CTET Paper 2 Maths & Science 23th Jan 2023 (English-Hindi-Sanskrit) (Previous Year Paper)

Key Points

• Assertion (A) states that it is not considered abnormal for a child to begin shedding their milk teeth at the age of five or seven, even though the average age for this process is around six years. This is because there is a normal range of individual variation in the timing of tooth eruption and shedding. Some children may experience these changes slightly earlier or later than the average, and it is still considered within the normal range.
• Reason (R) states that the patterns of growth and sequence of physical development are universal, meaning that there are general expectations for the order and timing of various developmental milestones. However, there is also a significant range of individual differences within these patterns. Each child has their unique developmental timeline, influenced by genetic, environmental, and other factors. This variability in individual development is considered normal.

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

The principles of development are general guidelines that describe the patterns, characteristics, and processes of human development. These principles help to understand and explain how individuals grow, change, and develop throughout their lifespan.

Key Points

• The Principle of Individuality recognizes that every child is unique and develops at their own pace.
• While children may follow a general sequence of development, the timing and rate of their development can vary.
• This principle acknowledges that each child has their individual strengths, abilities, and areas of growth, and their developmental journey should be respected and supported accordingly.

Thus, it is concluded that Principle of Individualilty states that each child develops at her own rate even though the direction of development is similar.

 Hint

• Principle of Cephalocaudal development: This principle describes the pattern of development where growth and development occur from the head down to the feet. It relates to the physical development of an individual.
• Principle of Proximo-distal development: This principle describes the pattern of development where growth and development occur from the center of the body outward to the extremities. It also relates to the physical development of an individual.

Secondary agencies of socialization typically include institutions and groups such as schools, peers, religious institutions, media, and community organizations. These secondary agencies contribute to the socialization process by providing additional social experiences, perspectives, and influences beyond the family unit.

Key Points

• Family is not considered a secondary agency of socialization but rather the primary agency of socialization.
• The family is the first and most influential social group that a child encounters, and it plays a crucial role in shaping a child's beliefs, values, attitudes, and behaviors.
• Family members, especially parents or guardians, serve as primary role models and provide initial socialization experiences for children.

Thus, it is concluded that Family is NOT an important secondary agency of socialization.

Jean Piaget was a Swiss psychologist known for his influential theory of cognitive development.

Key Points

• The formal operational stage is the fourth and final stage of Jean Piaget's theory of cognitive development.
• It typically begins around adolescence and continues into adulthood.
• During this stage, individuals develop the ability to think abstractly, hypothetically, and systematically.
• They can reason using formal logic, manipulate abstract concepts, understand hypothetical situations, and think about possibilities and consequences.

Thus, it is concluded that In the formal operational stage, children can reason not just with objects but with formally stated propositions.

Piaget's theory proposed that children actively construct their understanding of the world through a series of stages, each characterized by distinct cognitive abilities and ways of thinking.

Key Points

• Sensory Experience: This refers to the Sensorimotor Stage, which occurs from birth to about 2 years old. During this stage, infants learn about the world through their senses and motor actions.
• Symbolic and Intuitive Thoughts: This refers to the Preoperational Stage, which occurs from about 2 to 7 years old. In this stage, children acquire symbolic representation and language skills. They engage in pretend play and have egocentric thinking.
• Reversible Mental Operation: This refers to the Concrete Operational Stage, which occurs from about 7 to 11 years old. In this stage, children become capable of more logical and concrete thinking. They understand conservation and can perform mental operations that involve reversing actions or mentally manipulating objects.
• Hypothetical Thinking: This refers to the Formal Operational Stage, which typically begins around 11 years old and continues into adulthood. In this stage, individuals develop the ability to think abstractly, reason hypothetically, and engage in systematic and scientific thinking.

Thus, it is concluded that Sensory Experience, Symbolic and Intuitive Thoughts, Reversible Mental Operation, Hypothetical Thinking is the correct sequence of stage of cognitive development beginning from the birth.

Piaget's theory proposed that children actively construct their understanding of the world through a series of stages, each characterized by distinct cognitive abilities and ways of thinking.

Key Points

• According to Jean Piaget, in order for cognitive development to take place effectively, a child should be given opportunities for active exploration.
• Piaget's view is that children construct their understanding of the world through interactions with their environment.
• Piaget emphasized the importance of hands-on experiences, curiosity, and active engagement with the environment for cognitive development to occur.
• Through active exploration, children can engage in problem-solving, discovery, and assimilation of new information into their existing cognitive structures.

Thus, it is concluded that option 3 is the correct answer.

Lawrence Kohlberg was a psychologist known for his theory of moral development.

Key Points

• The pre-conventional level is the first level of moral development in Kohlberg's theory**.**
• It typically occurs during early childhood and is characterized by a focus on external consequences and rewards/punishments.
• At this stage, individuals make moral judgments based on self-interest and the potential for personal gain or avoidance of punishment.
• They may adhere to rules to avoid punishment or to gain rewards, and their moral reasoning is guided by obedience and self-interest.

Thus, it is concluded that  In Kohlberg's Pre-conventional level moral development theory, the stage in which what is considered good or bad is determined by the consequences of obeying or disobeying rules.

Lev Vygotsky was a Russian psychologist known for his sociocultural theory of cognitive development. Vygotsky's theory emphasizes the role of social interaction and cultural factors in the development of higher mental functions.

Key Points

• Vygotsky emphasized the importance of social interaction and collaboration in a child's cognitive development.
• He believed that learning occurs through the guidance and support of more knowledgeable individuals, particularly in the context of social interactions with peers and adults.
• Through social interaction, children can engage in shared activities, receive guidance, and internalize knowledge and skills from others.

Thus, it is concluded that According to Vygotsky, children learn through social interaction with their peers.

Lev Vygotsky was a Russian psychologist known for his sociocultural theory of cognitive development. Vygotsky's theory emphasizes the role of social interaction and cultural factors in the development of higher mental functions.

Key Points

• Scaffolding refers to the support provided by a more knowledgeable individual, such as a teacher, parent, or peer, to help a learner achieve a higher level of understanding or skill. The support is tailored to the learner's current level of ability and gradually adjusted as the learner becomes more competent.
• The key concept of scaffolding is that the adult or more capable peer provides assistance that is just beyond the learner's current ability level, within the learner's Zone of Proximal Development (ZPD).
• The adult varies the level of assistance, adapting to the learner's needs and gradually reducing support as the learner becomes more independent and proficient.

Thus, it is concluded that In Lev Vygotsky’s theory the idea of scaffolding means that the adults vary the amount and nature of assistance.

In a progressive classroom, the focus is on student-centered learning and providing a more holistic approach to education.

Key Points

• A progressive classroom emphasizes student-centered learning and values the unique abilities, interests, and needs of each child.
• Teachers in a progressive classroom foster an environment of respect and trust, where children are encouraged to explore, question, and take an active role in their own learning.
• The teacher acts as a facilitator, guiding and supporting students as they engage in hands-on activities, collaborative projects, and critical thinking.

Thus, it is concluded that In a progressive classroom, children are respected and teachers have trust in the capacity of each child.

Howard Gardner proposed the theory of multiple intelligences, which suggests that intelligence is not a single, unitary concept but rather a combination of various distinct intelligences.

Key Points

• Naturalistic intelligence, as proposed by Howard Gardner's theory of multiple intelligences, refers to the ability to recognize and categorize elements of the natural world, including plants, animals, geological formations, and ecosystems.
• Individuals with high naturalistic intelligence are often observant of their surroundings, have a deep connection to nature, and demonstrate a keen ability to identify and understand the patterns and relationships within the natural world.

Thus, it is concluded that Individuals having high naturalistic intelligence possess the ability to classify natural forms such as animal and plant species and rocks and mountain types.

Hint

• Linguistic intelligence refers to the ability to effectively use language, including verbal and written communication skills.
• Musical intelligence refers to the ability to understand, appreciate, and create music.
• Intrapersonal intelligence refers to self-awareness and understanding of one's own emotions, strengths, and weaknesses.

Gender is not solely determined by genetics, physical characteristics, or hereditary factors.

 Key Points

• Gender is primarily a social construct that encompasses the roles, behaviors, expectations, and identities that society assigns to individuals based on their perceived gender.
• Gender is shaped by cultural, historical, and societal norms and varies across different societies and time periods.
• Understanding gender as a social construct acknowledges that gender roles and identities are not fixed or universal but are influenced by cultural beliefs, social norms, and power dynamics.
• It recognizes that individuals may experience and express their gender in diverse and fluid ways beyond the binary understanding of male and female.

Thus, it is concluded that the statement that society determines the role of male, female and other genders articulates gender as a social construct.

Key Points

• The assertion states that teachers should emphasize using and implementing standardized curriculum and assessment methods. However, this is not a correct statement. There are diverse approaches to education, and not all educators believe that standardized approaches are the most effective for every student or in every context. Many educators advocate for personalized and differentiated instruction to accommodate individual differences and promote meaningful learning experiences.
• The reason suggests that schools should work towards removing individual differences among children rather than accepting them. This statement is also not correct. Recognizing and respecting individual differences is considered important in education. Schools aim to create inclusive environments that celebrate diversity and cater to the unique needs and strengths of each student.

Thus, it is concluded that Both (A) and (R) are false.

Assessment in education refers to the process of gathering evidence and information about students' knowledge, skills, and abilities to make informed judgments about their learning progress.

Key Points

• Assessment in education serves various purposes, such as understanding the readiness levels of children for learning, improving teaching processes, and helping understand what a child can and cannot do. These purposes are aligned with supporting student growth, identifying areas of improvement, and tailoring instruction to meet individual needs.
• Inculcating a competitive spirit among children is not an appropriate goal of assessment.
• While healthy competition can sometimes be motivating, the primary focus of assessment should be on promoting learning, growth, and understanding rather than fostering an overly competitive environment.
• Assessment should encourage collaboration, critical thinking, and the development of individual strengths rather than solely promoting a competitive mindset.

Thus, it is concluded that Assessment should NOT be undertaken to inculcate competitive spirit among children.

Assessment refers to the process of gathering evidence and information about students' knowledge, skills, and abilities to make informed judgments about their learning progress.

Key Points

• Formative assessment is an ongoing process of gathering evidence and information about students' learning progress throughout instruction.
• It involves various strategies such as observations, discussions, quizzes, questioning, and informal assessments.
• Formative assessment allows teachers to monitor student learning in real-time, identify areas of strength and weakness, and provide timely and specific feedback to students.
• It helps teachers understand how well students are comprehending the material, adjust their teaching strategies as needed, and guide students toward further improvement.

Thus, it is concluded that To provide constructive feedback to the students on their learning and reflect on their own pedagogy, the teachers should use formative assessment.

Inclusive schools promote an environment where all students are included and valued, regardless of their abilities, backgrounds, or differences.

 Key Points

• Questioning exclusion characterizes an inclusive school setup.
• They challenge the notion of exclusion and strive to create an inclusive culture that embraces diversity and provides equal opportunities for learning and participation.
• Inclusive schools encourage a sense of belonging, respect, and acceptance among students and aim to eliminate any form of discrimination or exclusionary practices.

Thus, it is concluded that option 1 is the correct answer.

Key Points

• It is important to include children from disadvantaged and deprived backgrounds in the classroom discussion because every child has a right to education.
• Regardless of their socio-economic, cultural, or religious background, every child deserves equal opportunities to participate, learn, and engage in classroom activities.
• Inclusion promotes equity and ensures that all students, regardless of their circumstances, receive the necessary support and opportunities to thrive academically and socially.

Thus, it is concluded that option 2 is the correct answer.

Hint

• ​ Options 1, 3, and 4 are incorrect as they are based on negative assumptions and stereotypes about children from disadvantaged backgrounds, which go against the principles of inclusion, equity, and respect for all students.

A learning disability refers to a neurological condition that affects the brain's ability to process and comprehend information effectively.

Key Points

• Dyslexia is a learning disorder that primarily affects reading and language processing.
• Individuals with dyslexia may struggle with phonological awareness, which can result in difficulties in recognizing and distinguishing between similar-sounding words.
• This can impact their reading, spelling, and overall language skills.

Thus, it is concluded that a child has difficulty in distinguishing words such as ‘WAS’ and ‘SAW’, ‘BATTLE’ and ‘BOTTLE’. Such a difficulty is a typical identifying characteristic of dyslexia.

Hint

• Dysgraphia refers to difficulties in writing.
• Dyscalculia refers to difficulties in mathematics.
• Dysphasia refers to language disorders often caused by brain damage.

Key Points

• Allowing them to sit near the teacher: This accommodation helps students with partial hearing loss have better access to the teacher's voice and visual cues, making it easier for them to hear and understand.
• Minimizing background noise: Background noise can be distracting and make it difficult for students with hearing loss to focus on the teacher's voice. Minimizing noise improves their ability to hear and comprehend.
• Giving handouts using graphic organizers and mind maps: Providing visual support through handouts using graphic organizers and mind maps helps students with hearing loss to access information visually, enhancing their comprehension.

Thus, it is concluded that (i) (ii) (iv) is the correct answer.

Creativity refers to the ability to generate new and valuable ideas, concepts, or solutions to problems.

Key Points

• A teacher can foster creativity in her students by encouraging multiple ideas and intuitive guesses.
• This involves creating an environment where students feel comfortable expressing their thoughts and ideas without fear of judgment or criticism.
• By encouraging divergent thinking and valuing different perspectives, teachers can stimulate creativity in students, allowing them to explore and generate unique solutions and insights.

Thus, it is concluded that a teacher can foster creativity in her students by encouraging multiple ideas and intuitive guesses.

Motivation refers to the internal or external factors that drive and direct an individual's behavior toward achieving a goal or satisfying a need. It is the energy and enthusiasm that fuels and sustains actions, effort, and perseverance toward a desired outcome.

Key Points

• ​Intrinsic motivation refers to engaging in an activity for the inherent satisfaction, enjoyment, or personal interest it brings. When students are intrinsically motivated, they are more likely to be self-driven, engaged, and motivated to learn for the sake of learning itself.
• In contrast, extrinsic motivation involves engaging in an activity for external rewards or to avoid punishment.

Thus, it is concluded that a teacher should encourage intrinsic motivation rather than extrinsic motivation.

Meaningful learning refers to the process of acquiring knowledge or skills in a way that is personally relevant, interconnected, and can be applied to real-life situations.

 Key Points

• Boredom hinders the process of meaningful learning. When students feel bored, they are disengaged and lack interest in the learning material or activities.
• This can lead to a lack of focus, reduced attention, and decreased motivation to learn.
• Boredom can be detrimental to meaningful learning as it inhibits active participation, curiosity, and exploration.

Thus, it is concluded that Boredom emotion hinders the process of meaningful learning.

 Hint

• Enjoyment, Happiness, and Pride are not emotions that hinder the process of meaningful learning.
• They can positively impact the learning experience.
• Enjoyment and happiness enhance engagement, motivation, and positive affect, leading to increased interest and deeper processing of information.
• Pride can foster a sense of accomplishment and self-efficacy, positively influencing the learning process.

Learned helplessness refers to a psychological condition in which an individual feels a sense of powerlessness and helplessness in the face of challenging or adverse situations.

 Key Points

• Students who exhibit learned helplessness believe that their ability is fixed and stable.
• They tend to have a belief that their intelligence, talents, or skills are predetermined and cannot be improved or changed through effort.
• This mindset can hinder their motivation, persistence, and willingness to take on challenges because they perceive their abilities as fixed limitations.

Thus, it is concluded that option 1 is the correct answer.

Key Points

• The child's learning, understanding, and ability to apply knowledge in different situations depend on the opportunities she has to observe and interact with objects and people.
• By actively engaging with the environment, exploring, experimenting, and interacting with others, children can acquire new knowledge, develop skills, and gain a deeper understanding of concepts.
• Hands-on experiences, social interactions, and exposure to a variety of stimuli provide rich learning opportunities and promote cognitive and socio-emotional development.

Thus, it is concluded that What the child learns, how well she learns it and how she is able to apply that learning to various situations depends on opportunities she has to observe and interact with objects and people.

Thinking refers to the cognitive process of mentally processing information, making sense of experiences, and generating thoughts, ideas, and solutions.

 Key Points

• Thinking about one's own thinking is known as metacognition, which refers to the ability to reflect on and be aware of one's own cognitive processes, strategies, and knowledge.
• Metacognition involves being able to monitor and regulate one's thinking, understanding, and problem-solving abilities.
• It includes skills such as self-awareness, self-monitoring, planning, goal-setting, evaluating, and adjusting one's learning strategies.
• Metacognitive abilities are considered higher-order cognitive processes as they involve higher-level thinking and self-regulation.

Thus, it is concluded that Thinking about one’s own thinking is known as metacognition and is a higher order ability.

Constructivism emphasizes active engagement, hands-on experiences, and collaborative learning.

Key Points

• Teachers can encourage students to explore, discover, and construct their own knowledge through inquiry-based activities, problem-solving tasks, group discussions, and interactive projects.
• By creating a stimulating and interactive learning environment, teachers promote student engagement, critical thinking, and the construction of meaning.

Thus, it is concluded that in a constructivist classroom, a teacher can facilitate learning by making the process of teaching and learning interesting and interactive.

Key Points

• Assertion (A) states that the primary role of a teacher in a middle school classroom is to transmit knowledge and correct wrong answers of the students. However, this is an outdated view of teaching. In modern education, the role of a teacher is much broader and encompasses facilitating learning, promoting critical thinking, fostering student engagement, and creating a supportive learning environment. The teacher's role extends beyond simply transmitting knowledge and correcting answers.
• Reason (R) states that learning is a process of acquisition of facts that take place through drill and repeated practice. However, this is an oversimplification of the learning process. While practice and repetition can be components of learning, true learning involves deeper understanding, critical thinking, problem-solving, and the application of knowledge to real-world contexts. Learning is not solely about acquiring facts but also about developing skills, fostering creativity, and promoting higher-order thinking.

Thus, it is concluded that Both (A) and (R) are false.

Meaningful learning refers to the process of acquiring knowledge or skills in a way that is personally relevant, interconnected, and can be applied to real-life situations. 

Key Points

• Explaining to a peer: Explaining concepts to a peer requires students to articulate their understanding in their own words. This process helps solidify their own understanding and promotes active engagement with the material.
• Making concept maps: Creating concept maps involves visually organizing and connecting key concepts, demonstrating relationships and hierarchies between ideas. This strategy enhances understanding by promoting the organization and integration of knowledge.
• Using imageries and creating flowcharts: Imageries and flowcharts can help visualize and represent complex information. These visual aids support comprehension and memory recall by presenting information in a clear and structured manner.
• Thinking of examples and non-examples: Thinking of examples and non-examples helps students develop a deeper understanding of concepts by considering their boundaries and variations. This strategy promotes critical thinking and conceptual clarity
• Self-questioning: Engaging in self-questioning involves asking oneself questions about the material being learned. This strategy promotes metacognition and reflection, encouraging deeper processing and understanding of the content.

Thus, it is concluded that (i) (ii) (iii) (iv) (v) is the correct answer.

Key Points

• Performance goals focus on achieving success in comparison to others, often with the intention of demonstrating superiority or outperforming others.
• In this scenario, Neha's motivation is driven by the desire to obtain higher marks than Rashmi, indicating a focus on external validation and competition rather than intrinsic motivation or learning for the sake of personal growth.

Thus, it is concluded that Neha is setting performance goals.

A socio-constructivist classroom is an educational setting that embraces the principles of socio-constructivism as a guiding framework for teaching and learning.

Key Points

• In a socio-constructivist classroom, children's learning should not be influenced by the marks and scores obtained by their friends.
• Socio-constructivism emphasizes collaborative learning, active engagement, and the construction of knowledge through social interactions.
• It encourages students to focus on the process of learning, understanding, and constructing meaning rather than solely on external measures such as grades or comparison with peers.

Thus, it is concluded that In a socio-constructivist classroom, children’s learning should NOT be influenced by marks and scores obtained by friends.

Hint

• Activities in the classroom, are intended to engage students and facilitate their learning in a socio-constructivist environment. These activities promote hands-on experiences, collaboration, and active participation.
• Content given in the curriculum and books, provides the foundation for learning and understanding in a socio-constructivist classroom. Students interact with the content to construct their own knowledge and understanding.
• Interaction with peer groups, is a crucial aspect of socio-constructivism. Collaborative learning, discussions, and interactions with peers foster the exchange of ideas, different perspectives, and social construction of knowledge.

Calculation:

The square root of 5774 we get,

Instead of taking 145 × 5, we will take 146 × 6 = 876, so we get 2 extra

Now, if we add 2 with 5774, the remainder will be zero and  (5774 + 2) = 5776 became a perfect square number.

∴ The correct answer is 2

Important Points If the question asked for the number which must be subtracted to 5774 to make it a perfect square,

Then we take 145 × 5 = 725, so (874 - 725) = 149 would be the number

Given:

A four-digit number 15y3 is a multiple of 3

Concept used:

If a number is a multiple of 3 then the sum of its digit must be divisible by 3

Calculation:

Sum of the four digits = (1 + 5 + y + 3) = 9 + y

If (9 + y) is divisible by 3 then all the possible values of y is 0, 3, 6, 9 [ y is a single digit number can't be 12 and more ]

The sum of all the possible values of y is (0 + 3 + 6 + 9) = 18

∴ The correct answer is 18

Given:

3.5 × 2.4 × 4.8

Calculation;

3.5 × 2.4 × 4.8

⇒ 35/10 × 24/10 × 48/10

⇒ 7/2 × 12/5 × 24/5

⇒ 7 × 6/5 × 24/5

⇒ 1008/25

∴ The correct answer is 1008/25

Given:

2-3 × (-7)-3

Concept used:

The value, which on adding with the original number results in zero value.

Calculation:

Let's assume the additive inverse of 2-3 × (-7)^-3 be k, then,

⇒ 2-3 × (-7)^-3 + k = 0

⇒ k = - [2-3 × (-7)-3] 

⇒ k = - [ 1/8 × -1/343] = 1/2744

∴ The correct answer is $\frac{1}{2744}$

Given:

 x and y are respectively the HCF and LCM of 135, 108, and 198,

Calculation:

135 = 3³ × 5, 108 = 2² × 3³, and 198 = 2 × 3² × 11

Now, x = HCF of (35, 108 and 198) = 3² = 9

So, y =  LCM of (35, 108 and 198) = 2² × 3³ × 5 × 11 = 5940

So, x/y = 9/5940 = 1/660

∴ The correct answer is $\frac{1}{660}$

Given:

$\rm p=\frac{1}{2}x^2y$ and q = 3xy - 5x3y4

Calculation:

pq + 2x3y2 

⇒ $[\frac{1}2 x^2 y \times (3xy - 5x^3 y^4)] + 2x^3 y^2$

⇒ $[\frac{3}{2}x^3y^2 - \frac{5}{2}x^5y^5] + 2x^3 y^2$

⇒ $\frac{7}{2}x^3y^2 - \frac{5}{2}x^5y^5$

∴ The correct answer is $\rm \frac{7}{2}x^3y^2-\frac{5}{2}x^5y^5$

Concept used:

a² - b² = (a + b) × (a - b)

Calculation:

(x + 2z)2 - 16x2

⇒ (x + 2z)2 - (4x)2

⇒ (x + 2z + 4x) × (x + 2z -  4x)

⇒ (5x + 2z) × (2z - 3x)

∴ The correct answer is (5x + 2z) (2z - 3x)

Calculation:

$\rm x + 7-\frac{16x}{3}=12-\frac{7x}{2}$

⇒ $x + \frac{7x}{2} - \frac{16x}{3} = 12 - 7$ 

⇒ $\frac{6x + 21x - 32x}{6} = 5$

⇒ - 5x = 30

⇒ 5x = - (26 + 4)

⇒ 5x + 4 = - 26

∴ The correct answer is  5x + 4 = - 26

Given:

Total cost pricer of two tables 9000 and total marked price of two tables is 10000

Calculation:

If 2% discount given on each table, then SP of two tables = 2× (5000 × 98/1000) = 9800

So, gain in the whole transaction is (9800 - 9000) = Rs.800

∴ The correct answer is Rs. 800 gain

Concept used:

A binomial is a polynomial that is the sum of two terms, each of which is a monomial

Calculation:

If we take m = 1, then 5x + 2x2 + 3x = 8x + 2x² [ which is a binomial ]

Again, if we take m = 2, then 5x² + 2x2 + 3x  = 7x² + 3x [ which is a binomial ]

∴ The correct answer is Both 1 and 2

Concept used:

• In a rhombus opposite angles are equal.

• Sum of four angles of a quadrilateral is 360°

• Diagonals of rhombus are angle bisector

Calculation:

If ∠PSR = 70° then, ∠PQR = 70° and 2∠PQR = 140° 

Now, ∠SPQ = (360 - 140)/2 = 110° So, ∠SPR = 110°/2 = 55° 

Then, 2∠PQR + 3∠SPR = (140 + 165) = 305° 

∴ The correct answer is 305°

Linear Symmetry : If we draw a line of segment in the middle of the drawing then one part becomes identical to other.

Rotational Symmetry : When drawing looks same after some rotation by a partial turn.​

Calculation:

Rhombus has two line of symmetry and rotational symmetry of order 2.

Rectangle has two line of symmetry and rotational symmetry of order 2.

Kite has one line of symmetry but no rotational symmetry.

∴ The correct answer is option 4.

Given:

Interior angles of triangle are 60° and x° 

Exterior angles 140° 

Concept used:

Exterior angle = sum of interior angles of triangle

Calculation:

According to question,

⇒ 140° = 60° + x° 

⇒ x° = 80° 

Now the value of 3x + 20° 

⇒ 3 × 80° + 20° 

⇒ 240° + 20° 

⇒ 260° 

∴ The correct answer is 260°.

Shortcut Trick

Corresponding angles of parallel lines are always equal.

∴ x = 70°

Substitute x in the required expression: 4x − 30°

4(70°) − 30° = 280° − 30° = 250°

∴ The correct answer is 250°.

Alternate Method

Given:

Parallel lines are intersected by a transversal.

Corresponding angles are x and 70°.

Formula Used:

When two parallel lines are cut by a transversal, the pairs of corresponding angles are equal in measure.

Calculations:

⇒ x = 70° (Property of corresponding angles)

⇒ To find: 4x − 30°

⇒ 4 × 70° − 30°

⇒ 280° − 30°

⇒ 250°

∴ The correct answer is 250°.

Additional Information

Alternate Interior Angles

Angles on opposite sides of the transversal and between the parallel lines are equal.

Consecutive Interior Angles

Angles on the same side of the transversal and between parallel lines are supplementary (Sum = 180°).

Vertically Opposite Angles

When two lines intersect, the angles opposite each other at the vertex are always equal.

Linear Pair

Angles that are adjacent and form a straight line add up to 180°.

Given:

∠PQS = 30° ∠SQR = 40° ∠SRP = 30° ∠PRQ = 40°

Calculation:

We want to establish congruence between ΔPQR and ΔSQR.

Option 1:

ΔPQR ≅ ΔSQR by SAS. For SAS congruence, we would need to have two pairs of congruent sides and the included angle to be congruent.

Sides:

QR (common to both triangles)

Angles:

∠PQR = 40° (given) ∠SQR = 40° (given)

However, we don't have a matching side for PQ and SR, so SAS congruence cannot be established. Option 1 is incorrect.

Option 2:

ΔPQR ≅ ΔSQR by ASA. For ASA congruence, we would need to have two pairs of congruent angles and the included side to be congruent.

Angles:

∠PQR = 40° (given) ∠SQR = 40° (given)

Side:

QR (common to both triangles)

We have two pairs of congruent angles and a congruent side, satisfying the ASA congruence condition. Therefore, ΔPQR ≅ ΔSQR by ASA. Option 2 is correct.

Option 3:

ΔPQR ≅ ΔSRQ by SAS. We cannot establish SAS congruence because we don't have two pairs of congruent sides and the included angle.

Option 4:

ΔPQR ≅ ΔSRQ by ASA. We cannot establish ASA congruence because we don't have two pairs of congruent angles and the included side.

Therefore, the correct option is 2) Δ PQR ≅ Δ SQR by ASA.

Given:

Rate of fencing : Rs. 5 per meter

Total cost of fencing: Rs. 440 π = 22/7

Formula used:

To find C, we use the formula C = 2πr

To find the area of the circle, we use the formula A = πr²

Calculation:

Let's assume the radius of the circular field is r.

Given that the cost of fencing is Rs. 440 at a rate of Rs. 5 per meter, we can set up the equation:

⇒ 440 = 5 × C

To find C, we use the formula C = 2πr:

⇒ 440 = 5 × 2πr

Dividing both sides by 10, we get:

⇒ 44 = πr

Now, we can substitute the value of π as 22/7:

⇒ 44 = (22/7) × r

Multiplying both sides by 7, we get:

⇒ 308 = 22r

Dividing both sides by 22, we get:

⇒ r = 14

The radius of the circular field is 14 meters.

To find the area of the circle, we use the formula A = πr²

⇒ A = (22/7) × (14)²

⇒ A = 22 × 28 

⇒ A = 616

Therefore, the area of the circular field is 616 square meters.

Given:

Length of the diagonal of the square: 12 cm

Length of the rectangle: 18 cm

Calculation:

Let's assume the side length of the square is "a".

From the given information, we know that the diagonal of the square is 12 cm. Using the formula for the diagonal of a square (d = a√2), we can write:

⇒ 12 = a√2

Dividing both sides by √2, we get:

⇒ a = 12/√2

To simplify the expression, we rationalize the denominator:

⇒ a = (12/√2) × (√2/√2)

⇒ a = 12√2/2

⇒ a = 6√2

Now, we know the side length of the square is 6√2 cm.

The area of the square is equal to the area of the rectangle, so we have:

Area of the square = Area of the rectangle

⇒ (a²) = (length × width)

⇒ (6√2)² = 18 × width

⇒ 36 × 2 = 18 × width

⇒ 72 = 18 × width

Dividing both sides by 18, we get:

⇒ 4 = width

Therefore, the width of the rectangle is 4 cm.

To find the perimeter of the rectangle, we use the formula:

Perimeter = 2(length + width)

Perimeter = 2(18 + 4)

Perimeter = 2(22)

Perimeter = 44 cm

Therefore, the perimeter of the rectangle is 44 cm.

The correct option is: 3) 44 cm.

Given:

Surface area of a cube is 1176 m2.

Formula used:

Surface area of cube = 6a²

Volume of cube = a³

Calculation:

According to question,

⇒ 6a² = 1176

⇒ a² = 196

⇒ a = 14

Volume of cube = 14 × 14 × 14

⇒ 2744 m³

∴ The correct answer is 2744 m³.

Given:

Numbers 15, 16, 17, . . . , 49, 50, 51 are written (one number on one slip).

Formula used:

Probability = Sum of all observation/Number of observation

Calculation:

Total number of observations = 37

Number of observations divisible by 2 : 18

Number of observations divisible by 3 : 13

Actual number of observations = (18 + 13) - 6 = 31 - 6 = 25

Probability = 25/37

∴ The correct answer is 25/37.

Given:

Observations: 13, 21, 17, 12, 15, 19, 19, 12, 20, 25, 17

Concept used:

To find the mean, we calculate the sum of all the observations and divide it by the total number of observations. To find the median, we arrange the observations in ascending order and find the middle value.

Calculation:

First, let's arrange the observations in ascending order: 12, 12, 13, 15, 17, 17, 19, 19, 20, 21, 25

There are 11 observations, so the middle value is the 6th observation, which is 17. Therefore, the median is 17.

Range = Upper Limit - Lower Limit

⇒ 25 - 12 = 13

Average = (13 + 17)/2

⇒ 30/2

⇒ 15

∴ The correct answer is 15.

Students are provided with real polyhedra, such as cubes or pyramids, and asked to count the vertices, edges, and faces.

Key Points

• By tabulating this data, they can explore the relationship V - E + F = 2.
• This hands-on experience fosters active learning, enabling students to visualize and comprehend the formula's significance.
• It encourages critical thinking, collaboration, and deeper understanding as students actively manipulate and analyze the solid shapes.
• This interactive approach creates a meaningful context for learning Euler's formula, helping students to internalize the concept and recognize its relevance in the realm of three-dimensional geometry.

Hence, it can be concluded that option 2 is the correct answer.

Transposition, is not appropriate to be taught using the given model (_______ + 5 = 24) as it lacks the necessary algebraic structure.

Key Points

• Transposition involves manipulating equations with variables, which are absent in this simple arithmetic representation.
• In transposition, we move terms from one side of an equation to the other to isolate the unknown variable.
• However, in this case, there is no variable to isolate.
• The given model is more suitable for teaching basic arithmetic concepts, such as addition and subtraction.
• To teach transposition effectively, students need equations containing algebraic variables like x, y, a, etc., so they can learn how to solve for unknowns using appropriate algebraic techniques.

Hence, it can be concluded that transposition is the correct answer.

The most important prerequisite knowledge required for students to construct a pie chart for a given set of data is ratio, proportion, and angle measures.

Key Points

• A pie chart represents data as a circle, and each category or component is represented as a portion (or slice) of the whole circle.
• To construct a pie chart, students need to understand how to calculate the angles that correspond to each category, and this involves knowledge of ratios and proportions.
• The angles in a pie chart are proportional to the frequencies or percentages of each category in the data set.
• While measures of central tendencies, frequency distribution, and bar graphs are relevant concepts in statistics and data representation, they are not the primary prerequisites for constructing a pie chart.
• Ratio, proportion, and angle measures are more directly related to the creation of a pie chart.

Hence, it can be concluded that 'ratio, proportion and angle measures' is the most important prerequisite knowledge required for students to construct a pie chart for a given set of data.

Making linkages between conceptual and procedural knowledge is essential for developing a deep understanding of mathematics.

Key Points

• It involves connecting the underlying concepts and principles with the procedures or algorithms used to solve problems.
• By explaining why specific methods work and how they relate to the broader mathematical concepts, students can see the meaning and relevance behind the procedures they are learning.
• This approach fosters a deeper understanding and promotes critical thinking, enabling students to apply their knowledge effectively in various problem-solving situations.

 Hence, it can be concluded that To build conceptual understanding among students in mathematics a teacher should make linkages between the conceptual and the procedural knowledge.

Open-ended problems are those that do not have a single correct answer and allow for multiple approaches and interpretations.

Key Points

• ​Draw a rectangle whose area is 36 cm². This is an example of an open-ended problem because there can be multiple correct answers.
• For example, you could draw a rectangle with dimensions 6 cm by 6 cm, 12 cm by 3 cm, 9 cm by 4 cm, or 18 cm by 2 cm, etc.
• The rectangle could have any dimensions where its length and width, when multiplied, equals 36.
• Write 10 multiples of 2 and 3. This is not an open-ended problem. It has a definite solution. The first ten multiples of 2 are 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, and of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30.
• Write all even numbers up to 20. This is not an open-ended problem. It also has a definite solution. The even numbers up to 20 are 2, 4, 6, 8, 10, 12, 14, 16, 18, 20.

Hence, we can conclude that the correct answer is only A.

By intentionally introducing a problem with multiple valid interpretations or approaches, the teacher aims to broaden students' understanding of mathematical concepts.

Key Points

• This approach encourages students to think critically and explore diverse perspectives, fostering a growth mindset towards problem-solving.
• Through respectful debates and discussions in the classroom, students learn that differing viewpoints can coexist, and there isn't always a single correct answer.
• This realization promotes intellectual curiosity, creativity, and analytical thinking.
• Moreover, it cultivates a positive learning environment where students feel comfortable expressing their thoughts and engaging in constructive dialogue with their peers.
• By embracing the idea of disagreements in mathematics, students become more confident and open-minded learners, unafraid to explore various strategies to tackle mathematical challenges.

Hence, it can be concluded that option 3 is the correct answer.

Mathematical reasoning is the process of using logical and systematic thinking to analyze and solve mathematical problems.

Key Points

• Syllogism involves drawing conclusions from two given propositions sharing a common term.
• Its deductive nature enables mathematicians to make specific inferences, like if "All A are B" and "C is an A," then logically, "C is B."
• Logical reasoning forms the backbone of mathematical analysis, using valid arguments and principles to derive conclusions from given premises.
• It ensures the coherence and consistency of mathematical proofs and problem-solving.
• Together, these methods enable mathematicians to construct robust arguments, make deductions, and prove theorems with confidence

Hence, it can be concluded that option 3 is the correct answer.

Calculus is not a part of the mathematics curriculum at the secondary level according to NCERT guidelines.

Key Points

• Calculus is an advanced branch of mathematics that involves studying rates of change, accumulation, and the properties of continuous functions.
• It includes concepts like derivatives, integrals, limits, and differential equations.
• While topics like Algebra, Probability, and Trigonometry are covered at the secondary level to build foundational mathematical skills, Calculus is typically introduced at higher education levels.
• It plays a crucial role in various fields like physics, engineering, economics, and more, making it an essential part of higher education for students pursuing careers in these disciplines.

Hence, it can be concluded that option 4 is the correct answer.

Geogebra is a powerful software tool that allows students to visualize and interact with mathematical concepts through dynamic graphs and visual representations.

Key Points

• Visually-challenged students require alternative teaching-learning resources that cater to their specific needs.
• While tactile materials like braille-based materials and tactile tiles can be useful,
• Geogebra's visual nature limits its accessibility.
• Instead, educators can focus on tactile approaches, verbal descriptions, and interactive technologies with auditory output to enhance the learning experience for visually-impaired students.
• Providing accessible and inclusive resources ensures that all students, including those with visual challenges, can actively participate and excel in mathematics education.

Hence, it can be concluded that geogebra is the correct answer.

In mathematics, a conjecture is a statement or proposition that is believed to be true based on evidence, observations, patterns, or experimental results, but it has not been formally proven or demonstrated as a theorem.

Key Points

• Conjectures often arise from patterns observed in numerical data, geometry, algebraic equations, or other mathematical structures.
• Mathematicians use conjectures as a starting point for further investigation and exploration.
• They attempt to prove or disprove the conjecture using rigorous mathematical reasoning and techniques.
• If a conjecture is successfully proven, it becomes a theorem and is considered a fundamental truth within the realm of mathematics.
• However, if it is shown to be false, counterexamples are used to disprove it.

Hence, it can be concluded that option 4 is the correct answer.

The Correct answer is Veins, carbon dioxide, thin.

Explanation:

• In a closed blood circulation system three types of blood vessels are present:
• Arteries:
• These carry pure oxygenated blood from the heart to different organs of the body.
• The wall of arteries are thick compared to veins due to higher blood pressure in Arteries
• Veins:
• These carry impure carbon dioxide-rich blood from body organs to the heart.
• The walls of veins are thin as compared to the arteries because the pressure of blood flow is low.
• Capillaries:
• These are present in organs, and these are the vessels through which exchange takes place.

Exceptions - 

• The pulmonary vein carries oxygenated blood from the lungs to the heart.
• The pulmonary artery carries deoxygenated blood from the heart to the lungs.

the correct answer is A-Sodium, B-Mercury, C-Phosphorus, D-Sodium hydroxide pellets.

Explanation:

• A - in kerosene: Sodium is a highly reactive metal that reacts vigorously with air and moisture, so it should be stored in kerosene to prevent these reactions.
• B - in a glass bottle: Mercury is a stable liquid metal and does not react with glass, making a glass bottle suitable for its storage.
• C - under water: Phosphorus is a highly reactive non-metal that can spontaneously ignite when exposed to air. To prevent this, it is stored underwater to keep it away from atmospheric oxygen.
• D - in a plastic bottle: Sodium hydroxide pellets are typically stored in a plastic bottle. Sodium hydroxide pellets are caustic and can react with certain metals, so a plastic bottle is a suitable container to avoid any adverse reactions.

The Correct answer is Bile juice.

Concept :

• The process of digestion includes both mechanical and chemical processes.
• Mechanical digestion includes churning or mastication of food.
• The chemical process includes the action of certain enzymes which break down the food and convert it into simpler forms.

Explanation :

Bile juice:

• The bile secreted by the hepatic cells passes through the hepatic ducts and is stored and concentrated in a thin muscular sac called the gall bladder.
• It does not contain any enzyme.
• Bile helps in the emulsification of fats, i.e**., breaking down the fats into tiny micelles.** Bile also activates lipases.

Pancreatic juice:

• The exocrine portion of the pancreas secretes an alkaline pancreatic juice containing enzymes and the endocrine portion secretes hormones, insulin, and glucagon.
• The pancreatic juice contains inactive enzymes – trypsinogen, chymotrypsinogen, procarboxypeptidases, amylases, lipases, and nucleases.

Salivary juice:

• The saliva secreted into the oral cavity contains electrolytes and enzymes, salivary amylase, and lysozyme.
• The chemical process of digestion is initiated in the oral cavity by the hydrolytic action of the carbohydrate-splitting enzyme, salivary amylase.

Gastric juice:

• Rennin is a proteolytic enzyme found in the gastric juice of infants which helps in the digestion of milk proteins.

Additional Information

• Trypsinogen is activated by an enzyme, enterokinase, secreted by the intestinal mucosa into active trypsin, which in turn activates the other enzymes in the pancreatic juice.
• The bile released into the duodenum contains bile pigments (bilirubin and biliverdin), bile salts, cholesterol, and phospholipids.

The Correct answer is glass container as it does not react.

Explanation;

• Glass container as it does not react: Glass containers are an excellent option for storing mango pickles. Glass is non-reactive and does not interact with the pickle's acidic components. It does not leach any harmful substances into the food, ensuring the pickle's taste and quality remain unaffected during storage.
• Glass containers are non-reactive, easy to clean, and do not alter the taste or quality of the pickle. They are also a safe choice for long-term storage, as they do not contain harmful chemicals that could potentially leach into the food.

Additional Information

• Steel container as steel does not rust: Stainless steel containers are a common choice for food storage, and they indeed do not rust easily. Stainless steel is a sturdy and durable material that can resist corrosion.
• However, when it comes to storing acidic foods like mango pickles, there is a potential concern. While stainless steel is resistant to rust, it can still react with acidic substances, causing a metallic taste in the food and compromising the quality of the pickle.
• Plastic container as it is inexpensive: Plastic containers are widely available and often inexpensive. However, using plastic containers to store acidic foods like mango pickles can be problematic. Some plastics may contain chemicals, such as BPA (bisphenol-A), that can leach into the food, especially when exposed to acidic substances. These chemicals could pose health risks over prolonged exposure
• Tin container as it does not react: Tin containers are not commonly used for food storage, particularly for acidic foods like pickles. Tin can react with acidic substances, leading to off-flavors in the food and potential health risks if harmful compounds are released into the pickle.

The Correct answer is (B) and (C).

Concept:

• Adaptation refers to the presence of specific features and habits which enable a plant or animal to live in a particular habitat and its geographical conditions.
• Adaptation is long term gradual and continuous process.
• Habitat refers to the surroundings where plants and animals live.
• The plants or trees species survive in their environment such as underwater, in deserts, on grassland, on the mountain range, etc
• For example, seaweed is a plant adapted for its underwater environment, cacti are adapted for a desert environment, conifers plants are adapted for a snowy environment, etc.

Explanation:​

• Characteristic features of trees in the mountain range:
• Plants or trees such as pines, firs, spruces, etc are adapted for a mountain environment.
• These trees are tall. straight and cone-shaped.
• They have sloping branches so that snow slides off easily without damaging the branches and leaves.
• The leaves are needle-shaped with a wax-like coating.
• The trees have thick bark which helps the tree to withstand the cold.
• Whereas the desert plant has a waxy coating on the stem which helps to retain water as well as long penetrating roots for absorbing water.

Additional Information Long penetrating roots:

• This is an essential adaptive feature of desert plants like cactus.
• These deep roots help them reach the lower levels of groundwater.

stems and leaves have a thick waxy coating

• Cactus are dicots with a fleshy, green photosynthetic stem called the cladophyll.
• A cactus has a thick waxy coating that helps it retain water.
• A cactus has a thick, folded stem that allows it to store as much water as possible during short periods of wet weather.
• The water inside the cactus is kept from evaporating by a thick, waxy coating on the stems and leaves.
• Example - Lotus leaves.

The Correct answer is (A) and (C).

Concept:

Chemical change:

• During a chemical change, the molecules of the reactants ( original substances) change to form molecules of the products which are substances that undergo chemical transformation to form new substances.
• It is generally irreversible.
• For example: burning of fuels like LPG, petrol, etc, curdling of milk, rusting of iron, etc.

Physical change:

• During a physical change, substances undergo a change in their physical properties, and the formation of no new substance takes place.
• It is generally reversible.
• For example melting of wax, freezing of water, etc.

Explanation:

• (A) Dissolving sugar into milk:  Sugar breaks down into its individual molecules and disperses uniformly throughout the milk. * No new chemical bonds are formed, and both sugar and milk retain their individual chemical properties. This is a physical change.
• (B) Setting milk into curd:  Lactic acid bacteria in milk convert lactose (milk sugar) into lactic acid. The casein proteins in milk react with the lactic acid, causing them to coagulate and form a gel-like structure. * New chemical bonds form between the lactic acid and casein, creating curd with different properties than milk. This is a chemical change.
• (C) Making buttermilk from curd:  Water and fat are separated from the curd, resulting in buttermilk. * No new chemical reactions occur, only a physical separation of components. This is a physical change.
• (D) Making cottage cheese from milk: Similar to curd formation, lactic acid bacteria ferment milk sugar, causing casein proteins to coagulate. * The curds are then cut and whey (liquid) is drained, leaving behind cottage cheese. * New chemical bonds form between lactic acid and casein, creating cottage cheese with different properties than milk. This is a chemical change.

Therefore, the correct answer is A and C.

The Correct answer is **fertilisation of two eggs by two sperms.**Concept:

• The process of combining the male gamete (sperm) with the female gamete (ovum) is known as fertilization.
• Fertilization of the ovum by sperm normally occurs in the fallopian tubes in humans.
• The product of fertilization is a zygote.
• The zygote becomes an embryo which then develops into a fetus.

Explanation:

• There are two types of twins –
• identical (monozygotic)
• fraternal (dizygotic)

Identical twins

• Identical twins develop from a single fertilised egg.
• Fertilization of a single egg takes place by a single sperm.
• This fertilized egg then splits into two and develops as two embryos.
• Identical twins share the same genomes and are always of the same sex.

Fraternal twins

• Fraternal twins are also called dizygotic twins.
• They result from the fertilization of two separate eggs with two different sperm during the same pregnancy.
• Fraternal twins may or may not be of the same sex or have similar appearances.

The Correct answer is The pressure due to water increases as one goes down.

Explanation:

• Divers wear special suits in order to protect them from High pressure.
• The pressure increases as the depth increase.
• The pressure exerted in deep water under the sea is much greater than at sea level.
• So divers need a proper suit to bear that extra pressure.
• Divers wear special suits and carry oxygen cylinders when they go underwater diving primarily because the pressure of water increases as one descends deeper into the water.
• This increase in pressure is due to the weight of the water above pushing down on the diver. Without proper equipment, the increasing pressure can have adverse effects on the human body, such as causing decompression sickness ("the bends") or lung overexpansion injuries.
• The special suits and oxygen cylinders help divers to adapt to the changing pressure and provide them with a controlled supply of breathing gas, enabling them to explore the underwater environment safely.

The Correct answer is Heat is added to the system.

Explanation:

• When ice melts into water, it undergoes a phase change from a solid (ice) to a liquid (water). During this process, the temperature remains constant even though the physical state of the substance is changing.
• The temperature at which a solid changes into a liquid is known as the melting point. For water, the melting point is 0 degrees Celsius (32 degrees Fahrenheit) at standard atmospheric pressure.
• To melt ice into water, heat energy is added to the system. This added heat energy breaks the intermolecular forces holding the water molecules in a fixed lattice structure as ice and allows the molecules to move more freely, resulting in the transition to the liquid state. However, the temperature remains constant at the melting point until all the ice has completely melted.
• Once all the ice has melted into water, any further addition of heat energy will cause the temperature of the water to increase.

Note:-  This answer is according to the statement provided in this question, but according to official answer key is option 2.

The Correct answer is Strong and temporary.

Explanation:

• An electromagnet is a type of magnet in which the magnetic field is produced by an electric current.
• The magnetic field disappears when the current is turned off.
• Therefore, it is known as a temporary magnet because its magnetism is in effect only for the period during which an electric current is flowing.
• The strength of the magnetic field produced by such a magnet can be changed by changing the amount of electric current that passes through it.
• This is different from a permanent magnet, which produces its own persistent magnetic field without the need for an external electric current.
• The strength of an electromagnet can be much greater than that of a permanent magnet.
• This strength can be adjusted by varying the current flowing through the electromagnet, the number of coils in the electromagnet, or the material of the core.

The Correct answer is (A) - (iv), (B) - (iii), (C) - (i), (D) - (ii).

CONCEPT:

Convex mirror:

• If the outer surface of the spherical mirror is the reflecting surface then it is called a convex mirror. It is also called the diverging mirror.
• The nature of the image formed by a convex mirror does not depend on the distance of the object from the; mirror. These images are always virtual, smaller than the object, and situated behind the mirror.

Concave mirror:

 If the inner surface of the spherical mirror is the reflecting surface, then it is called a concave mirror. It is also called a focusing mirror/converging mirror.

• The size of the image produced by these mirrors can be larger or smaller than the object, depending upon the distance of the object from the mirror.
• The concave mirror can form both real as well as virtual images of any object.

Explanation:

• Convex mirror -used for rear view in vehicles: A concave mirror is a mirror with a reflecting surface that curves inward like the inside of a bowl.
• When used as a rear-view mirror in vehicles, it allows the driver to see a wider field of view. The mirror's curved shape converges the light rays, making objects appear smaller but also allowing a larger area to be visible in the reflection.
• Concave lens - used for near-sightedness: A concave lens is thinner at the center and thicker at the edges. It is used to correct near-sightedness or myopia. Near-sightedness occurs when light entering the eye is focused in front of the retina, causing distant objects to appear blurry.
• A concave lens diverges light rays, allowing them to focus properly on the retina, thus improving distant vision**.**
• Concave mirror - used in torch lights: A convex mirror is a mirror with a reflecting surface that curves outward.
• Convex mirrors have a wider field of view compared to flat mirrors and are often used in torch lights or flashlights to provide a broader spread of light. They scatter light rays, allowing a larger area to be illuminated.
• Convex lens -used in microscopes: A convex lens is thicker at the center and thinner at the edges. It converges light rays and is commonly used in microscopes to magnify small objects. When light passes through a convex lens, it converges and forms a real, enlarged, and inverted image of the object being observed, which allows for detailed examination in microscopes.

The Correct answer is Object is at rest.

Concept:

• 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, it moves with uniform speed.
• This shows that the distance traveled by the object is directly proportional to the time taken.

Explanation:

• Thus, for uniform speed, a graph of distance traveled against time is a straight line.
• If this straight line is parallel to the time axis it means the object is at the rest.
• But if the line is a straight line not parallel to the time axis then the object has no acceleration and therefore it is moving with a "constant velocity".
• If a body is at rest, then as time passes, there is no change in the distance traveled by the body. Hence, the distance-time graph of a body at rest is a horizontal line parallel to the time axis.

Additional Information Uniform Motion:

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

Non-uniform Motion:

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

Uniformly accelerated motion:

• The graph would be a straight line with its slope indicating the amount of acceleration when a body is in uniformly accelerated motion (Uniform speed).

The Correct answer is Both (A) and (B) are true.

Explanation:

on a new moon day, the moon is in between the earth and the sun is 

• A new moon occurs when the Moon is between Earth and the Sun, and thus the side of the Moon that is in shadow faces Earth.
• The new moon is the first lunar phase when the Moon and Sun have the same ecliptic longitude.
• On the fifteenth day, the moon is not visible. This day is known as the ‘new moon day’.

​on a full moon day, the Earth comes between the sun and the moon

• A full moon occurs about once a month when the earth, sun, and moon are in a line and the earth is between the other two.
• The day on which the whole disc of the moon is visible is known as the full moon day.
• A full moon occurs when we can see the entire illuminated area of the moon.
• Thereafter, every night the size of the bright part of the moon appears to become thinner and thinner.

The Correct answer is Both (A) and (R) are true and (R) is the correct explanation for (A).

Concept:

• Refraction of light: Refraction is the bending of light when it passes from one medium to another with a different refractive index. The refractive index is a measure of how much light slows down when passing through a medium. When light travels from a medium with a higher refractive index to a medium with a lower refractive index (such as water to air), it bends away from the normal (an imaginary line perpendicular to the surface).

**Explanation:**​

• The changes in refractive index, the light rays from the fish bend away from the normal (an imaginary line perpendicular to the water surface) as they exit the water and enter the air. This bending of light causes the rays to spread out more, making the fish appear larger than it actually is when viewed from above the water's surface.
• Larger appearance: The bending of light makes the fish's image appear higher than its actual position. As a result, the observer sees the top part of the fish (closer to the water's surface) first and then the lower part. This effect creates an elongated image of the fish, making it appear larger than its real size.
• Raised position: Since the light rays bend away from the normal, the apparent position of the fish is higher than its actual position. This is why the fish appears to be raised or lifted up relative to its actual location in the water.

The correct answer is maximum.

Concept:

• When a parachute descends through the air, it experiences air resistance or air friction. Air resistance is a force that opposes the motion of the parachute and is caused by the collision of air molecules with the surface of the parachute.
• The shape of the parachute is specifically designed to maximize air resistance, also known as drag.

Explanation:

• A parachute typically has a large surface area and a wide, open canopy. This design allows a significant amount of air to interact with the parachute as it falls through the atmosphere. When air molecules collide with the large surface area of the parachute, they exert a force that opposes the parachute's motion, causing it to slow down and descend at a controlled rate.
• By maximizing air resistance, the parachute can slow down the descent of the person or object attached to it, ensuring a safe landing. If the parachute were to experience minimal friction due to air or no friction due to air it would not be effective in slowing down the descent, and the person or object would fall too quickly, potentially leading to a dangerous impact upon landing.
• "infinite," is not correct either because infinite friction due to air is not physically possible. Friction, in any scenario, is always finite and depends on various factors such as the shape, size, and speed of the object moving through the medium.

Therefore, the shape of a parachute is designed to experience maximum friction due to air, allowing it to effectively slow down the descent and ensure a safe landing for the user.

The correct answer is: outermost, blue, complete  

Explanation:

A - "Outermost zone": The outermost layer of a flame, also known as the non-luminous zone, is the hottest part of the flame. Goldsmiths will often use this hotter zone to melt gold as it will do so more efficiently.

B - "Blue": The color of this zone is blue. This outermost zone is blue due to the complete combustion of gas, emitting light of this color.

C - "Complete combustion": Because this outermost layer has the highest oxygen concentration, it is the zone of complete combustion. This means that the gas in this part of the flame is entirely consumed by the reaction, and results in a clean burn with minimal soot or unburnt fuel.

The Correct answer is Z > X > Y > W

Concept;

• Metal activity series: The metal reactivity series is an array of metals arranged in descending order of their reactivities. It is also known as the metal activity series.
• The top metals in the series (K, Na, Ca, Mg, and Al) are so reactive that they are never found as free elements in nature.
• The metals at the bottom of the activity series are the least reactive.
• Some of these metals can be found in their natural state in the earth's crust.

Explanation:

• Metal X displaces metal Y from its salt solution but is not able to displace metal Z from its salt solution. This suggests that metal X is more reactive than metal Y but less reactive than metal Z.
• Metal Y displaces metal W from its salt solution. This implies that metal Y is more reactive than metal W.
• Based on the above information, we can determine the relative reactivity of the metals as follows:
• Most Reactive → Least Reactive:
• Metal Z> Metal X> Metal Y> Metal W

So, the correct order of reactivity of metals is: Z > X > Y > W

The Correct answer is Iron, Vitamin-C.

Explanation:

• Iron, Vitamin-C: This option is correct. Milk does not contain a significant amount of iron and vitamin C. Iron is an essential mineral for the formation of hemoglobin and red blood cells, and it is commonly found in meat, legumes, and fortified cereals**, but not in milk. Vitamin C is an antioxidant that enhances iron absorption**, but it is also not present in significant amounts in milk. Instead, vitamin C is commonly found in citrus fruits, tomatoes, and other fruits and vegetables.
• Iron, Vitamin-A: This option is incorrect. Milk contains a good amount of vitamin A. Vitamin A is important for vision, immune function, and maintaining healthy skin. It is commonly found in dairy products like milk, cheese, and butter.
• Phosphorus, Vitamin-C: This option is incorrect. Milk is a good source of phosphorus, which is vital for bone health, energy production, and DNA synthesis. However, it does not contain a significant amount of vitamin C, as mentioned earlier.
• Phosphorus, Vitamin-A: This option is incorrect. Milk does contain phosphorus, so it is not lacking in this mineral. As mentioned before, milk is also a good source of vitamin A.

The Correct answer is (D)

Explanation:

Animal Cell:

• An animal cell lacks a cell wall and is only bound by the cell membrane.
• It contains important organelles like the nucleus, mitochondria, vacuoles, Golgi bodies, and endoplasmic reticulum.
• Plastids are not found in animal cells.
• However, they usually contain lysosomes and centrioles, unlike plant cells.
• Animal cells are characterized by having a cell membrane (plasma membrane) that surrounds the cell, a well-defined nucleus that contains the genetic material (DNA), mitochondria responsible for energy production (ATP synthesis), and a cytoplasm that holds various organelles and cellular structures.

The Correct answer is pituitary, ovary, estrogen.

Explanation:

• A is the source of hormones that stimulate B. In this case, the pituitary gland is known to secrete hormones that regulate various processes in the body.
• B is the target organ or tissue that is stimulated by the hormones from A. In this context, it is the ovary.
• C is the substance that is released by B in response to the stimulation from A. In this case, the substance released by the ovary is estrogen.
• Estrogen This hormone is responsible for female physical features and reproduction.
• The ovaries, adrenal glands, and fat tissues produce estrogen.
• Both female and male bodies have this hormone, but females create more of it.
• It contributes to cognitive health, bone health, the function of the cardiovascular system, and other essential bodily processes.

If there were no stems in plants, the repercussions would be significant.

Key Points

• Stems play a crucial role in supporting the plant's structure and facilitating the transportation of water, nutrients, and photosynthetic products between leaves and roots.
• Without stems, plants would lose their ability to grow upright, resulting in a lack of access to sunlight and limited nutrient absorption.
• This question allows for various possible answers and interpretations, encouraging a more extended and thoughtful response rather than a simple one-word or factual answer.
• Respondents can explore different scenarios and consequences related to the absence of a stem.

Hence, it can be concluded that option 4 is the correct answer.

Asking students to conduct a water audit in the neighborhood is best suited to sensitize learners regarding water conservation in grade VI.

Key Points

• This activity actively engages students in understanding the water usage patterns and wastage in their immediate surroundings.
• By conducting a water audit, students can collect data, analyze water consumption, identify areas of improvement, and propose water-saving strategies.
• This hands-on approach promotes critical thinking and problem-solving skills while fostering a practical understanding of water conservation.

Hence, it can be concluded that option 2 is the correct answer.

Observations are direct and concrete pieces of information that you perceive through your senses. Inference involves drawing conclusions or making interpretations based on the observations you have made.

Key Points

• Statement (A) "North-Pole of magnet 'A' moves away from North-Pole of magnet 'B’." is an observation because it directly describes a phenomenon that can be observed using one's senses. It reports what can be seen in a straightforward manner.
• Statement (B) "Like poles of magnets repel each other." is an inference. It goes beyond a direct observation and draws a conclusion based on observed behavior. This statement generalizes the behavior of magnets with like poles based on observed instances.

Hence, (A) is observation, (B) is inference.

Both (A) and (R) are true statements, and (R) indeed provides a correct explanation for (A).

 Key Points

• A) The assertion states that learners' misconceptions in science topics tend to be stable and resistant to change.
• This is a well-documented phenomenon in science education, where students may hold incorrect or alternative conceptions that persist over time, even when confronted with contradictory evidence.
• (R) The reason explains that these misconceptions may draw on more than one scientific concept.
• This is a crucial aspect of why misconceptions can be challenging to correct.
• Misconceptions often arise when learners try to make sense of new information based on their existing mental models and prior knowledge, which may involve mixing or misinterpreting multiple scientific concepts.

Hence, it can be concluded that option 1 is the correct answer.

In the context of scientific investigations, data and evidence are related but not identical.

Key Points

• Data refers to the raw information and observations collected during an experiment or study. It can be quantitative or qualitative in nature.
• On the other hand, evidence is the interpretation and analysis of the data to support or refute a hypothesis or claim.
• Evidence is the result of critically evaluating and analyzing the data, making connections, and drawing conclusions based on the findings.
• While data provides the foundation for generating evidence, the two terms have distinct roles in the scientific process.

Hence, it can be concluded that data and evidence are same is not the correct statement.

In science, a law is a statement or mathematical equation that describes a consistent and predictable relationship between observable phenomena.

Key Points

• It summarizes a pattern found in nature without providing an in-depth explanation for why it occurs.
• On the other hand, a theory is a well-substantiated and comprehensive explanation that integrates multiple observations, experimental results, and evidence to describe and understand a particular aspect of the natural world.
• Theories go beyond laws by providing a broader framework that explains the underlying mechanisms and reasons behind the observed patterns and phenomena.

Hence, it can be concluded that option 1 is the correct answer.

Both statements A and B are true. 

Key Points

• (A) Science is parsimonious:
• In the pursuit of understanding natural phenomena, science seeks the simplest explanations that can account for observed data.
• This principle, known as parsimony or Occam's razor, suggests that the most straightforward hypotheses with the fewest assumptions are preferred.
• By favoring simplicity, scientists aim to avoid unnecessary complexity and ensure that explanations are concise and elegant.
• (B) Science is skeptical:
• Skepticism is an integral part of the scientific process.
• Scientists approach new claims, theories, and evidence with a critical mindset, subjecting them to rigorous testing and scrutiny.
• The skeptical inquiry helps identify errors, biases, or unsupported claims, ensuring that only well-founded and reliable information becomes part of scientific knowledge.
• This commitment to skepticism safeguards the integrity and credibility of scientific discoveries and allows for continuous refinement and improvement of scientific understanding.

Hence, it can be concluded that option 3 is the correct answer.

Process skills should be part of formal assessment reflects contemporary understanding of assessment in Science.

Key Points

• Including process skills in formal Science assessments ensures that students' scientific thinking and problem-solving abilities are evaluated alongside their content knowledge.
• By assessing skills like observation, experimentation, data analysis, and reasoning, educators gain insights into students' capacity for scientific inquiry and application.
• This approach fosters a deeper understanding of Science as a dynamic and hands-on discipline, encouraging students to think critically and approach challenges methodically.
• Incorporating process skills in assessment promotes a well-rounded and practical learning experience, preparing students to engage effectively in scientific investigations and equipping them with essential skills for future academic and real-world endeavors.

Hence, it can be concluded that option 3 is the correct answer.

In an inclusive Science classroom, self-paced learning encourages students to progress at their individual speed, catering to diverse learning styles and abilities.

Key Points

• By offering flexible learning paths, students can delve deeper into topics of interest or seek additional support as needed.
• This approach fosters a sense of autonomy, empowering learners to take responsibility for their education while reducing feelings of stress and inadequacy.
• Teachers can provide differentiated materials and personalized guidance, addressing each student's strengths and weaknesses.
• Embracing self-paced learning promotes a positive learning environment, enhances engagement, and maximizes the potential for academic success among all students, regardless of their learning profiles.

Hence, it can be concluded that option 2 is the correct answer.

Giving the opportunity to handle various objects of different shapes, sizes, and materials is the most desirable activity to explain the difference between density and heaviness.

 Key Points

• This is the most desirable activity as it allows individuals to physically interact with objects and experience their differences in weight and density.
• By holding objects of different materials and sizes, people can directly feel the effect of density and heaviness.
• This hands-on experience enhances understanding and provides a concrete basis for grasping the concepts.

Hence, it can be concluded that option 3 is the correct answer.

The correct answer is 'goes to a fair in the company of his parents.'

Key Points

• The first part of the passage discusses the journey to the fair. It mentions the crowds, the method of travel (some walking, some on horseback, some in carts), and includes the child running between his parents' legs. This all points to the child being accompanied by his parents on the way to the fair.
• There is no evidence in the text to suggest that the child was forbidden from going near the flowers, that he refused to be controlled by the strict behaviour of his father, or that he got lost outside the city gates.
• The later part of the passage, where the child is shown interacting with his parents regarding a toy he sees, further supports the idea that the child is with his parents throughout the journey.
• In addition, there is no indication in the passage that the child separates from his parents at any point.

Therefore, the correct answer is Option 1.

The correct answer is 'The child was persistently expressing his desire for a toy.​'

Key Points

• The passage describes how the child was "arrested by the toys in the shops" and pleads to his parents, "I want that toy," indicating that the child has a desire for the toys he sees in the shops.
• The father's 'red-eyed' and 'familiar tyrant’s way' gaze could be interpreted as a stern or strict look, often associated with denying a child's request, supporting the idea that the child wanted something from the shops.
• There is no evidence in the passage that suggests the child was lost, the mother was indulgent to him, or they were getting late for the fair.
• The father's look is described as 'familiar', indicating that the child is used to his father responding this way when he asks for something.

Therefore, the correct answer is Option 1.

he correct answer is 'divert her child's attention.'

Key Points

• After the child pleads for a toy and the father gives him a stern look, the mother responds by pointing out something else to the child, saying "Look, child, what is before you." This suggests that she is trying to divert his attention away from the toys he wants.
• There's no evidence in the text to suggest that the mother reprimanded her husband for scolding the child, dragged the child, or tried to control his sobs.
• By pointing out something else, the mother was able to distract the child from his unfulfilled desire and interest him in what lay before them, the footpath in the field.

Therefore, the correct answer is Option 2.

The correct answer is 'as he was arrested by the toys in the shops.'

Key Points

• The passage states clearly that the child lags behind because he is "arrested by the toys in the shops," meaning that he is stopped or distracted by the toys.
• There's no suggestion in the text that he wanted to escape his parents, was trying to avoid his father's rebuke, or wished to weep in silence. He is simply captivated by the toys he sees in the shops they pass.
• This interaction is what leads to the dialogue with his parents about wanting a toy, the father's stern look, and the mother's diversionary tactic.
• His lagging behind is the direct result of his interest in the toys, not any emotional or behavioral reaction to his parents.

Therefore, the correct answer is Option 2.

The correct answer is 'Despot'.

Key Points