Mathematics and Science PYQs

Concept:

• Neils Bohr proposed Bohr's postulate which explained that a nucleus (positively charged) is surrounded by negatively charged electrons.
• According to Bhor, Electron which is moving in an orbital does not lose or radiate energy and atom came as a modification to Rutherford’s model of an atom.
• Postulates of Bohr’s model of an atom are:
• In an atom, electrons move in a fixed circular path around a positively charged nucleus. This path is known as orbits or shells
• These orbits or shells have fixed energy.
• The energy levels are represented by an integer (n = 1, 2, 3, 4, …) known as a principal quantum number.
• If an electron moves from lower energy level to higher energy level, then it will do so by gaining energy and if it moves from higher energy level to lower energy level then it will do so by losing energy.

Explanation:

• Quantum number are those numbers that designate and distinguish various atomic orbitals and electrons present in an atom.
• There are four types of quantum number:
• The angular quantum number determines the three-dimensional shape of the orbital quantum number.
• Denoted by the symbol ‘l’ is also known as orbital angular momentum or subsidiary quantum number.
• It defines the three-dimensional shape of the orbital.
• Principal quantum number
• ​Denoted by the symbol ‘n’.
• Determines the size and to a large extent the energy of the orbital.
• Magnetic orbital quantum number
• ​Denoted by the symbol ‘ml’.
• Gives information about the spatial orientation of the orbital concerning standard set of co-ordinate axis.
• Electron Spin quantum number
• ​Denoted by the symbol (ms) refers to the orientation of the spin of the electron.

Scurvy:

• Severe and continuous deficiency of vitamin C causes scurvy:
• Following are the symptoms of Scurvy:
• Anaemia
• Bleeding gums and gingivitis.
• Bruised hair follicles and skin haemorrhages.
• Swollen joints.
• Oral vitamin C supplements and foods containing vitamin C help treating scurvy.

Additional Information

Concept:

Acid and Base

Explanation:

• Strong and weak acid
• Strong acids have a very high concentration of H ⁺ ions. Sulphuric acid, hydrochloric acid, Nitric acid are some examples of strong acids.
• Weak acids have comparatively low concentrations of H ⁺ ions. Citric acid, tartaric acid, acetic acid are some examples of strong bases.

So, citric acid is a weak acid. 

Important Points Strongness of an acid or base is determined by its pH value. 

pH = - log [H ⁺] 

It is measured from a scale of 0 - 14

Strong acids have pH : 0 - 3

Weak acids have pH: 3 - 6

Neutral solutions have pH = 7

Weak bases have pH: 8 - 11

Strong bases have pH 11 - 14

Additional Information

• Strong bases have a very high concentration of OH ^- ions.
• Strong acids have a very high concentration of H + ions. Sulphuric acid, hydrochloric acid, Nitric acid are some examples of strong acids.
• Weak acids have comparatively low concentrations of H + ions. Citric acid, tartaric acid, acetic acid are some examples of strong bases.
• Strong bases have a very high concentration of OH - ions.

John Ray developed a 'key' for the identification of Animals.

Key Points

• Keys is used for the identification of plants and animals based on their similarities and dissimilarities.
• The keys are based on the contrasting characters generally in a pair called a couplet.
• It represents the choice made between the two opposite options.
• This results in acceptance of only one and rejection of the other.
• Each statement in the key is called a lead.
• Keys are generally analytical in nature.

Additional InformationHerbarium

• It is a storehouse of collected plant specimens that are dried, pressed, and preserved on sheets.

Botanical Gardens

• Plant species in these gardens are grown for identification purposes and it is labelled indicating its scientific name and its family.

Museum

• It has collections of preserved plants and animals for study.

Concept-

• The seeds are protected inside the fruit.
• The ripened ovule is known as a seed.
• A mature seed is having three main parts - Seed coat, embryo, and endosperm.
• Fruits are the results of fertilization, there are a few species in which fruits develop without fertilization. Such fruits are called parthenocarpic fruits.
• Parthenocarpy can be induced through the application of growth hormones and such fruits are seedless.

Explanation-

• In coconut parthenocarpy is useless.
• Because its edible part is the endosperm and endosperm is the part of the seed.
• Its edible endosperm is what it is valued for.

Therefore seedless fruits are of no use in Coconut.

Additional InformationTomato

• Tomato is a berry fruit.
• These fruits develop from mono or multicarpellary, syncarpous ovary.
• Tomato is a true berry (Plant with superior ovary).

Banana

• Banana is a false berry (Plant with inferior ovary).

The correct option is seed coat.

About Cotton fibre:

• It is a very Soft, Fluffy staple Fiber that Grows in a Protective Capsule or Ball like structure, around the Seeds of Cotton plants of the genus Gossypium in the family of Malvaceae. The Fiber of Cotton is almost like a Pure Cellulose.
• Under the Natural conditions, the Cotton Bolls will tend to Increases in the Dispersion of the Seeds. It is a seed Hair fibre produced from the Epidermal Seed Coat. These Fibers are not obtained from Stem Hairs, Root Hairs, or Leaf of Cotton Plant.
• The Cotton Plant is a Shrub Native to Tropical and Subtropical regions around the world, including countries like the Americas, Egypt, Africa, and India.
• The greatest Diversity of Wild Cotton Species is found in Mexico, followed by Africa and Australia. Cotton was independently domesticated in the Old times and very much diversified in New Worlds.
• India is the world's Largest Producer of Cotton. In Asian countries like India and Pakistan (less than 2%) Gossypium Arboreum types of Cotton Plants are found.

Concept:

Life Cycle of Silkworm: 

• Stage 1:The cycle starts when female silk moth lays eggs.
• Stage 2: The caterpillar of larvae is hatched from the eggs of the silkmoth and they feed on mulberry leaves and consume a large amount of these leaves for around 30 days.
• Stage 3::The silkworm spin a protective cocoon around itself.it is the size of a small cotton ball and is made of a single thread of silk.
• Stage 4: Then Pupa changes into an adult moth. The female moth lays eggs after mating and thus the life cycle of silkworm begins again.

Explanation:

• Silk is extracted from the cocoon that is spun by the pupa.
• The word caterpillar is applied to the larval stages of all species in the insect.
• "Silkworms" are the caterpillars of a particular species of a moth: namely Bombyx mori.
• Silkworm is the larval stage of silk moth and is a more specific term whereas, the caterpillar is a broad term representing the larval stage of any lepidopteran insect.​​

The correct answer is Mangrove plants.

Explanation-

Vivipary germination- 

• It is a special case of germination occurring in the Mangrove (halophytes) plants.
• Mangrove plants grow in swampy places around the seashore.
• Halophyte plants can survive in highly salinized soils or water.
• In this particular type of germination, the seed germinates inside the fruit while it is still attached to the parent plant.
• The embryo comes out of the fruit with a massive radicle pointing downwards.
• Due to increased weight, the seedling separates from the parent plant and establishes itself in the muddy soil.
• Examples- Mangrove trees, Rice grass (Spartina)

Additional InformationAquatic plants- 

• Aquatic plants are also known as hydrophyte plants.
• Hydrophyte plants are those plants that grow in freshwater habitats (pond, lakes, and streams).
• They are partially or completely submerged in water.
• Examples- Lotus, Vallisneria

Xerophyte plants- 

• Xerophyte are plants that survive in very dry conditions.
• They are generally found in deserts.
• They face a shortage of water.
• Examples- Aloe vera, cactus.

Shrubs- 

• Shrub are woody plant which is smaller than a tree and has several stems.
• They can be evergreen or deciduous.
• They are distinguished from trees by their multiple stems and shorter height.
• They differ from trees in their multiple stems and shorter height.

The correct answer Helper T-lymphocytes.

Key Points

• Human Immuno Deficiency (HIV) is a virus that attacks cells in the body.
• Human Immuno Deficiency is a member of a group of viruses called a retrovirus.
• It has an RNA genome enclosed in an envelope.
• AID (Acquired Immuno Deficiency Syndrome) is caused by Human Immuno Deficiency.

Explanation-

HIV infection- 

• The HIV virus mainly affects the Helper T-lymphocytes (immune cells of the human body).
• After getting HIV into the body of a person, the virus enters the macrophages.
• Here, RNA is replicated to form viral DNA by enzyme reverse transcriptase.
• The viral DNA now gets incorporated into the host cell's DNA and directs the infected cells to produce viruses.
• The macrophages continue to produce virus particles.
• The virus particles enter Helper T-lymphocytes (T_H cells) in the blood, where they continue to replicate and produce viral progenies.
• The virus released in the blood also affects the other Helper T-lymphocytes.
• Thus, the number of Helper T-lymphocytes progressively decreases in the body of the infected persons.
• With the decrease in the number of T-cells, immunity also decreases.
• The person is unable to produce any immune response.

Thus, HIV mainly infects Helper T-lymphocytes.

Additional Information

Following preventive measures are used to prevent the spread of HIV infection.

• Making blood from blood banks safe from HIV.
• Ensure the use of only disposable needles and syringes.
• controlling drug abuse.

Enzyme-linked immunosorbent assay (ELISA) is the widely used diagnostic test for AIDS.

Explanation-

• In general, human cells contain 23 pairs of chromosomes. One chromosome in each pair comes from father and mother.
• About 95 percent of the time, Down syndrome is caused by trisomy 21.
• In this, the person has three copies of chromosome 21.
• It is a result of abnormal cell division involving chromosome 21 occurs.

The correct answer is Cactus.

Concept:

Stomata

• The Stomata are openings in the epidermis of most of the aerial parts of the plants, especially the leaves.
• Stomata regulate the process of transpiration and gaseous exchange.
• Stomata consists of two bean-shaped cells known as guard cells.
• It regulates the opening and closing of stomata.

Explanation:

• The cactus is a desert or a succulent plant that can live under harsh circumstances.
• The stomata present in the cactus close during the day and open only at night.
• During the daytime, they receive an excessive amount of sunshine, and their rate of transpiration tends to rise.
• Transpiration is the loss of water in the form of vapors from the plant parts through stomata.
• If the rate of transpiration increases, the cactus plant will dry out quickly.
• To avoid this, they have changed their system in which they open at night and take in carbon dioxide from the atmosphere, and the gaseous exchange occurs before the sunlight.
• During the daytime, they close their stomata to reduce transpiration.
• Such adaptability has enabled them to live in harsh environments.

Explanation:

• Photosynthesis is the process of manufacturing carbohydrates by autotrophs using water, and carbon dioxide in presence of sunlight.
• During photosynthesis, light energy is converted into chemical energy which is used by the plants to carry the vital functions.

The reaction for photosynthesis is:

6CO2 + 12H2O → C6H12O6 + 6O2 + 6H2O

The possession of skills is an essential feature of any profession. Skills provide a means for professionals to put theoretical knowledge into practice. Effective teachers should possess skills and competence that set them apart not only from non-professionals, i.e., non-teachers but also from ineffective teachers.

• The teachers we need can be made available through appropriate education and training.
• The skills required by them can be taught, practiced, evaluated, predicted, and controlled.

Key Points

• Teaching Skills are defined as a group of teaching acts or behaviors intended to facilitate students learning directly or indirectly. It is employed extensively in daily teaching.
• Unification means to make the things combined or make them a whole. Unification of teaching skills is to choose proper teaching skills in one lesson.
• If the teacher unifies all his/her skills in the lecture, he/she will be able to summarise the whole topic in one attempt.
• The teacher will teach with great accuracy and knowledge if she/he unifies all teaching skills.

Thus, it is concluded that the meaning of unification of teaching skills is to choose proper teaching skills in one lesson.

Benjamin Bloom's taxonomy is a set of three hierarchical models that refers to the classification of educational learning objectives. In the taxonomy, Bloom identified three domains of learning which include cognitive, affective, and psychomotor.

 

These three domains have been divided in a way that proceeds from the simplest process to the complex.

• Cognitive domains: In this domain, a child deals with knowledge and hence, learns to create, evaluate, analyze, etc.
• Psychomotor domains: It is concerned with acquiring skills that require the integration of mental and physical movements.
• Affective domains: This domain comes into play when we grow in emotional areas such as feelings, attitudes, etc. It includes how we deal with things emotionally, such as feelings, values, appreciation, enthusiasms, motivations, and attitudes.

Key Points

Let's Understand  the Levels of Affective Domain in Brief:

• Receiving: When a learner shows sensitivity to certain stimuli.
• Responding:  It is defined as the tendency to respond to an object or stimuli.
• Valuing: It refers to the acceptance of behavior and commitment to it. One values certain behaviors not by desires but by commitment.
• Organizing: It refers to organizing the value system which is attained when one develops one’s code of conduct or standard of public life.
• Characterizing: It deals with behavior as per values or attitudes a child has imbibed; children show teamwork.

Hence, it could be concluded that the is Analysis is not included in the affective aspect.

Hint

• Analysis is related to the cognitive aspect/domain of Bloom's taxonomy of educational objectives.

The teaching of anything is considered effective only when the students learn meaningfully. To make teaching effective, teachers need to carefully plan and prepare for each lesson. Usually, a lesson is transacted in the classroom in one period of 35 to 40 minutes duration.

• A lesson plan needs to have three distinct phases i.e. activities before teaching-learning, activities during teaching-learning, and activities after teaching-learning.
• A lesson plan refers to the written expression of the details of planned activities to be undertaken during classroom transactions of a particular lesson or topic.

Key Points

​A lesson plan must be started with a clear and descriptive objective.  It is a statement or purpose of the lesson.

Some of the major characteristics of objectives can be:-

• The objective is the overall idea of what the teacher sets to achieve in the lesson.
• The objective is what the teacher thinks students should be able to do better by the end of the lesson.
• Having the aim in mind will prevent from losing focus or just teaching the favorite topics.

Some lessons may require more than one objective.

• The objective should be written at the top of the lesson plan to serve as a guide to other things that will go into the plan. Clear and realistic objectives are essential in making a lesson successful.

Important Points​ The lesson plan should have at least the following four characteristics:

• Objective-based: A lesson plan should be objective-based. A limited number of objectives pertaining to a lesson that could be realized within the time available in a period should be determined.
• Comprehensive: A lesson plan should be comprehensive, brief, and simple.

All your efforts for the realization of the set objectives may be reflected in the lesson plan. As far as possible, this must be short and precise so that you can prepare and use it with ease.

• Flexible: A lesson plan should be flexible with the scope to incorporate changes that would be instantly required at the time of transacting the teaching-learning activities in the classroom. For example, you may have come across a recent development in science that is not indicated in the lesson plan and you realize that you must share this to make a concept relevant, then you can immediately incorporate this in the lesson plan for better classroom transaction.
• Implementable: A lesson plan must be practical, i.e., it can be implemented in real situations. The teaching-learning activities and strategies proposed in the plan should be beneficial to the students and can be implemented within the stipulated available time.

Thus, it is concluded that the first thing which is considered in the lesson plan is the Objective.

Science as a discipline has its unique perspective. Science is not limited to observation, experimentation, and analysis only rather it is a way of life. Science is an expanding body of knowledge through the process of inquiry.

 Key Points

Nature of Science:

• Science is socially and culturally embedded.
• Science is inferential, imaginative, and creative. It is subjective and theory-laden.
• Science is empirical (based on or derived from developed observation of the natural world).
• Science is not merely a collection of evidence of happenings rather it attempts to understand happening through analysis, testing, and verification.

Important Points

• The value of science comes from its economical and political importance,  but science seeks the truth by observing important values: a scientist must be honest, modest, always critical, rejecting any dogmatism and any fraud,  but also creative, imaginative, and able to work collectively.
• The main values of science to be rigorous, rational, honest, critical, creative, etc. can explain how science aims as far as possible at the truth (even if the scientific knowledge is always under construction) but it is impossible to say that science is the only truth in our world.

Thus, it is concluded that Reality is the value of science for nature.

Creativity is a cognitive ability to produce something original by offering a fresh perspective. It is the ability possessed by people who are creative, persistent, and imaginative.

• Creativity is related to divergent thinking which refers to a way of solving problems by more than one approach.
• It is goal-directed thinking which is unusual, novel, and useful and includes brainstorming and out-of-the-box thinking in it.

Key Points

Creative children: 

• The creative children are those who show high-performance capability in several areas such as artistic and creative work, leadership quality, keen power of observation, etc.
• These children have divergent thinking and are very curious in nature that's why sometimes the classroom seems monotonous to them because they grab things fastly than of their age-peers.

Quality of a creative child:

• Abstracting ability
• Fluency & Flexibility
• Originality & Novelty
• Independencey in thought

Important Points 

Characteristics of Creative Children:

• Perceive relation between impossible things.
• Curious, extrovert, and ambitious in nature.
• Think quickly and solve problems in a novel way.
• Convert imaginative and original ideas into reality.
• Try new things and risk failure in executing innovative ideas.
• Use divergent and out of the box thinking in different situations.

Hence, it could be concluded that the quality of creative students is Originality.

Concept: 

Temperature

• The degree of hotness or coldness of a body is given by the temperature.
• The heat is transferred from a hotter body to a colder body until the temperature of both comes to an equilibrium.
• The SI unit of temperature is Kelvin (K).
• Degree centigrade is another unit of measuring temperature which is based on the freezing and boiling point of water.
• 0° C is the freezing point, and 100° C is the boiling point of the water.
• Kelvin is used for scientific measurements.
• 0 Kelvin is said to be absolute temperature. The temperature below this cannot be achieved.
• The relationship between Kelvin and ° C is given as K = C + 273

Explanation:

So, the relationship between Kelvin and ° C is

K = C + 273 

We need to add 273 in ° C to obtain the value of temperature in Kelvin. 

Now, the difference between the two temperatures in Kelvin will be the same as that of  ° C. 

For example, we have to find the difference in temperature between 50 °C and 100 °C

In Kelvin, we have to find the difference between (50 + 273) and (100 + 273) K

Let's find the difference in Kelvin

(50 + 273) K - (100 + 273) K = 50K + 273 K - 100 K - 273 K = 50 K

So the difference in two temperature is 20 K (273 gets cancelled in above expression)

This also difference is °C (100 ° C - 50 °C ) = 50 ° C

So, correct option is 50.

Important Points

The change in temperature in Kelvin and degree Celcius will always be the same.

Concept:

• Equivalent Resistance: Equivalent Resistance between two Points is the ratio of Potential Difference between them and the amount of current passing through them.
• Equivalent Resistance can also be defined as the resistance of the resistor which will replace all the resistors between two points and will draw the same current between these two points as it was flowing Earlier. 
• Symmetry: A group of the same set of resistors connected in series with a similar group then we can say, there is symmetry in Circuit.

Different Types of Connections are Series connections and Parallel connections.

Calculation:

Given:  

Resistors are in parallel,

\(\frac{1}{R} = \frac{1}{R_{1}} +\frac{1}{R_{2}} + \frac{1}{R_{3}}.....+ \frac{1}{R_{n}}\)

The equivalent resistance will be 

\(\frac{1}{R} = \frac{1}{2 \Omega } +\frac{1}{3\Omega} + \frac{1}{1\Omega}\)

\(\implies \frac{1}{R} = \frac{2+3+6}{6 \Omega } = \frac{11}{6 \Omega } \)

\(\implies R = \frac{6}{11} \ \Omega \)

The correct option is 1.

Concept:

• The equation for the speed of sound in a gas is given by

\(v =\sqrt\frac{γ RT}{M}\)

Where γ = Ratio of specific heat, R = Universal gas constant, T = Temperature in Kelvin, M = Mass

• The γ at NTP is the same for all the gases.

Explanation:

γ, R, and M are constant. 

So, we can say

ν ∝ √T