a - b - 14} = (17 + 3)^{17 - 3 - 14} = 20⁰ = 1

∴ The correct answer is 1

Given:

Four angles of a quadrilateral are in the ratio of 1 ∶ 2 ∶ 3 ∶ 4

Concept used:

The sum of the four angles of a quadrilateral is 360° 

Calculation:

Let's assume that the four angles of a quadrilateral are k, 2k, 3k, 4k

According to the concept,

(k + 2k + 3k + 4k) = 360°

⇒ 10k = 360° 

⇒ k = 36° 

So, the measure of the smallest angle is 36°

∴ The correct answer is 36°

Concept use:

Euler's Formula for Polyhedron:

The theorem states a relation of the number of faces, vertices, and edges of any polyhedron. Euler's formula can be written as F + V = E + 2, where F is equal to the number of faces, V is equal to the number of vertices, and E is equal to the number of edges.

Calculations:

F = 6, E = 12 , V = ?  Here, F = faces, E = edges, V = Vertices

F + V = E + 2

6 + V = 12 + 2 

V = 14 - 6 = 8

Hence, the Correct Answer is 8

Concept used:

In a rectangle two diagonals are equal.

Calculation:

According to the concept,

(2x + 3) = (3x - 5)

⇒ x = 8

So, the value of (2x + 9) = (2 × 8 + 9) = 25

∴ The correct answer is 25

Concept used:

In the ΔABC, if BO and CO are the angle bisectors, then ∠BOC = 90 + 1/2∠A

Calculation:

According to the given concept,

∠BOC = 90 + 1/2∠BAC

⇒ 105 = 90 + 1/2∠BAC

⇒ 1/2∠BAC = 15

⇒ ∠BAC = 30° 

∴ The correct answer is 30°

Shortcut Trick

Supplement of an angle = 180° − Angle

⇒ x = 180° − 60° = 120°

Complement of an angle = 90° − Angle

⇒ y = 90° − 60° = 30°

⇒ x + y = 120° + 30° = 150°

∴ The correct answer is 150°.

Alternate Method

Given:

Original angle = 60°

x = Supplement of 60°

y = Complement of 60°

Formula Used:

Supplement of an angle θ = 180° − θ

Complement of an angle θ = 90° − θ

60° x x = 180° − 60° = 120°

60° y y = 90° − 60° = 30°

Calculations:

⇒ x = 180° − 60°

⇒ x = 120°

⇒ y = 90° − 60°

⇒ y = 30°

⇒ (x + y) = 120° + 30°

⇒ (x + y) = 150°

∴ The correct answer is 150°.

Additional Information

Supplementary Angles

Two angles are supplementary if their sum is exactly 180°. When placed adjacent to each other, they form a straight line.

Complementary Angles

Two angles are complementary if their sum is exactly 90°. When placed adjacent to each other, they form a right angle.

Reflex Angle

The reflex angle of any given angle θ is the remaining angle required to complete a full circle. It is calculated as 360° − θ.

Concept used:

Area of rhombus = 1/2 × product of two diagonals

Calculation:

From the given concept,

Area of rhombus = 1/2 × 12 × 25 = 150 cm²

∴ The correct answer is 150 cm2

Shortcut Trick

Area of trapezium = 1/2 × (Sum of parallel sides) × Height

336 = 1/2 × (24 + 18) × h

336 = 1/2 × 42 × h ⇒ 336 = 21 × h

h = 336 ÷ 21 = 16 units.

∴ The correct answer is 16 units.

Alternate Method

Given: Parallel sides MO = 24 units, RE = 18 units, Area = 336 sq units.

Formula: Area = [ (a + b) ÷ 2 ] × h, where a and b are parallel sides and h is the distance between them.

⇒ Sum of parallel sides = 24 + 18 = 42 units

⇒ 336 = (42 ÷ 2) × h

⇒ 336 = 21 × h

⇒ h = 336 ÷ 21

⇒ h = 16 units

∴ The correct answer is 16 units.

Additional Information

Trapezium Properties

A quadrilateral with at least one pair of parallel sides. If non-parallel sides are equal, it is an Isosceles Trapezium.

Median of Trapezium

The segment connecting midpoints of non-parallel sides is the Median. Length = (Sum of parallel sides) ÷ 2.

Area via Median

Area can also be calculated as Median × Height.

Shortcut Trick

Sum of areas of 3 adjacent faces = (8 × 3) + (3 × 5) + (5 × 8) = 24 + 15 + 40 = 79 cm².

Total Surface Area = 2 × 79 = 158 cm².

Total Cost = 158 × 0.50 = ₹ 79.00.

∴ The correct answer is ₹ 79.00.

Alternate Method

Given: Length (l) = 8 cm, Breadth (b) = 3 cm, Height (h) = 5 cm, Cost rate = ₹ 0.50 per cm².

Formula Used: Total Surface Area (TSA) of Cuboid = 2(lb + bh + lh)

l = 8 cm b = 3 cm h = 5 cm

⇒ TSA = 2 × (8 × 3 + 3 × 5 + 5 × 8)

⇒ TSA = 2 × (24 + 15 + 40)

⇒ TSA = 2 × 79

⇒ TSA = 158 cm²

⇒ Total Cost = Total Surface Area × Rate per unit area

⇒ Total Cost = 158 × 0.50

⇒ Total Cost = ₹ 79.00

∴ The correct answer is ₹ 79.00.

Additional Information

Lateral Surface Area of a Cuboid

The area of the four side walls is given by 2h(l + b).

Volume of a Cuboid

The capacity or space occupied by the box is calculated as l × b × h.

Longest Diagonal of a Cuboid

The length of the longest rod that can fit inside the box is √(l² + b² + h²).

Shortcut Trick

Identify the middle term in the set of 9 observations (n = 9).

The median is the ((9 + 1) ÷ 2)^th term, which is the 5^th observation.

5^th observation = x + 2 = 21 ⇒ x = 19.

Target value = 3x + 7 = 3(19) + 7 = 57 + 7 = 64.

∴ The correct answer is 64.

Alternate Method

Given observations: 11, 12, 14, 18, (x + 2), 22, 22, 25, 61 (arranged in ascending order).

Formula Used: For an odd number of observations (n), Median = ((n + 1) ÷ 2)^th term.

Calculations:

⇒ Total number of observations (n) = 9

⇒ Median position = (9 + 1) ÷ 2 = 10 ÷ 2 = 5^th observation

⇒ Value of 5^th observation = x + 2

⇒ x + 2 = 21 (Given)

⇒ x = 21 − 2 = 19

⇒ Required value = 3x + 7

⇒ 3(19) + 7 = 57 + 7 = 64

∴ The correct answer is 64.

Additional Information

Median for Even n

If the number of observations is even, the median is the average of the (n/2)^th and (n/2 + 1)^th terms.

Mean Calculation

Mean = (Sum of all observations) ÷ (Total number of observations).

Mode of Data

The observation that appears most frequently in the data set is called the mode.

Relationship between Mean, Median, and Mode

Empirical formula: Mode = 3 × Median − 2 × Mean.

Concept used:

Probability of an event P(a) = Number of favorable cases/Total number of cases

Calculation:

According to the question, from 3 to 47 there are total 45 number of cases

The number of cases divisible by 6 are 6, 12, 18, 24, 30, 36, 42

So, the number of favorable cases = 7

Required probability = 7/45

∴ The correct answer is 7/45

A mathematical proof is a logical argument that conclusively establishes the truth of a mathematical statement or theorem.

Key Points

• Mathematics relies on logical deduction rather than observation of the natural world.
• Deductive reasoning is a fundamental method used in mathematical proofs, where conclusions follow logically from previous statements, theorems, or axioms.
• Logical reasoning is the process of using a rational, systematic series of steps based on sound mathematical procedures and given statements to arrive at a conclusion.
• Verification involves ensuring that each step of the proof follows logically from the previous steps, adheres to the rules of logic, and that the entire argument leads to the correct conclusion.

Hence, we can conclude that empirical Observations are not involved in mathematical proofs.

Assessment and evaluation in mathematics have various purposes, but the main focus is typically on understanding students' comprehension, skills, and progress, and then adapting instruction accordingly.

Key PointsAssessment and evaluation in mathematics serve several crucial purposes:

• Identifying Strengths and Weaknesses: Through assessments, educators can determine which mathematical concepts or skills students have mastered and where they might need extra help.
• Guiding Instructional Strategies: Evaluation of student performance helps teachers to adapt their teaching methods. If students are struggling with a particular concept, the teacher might need to reteach it using a different approach or provide additional examples and practice.
• Monitoring Progress Over Time: Regular assessments enable teachers to track student's progress throughout the academic year. This helps to ensure that students are making the expected gains and allows for adjustments if they are not.
• Motivating and Engaging Students: When used effectively, assessments can encourage students to reflect on their learning and set goals for improvement. Some students may find assessments motivating, as they provide clear indicators of growth and success.
• Creating a Record of Learning: Accumulating assessment data over time creates a record of a student's learning journey. This can be valuable for future educational decisions, such as placement in advanced courses.

Hence, we can conclude that to find out the intelligence quotient of students to identify talented students is not a purpose of conducting assessment and evaluation in mathematics.

The most appropriate teaching-learning resource for introducing the concept of similarity in geometry would be differently-sized photographic images of the same objects.

Key Points

• This resource allows students to clearly visualize and understand the principle of similarity.
• That two shapes are similar if their corresponding angles are congruent and the ratios of the lengths of their corresponding sides are equal, which often holds true with differently-sized photographic images of the same object.
• This approach is hands-on and likely to engage students more effectively than just explaining the theory, as it allows them to discover the concept for themselves.

Hence, we can conclude that using differently-sized photographic images of the same objects is the most appropriate teaching-learning resource.

According to Jean Piaget's theory of cognitive development, children begin to show more advanced mathematical reasoning skills during the Concrete Operational Stage.

Key Points

• During the Concrete Operational Stage (typically occurring between the ages of 7 and 11), children become more capable of understanding and applying logical operations to concrete tangible objects and situations.
• This stage is marked by the development of conservation (understanding that the quantity of an object remains the same despite changes in appearance), reversibility (understanding that actions can be undone), and the ability to think more systematically about concrete problems.
• In terms of mathematics, children in the Concrete Operational Stage start to grasp concepts such as the conservation of numbers, understand basic mathematical operations, and begin to solve problems in a more logical and organized manner.
• They move beyond the limitations of the Pre-operational Stage, where thinking is more egocentric and cannot understand conservation and reversibility.

Hence, we can conclude that at the Concrete Operational Stage, children begin to show mathematical reasoning skills.

The narrow aim of mathematics education is concerned with the development of basic mathematical skills, such as addition, subtraction, multiplication, and division. 

Key Points

• The statement that Learning mathematics helps in developing logical thinking is the most appropriate statement with respect to the narrow aim of mathematics education.
• Logical thinking is the ability to think clearly and rationally, and it is essential for solving mathematical problems.
• The other statements are also important, but they are more related to the broad aim of mathematics education.
• Learning mathematics helps in generating curiosity and enjoyment among children and is related to the development of mathematical power.
• Learning mathematics would turn out employable adults who will contribute to socio-economic development related to the application of mathematics in the real world.

Hence, we can conclude that learning mathematics helps in developing logical thinking is the most appropriate statement with respect to the narrow aim of mathematics.

A biconditional statement is a statement that is true if both parts of the statement are true or both are false. It is often expressed with the phrase "if and only if."

Key Points

• The "if and only if" means that the truth of "one is less than seven" is exactly the same as the truth of "two is less than eight."
• In this case, both parts of the statement are true, so the biconditional statement is true.
• In this case, both statements p and q are true and also have "if and only if".

Hence, we can conclude that "One is less than seven, if and only if two is less than eight" is a biconditional statement.

In mathematics, equality is a relationship between two quantities or expressions that are the same in value.

Key Points

• In the given scenario, where the students are attempting to solve the equation
• x+2=8, their incorrect solutions indicate a misunderstanding of how to manipulate equations to isolate the variable and find its value.
• The correct approach to solving this equation involves using the concept of equality and inverse operations.
• Specifically, you would subtract 2 from both sides of the equation to isolate the variable x, resulting in x=6.
• The students' mistakes don't involve proportionality, multiplication, or subtraction as such, but rather a misunderstanding of the equality concept, which governs how you can manipulate both sides of an equation to solve for a variable.

Hence, we can conclude that the students have not acquired the concept of Equality.

The numbers that can be expressed as the sum of two cubes in two different ways are called Ramanujan Numbers.

Key Points

• The term "Ramanujan Number" has since been used to describe any positive integer that can be expressed as the sum of two cubes in two different ways.
• The Ramanujan Numbers are also an interesting example of Diophantine equations, where solutions are sought in integers.
• Diophantine equations are a rich field in number theory with many intriguing and often highly challenging problems.
• The smallest Ramanujan number is 1729, which can be expressed as 1729 = 1³ + 12³ = 9³ + 10³.

Hence, we can conclude that Ramanujan Numbers can be expressed as a sum of two cubes in two different ways.

Connecting teaching to the surroundings of a student is a teaching approach that builds on the existing knowledge and experiences of the students.

Key Points

• Statement (A): Connecting mathematical concepts with objects around the students can indeed help in developing the student's understanding of mathematics.
• By relating abstract ideas to concrete examples, teachers can make the concepts more accessible and relatable to students. Thus, statement (A) is true.
• Statement (R): Students come to the classroom with a variety of experiences and prior knowledge from their environment.
• This background knowledge can be leveraged to help them understand new concepts, especially if the teaching is connected to things they have already seen or experienced. Thus, statement (R) is also true.

Hence, we can conclude that both (A) and (R) are true and (R) is the correct explanation of (A).

A diagnostic test is used to identify a student's understanding and skills in a particular subject or content area.

Key Points

• By focusing on a specific content, the diagnostic test is designed to detect specific strengths and weaknesses in that content area.
• The main purpose of these tests is to inform instruction by identifying what students already know and where they need help.
• The diagnostic test is different from the achievement test in that it delves deeper into a particular area, identifying specific difficulties or misconceptions.
• While an achievement test measures the overall understanding and mastery of a subject, a diagnostic test focuses more intensely on specific content, often with the goal of informing targeted interventions or instructional adjustments.

Hence, we can conclude that the Diagnostic Test covers most questions from a specific content.

The correct answer is (A) and (B).

Explanation:

(A) Charge becomes used up as it flows through a circuit. (FALSE)

• Charge is conserved in a closed circuit.
• It doesn't get used up; instead, it flows continuously from one point to another.

(B) Charge flows through circuits at very high speeds. (FALSE)

• In most circuits, the charge carriers (usually electrons) move relatively slowly.
• Although the electrical signals (changes in voltage and current) can travel at close to the speed of light in conductors, the actual movement of electrons is much slower.

(C) A light bulb transforms the electrical energy of moving charge into other forms of energy. (TRUE)

• When an electric current passes through a light bulb, the filament heats up and emits light, converting the electrical energy into light energy and some heat energy.

(D) The charge carriers in wires are simply the electrons possessed by the atoms that make up the wires. (TRUE)

• In most electrical wires, the charge carriers are electrons, which are the negatively charged particles orbiting the atoms in the wire.
• These electrons move through the wire, creating an electric current when a voltage is applied.

The correct answer is Option 1 i.e. 30 degrees & 60 degrees respectively.

Explanation:

• Two mirrors A & B are at right angles to each other.
• If a ray of light strikes mirror A at 30 degrees to the normal and then strikes mirror B, find the angle of reflection of the ray reflected from both mirrors A & B.

Reflection from Mirror A:

• Angle of incidence on mirror A is 30°.
• -Using the laws of reflection, angle of reflection is equal to the angle of incidence.
• Thus, the reflection angle for Mirror A is 30°.

Reflection from Mirror B:

• Angle of incidence on mirror B is 60°.
• Using the laws of reflection, the angle of reflection will be equal to the angle of incidence. Therefore, the reflection angle for Mirror B is 60°.
• The ray reflects off mirror A at an angle of 30° and off mirror B also at an angle of 60°.

The correct answer is Blanket in both the cases.

Explanation:

• Blankets are good thermal insulators that can reduce thermal energy conduction and radiation.
• Using a blanket to wrap a box of ice cream can help to some extent in both summer and winter by minimizing heat transfer and maintaining the temperature inside the box, which can slow down the melting process in summer and prevent excessive freezing in winter.
• So, based on the thermal insulating properties of blankets, using a blanket in both cases (summer and winter) can be a reasonable and effective choice to prevent the ice cream from melting or freezing too quickly.

The Correct answer is Speed of A is greater than speed of B.

Concept:

• The distance-time graph of a moving object is a straight line if the object is moving at a uniform speed.
• The steeper the line, the greater the speed of the object.

Explanation:

• In the given graph, the line for A is steeper than the line for B. This means that A is moving at a greater speed than B.
• Being steeper or less steep doesn't necessarily imply that one car has traveled a greater distance than the other; it merely shows their speed in the given time frame.
• if both cars were driven for the same amount of time, then the car with the higher speed (A) would have covered a greater distance. Conversely, if car B traveled for a longer time, even at a slower speed, it might have covered more distance.
• The information given doesn't provide enough detail to determine  Thus, based on the distance-time graph and the information provided, we can only conclusively infer the comparative speeds of cars A and B.

Therefore, the only inference that we can make from the graph is that the speed of A is greater than the speed of B.

Additional Information

• The speed of an object is the rate at which it is moving. It is measured in meters per second (m/s).
• The distance traveled by an object is the total length of the path that it has covered. It is measured in meters (m).
• The area under a distance-time graph represents the total distance traveled by the object.
• The steeper the line on a distance-time graph, the greater the speed of the object.​

The correct answer is Float over mercury but sink in corn oil.

Explanation:

When a copper coin is dropped in a glass filled with mercury and corn oil, the following will happen:

Mercury:

• With a density of 13550 kg/m³, mercury is much denser than copper coin (8960 kg/m³).
• The copper coin will float on the surface of the mercury because it is less dense than mercury.

Corn oil:

• Corn oil has a density of 900 kg/m³, which is much less dense than both mercury and copper.
• When the copper coin is dropped into the glass filled with corn oil, it will sink to the bottom of the glass due to its higher density compared to corn oil.
• This is mainly because the density of mercury is higher than that of a copper coin, while the density of corn oil is less than that of a copper coin.

Thus, the copper coin will float on the mercury and sink in the glass filled with corn oil.

The correct answer is Both assertion and reason are correct and reason is not the correct explanation of the assertion.

Explanation:

Assertion: Larger the amplitude of vibrations, louder is the sound.

• Loudness of sound is proportional to the square of the amplitude of the vibration producing the sound.
• Loudness ∝ (amplitude)²
• For example, if the amplitude becomes twice, the loudness increases by a factor of 4.
• The loudness is expressed in a unit called decibel (dB).
• The loudness of sound depends on its amplitude.
• When the amplitude of the vibration is large, the sound produced is loud.
• When the amplitude is small, the sound produced is feeble.
• The greater the amplitude, the greater the loudness.

Reason: Higher the frequency of vibration, higher is the pitch.

• The frequency determines the shrillness or pitch of a sound.
• If the frequency of vibration is higher we say that the sound is shrill and has a higher pitch.
• If the frequency of vibration is lower, we say that the sound has a lower pitch.

The pitch of a sound is determined by its frequency, not by the amplitude. While the amplitude affects the loudness of the sound, it does not have any direct relation to the pitch. So, the Reason is not the correct explanation of the Assertion.

The correct answer is Heat causes air inside the bottle to expand.

Explanation:

• The activity demonstrates the effect of temperature on the volume of gases.
• This activity is a simple example of Charles's Law, which states that the volume of a given amount of gas is directly proportional to its absolute temperature when the pressure and the amount of gas are kept constant.
• When the deflated balloon is placed on the mouth of the glass bottle and the bottle is immersed in a bath of boiling water, the temperature of the air inside the bottle increases.
• As the temperature of a gas increases, its particles gain kinetic energy and move more vigorously, leading to an increase in the average speed of the particles.
• As a result of the increased kinetic energy and particle movement, the heat causes air inside the glass bottle to expand.
• This increase in volume causes the balloon to inflate or change its shape, showing that the gas inside the bottle has expanded.
• Thus, the change in the shape of the balloon when the glass bottle is immersed in boiling water demonstrates that gases expand when their temperature increases due to the increased kinetic energy of their particles.

The correct answer is M is acid and N is base.

Concept:

• Turmeric solution acts as an indicator.
• An indicator is a substance that changes its color in the presence of different pH levels (acidity or basicity) of a solution.
• Turmeric is a natural indicator that turns yellow in acidic solutions and brick red in basic solutions.

Explanation:

• When turmeric solution is added to solution M, it turns yellow.
• This indicates that solution M is acidic because turmeric turns yellow in acidic conditions (pH below 7).
• When turmeric solution is added to solution N, it turns brick red.
• This shows that solution N is basic because turmeric turns brick red in basic conditions (pH above 7).
• Red color in solution N gradually fades when solution M is added to it, it indicates that solution N is a base.
• The acidic nature of solution M neutralizes the basic nature of solution N, leading to the fading of the red color.

The correct answer is Option 1 i.e. Iron oxide and Potassium permanganate.

• Food preservatives are chemicals that are added to food to protect it from microbes that could contaminate or rot it.
• They keep food looking and tasting fresh while protecting it from contamination.
• Salts, sugars, edible oils, vinegar, etc. are referred to as preservatives.
• The most common chemicals used to inhibit the growth of microorganisms are salts and edible oils.
• To prevent microbes from attacking pickles, we add salt or acid preservatives.
• Common preservatives also include sodium benzoate and sodium metabisulphite.

Explanation:

​Iron oxide:

• Iron oxide, also known as rust, is not used as a food preservative.
• It is a chemical compound that consists of iron and oxygen, and it is commonly found in nature as a reddish-brown or black mineral.

Potassium permanganate:

• Potassium permanganate (KMnO₄) is a powerful chemical compound that is used for a variety of purposes, including water treatment, disinfection, and oxidation.
• It has disinfectant properties**.**
• It is highly toxic if ingested in significant amounts.
• It should never be used as a food preservative due to its toxicity and potential harm to human health.

Additional InformationSodium benzoate and sodium metabisulphite:

• Sodium benzoate is used as a food preservative because of its anti-fungal properties. This chemical compound enters each cell and balances the pH of the food, effectively increasing the acidity of the food and assisting in food preservation.
• Sodium metabisulphite is widely used as a preservative and disinfectant in food.

Sodium chloride and citric acid:

• Sodium chloride (Salt) is one of the oldest and most widely used food preservatives. It is commonly used in pickling, curing meats, and preserving various food products.
• Citric acid is a weak organic acid found naturally in citrus fruits like lemons, limes, and oranges. It is widely used in the food industry as a preservative, flavor enhancer.

Vit C (ascorbic acid) and sugar:

• Ascorbic acid, commonly referred to as vitamin C, acts as an antioxidant in foods.
• Sugar has long been used as a traditional method of food preservation, especially in the form of jams, jellies, and fruit preserves.

Hence, the correct option is 1.

The correct answer is Rusting of iron, burning of paper, cooking of food.

Concept:

Physical Change:

• A change in which a substance's physical properties change is referred to as a physical change.
• It is usually reversible.
• In the physical change, no new products are formed.

Chemical Change:

• When one chemical substance is transformed into one or more different substances, this is referred to as a chemical change.
• It is usually irreversible.
• In the chemical change, new products are formed.

Explanation:

Rusting of iron:

• Rusting of iron is a chemical change that occurs when iron reacts with oxygen and moisture in the atmosphere, resulting in the formation of a reddish-brown layer (rust) on the surface of iron.
• The chemical composition of iron changes during this process, and a new substance, rust, is formed.

Burning of paper:

• When we burn paper, it undergoes the combustion reaction, and the state of substances changes from solid to liquid to gaseous during the combustion reaction.
• As a result, burning paper is considered a chemical change because the paper after burning transforms into ashes and gas fumes evolve.

Cooking of food:

• Cooking of food is an irreversible chemical change.
• Cooking causes the molecules in food to change and form new substances.
• Furthermore, cooked food cannot be returned to its raw state.

The correct answer is Both assertion and reason are correct and reason is the correct explanation of the assertion.

Concept:

Metal activity series:

• The metals are arranged in an activity order that is known as metal activity series.
• The more active metals are present at the top of the series whereas the less active metals are present at the end of the series.

Importance of the series-

• The metal activity series is used to predict displacement reactions.
• Metals that are above hydrogen in the series can displace hydrogen from acids.
• Metals that are below hydrogen in the series cannot displace hydrogen from the acids.
• Metals that are higher in the activity series can displace metals that are lower to them from their salts.

Explanation:

Assertion: If an iron blade is put in a blue copper sulfate solution, copper will get deposited over the iron blade.

• This statement is correct.
• When iron is placed in a copper sulfate solution (CuSO₄), a displacement reaction occurs.
• The more reactive metal, which is iron in this case, displaces the less reactive metal, which is copper, from its compound.
• As a result, copper ions (Cu²⁺) in the copper sulfate solution gain electrons and get reduced to form copper metal, which gets deposited on the iron blade.

Reason: The reactivity of iron is greater than that of copper, and hence copper is displaced from copper sulfate solution.

• This statement is also correct.
• In the reactivity series of metals, iron is placed higher than copper.
• This means iron is more reactive than copper.
• When a metal is more reactive than another metal, it can displace the less reactive metal from its salt solution in a displacement reaction.
• In this case, iron, being more reactive, displaces copper from the copper sulfate solution, leading to the deposition of copper on the iron blade.

Thus, both the Assertion and Reason are correct and reason is the correct explanation of the assertion, Option (A) is the correct option.

The correct answer is (A) and (D).

Explanation:

• When zinc powder is added to dilute hydrochloric acid (HCl) in a test tube, a rapid chemical reaction takes place.
• Zinc reacts with hydrochloric acid to produce hydrogen gas (H₂) and zinc chloride (ZnCl₂).
• This is a typical example of a single displacement or redox reaction, where zinc replaces hydrogen in the acid.
• The balanced chemical equation for the reaction is:

Zn(s) + 2HCl(aq) → ZnCl₂(aq) + H₂(g)

• So, when zinc powder is added to dilute hydrochloric acid in a test tube, you can expect the release of hydrogen gas.
• To form bubbles of hydrogen, zinc reacts rapidly with the acid.
• The reaction may be visible as bubbles forming in the test tube.

Key Points

• Digestion is the process by which large insoluble macromolecules of food are broken down into small water-soluble food molecules that can be absorbed by the blood plasma.
• Digestion occurs in the digestive system that starts with the mouth and ends with the anus.
• The digestive system comprises different structures such as the mouth, oesophagus, stomach, pancreas, liver, gall bladder, small intestine, large intestine, rectum, and anus.
• The digestive system is anatomically made up of the gastrointestinal tract or alimentary canal and the accessory digestive organs, viz. liver and pancreas.
• There are various digestive juices and enzymes that also help in the digestion of food.
• Digestive juices and enzymes are secreted by the buccal cavity, stomach, liver, pancreas, etc.
• The whole digestion process completes in the following steps- ingestion, secretion, digestion, absorption, and excretion.

Explanation:

A Gets broken into simple sugars

• A indicates Carbohydrates.
• Carbohydrate digestion starts in the mouth. Salivary amylase from the salivary gland starts the breakdown of carbohydrates into maltose.
• With the help of the maltase enzyme maltose breaks down into two glucose molecules in the mucosal epithelial cells of the intestine.

B Gets broken into glycerol

• B indicates Fats.
• Firstly fats are emulsified, i.e. breaking down of the fats into very small micelles by bile juices from the liver.
• Bile also activates the lipase enzyme that breaks down fats into glycerol and fatty acids.

C Breaks into simpler amino acids

• C indicates Proteins.
• Protein digestion starts in the stomach and completes in the small intestine.
• Pepsin is a protein-digesting enzyme that is secreted by the stomach in an inactive form.
• The inactive form is called pepsinogen and it gets activated by HCl.
• Pepsin then converts proteins into proteases and peptides.
• With the help of trypsin, chymotrypsin converts proteases and peptides into dipeptides.
• Lastly, the dipeptidase enzyme breaks down dipeptide into amino acids.

Hence, the correct option is (3) A - Carbohydrates, B - Fats, and C - Proteins.

The correct answer is Option 2.

Explanation:

Drive at a moderate speed as far as possible. (CORRECT)

• Driving at a moderate speed (neither too fast nor too slow) can help improve fuel efficiency.
• High speeds often lead to increased aerodynamic drag, which requires more energy to overcome and leads to higher fuel consumption.
• Driving at a moderate speed allows the engine to operate more efficiently, leading to better fuel economy.

Ensure that the tyre pressure is moderately low. (INCORRECT)

• This statement is incorrect. The correct suggestion is to ensure that the tyre pressure is at the recommended level or moderately high.
• Properly inflated tyres reduce rolling resistance, which can improve fuel efficiency.
• Under-inflated tyres increase rolling resistance, causing the engine to work harder and consume more fuel.

Ensure regular maintenance of the vehicle. (CORRECT)

• Regular vehicle maintenance is crucial for optimal fuel efficiency.
• A well-maintained vehicle performs more efficiently, and issues like clogged air filters, faulty spark plugs, or engine problems can decrease fuel economy.
• Regular servicing and maintenance checks help ensure that the vehicle is running at its best, leading to better fuel efficiency.

Switch off engine at red light. (CORRECT)

• This is a valid suggestion to save petrol/diesel.
• When your vehicle is stationary at a red light or during prolonged stops, switching off the engine can save fuel.

Thus, to save petrol/diesel, it's essential to adopt fuel-efficient driving habits and perform regular maintenance on the vehicle. Keeping tyres properly inflated, driving at moderate speeds, and turning off the engine during prolonged stops are effective ways to improve fuel efficiency and reduce fuel consumption.

Key Points

• The roots of the plants are the underground structures that provide anchoring and absorption.
• There are three types of roots present in plants- Tap roots, Fibrous roots, and Adventitious roots.
• The tap roots develop from the radicle of a developing embryo.
• A taproot system comprises one thick, cylindrical main root, called the primary root.
• The small roots that branch out from the primary root are known as secondary and tertiary roots.
• The primary function of the tap root is to provide strong anchorage to plants.

Explanation:

• Turnips and tapioca are examples of tap roots.
• In turnips, tap roots perform the storage function.
• The tap roots are modified in such a way that they can store food synthesized by the plants.
• In tapioca also tap roots are modified to perform storage functions.
• Starch is stored in the tap roots of tapioca.

Additional Information

• Maize and onion contain fibrous roots.
• Carrots have tap roots but potatoes are modified underground stems.
• Ginger is an example of a nodulose root.

Hence, the correct option is (3) Turnip, tapioca.

Key Points

• Photosynthesis is the process by which autotrophs produce their own food and transforms solar energy into chemical energy.
• During photosynthesis, chlorophyll present on the green leaves traps the sunlight, roots absorb water and minerals, and CO₂ from the atmosphere forms food.
• The representation of photosynthesis-

         6CO₂ + 12H₂O + Sunlight → C₆H₁₂O₆ + 6O₂ + 6H₂O

Explanation:

Statement (A): The presence of starch in leaves indicates the occurrence of photosynthesis.

• During photosynthesis, glucose is produced.
• The presence of starch in leaves indicates the occurrence of photosynthesis.
• Starch is a polysaccharide made up of glucose monomers.
• In starch, glucose units are joined together by glycosidic bonds.
• Thus, the assertion is true.

Statement (R): Oxygen formed during photosynthesis ultimately gets converted to starch.

• Oxygen is one of the end products formed during photosynthesis.
• Oxygen is a gaseous bi-product that goes out to the atmosphere through the stomata.
• Oxygen formed during photosynthesis does not get converted to starch.
• Thus, the reason is false.

Hence, the correct option is (3) (A) is true but (R) is false.

Key Points 

Statement (A) Mustard, rose and petunia have unisexual flowers.

• The flowers have only male or female reproductive parts, i.e., either stamens or carpels present, are known as unisexual flowers.
• Mustard, rose, and petunia have bisexual flowers.
• Thus, this statement is false.

Statement (B) Corn, papaya, and cucumber produce bisexual flowers.

• The flowers contain both the male and female reproductive parts that is stamens and carpels, and are known as bisexual flowers.
• Corn, papaya, and cucumber produce unisexual flowers.
• Thus, this statement is false.

Statement (C) The female gamete is formed in an ovule.

• The ovule is a structure of a flowering plant that develops into a seed during fertilization.
• The female gamete is formed in an ovule also known as an egg.
• Thus, this statement is true.

Statement (D) After fertilization, the ovary grows into a seed of the plant.

• The process of fusion of a paternal sperm nucleus with a maternal egg nucleus to form a zygote is known as fertilization.
• After fertilization, ovules develop into seeds and the ovary develops into fruit that encloses the seeds.
• Thus, this statement is false.

Hence, the correct option is (3) Only (C).

The correct answer is Option 1.

 Key Points

(A) Citrus canker - (ii) Bacteria

• Citrus canker is a bacterial disease of citrus plants.
• The disease leads to the premature fall of fruits and leaves.
• The disease is caused by Xanthomonas bacteria.

(B) Polio - (i) Virus

• Polio is a viral disease caused by poliovirus.
• It is an infectious disease.
• Polio affects children by causing limb paralysis of them.

(C) Malaria - (iv) Protozoa

• Malaria is a mosquito-borne infectious disease.
• It is caused by Plasmodium protozoa.
• Plasmodium proliferates in the gut of the female Anopheles and acts as a vector for malaria.

(D) Rust of wheat - (iii) Fungi

• Rust of wheat is a fungal disease of wheat, barley, etc.
• It is caused by Puccinia graminis.
• Puccinia graminis belong to the Basidiomycetes group of the kingdom fungi.

Explanation:

Hence, the correct option is 1.

The correct answer is Option 2 i.e. A- Xylem, B- Phloem, C- stomata.

Concept:

• Vascular tissues are present in plants that transport water, minerals, food, etc.
• Vascular tissues are complex conducting tissues.
• Xylem and phloem tissues are vascular tissues.
• These tissues are mainly responsible for the transport of water and nutrients throughout the plant body.

Explanation:

A. are vascular tissues for the transportation of water and nutrients in plants-

• 'A' indicates Xylem.
• The xylem is one of the conducting tissues that are responsible for the transport of water and minerals from the roots to the leaves of the plants.
• Xylem is composed of treachery elements.
• The components of the xylem include tracheid, vessels, xylem parenchyma, and xylem fibers.

B. are vascular tissues that transport food in plants-

• 'B' indicates Phloem.
• The phloem is one of the vascular tissues that transport food prepared during photosynthesis from the leaves to all the parts of the plant.
• The components of the phloem include sieve elements, companion cells, and phloem parenchyma.
• Sieve tubes and sieve plates together form sieve elements.

C. are tiny pores present on the surface of leaves-

• 'C' indicates Stomata.
• Stomata are the tiny pores present on the surface of the leaves.
• Stomata play an important role in gaseous exchange and transpiration.
• The opening and closing of stomatal pores are maintained by guard cells.

Hence, the correct option is (2) A - Xylem, B - Phloem, C - Stomata.

The correct answer is Option 2 i.e. Cell wall is absent in plant cell while present in animal cell.

Concept:

• A cell is the fundamental structural and functional unit of life.
• All living organisms are made of cells and products of cells.
• Some organisms are made up of a single cell, called a unicellular organism and some are made up of many cells called multicellular organisms.
• Each cell contains a semi-fluid matrix, cytoplasm that is enclosed by a defined cell membrane.
• In the presence or absence of a well-distinct nucleus, cells are divided into Eukaryotic and Prokaryotic cells.
• Mitochondria, ribosomes, endoplasmic reticulum, lysosomes, vacuoles, Golgi bodies, etc. are the cell organelles present inside the cell.

Explanation:

Option 1: Cell membrane is present in both animal and plant cells.

• The cell membrane supports the cell's shape and size and protects the inner environment of the cell.
• The cell membrane is found in both animal and plant cells.
• The membrane is semi-permeable.
• It is made up of lipids that are arranged in a bilayer and proteins.
• The membrane proteins are classified as integral and peripheral proteins.
• Thus, this statement is correct.

Option 2: The cell wall is absent in plant cells while present in animal cells.

• The cell wall is the non-living outer covering for the cell membrane that is present in plants and fungi.
• The cell wall is absent in animal cells.
• It maintains the shape of the cell and also protects the cell from mechanical injuries and damage.
• The cell wall is composed of cellulose, hemicellulose, and proteins.
• Thus, this statement is incorrect.

Option 3: Plastids are present in plant cells only.

• Plastids are the double membrane-bound cell organelles present in plant cells only.
• Plastids contain some specific pigments and based on pigments plastids can be divided into- chloroplasts, chromoplasts, and leucoplasts.
• Thus, this statement is correct.

Option 4: Cytoplasm is present in both animal and plant cells.

• Cytoplasm is the thick, clear, semi-fluid matrix that is present inside the cell membrane.
• It is present in both animal and plant cells.
• It holds the cell organelles and is the site of various biochemical reactions.
• Thus, this statement is correct.

Hence, the correct option is (2).

The nature of science includes understanding that scientific ideas are tentative and can be modified or disproved and that science is a creative endeavor that requires imagination.

Key Points

• Some phenomena are studied through observation, modeling, or other methods. not all scientific ideas can be tested by controlled experiments.
• A theory does not become a law, even if strongly supported. Laws describe consistent relationships in nature, while theories explain those relationships.
• Science is an evolving field, and ideas can change as new evidence becomes available. Scientific ideas are tentative and can be modified or disproved.
• Scientists often need creativity to design experiments, interpret data, and formulate theories.

Hence, we can conclude that statements (C) and (D) represent a correct understanding of the nature of science.

The detailed observation of flowers in an educational context, especially in middle school like grade 7, serves multiple purposes and aims.

Key Points

• To identify flower parts: Correct. Detailed observation can teach students the various parts of a flower, like the petals, stamen, pistil, etc.
• To help instill a sense of empathy for plants: Not Directly Correct. While studying nature may foster a greater appreciation and care for it, this isn't a direct objective of studying the structure of flowers.
• To prepare students for an understanding of pollination: Correct. By understanding the different parts of a flower, students can better understand how pollination works.
• To appreciate the diversity of flowers around: Correct. Observing various types of flowers can enhance students' appreciation of the diversity within the plant kingdom.
• To observe xylem and phloem closely: Not Likely Correct. While these are essential parts of plant biology, a detailed observation of flowers specifically might not enable grade 7 students to study these microscopic structures without specialized equipment.

Hence, we can conclude that statements (A), (C) and (D) are correct.

Ethical validity in science education refers to promoting and instilling values that reflect the ethical norms of the scientific community. 

Key Points

This includes:

• Honesty: Encouraging students to report findings truthfully, without fabrication, falsification, or plagiarism.
• Objectivity: Teaching students to approach scientific inquiry without bias, ensuring that conclusions are based on evidence and not personal or societal beliefs.
• Integrity: Emphasizing the importance of consistency in methods, data recording, and reporting.
• Fairness: Encouraging collaborative work, proper citation, and respectful disagreement.
• Responsibility: Highlighting the scientist's responsibility to society, the environment, and the broader scientific community.

Hence, we can conclude that Ethical validity in science curriculum means promoting the values of honesty, objectivity, etc.

The phenomenon of moonrise refers to the appearance of the Moon as it ascends above the horizon as observed from a specific location on Earth.

Key Points

• The moon rises in the east and sets in the west, although the exact angles can vary depending on your geographical location and the time of year.
• Moonrise does not happen at the same time every day. The time it rises and sets changes throughout the lunar month (approximately 29.5 days).
• After the new moon phase, the portion of the moon that is illuminated as viewed from Earth does indeed increase. but in the question, it is not mentioned the observations were done at the time of the new moon.
• The phases of the moon are not caused by the Earth blocking sunlight from reaching the moon.

Hence, we can conclude that statements (A) and (B) are correct inferences made by Ronak based on his observations.

Concept maps are visual representations of knowledge that can be used to assess students' understanding of a topic.

Key Points

• Concept maps can be used to identify areas where students are struggling to understand the concepts, and they can also be used to track students' progress over time.
• Observing practical skills can be helpful for assessing students' ability to apply concepts, but it does not provide as much information about their understanding of the concepts themselves.
• Organizing quiz sessions can be helpful for assessing students' knowledge of specific facts, but they do not provide as much information about their understanding of the relationships between concepts.
• Giving homework regularly can be helpful for reinforcing concepts, but it does not provide as much information about students' understanding of the concepts themselves.

Hence, we can conclude that Using concept maps is best the strategy.

Open-book questions are designed to allow students to refer to their textbooks or notes during an examination. 

Key Points

• The idea is to assess students' ability to find and apply knowledge, rather than simply recall facts.
• This can help to reduce stress, as students know that they will have the information available to them, and encourage a deeper understanding of the material, as they need to know how to apply what they have learned.
• Open-book exams aren't about encouraging students to memorize books. Instead, they emphasize understanding and application.
• Open-book exams recognize that having access to the book can reduce the fear associated with exams.
• Open-book exams emphasize exploration and utilization of the book to solve problems.
• Open-book exams can actually help gauge conceptual understanding by assessing students' ability to apply knowledge.

Hence, we can conclude that statements (B), and (C) align with the spirit of open-book questions.

The given paragraph tells the story of the discovery of silk, including some historical context and the process of discovery. 

Key Points

• (A) The paragraph provides historical context to the discovery of silk, so this objective is fulfilled.
• (B) It details how a chance incident led to a significant discovery, allowing students to appreciate how ideas and accidental occurrences can lead to significant discoveries.
• (C) It might be considered part of a holistic understanding of science in that it connects biology (silkworms and mulberry trees) with technology (the production of silk) and history (the silk route), although this is somewhat debatable depending on the broader context of the lesson.
• (D) The paragraph doesn't specifically focus on a fun element of science, so this option is not fulfilled.

Hence, we can conclude that statements (A), (B), and (C) are the objectives of science teaching-learning that are fulfilled by including the above in the textbook.

A debate is a structured argument where two or more people present opposing views on a specific topic or issue.

Key Points

• The purpose of organizing a debate, especially on a subject like "Destruction of animal habitat due to encroachment," is typically to encourage:
• Critical thinking.
• Allow students to express their views.
• Foster the development of various perspectives.
• Assess the children's understanding and ability to articulate their thoughts.
• However, debates are not meant to arrive at one correct or universally accepted opinion.
• They are meant to expose students to different viewpoints and help them understand that complex issues may not have a simple or singular solution.

Hence, we can conclude that helping in arriving at one correct opinion about the problem of encroachment is not the purpose of having these kinds of activities.

The National Curriculum Framework (NCF) 2005 emphasizes a constructivist approach to learning, promoting understanding and application of concepts rather than rote memorization.

Key PointsFor the upper primary stage science curriculum, the focus is on:

• (A) Relating science concepts to real-life situations, so that students can see the relevance and application of what they are learning.
• (C) Creating situations for students to construct their own knowledge, fosters a deeper understanding and encourages critical thinking skills.
• The other options (B) and (D) are not aligned with the NCF 2005's recommendations, as they lean more towards direct instruction and avoid traditional resources, which doesn't fully reflect the framework's emphasis on a balanced and student-centered approach.

Hence, we can conclude that statements (A) and (C) are correct recommendations according to N. C. F. 2005 for the upper primary stage science curriculum.

Equity in science education refers to the principle that all students should have fair and equal access to quality science instruction, resources, opportunities, and support.

Key Points

• Assertion (A) is indeed correct. Equity in science education refers to ensuring that every student has an equal opportunity to access quality science education, regardless of their background, ethnicity, gender, or special needs.
• Reason (R) is also correct. One of the objectives of science education is to prepare all students for participation in an equitable society, where everyone has an equal opportunity to contribute and benefit.
• However, while both statements are true, (R) is a broader objective and doesn't specifically explain why equity in science education is defined the way it is in (A).
• The focus of equity in education is more comprehensive than just preparing students for a modern equitable society; it's about fairness, inclusion, and ensuring that all students have the same educational opportunities.

Hence, we can conclude that Both (A) and (R) are correct but (R) is not the correct explanation of the (A).

The correct answer is: providing food to pilots in space.

Key Points

• Let us look at the statements given in option section.
• ​"Sending information for the weather forecast" - This is mentioned in the first sentence of the passage: "e.g. the weather forecasts are sent by satellites."
• "Providing food to pilots in space" - There is no reference to this in the passage. It is not mentioned as one of the functions or uses of satellites.
• "Taking photographs of the earth" - This is mentioned in the first paragraph: "Some satellites have cameras that take photographs of the earth to show how clouds move."
• "Sending TV pictures" - This is mentioned in the second paragraph: "We use satellites to send television pictures from one part of the world to another."
• Therefore, it is clear that the passage discusses the various functions and uses of satellites, such as sending weather forecasts, taking photographs of the earth, and sending TV pictures.
• However, there is no mention of satellites being involved in providing food to pilots in space.

Hence, the correct answer is option 2.

The correct answer is: to stay in a certain position in the orbit.

Key Points

• According to the passage, the satellite moves in the sky at the same velocity as the earth rotates to stay in a certain position in the orbit.
• This is mentioned in paragraph 2 of the passage: "Sometimes we can see a satellite in the sky and it seems to stay at the same place. This is because it is moving at around 11,000 kms an hour, exactly the same speed that the earth rotates."
• The matching velocity allows the satellite to stay in a fixed position relative to the Earth's surface, which is essential for many satellite applications, including communication and observation tasks.

Therefore, the correct answer is option 4.

Additional Information

• Option 1 is not the correct reason why the satellite moves in the sky at the same velocity as the earth rotates. The satellite's movement is not directly related to taking photographs of the Earth
• Option 2 is not correct either as the satellite's velocity matching the earth's rotation speed does not make it easier for the satellite to move away from its orbit.
• Option 3 is not the correct reason either because the satellite's velocity is not primarily related to sending television pictures.

The correct answer is: (A) is true and (B) is false

Key Points

• The passage mentions that satellites have little rockets on them, which are used to put the satellite back in the right position if it moves away from its orbit.
• So, the rockets in a satellite help keep it in a proper position.
• Hence, statement A is correct.
• The passage states that broken satellites are sometimes repaired by astronauts or brought back to Earth to be repaired.
• However, if they are very old or cannot be repaired, they are often left in space to orbit the earth for a long time.
• So, disabled satellites can be repaired in some cases, but if not feasible, they are left in space.
• Hence, statement B is incorrect.

Therefore, the correct answer is option 1, i.e. "(A) is true and (B) is false."

The correct answer is: both (1) and (2)

Key Points

• The passage mentions that most satellites use solar power to produce electricity and a few use nuclear power.
• So, orbiting satellites can be powered by either solar power or nuclear power, or sometimes a combination of both depending on the design and purpose of the satellite.
• The choice of power source for a satellite depends on its mission requirements, duration in space, power needs, and other design considerations.
• Solar power is commonly used for most satellites due to its reliability and accessibility in space, while nuclear power is utilized for specific missions that demand extended durations or higher power output.

Therefore, the correct answer is option 4, i.e. "both 1 and 2."