Mathematics and Science PYQs

The factors of a trinomial expression can be numbers, variables, or expressions. For example, the factors of the trinomial x² +3x+2 are 1,x,2,x+2.

Key Points

Therefore, the factors of a trinomial expression can be any of the following: 

• A number
• A variable
• An expression

Hence, we can conclude that (A), (B), and (C) is the correct factors of a trinomial expression.

The higher aims of teaching mathematics are to develop mathematical power, mathematical literacy, and positive attitudes towards mathematics.

Key Points

• Mathematical power is the ability to think mathematically, to reason logically, and to solve problems.
• Mathematical literacy is the ability to understand and use mathematical concepts and skills in everyday life.
• Mathematics helps learners move beyond concrete objects and understand abstract concepts, symbols, patterns, and relationships.

It develops the ability to think logically and work with mathematical ideas that may not be directly observable.

• Positive attitudes towards mathematics include an appreciation for the beauty and usefulness of mathematics and a willingness to use mathematics to solve problems.

 Hint

• The right attitude for problem solving is important, but it is not the highest aim of teaching mathematics. It is a prerequisite for learning mathematics, and it is something that should be developed alongside the development of mathematical power and mathematical literacy.

Thus, option 1 is the correct answer.

Visually-challenged students are those who have significant difficulty seeing, even with the aid of corrective lenses, or are completely blind. This visual impairment affects their ability to perform tasks that require sight, such as reading, writing, and interpreting visual information.

Key Points

For helping visually-challenged students in a mathematics classroom, the following teaching-learning resources can be used: 

• (A) Taylor's abacus: This device is specifically designed for visually impaired students to perform mathematical calculations.
• (B) Computer: Computers can be used with screen readers and other assistive technologies to aid visually impaired students.

Hint

• GeoGebra is a dynamic mathematics software that provides interactive geometry, algebra, statistics, and calculus applications.
• While it is a powerful tool for visualizing mathematical concepts, it primarily relies on visual interaction and graphical representations, making it less accessible for visually-challenged students without significant adaptations.

Hence, it can be concluded that the correct answer is (A) and (B).

In a constructivist classroom, the emphasis is on hands-on, experiential learning and active participation of students in the learning process.

Key Points

• By bringing in solid shapes and providing graph sheets and measuring devices, the teacher allows learners to engage in exploratory activities.
• Students can manipulate the shapes, measure their dimensions, and experiment with different formulae to understand the concepts of area and volume.
• This approach encourages students to construct their own understanding through direct experiences and interactions with the materials.
• It promotes a deeper understanding of spatial quantities by providing concrete experiences that students can relate to abstract formulas.

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

The table can be used to teach two mathematical concepts: data handling and integers.

Key Points

• Data handling involves organizing, analyzing, and interpreting data.
• In this case, students can learn to organize the temperature readings for different cities, create frequency distributions, calculate measures of central tendency, and represent the data using graphs or charts.
• They can explore patterns, relationships, and trends in temperature data, enhancing their skills in data analysis and interpretation.
• Integers come into play as the temperature readings in the table include both positive and negative values.
• Students can learn about the concept of integers, and understand the meaning of negative temperatures representing temperatures below freezing point, and positive temperatures representing temperatures above freezing point.

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

Open-ended tasks in mathematics are valuable for fostering conceptual understanding, providing opportunities for multiple answers, and stimulating students' excitement for exploring mathematical ideas. 

Key Points

• While it is true that open-ended tasks may take longer to solve compared to closed-ended questions, the time aspect alone does not justify their use.
• Open-ended tasks are valuable in the classroom because they promote critical thinking, problem-solving skills, creativity, and deeper engagement with mathematical concepts.
• They encourage students to think flexibly, explore different strategies, and communicate their reasoning effectively.

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

A line graph is a powerful tool for visualizing data and displaying trends over time.

Key Points

• It consists of a series of data points connected by lines, with the x-axis representing time and the y-axis representing the numerical values.
• This type of graph allows for the representation of continuous data, making it ideal for showing smaller changes in trends.
• The advantage of a line graph lies in its ability to display gradual shifts, fluctuations, and patterns in the data set over time.
• The line connecting the data points provides a visual representation of the trend's direction and magnitude, enabling viewers to observe and analyze even subtle changes or variations in the data.

Hence, it can be concluded that a line graph is the correct answer. 

Hint

• A bar graph represents data using separate bars and is useful for comparing distinct categories, but it does not show small trends in time as smoothly as a line graph.
• A pie chart displays parts of a whole at a single point in time and cannot show changes across time or highlight minor variations.
• A pictograph uses images or symbols to represent numbers and is best for young learners, but it cannot handle large datasets or capture subtle changes effectively.

At the primary level, students are in the early stages of learning mathematics, and their foundational understanding is still developing.

Key Points

• It is important to prioritize building a strong conceptual foundation and fostering a love for mathematics rather than expecting them to solve complex questions.
• Instead of complex questions, assessments should emphasize students' grasp of fundamental concepts, their ability to apply basic mathematical procedures, and their conceptual knowledge.
• Assessments should be designed to encourage critical thinking, problem-solving skills, and a deep understanding of core mathematical concepts.
• By avoiding complex questions and focusing on age-appropriate content, assessments can create a supportive environment that nurtures students' mathematical abilities and allows them to progress gradually in their mathematical journey.

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

Using real-life contexts is an effective strategy to enhance students' understanding of concepts and their practical application.

Key Points

• By engaging Kamal in real-life situations where area and volume measurements are relevant, he can develop a deeper understanding of these concepts and their associated units.
• For example, teachers can involve Kamal in activities such as measuring the area of his classroom or calculating the volume of a water tank.
• By relating these concepts to everyday situations, Kamal can see the practical significance of using appropriate units for area and volume.
• This strategy encourages Kamal to connect mathematical concepts to real-world scenarios, enabling him to develop a more intuitive understanding of area and volume measurements.
• It also promotes conceptual understanding and long-term retention of knowledge.

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

Problem-solving strategies in mathematics require various cognitive processes and mathematical thinking skills. While formulas and equations can be useful tools in problem-solving, the emphasis is on understanding and applying mathematical concepts rather than relying solely on rote memorization.

Key Points

• Effective problem-solving involves analyzing the problem, identifying relevant mathematical principles, and selecting appropriate strategies.
• It requires critical thinking, logical reasoning, and creativity to approach problems from multiple angles and devise innovative solutions.
• Rote memorization of formulas may hinder the development of problem-solving skills as it does not foster a genuine understanding of the underlying concepts.
• Instead, problem-solving strategies in mathematics encourage students to think critically, make connections, and develop a strong conceptual foundation, enabling them to tackle a wide range of mathematical challenges effectively.

Hence, it can be concluded that Problem solving strategies in Mathematics do not necessarily involve Learning and rote memorising formulae to solve problems.

The Correct answer is Frog, snake, hen

Explanation:

• Oviparous animals are those which lay eggs.
• Examples of Oviparous animals include birds, reptiles, amphibians, fish, etc.
• Viviparous animals give birth to completely developed living young animals. examples- cattle, humans, etc.
• Scorpion, Snake, Rat: Among these animals,only Snake is  oviparous. Scorpions, some snakes, and rats are viviparous animals, which means they give birth to live young.
• Frog, Hen and Snake : Among these animals, the frog and hen are oviparous. Frogs lay eggs, which hatch into tadpoles and eventually develop into adult frogs. Hens, which are female chickens, also lay eggs.
• Rat, Scorpion, Penguin: None of these animals are oviparous. Rats and Scorpions are viviparous, while penguins are unique among birds as they are ovoviviparous. Penguins lay eggs, but instead of incubating them externally, they keep the eggs warm by balancing them on their feet and covering them with a special brood pouch.
• Penguin, frog, kangaroo: Among these animals, only the frog is oviparous. Penguins, as mentioned earlier, are ovoviviparous, and kangaroos are marsupials that give birth to live but relatively undeveloped young ones, which then continue to develop in their mother's pouch.

 

Additional InformationViviparous and Oviparous Animals: 

• Oviparous and viviparous animals are two different groups of animals, which are classified on the basis of fertilization.
• The main difference between oviparous and viviparous animals is listed below.

The Correct answer is (A) & (B)

Concept:

• Reproduction is the biological process in which the organism gives rise to young ones or offspring similar to itself.
• It is responsible for the continuity of species generation after generation.
• Reproduction is mainly divided into two types:

Sexual reproduction: 

• Involves the formation of the male and female gametes, either by the same individual or by different individuals of the opposite sex.
• These gametes fuse to form the zygote which develops to form the new organism.
• It is an elaborate, complex, and slow process as compared to asexual reproduction. (E.g. Mammals).
• The offsprings show characteristics of both male and female parents and show variation.

Asexual reproduction:

• The reproduction in which an offspring is produced by a single parent without the fusion of gametes is called asexual reproduction. (E.g. Amoeba, Hydra)
• The offsprings are exact replicas of their parents and genetically identical.
• Asexual reproduction is of many types: Sporulation, Fission, and Fragmentation. Budding, Plasmotomy, vegetative propagation, Apomixis & Parthenogenesis

Explanation:

Budding: 

• The small bulb-like projection coming out from the yeast cell is called a bud.
• The bud gradually grows and gets detached from the parent cell and forms a new yeast cell.
• Example-yeast, are sponges, and hydra.

Binary Fission:

• It is asexual reproduction by a separation of the body into two new bodies.
• Under this, an organism duplicates its genetic material, and then divides into two parts (cytokinesis), with each new organism receiving one copy of DNA.
• Binary fission is seen in Single-celled organisms like protozoa

On the basis of the plane of division binary fission in protozoa is of the following types:

• Irregular Binary fission: This type of binary fission is seen in protozoans with irregular body forms. Here the body divides into two parts without any defined plane of fission. Eg - Amoeba

Additional Information

• In vitro fertilization (IVF) is an option for women to have their own children who cannot reproduce naturally.
• The zygote is allowed to develop through fertilization in the laboratory for about a week and then implanted in the mother's uterus.
• In some cases, women cannot reproduce naturally due to the blockage of the oviduct. Therefore, sperm cannot reach the egg for fertilization and women become unable to give birth to children. In vitro fertilization (IVF) is an option for such cases.
• During in vitro fertilization, collects the freshly released eggs and sperm and allows them to be fertilized by placing them together in laboratory conditions for a few hours.
• Fertilization takes place and the zygote is allowed to develop for about a week and then it is implanted in the mother's uterus for the full development of the embryo.
• The baby is born like any other baby and the babies born with this technique are called test tube babies.

The Correct answer is Like charges repel each other.

Explanation:

• There are two types of charges found in nature -

1. Positive charge
2. Negative charge

Properties of charges:

• Like charges (same charges) repel each other.
• Unlike charges (different charges) attract each other.
• The electroscope is a device that can be used to test whether an object is carrying a charge or not.
• It was invented by British physician William Gilbert.
• The working principle of an electroscope is based on the atomic structure of the elements, charge induction, the internal structure of metal elements, and the idea that like charges repel each other while unlike charges attract each other.

The Correct answer is  It is a non-contact force.

Concept;

• Gravitational force is a non-contact force.
• It is the force of attraction between two objects with mass.
• It acts at a distance without the need for physical contact between the objects.
• The force of gravity is responsible for the motion of celestial bodies, such as the planets orbiting the sun, and the gravitational attraction between objects on Earth.
• It follows Newton's law of universal gravitation, which states that the force of gravity is proportional to the product of the masses of the objects and inversely proportional to the square of the distance between them.

Explanation:

• "It can be attractive as well as repulsive" is incorrect. The force of gravitation is always attractive and never repulsive. Gravitational attraction occurs between two objects with mass. The larger the mass of the objects, the stronger the gravitational force between them. This force always pulls objects toward each other, never pushing them away.
• "It is a unique force which only the Earth possesses" is incorrect. Gravitation is a universal force that exists between all objects with mass. It is not exclusive to the Earth.

Every object in the universe exerts a gravitational force on other objects. However, the magnitude of the force depends on the masses of the objects involved and their separation.

• "It is a strong force" is incorrect. Compared to other fundamental forces, such as the electromagnetic force and the strong nuclear force, the force of gravitation is relatively weak. It is the weakest of the four fundamental forces in nature. Its strength is evident in everyday life due to the large masses involved, such as the Earth's gravitational pull on objects on its surface or the gravitational attraction between celestial bodies, but on a microscopic scale, other forces dominate.

The Correct answer is It will boil above 100°C.

Concept;

• The boiling point of water is 100°C.
• At sea level, vapor pressure is equal to the atmospheric pressure at 100 ˚C, and so this is the temperature at which water boils.
• Due to this, the temperature required to reach the necessary vapor becomes lower and lower as we get higher above sea level, and the liquid will therefore boil at a lower temperature.

Explanation:

• The boiling point of water at normal temperature and pressure is 100°C. This means that, under normal conditions, water changes from a liquid state to a gaseous state (vapor) at 100°C.
• However, the information provided states that the water begins to freeze at -3°C. This implies that the temperature of the water is below the freezing point of 0°C.
• When the temperature of the water is below its freezing point, it transitions from a liquid state to a solid state (ice). This indicates that the water is in a solid state at temperatures below -3°C.
• Since the water is in a solid state at -3°C, it is not at the boiling point, and therefore it will not boil at this temperature.

Therefore, we can conclude that the boiling point of the water sample will be above 100°C, as it must transition from a solid (ice) to a liquid (water) state before it can reach the boiling point of 100°C.

The Correct answer is (i) - Starch, (ii) - Proteins, (iii) - Bile, (iv) - Fats.

Explanation:

• Mouth: The mouth is responsible for the initial stage of digestion. Saliva, secreted by the salivary glands in the mouth,  It helps in the mechanical breakdown of food through chewing and the chemical breakdown of starches by the enzyme amylase, which converts starch into sugar.
• Stomach: The stomach is involved in the mechanical and chemical digestion of food. It secretes gastric juices, including hydrochloric acid and enzymes, which help break down proteins and kill bacteria present in the food.
• Liver: Although not directly a part of the digestive tract, the liver plays a crucial role in digestion. It produces bile, a substance stored in the gallbladder and released into the small intestine. Bile aids in the digestion and absorption of fats by emulsifying them into smaller droplets.

The Correct answer is Paddy, cotton, groundnut.

Concept:

• When plants of the same kind are grown and cultivated at one place on a large scale, it is called a crop.
• Crops can be classified on the basis of the season in which they grow.
• India is a vast country. The climatic conditions like temperature, humidity, and rainfall vary from one region to another.
• Accordingly, there is a rich variety of crops grown in different parts of the country.
• Despite this diversity, two broad cropping patterns can be identified. These are Kharif Crops and Rabi Crops.

Explanation:

Kharif Crops :

• Kharif crops also are known as monsoon crops as they are cultivated in the monsoon season.
• Their cropping season starts in June and ends in October.
• These crops are sown at the beginning of the rainy season.
• Rice, maize, bajara, ragi, sorghum, soybean, groundnut, cotton, etc. are all Kharif types of crops.

Rabi Crops:

• The crops grown in the winter season are called rabi crops.
• Their time period is generally from October to March.
• Examples of rabi crops are wheat, gram, pea, mustard, and linseed.

The Correct answer is Shimla

Concept:

• Weather and climate data can be used to identify or describe specific geographic locations. Key data include temperature ranges and precipitation levels, which can vary significantly by location due to factors such as latitude, elevation, and proximity to bodies of water. Understanding regional climatic patterns can help to narrow down the options.

Here are brief descriptions of the climatic conditions of the four Indian cities listed:

• New Delhi: New Delhi experiences a wide range of temperatures throughout the year, with extremely hot summers and cold winters. The average maximum temperature in July is 38.2°C, which aligns with the hot summer season in Delhi. However, the minimum temperature in July is stated as 33.7°C, which seems unusually high for New Delhi. Moreover, the precipitation in July is mentioned as 208mm, which is relatively high compared to the average rainfall in Delhi. Therefore, the given data does not match New Delhi's temperature and precipitation patterns.
• Chennai: Chennai, located on the southeastern coast of India, has a tropical wet and dry climate. The city experiences a relatively consistent temperature throughout the year. The average maximum temperature in July is mentioned 26.6°C, which is consistent with Chennai's climate.
• However, the minimum temperature in July is stated as 33.7°C, which seems unusually high for Chennai. Additionally, the precipitation in July is mentioned as 208mm, which is significantly higher than Chennai's average rainfall. Therefore, the given data does not match Chennai's temperature and precipitation patterns.
• Bikaner: Bikaner is a city in the western state of Rajasthan, known for its extreme desert climate. The city experiences scorching summers and chilly winters. The average maximum temperature in July is stated as 26.6°C, which aligns with Bikaner's climate. However, the minimum temperature in July is mentioned as 33.7°C, which is unusually high for Bikaner. Additionally, the precipitation in July is mentioned as 208mm, which is significantly higher than the minimal rainfall Bikaner receives. Therefore, the given data does not match Bikaner's temperature and precipitation patterns.
• Shimla: Shimla is a city in the northern Indian state of Himachal Pradesh, located in the Himalayan region. It has a subtropical highland climate with cool summers and cold winters. The average maximum temperature in July is stated as 26.6°C, which aligns with Shimla's climate.
• The minimum temperature in July is mentioned as 33.7°C, which seems unusually high for Shimla, as the city typically experiences cooler temperatures during that time. However, considering that this might be an outlier or anomaly, we will consider Shimla as a potential candidate. The precipitation in July is mentioned as 208mm, which indicates a relatively high amount of rainfall, which is common during the monsoon season in Shimla.

​Based on the given data, the city that seems to match the temperature and precipitation patterns most closely is Shimla.

The Correct answer is The eye sees in three dimensions & while a camera sees in two dimensions.

Explanation:

• Both the eye and the camera have lenses that focus light onto a light-sensitive surface. The light-sensitive surface in the eye is called the retina, and it converts light into electrical signals that are sent to the brain. The brain interprets these signals and creates the image that we see.
• The eye can see in three dimensions because it has two retinas, one in each eye.
• The two retinas are slightly offset from each other, which allows the brain to calculate the depth of objects.
• On the other hand, cameras only have one light-sensitive surface, so they can only see in two dimensions.
• The other options are not correct. The eye does not form an erect image, but rather an inverted image. The camera can have either a concave or convex lens, depending on the type of camera. And the focal length of the human eye can be adjusted slightly, by contracting or expanding the lens.

 

 similarities and differences between the eye and the camera:

The Correct answer is (A) - (III), (B) - (I), (C) - (V), (D) - (II), (E) - (IV)

Explanation: