Author: abhishekinbh
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10th Question Bank 2026-27
CBSE Class 10 Question Bank CBSE Official ResourcesClass 10 Question Bank
Direct PDF downloads from CBSE Academic · Curated by Abhishek Sir
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Chapter 2: Cell — The Building Block of Life
PAUSE AND PONDER (In-chapter Questions)
Q1. What argument would you give for the necessity of a cell wall in plants (fixed) vs animals (moving)?
Plants are stationary and face mechanical stresses like wind, rain, and gravity. The rigid cell wall provides structural support to withstand these forces and maintain upright posture. Animals move actively, so their cells need flexibility to change shape — a rigid wall would hinder movement of tissues like muscles. Thus, a cell wall is essential for plants but would be a disadvantage for animals.
Q2. What consequences if a plant cell’s cell wall became as flexible as the cell membrane?
- The cell would lose its fixed shape and rigidity.
- Plants would become unable to stand upright and would wilt permanently.
- Leaves and flowers would collapse.
- When placed in hypotonic solution, the cell could burst (like animal cells) since the wall wouldn’t resist excessive water entry.
- Overall structural integrity of the plant body would be lost.
Q3. Why is it important to cut potato pieces in roughly equal size and measure initial weight?
This ensures a fair and controlled experiment. If sizes differ, the surface area exposed to solution differs, affecting the rate of osmosis. Measuring initial weight allows accurate calculation of water gain or loss. Without these controls, results cannot be reliably compared between the two beakers.
Q4. Do white flowers contain any pigment? Give reasons.
Yes, white flowers do contain pigments, but they reflect all wavelengths of visible light rather than absorbing any specific colour, which makes them appear white. Some white flowers contain flavonoids or other colourless/UV-absorbing pigments. The whiteness may also result from air spaces in petals that scatter light. So white does not mean absence of all pigments.
Q5. Draw a well-labelled schematic diagram of a plant or animal cell.
(This is a drawing-based question — draw referring to Fig. 2.10 in the textbook.)
For a plant cell, include: cell wall, cell membrane, nucleus (dark round body), cytoplasm, ER (network extending from nuclear envelope), mitochondria (rod-shaped), chloroplasts (rod-shaped, green), vacuole (large, central), Golgi apparatus, ribosomes.
For an animal cell, include: cell membrane, nucleus, cytoplasm, ER, mitochondria (rod-shaped), Golgi apparatus, lysosomes, ribosomes, small vacuoles.
Q6. Why does a cell not have one giant mitochondrion instead of many small ones? (Surface area concept)
Many small mitochondria provide a much greater total surface area than one large mitochondrion of the same combined volume. The inner membrane (with cristae) is where ATP production occurs. More surface area means more space for chemical reactions, leading to greater and more efficient energy production. A single giant mitochondrion would have far less surface-area-to-volume ratio and would be metabolically inefficient.
Q7. If skin cells divide by meiosis instead of mitosis, what would happen to a skin cut?
Meiosis produces cells with half the chromosome number. If skin cells used meiosis for repair:
- Daughter cells would have only half the genetic information needed.
- They would be genetically different from the parent skin cells.
- Proper healing would not occur since the new cells would be abnormal and non-functional.
- The wound would not heal correctly, and skin integrity would be permanently compromised.
REVISE, REFLECT, REFINE (End-chapter Questions)
Q1. Differentiate between the following:
(i) Cell membrane vs Cell wall (permeability)
Cell Membrane Cell Wall Selectively permeable — allows only certain substances Fully permeable — water and dissolved minerals pass freely Present in all cells Present only in plant, fungal, and bacterial cells Made of lipids and proteins Made primarily of cellulose (in plants) Thin, flexible Thick, rigid (ii) RER vs SER (structure)
RER (Rough ER) SER (Smooth ER) Has ribosomes attached on its surface No ribosomes on surface Appears rough under electron microscope Appears smooth under electron microscope Involved in protein synthesis and secretion Involved in synthesis and storage of fats and hormones (iii) Chloroplasts vs Chromoplasts (pigments)
Chloroplasts Chromoplasts Contain green pigment chlorophyll Contain yellow, orange, or red pigments (not chlorophyll) Found in green parts of plants Found in flower petals and fruits Responsible for photosynthesis Responsible for bright colours attracting pollinators/animals
Q2. Cell X in pure water swells; Cell Y in concentrated salt solution shrinks. Which statement is correct?
Answer: (iii) — Water moved into Cell X and moved out of Cell Y through the cell membrane.
Explanation: The cell membrane is selectively permeable and allows water (not salt/sugar molecules) to move by osmosis. Pure water (hypotonic outside) causes water to enter Cell X → it swells. Concentrated salt solution (hypertonic outside) causes water to leave Cell Y → it shrinks. Option (i) is wrong because salt molecules don’t move in. Option (ii) is partially wrong. Option (iv) is wrong because osmosis involves water movement, not solute movement.
Q3. Identify parts (a) to (g) in Fig. 2.20 (plant cell diagram) and match functions:
Based on a standard plant cell diagram with labels (a) through (g):
Label Organelle Function (a) Chloroplast (vii) Helps in manufacturing food (b) Nucleus (i) Controlling all activities of a cell (c) Endoplasmic Reticulum (transport network) (d) Cell Wall (v) Provides structural rigidity (e) Cell Membrane (iv) Separates cell contents from surroundings (f) Golgi Apparatus (vi) Packs and stores materials received from ER (g) Vacuole (iii) Storage organelle that also provides rigidity Mitochondria Mitochondria (ii) Site of cellular respiration (Exact matching depends on the actual figure; match accordingly using the functions above.)
Q4. Which option correctly pairs cell organelles present in plant cells / absent in animal cells?
Answer: (i) — Leucoplast (present in plant cells) and Cell wall (absent in animal cells).
Explanation: Leucoplasts are plastids found only in plants. Cell wall is present in plants but absent in animals. Option (ii) is wrong — both mitochondria and ribosomes are present in animal cells. Option (iii) is wrong — Golgi apparatus is present in animal cells. Option (iv) is wrong — both lysosomes and ER are present in animal cells.
Q5. Renu says plastids are in all plant parts including roots. Rohit says roots have no plastids. Who is correct?
Rohit is partially correct, but Renu is more accurate overall.
Plastids are indeed present in root cells, but they are leucoplasts (colourless, storage plastids), not chloroplasts. Roots do not receive sunlight, so chloroplasts are absent. However, saying plastids are entirely absent in roots is incorrect. Leucoplasts in root cells store starch and other food materials. So Renu is correct that plastids are present in roots, but they are non-photosynthetic leucoplasts rather than chloroplasts.
Q6. Compare mitochondria and chloroplasts — similarities and differences:
Similarities:
- Both are double-membrane-bound organelles.
- Both contain their own DNA and ribosomes, so they can synthesise some proteins independently.
- Both are involved in energy-related processes.
- Both are rod-shaped.
- Both show evolutionary relationship with ancient bacteria (endosymbiotic theory).
Differences:
Mitochondria Chloroplasts Found in both plant and animal cells Found only in plant cells Inner membrane folded into cristae Has stroma with disc-shaped thylakoid membranes containing chlorophyll Carries out cellular respiration — breaks down glucose to release ATP Carries out photosynthesis — converts light energy into glucose Uses oxygen, releases CO₂ Uses CO₂, releases oxygen Active in all living cells 24 hours Active only in the presence of light
Q7. Which pair of cell organelles contains DNA?
Answer: (ii) Mitochondria and Nucleus
Explanation: The nucleus contains chromosomal DNA carrying the cell’s genetic information. Mitochondria have their own circular DNA (inherited maternally). Chloroplasts also have DNA, but they are not listed here. Ribosomes, Golgi bodies, and lysosomes do not contain DNA.
Q8. Researcher’s carrot experiment (plain water vs concentrated salt solution):
(i) Hypothesis she wants to test:
The hypothesis is: Cell membranes are selectively permeable, and water moves by osmosis from a region of lower solute concentration to higher solute concentration. Specifically: a carrot in plain water will remain firm (water entry) while a carrot in salt solution will become limp (water loss).(ii) Suggestions for improvement:
- Use carrots of identical size, shape, and weight to ensure a controlled experiment.
- Record initial and final weights to quantify water gain/loss.
- Specify exact concentration of salt solution for reproducibility.
- Use multiple trials and calculate average results.
- Keep temperature constant throughout the experiment.
(iii) Why does carrot in plain water stay stiff but carrot in salt solution become rubbery?
In plain water (hypotonic solution), water enters the carrot cells by osmosis (water concentration outside > inside), making cells turgid → carrot stays stiff and crunchy. In concentrated salt solution (hypertonic), water moves out of carrot cells by osmosis (solute concentration outside > inside), cells lose turgor pressure → carrot becomes flaccid, rubbery, and limp.
Q9. Presence/absence of structures in bacterial and animal cells:
Structure Bacterial Cell Animal Cell Chromosome Present (circular, in nucleoid, no membrane) Present (linear, enclosed in nucleus) Nucleus Absent (nucleoid present instead) Present (well-defined, membrane-bound) Mitochondria Absent Present Golgi complex Absent Present Chromoplasts Absent Absent
Q10. Potato cup experiment (Cups A, B, C, D):
(i) Why does water gather in Cup B (sugar) and Cup C (salt)?
Sugar and salt create a concentrated solution inside the potato cup. The surrounding potato cells have a lower solute concentration inside. By osmosis, water moves from the potato cells (higher water concentration) into the hollow cup (lower water concentration / higher solute concentration). This is why water accumulates in the hollow of Cup B and Cup C.(ii) Why is Cup A (empty) necessary?
Cup A is the control. It shows that water does not enter an empty potato cup by itself, confirming that the presence of solute (sugar/salt) is what drives water movement. Without a control, we cannot attribute the water gathering to osmosis specifically.(iii) Why does water not gather in Cup A and Cup D?
- Cup A (empty): No solute inside the cup, so no concentration gradient exists. No osmosis occurs; water has no driving force to enter.
- Cup D (boiled potato with sugar): Boiling kills the cells and denatures the cell membrane proteins, destroying selective permeability. The cell membranes are no longer functional, so osmosis cannot occur even though sugar is present. Therefore, water does not accumulate.
Q11. Identify the incorrectly matched pair:
Answer: (ii) SER — Lipid and cellulose synthesis
Explanation: SER is involved in synthesis of lipids and hormones — not cellulose. Cellulose synthesis occurs at the cell wall level involving Golgi apparatus. Options (i) and (iii) are correct: ribosomes do synthesise proteins, and lysosomes do digest foreign agents and waste materials.
Q12. What if all mitochondria are removed from a eukaryotic cell?
- Mitochondria are the powerhouses that produce ATP through cellular respiration.
- Without mitochondria, ATP production would stop almost entirely.
- The cell would have no energy currency to carry out any activity — protein synthesis, active transport, movement, division, etc.
- The cell would quickly become non-functional and die.
- Some minimal anaerobic energy production (glycolysis in cytoplasm) might occur briefly, but it would be insufficient to sustain the cell.
Q13. Which phenomenon inhibits tumour formation in humans? Can plants develop tumours?
Phenomenon: Contact Inhibition. When normal animal cells come in contact with neighbouring cells, they stop dividing. This prevents uncontrolled growth and tumour formation. Cancer cells lose this property and keep dividing uncontrollably.
Can plants develop tumours? Yes, plants can develop tumours, but through a different mechanism. Plant cells do not show contact inhibition because their rigid cell walls regulate growth differently. A well-known example is Crown Gall Disease, caused by the bacterium Agrobacterium tumefaciens, which inserts its DNA into plant cells causing uncontrolled cell proliferation and tumour formation. So plants can have tumours, but the regulatory mechanism differs from animals.
Q14. Which organelles help synthesise cell membrane? Trace the path of synthesis:
Cell membrane is made of proteins and lipids.
Organelles involved:
- Ribosomes (on RER) — synthesise proteins
- SER — synthesises lipids
- Golgi apparatus — modifies, packages, and transports both
Path:
- Proteins are synthesised on ribosomes attached to RER.
- Lipids are synthesised in SER.
- Both are transported to the Golgi apparatus via vesicles.
- Golgi apparatus modifies, sorts, and packages them into vesicles.
- These vesicles move toward and fuse with the cell membrane, adding new lipid and protein components to it.
(Draw a labelled diagram showing: Ribosome → RER → Vesicle → Golgi → Vesicle → Cell membrane, with SER also contributing lipids to Golgi.)
Q15. What would happen if gametes are formed by mitotic divisions?
Normally, gametes are formed by meiosis, which halves the chromosome number. If gametes were formed by mitosis instead:
- Each gamete would have the full (diploid) chromosome number instead of half (haploid).
- Upon fertilisation, the zygote would have double the normal chromosome number (tetraploid).
- With each successive generation, chromosome numbers would keep doubling.
- This would cause severe genetic abnormalities, developmental disorders, and would disrupt the normal chromosome balance essential for proper gene function.
- Genetic diversity (normally created by meiosis through crossing over and random segregation) would also be eliminated.
Q16. Farmer Deepa’s amla and lemon preservation:
(i) Which scientific concept has she applied?
She has applied the concept of osmosis and hypertonic solutions. Adding high concentrations of salt, sugar, or jaggery creates a hypertonic environment. By osmosis, water is drawn out of the cells of microorganisms (bacteria, fungi) that cause spoilage, dehydrating and killing them, thereby preserving the produce.(ii) How does high salt/sugar prevent microbial growth?
High concentrations of salt or sugar create a hypertonic external environment around microbial cells. Water moves out of the microbial cells by osmosis (plasmolysis), causing them to shrink and dehydrate. Without adequate water, enzymes of spoilage microorganisms cannot function, their metabolic processes stop, and they cannot grow or reproduce. This is called osmotic preservation.(iii) Suggest a healthy preservation recipe:
Raw Mango Preserve (Aam ki launji): Take raw mango pieces, add jaggery (natural sweetener, rich in iron) and a small amount of salt. Cook gently until jaggery dissolves and coats the mango. Store in a clean glass jar. The high sugar/jaggery concentration preserves the fruit while providing nutritional value. Alternatively, lemon in salt brine (lemon pieces immersed in concentrated salt water) preserves lemons for months and serves as a healthy condiment.(iv) Scientific values addressed:
- Observation and inquiry — noticing post-harvest loss and seeking solutions.
- Application of scientific knowledge — using osmosis practically.
- Sustainability — reducing food waste and environmental impact.
- Economic thinking — converting waste into value-added products.
- Traditional knowledge integration — combining indigenous methods with scientific understanding.
- Food security — ensuring produce reaches consumers rather than being wasted.
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Chapter 2: Cell 🔬Class-9th
Chapter 2: Cell – The Building Block of Life | Complete Master Notes © ABHISHEK.io.inChapter 2: Cell 🔬
The Building Block of Life – Master Academic Notes1. The Origin of Life & Introduction
It is widely accepted amongst the scientific community that life originated in water. Some researchers believe it began in small water pools with changing environmental conditions rather than vast oceans.
- Puga Valley, Ladakh: The hot springs here maintain near-boiling temperatures even in a cold climate, mimicking the early Earth (about 3.5 billion years ago).
- Thermophiles: Heat-loving, mostly unicellular bacteria found in these hot springs.
- Birbal Sahni Institute of Palaeosciences (Lucknow): Scientists studied these springs and found rapid calcium carbonate deposition. These deposits likely protected early organic molecules from harmful radiation, aiding the formation of the first protective membrane (the barrier defining a cell).
Hierarchical Organisation: Cells → Tissues → Organs → Organ Systems (e.g., nasal pores, cavity, trachea, and lungs form the respiratory system). The cell remains the fundamental unit of structure and function.
2. How to Study Cells? (Microscopy) 🔍
The limit of resolution of the human eye is 0.1 mm (when viewed from the near point of 25 cm). Objects closer or smaller appear as a single point. To study cells, microscopes are essential:
Types of Microscopes
1. Light Microscope: Uses visible light and a combination of lenses (objective and eyepiece). Magnification is the product of both lenses (e.g., 10X eyepiece × 10X objective = 100X total magnification). It improves resolution, contrast, and magnification.
2. Electron Microscope: Uses a powerful beam of electrons instead of light to produce highly magnified images, revealing fine details at the nanometre scale (1 nm = one-billionth of a metre).
🧪 Activity 2.1: Estimating the Size of a Cell
Procedure: Focus a transparent millimetre ruler under a light microscope. Measure the diameter of the circular field of view in mm and convert to micrometres (1 mm = 1000 µm). Replace the ruler with an onion peel slide. Count the number of cells across the diameter.
Calculation Formula:
Size of one cell =Diameter of visible field (in µm) Number of cells along the diameterExample: If the diameter is 5000 µm and you see 25 cells…
Size = 5000 / 25 = 200 µm per cell!👨🔬 Historical Milestone
Robert Hooke (1665) observed a thin slice of cork under a self-designed microscope (200-300X magnification). He saw box-like compartments and coined the term “cells”.3. Structure of a Cell: The Boundary
a. Cell Membrane (Plasma Membrane)
The universal, extremely thin (7 to 10 nm thick) boundary that protects cellular contents and defines the cell’s individuality.
- It is selectively permeable: allows some substances to pass while blocking others.
- Fluid-Mosaic Model: Explains its structure. It consists of a lipid bilayer (fats with water-attracting heads facing outwards and water-repelling tails inwards) with embedded proteins.
- It is “fluid” because molecules can move sideways, flip, and rotate. The proteins act as gatekeepers facilitating the passage of specific substances.
Diffusion vs. Osmosis
Diffusion: The net movement of particles from a region of higher concentration to lower concentration (concentration gradient). *E.g., O₂ and CO₂ exchange in alveolar cells.*
Osmosis: The diffusion of water across a selectively permeable membrane from a dilute solution (more water, less solute) to a concentrated solution (less water, more solute).
Extracellular Solution Type Condition Result on Cell Isotonic Outside concentration = Inside concentration No net movement. Cell stays the same. Hypotonic Outside is dilute (less solute, more water) Water enters cell. Cell swells. Hypertonic Outside is concentrated (more solute, less water) Water leaves cell. Cell shrinks. 🧪 Activity 2.2: Potato Osmometer
Two roughly equal potato pieces are weighed. Piece A is placed in plain water (Hypotonic); Piece B is placed in a 20% salt/sugar solution (Hypertonic). After an hour, Piece A swells (gains weight due to endosmosis), while Piece B shrinks (loses weight due to exosmosis).
b. Cell Wall (Outer Covering)
Plants, fungi, and bacteria possess an additional covering outside the cell membrane called the cell wall. Plants require this rigid structure to withstand environmental stresses (wind, rain) since they are immotile.
- In plants, it is primarily composed of Cellulose (a carbohydrate of linked glucose units that acts as roughage in human digestion).
- It helps leaves/flowers remain firm, maintains shape, and keeps plants upright.
- Unlike the membrane, the cell wall is permeable, allowing water and dissolved minerals to pass through.
🧪 Activity 2.3: Onion/Rhoeo vs. Human Cheek Cells
Observations: Onion peel or Rhoeo (Cradle lily) leaf cells are box-shaped and regularly arranged. Human cheek cells are irregularly arranged because animal cells lack a rigid cell wall. When 20% sugar solution is added to Rhoeo cells, the inner contents shrink away from the rigid cell wall (plasmolysis), but the overall boundary size remains the same.
4. Prokaryotic vs. Eukaryotic Cells 🦠
All cells possess a plasma membrane, cytoplasm (semi-fluid, jelly-like substance), and genetic material. Based on nuclear organisation, cells are classified as:
Characteristics Prokaryotic Cell (e.g., Bacteria) Eukaryotic Cell (e.g., Plants, Animals) Nucleus Primitive. Genetic material (single circular DNA) lies in an undefined region called the Nucleoid. True, well-defined nucleus enclosed by a double nuclear membrane. Size Typically 1 to 10 µm. Typically 10 to 100 µm. Organelles Lacks membrane-bound organelles. Cellular activities occur directly in cytoplasm. Contains specialised membrane-bound organelles (Mitochondria, ER, etc.). Organism Type Usually unicellular. Can be unicellular or multicellular. 🦠 Acellular Infectious Agents (Exceptions)
Viruses: Genetic material enclosed in a protein coat.
Viroids: Infectious RNA lacking a protein coat.
Prions: Infectious, misfolded proteins lacking genetic material.5. The Cell Interior: Organelles ⚙️
Eukaryotic cells are like tiny living factories. They use a network of fine fibres called the Cytoskeleton for structural support, shape maintenance, internal transport, and movement. Cells may also contain Cell Inclusions (stored inactive materials like starch, calcium oxalate, or silica crystals in plants).
🧠 1. Nucleus: House of Coded Instructions
Surrounded by a double-layered nuclear membrane with pores to allow material transfer to the cytoplasm. It contains a dense round body, the Nucleolus, which is the site of ribosomal subunit synthesis.
- Contains DNA (Deoxyribonucleic acid) which holds genetic information. Functional segments of DNA are called genes.
- In a non-dividing cell, DNA is an entangled mass called Chromatin.
- When dividing, chromatin organises into rod-shaped Chromosomes (composed of DNA and specific proteins).
Threads of Curiosity: Mature Red Blood Cells (RBCs) in humans are enucleate (lack a nucleus). This provides more space for haemoglobin to transport oxygen. Because they lack a nucleus, they cannot repair or divide, giving them a short lifespan of about 120 days.🏭 2. Endoplasmic Reticulum (ER) & 🔵 3. Ribosomes
Ribosomes are tiny structures (free in cytoplasm or attached to ER) responsible for protein synthesis.
The Endoplasmic Reticulum is a large continuous network of tubes connected to the outer nuclear envelope. It transports and synthesises materials.
- Rough ER (RER): Appears rough under an electron microscope due to attached ribosomes. Synthesises and secretes proteins (e.g., in pancreatic gland cells).
- Smooth ER (SER): Lacks ribosomes. Involved in the synthesis and storage of fats (lipids) and certain hormones.
📦 4. Golgi Apparatus
Observed first by Camillo Golgi (1898) in the nerve cells of a barn owl using special staining techniques. It consists of stacks of flattened, sac-like structures. It acts as the cell’s post office: it modifies, sorts, and packages proteins and lipids into vesicles for transport, secretion, or lysosome formation.
🗑️ 5. Lysosomes: The Clean-up System
Single membrane-bound sacs filled with powerful digestive enzymes. They break down unwanted proteins, carbohydrates, fats, worn-out organelles, and damaged parts, keeping the cell clean.
*Fun Fact: Human sperm cells contain lysosomal enzymes to break down the outer layer of the egg, allowing fertilisation!⚡ 6. Mitochondria: Powerhouse of the Cell
Responsible for energy supply via cellular respiration (breaking down glucose to release energy). The energy is stored as ATP (Adenosine Triphosphate), the energy currency of the cell.
- Surrounded by two membranes. The outer is smooth and porous.
- The inner membrane is folded into finger-like projections called Cristae, which drastically increase the surface area for energy-producing chemical reactions.
- Unique feature: They have their own DNA and ribosomes!
🌿 7. Plastids (Only in Plant Cells)
Used for food synthesis and storage. Like mitochondria, plastids possess their own DNA and ribosomes, suggesting a shared evolutionary history with bacteria.
- Chloroplasts: Double-membrane bound. Contain a semi-fluid stroma and disc-shaped structures bearing green chlorophyll. They absorb light energy for photosynthesis. Sugars synthesised are stored in the stroma as starch granules.
- Chromoplasts: Contain pigments (yellow, orange, red) providing bright colours to flower petals and fruits to attract pollinators and seed-dispersing animals.
- Leucoplasts: Colourless plastids that store food materials like starch, oils, or proteins (e.g., found in potato and Colocasia/taro).
💧 8. Vacuoles: Storage and Support
In mature plant cells, there is usually one large central vacuole surrounded by a single selectively permeable membrane. It is filled with a watery fluid called cell sap.
- Stores water, minerals, sugars, and waste.
- By storing large amounts of water, it maintains internal pressure, keeping the plant cell firm (turgid). Loss of water causes the plant to wilt.
- In animal cells, vacuoles are smaller and used only for temporary storage.
🧬 Synthetic Biology (J. Craig Venter, 2010)
His team sequenced the DNA of a bacterium (*Mycoplasma mycoides*). They chemically synthesised an exact copy of this DNA in a lab and inserted it into a closely related cell (whose own DNA was removed, keeping the cytoplasm and membrane intact). The cell grew and divided following instructions from the synthetic DNA! This proved that DNA masterminds the structure and activities of the cell.6. How do Normal Cells Grow and Divide? 🧬
Every day, an estimated hundreds of billions of cells in our body are replaced (almost 1% of total cells). Cells cannot grow indefinitely in size; growth occurs through cell division. In eukaryotes, this is an orderly process called the Cell Cycle.
🧪 Activity 2.5: Onion Root Tip Experiment (Studying Cell Division)
1. Grow an onion bulb over a water jar.
2. Cut the freshly grown root tips (2-3 cm) and place them in freshly prepared aceto-alcohol (glacial acetic acid : ethanol :: 1:3) for 24 hours. Transfer to 70% ethanol for preservation.
3. Soften the tissue with dilute Hydrochloric acid (HCl) for 10-15 mins.
4. Add 2-3 drops of aceto-carmine stain, warm gently over a spirit lamp.
5. Squash the coverslip to spread the cells and observe. The cells of a growing tip divide continuously, displaying various structural stages of cell division.A. Mitosis
Purpose: Normal growth, repair of damaged tissues, maintenance, and asexual reproduction.
- One parent cell divides once to form two genetically identical daughter cells.
- Each new cell gets the same DNA and the same number of chromosomes as the parent cell.
B. Meiosis
Purpose: Occurs only in reproductive organs to produce gametes for sexual reproduction (creates genetic diversity!).
- In animals: occurs in male testes (produces sperm) and female ovaries (produces eggs).
- In plants: occurs in anthers (pollen/sperm) and ovaries (eggs).
- It is a two-step division resulting in four daughter cells.
- The number of chromosomes in each gamete is reduced to half. When gametes fuse during fertilisation, the original number is restored.
👨🔬 Meet a Scientist
Arun Kumar Sharma was a famous Indian botanist renowned for his work on chromosomes, plant taxonomy, and evolution. He invented useful lab methods to study plant chromosomes and received the Shanti Swarup Bhatnagar award and Padma Bhushan.7. Cell Theory & Regulatory Mechanisms ⚖️
The Classical Cell Theory
Formulated by combining the findings of three prominent scientists:
- Matthias Schleiden (1838, Botanist): All plants are made of cells.
- Theodor Schwann (1839, Zoologist): All animals are made of cells.
- Rudolf Virchow (1855): Proposed that all cells arise from pre-existing cells.
Totipotency (Gottlieb Haberlandt, 1902): Proposed that any living plant cell (even a mature one) can develop into a complete plant if provided suitable nutrients and conditions. This is the foundation of modern Plant Tissue Culture Technology.
Do cells grow and reproduce forever?
No. Cells grow in a controlled way, carry out functions, and die when no longer needed. They have a definite lifespan.
- Contact Inhibition: In many animal cells, cell division stops when they physically touch neighbouring cells. Plant cells grow differently due to rigid walls and do not show contact inhibition.
- Tumours & Cancer: When normal regulatory systems fail (often due to errors in mitosis), cells lose contact inhibition and divide uncontrollably, forming tumours (benign or malignant). Cancerous cells can invade nearby tissues and spread.
- Programmed Cell Death (PCD): A genetically regulated, highly organised process of selective cell destruction. Essential for quality control, immune function, and normal development (e.g., PCD eliminates cells between digits during embryonic development to prevent webbed hands).
- Errors in Meiosis: Faulty meiosis can lead to abnormal chromosome numbers, causing genetic disorders, distinctive physical features, early pregnancy loss, or reduced fertility.
🔬 Bridging Science and Society: Cell Culture
Scientists have developed methods to grow plant and animal cells outside the body in special conditions, known as cell culture. Cells are placed in a nutrient-rich medium maintaining specific temperature, pH, moisture, and sterile conditions. It is crucial for producing biochemicals, food, medicines, and vaccines.
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Applications to Principal Via Class Teacher
NRK Public School, Barkurwa, Sonwal
🤒 APPLICATION 1 — Absent Yesterday Due to Fever (Back Today)
Date: 2 May 2025 To, The Principal, NRK Public School Barkurwa, Sonwal Via: The Class Teacher, Class X-A Subject: Application for Rejoining Classes After Absence Due to Fever Respected Madam, I am Ananya Sharma, a student of Class X-A, Roll No. 18. I wish to inform you that I was absent on 1st May 2025 due to sudden high fever and was advised rest by our family doctor. I have recovered fully and have come to school today. I request you to kindly permit me to attend classes from today onwards. I will complete all missed work at the earliest. Yours obediently, (Signature) Ananya Sharma Class X-A | Roll No. 18
📅 APPLICATION 2 — Leave for Upcoming Days Due to Fever
Date: 4 May 2025 To, The Principal, NRK Public School Barkurwa, Sonwal Via: The Class Teacher, Class X-B Subject: Application for Medical Leave from 5th May to 7th May 2025 Respected Sir, I am Rohan Verma, a student of Class X-B, Roll No. 07. I am suffering from viral fever and our family doctor has advised me complete bed rest for three days. I am therefore unable to attend school from 5th May to 7th May 2025. I request you to kindly grant me leave for the said period. I will complete all missed classwork immediately upon my return. Yours obediently, (Signature) Rohan Verma Class X-B | Roll No. 07
💍 APPLICATION 3 — Marriage in the Family
Date: 2 May 2025 To, The Principal, NRK Public School Barkurwa, Sonwal Via: The Class Teacher, Class X-C Subject: Application for Leave to Attend a Family Marriage Ceremony Respected Madam, I am Divya Rajput, a student of Class X-C, Roll No. 22. I wish to inform you that my cousin's marriage ceremony is scheduled on 8th May 2025, and the related family functions begin from 7th May onwards. My presence is essential as I am closely related to the family. I request you to kindly grant me leave from 7th May to 9th May 2025. I assure you I will cover all missed lessons upon returning to school. Yours obediently, (Signature) Divya Rajput Class X-C | Roll No. 22
🪔 APPLICATION 4 — Religious Ritual / Puja at Home
Date: 2 May 2025 To, The Principal, NRK Public School Barkurwa, Sonwal Via: The Class Teacher, Class X-A Subject: Application for Leave to Attend Religious Ceremony at Home Respected Sir, I am Arjun Tiwari, a student of Class X-A, Roll No. 09. I wish to inform you that a religious ceremony (Satyanarayan Puja) has been organised at our home on 5th May 2025. It is a significant family ritual and my presence is required throughout the day to assist my parents. I request you to kindly grant me leave for one day on 5th May 2025. I will ensure no academic work is left incomplete. Yours obediently, (Signature) Arjun Tiwari Class X-A | Roll No. 09
✝️ APPLICATION 5 — Death / Bereavement in Family
Date: 2 May 2025 To, The Principal, NRK Public School Barkurwa, Sonwal Via: The Class Teacher, Class X-B Subject: Application for Leave Due to Bereavement in Family Respected Madam, I am Priya Mehta, a student of Class X-B, Roll No. 15. It is with deep sorrow that I inform you that my grandfather passed away on 30th April 2025. The last rites and post-funeral rituals are to be observed over the next few days and my presence at home is necessary to support my family during this difficult time. I request you to kindly grant me leave from 1st May to 4th May 2025. I humbly seek your compassion and understanding. Yours obediently, (Signature) Priya Mehta Class X-B | Roll No. 15
🏥 APPLICATION 6 — Parent’s Hospitalisation
Date: 2 May 2025 To, The Principal, NRK Public School Barkurwa, Sonwal Via: The Class Teacher, Class X-C Subject: Application for Leave Due to Parent's Hospitalisation Respected Sir, I am Harpreet Singh, a student of Class X-C, Roll No. 14. I wish to inform you that my mother has been admitted to the hospital for a surgical operation scheduled on 5th May 2025. As my father is out of town on work, I am the only family member available to be present at the hospital and look after her. I request you to kindly grant me leave from 5th May to 7th May 2025. I will make up for all missed work as soon as I return. Yours obediently, (Signature) Harpreet Singh Class X-C | Roll No. 14
🎭 APPLICATION 7 — Inter-School Competition
Date: 12 May 2025 To, The Principal, NRK Public School Barkurwa, Sonwal Via: The Class Teacher, Class X-A Subject: Application for Permission to Participate in Inter-School Debate Competition Respected Madam, I am Varun Khanna, a student of Class X-A, Roll No. 11. I have been selected to represent our school in the Inter-School Debate Competition being held at a nearby school on 14th May 2025. I will need to leave school by 11:00 AM on that day. I request you to kindly grant me permission and excuse my absence from afternoon classes. I assure you I will bring credit to our school. Yours obediently, (Signature) Varun Khanna Class X-A | Roll No. 11
🏃 APPLICATION 8 — State-Level Sports Championship
Date: 13 May 2025 To, The Principal, NRK Public School Barkurwa, Sonwal Via: The Class Teacher, Class X-A Subject: Application for Leave to Participate in State-Level Athletics Championship Respected Sir, I am Rahul Kumar, a student of Class X-A, Roll No. 05. I am honoured to inform you that I have been selected to represent our district in the State-Level Athletics Championship to be held from 15th to 17th May 2025. I request you to kindly grant me leave for three days for the above purpose. I assure you I will put in my best efforts to bring honour to NRK Public School. Yours obediently, (Signature) Rahul Kumar Class X-A | Roll No. 05
🧳 APPLICATION 9 — Family Pilgrimage / Outstation Trip
Date: 2 May 2025 To, The Principal, NRK Public School Barkurwa, Sonwal Via: The Class Teacher, Class X-B Subject: Application for Leave for a Family Pilgrimage Respected Madam, I am Sneha Sharma, a student of Class X-B, Roll No. 27. My family has planned a pilgrimage to Vaishno Devi from 10th May to 13th May 2025. This trip holds deep religious significance for our family and has been planned well in advance. My parents wish me to accompany them. I request you to kindly grant me leave for four days from 10th May to 13th May 2025. I will ensure that all pending work is completed promptly upon my return. Yours obediently, (Signature) Sneha Sharma Class X-B | Roll No. 27
🎊 APPLICATION 10 — Thread Ceremony (Mundan / Janeu)
Date: 2 May 2025 To, The Principal, NRK Public School Barkurwa, Sonwal Via: The Class Teacher, Class X-A Subject: Application for Leave to Attend Younger Brother's Thread Ceremony Respected Sir, I am Kartik Pandey, a student of Class X-A, Roll No. 33. I wish to inform you that my younger brother's sacred thread ceremony (Yagyopavit Sanskar) is being performed on 6th May 2025 at our residence. This is an important religious occasion for our family and my presence is required for the entire day. I kindly request you to grant me leave for one day on 6th May 2025. I will complete all academic work without any delay after returning. Yours obediently, (Signature) Kartik Pandey Class X-A | Roll No. 33
💰 APPLICATION 11 — Fee Concession Request
Date: 2 May 2025 To, The Principal, NRK Public School Barkurwa, Sonwal Via: The Class Teacher, Class X-B Subject: Application for Fee Concession Due to Financial Hardship Respected Madam, I am Pooja Tiwari, a student of Class X-B, Roll No. 31. My father, who is the sole earning member of our family, lost his job last month. Due to this financial difficulty, my family is currently unable to pay the full school fees for this quarter. I am a sincere and regular student and do not wish my education to be disrupted. I humbly request you to kindly consider granting me a temporary fee concession until our situation improves. Yours obediently, (Signature) Pooja Tiwari Class X-B | Roll No. 31
🚌 APPLICATION 12 — Complaint About Late School Bus
Date: 2 May 2025 To, The Principal, NRK Public School Barkurwa, Sonwal Via: The Class Teacher, Class X-B Subject: Complaint Regarding Late Arrival of School Bus on Route No. 7 Respected Sir, I am Manpreet Kaur, a student of Class X-B, Roll No. 20, writing on behalf of students travelling by School Bus No. 7. For the past two weeks, our bus has been arriving 30 to 40 minutes late, causing us to miss the first period regularly and receive late marks in attendance. I request you to kindly look into this matter and direct the transport department to ensure the bus runs on time. We are always present at the stop punctually. Yours obediently, (Signature) Manpreet Kaur Class X-B | Roll No. 20
🔑 APPLICATION 13 — Lost School Identity Card
Date: 2 May 2025 To, The Principal, NRK Public School Barkurwa, Sonwal Via: The Class Teacher, Class X-C Subject: Application for Issue of Duplicate School Identity Card Respected Madam, I am Nisha Choudhary, a student of Class X-C, Roll No. 19. I regret to inform you that I lost my school identity card during the school picnic on 30th April 2025. I searched thoroughly but was unable to find it. I request you to kindly arrange for a duplicate identity card at the earliest. I will pay the applicable charges as per school rules and will be more careful in future. Yours obediently, (Signature) Nisha Choudhary Class X-C | Roll No. 19
📊 All 13 Applications — Quick Reference
# Scenario Days 1 Fever — absent yesterday, back today Rejoining 2 Fever — upcoming leave 3 days 3 Cousin’s marriage ceremony 3 days 4 Religious puja / ritual at home 1 day 5 Death / bereavement in family 4 days 6 Parent’s hospitalisation 3 days 7 Inter-school competition Half day 8 State-level sports championship 3 days 9 Family pilgrimage / outstation 4 days 10 Thread ceremony (Mundan/Janeu) 1 day 11 Fee concession request No leave 12 Late bus complaint No leave 13 Lost identity card No leave All applications addressed to NRK Public School, Barkurwa, Sonwal ✅
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5 Formal + 5 Informal Letter Examples — Class 10 CBSE PYQs
5 Formal + 5 Informal Letter Examples — Class 10 CBSE PYQs
✉️ FORMAL LETTERS
📄 Example 1 — Letter to the Editor (PYQ: CBSE 2020)
Q. Write a letter to the Editor of a national daily about the increasing menace of noise pollution in your city.
12, Rajpur Road Dehradun, Uttarakhand – 248001 Date: 15 March 2024 The Editor The Hindustan Times New Delhi – 110001 Subject: Growing Menace of Noise Pollution in the City Sir, Through the columns of your esteemed newspaper, I wish to draw the attention of the concerned authorities towards the alarming rise in noise pollution in our city. Loudspeakers blaring at odd hours, incessant honking on roads, and the indiscriminate use of firecrackers have made life extremely difficult for residents. The elderly and students preparing for examinations are the worst affected. Studies have shown that prolonged exposure to such noise leads to stress, hearing impairment, and sleep disorders. I earnestly request the authorities to strictly enforce noise pollution norms, limit the use of loudspeakers after 10 PM, and penalise traffic violators. I hope your newspaper will highlight this issue so that prompt action is taken. Yours faithfully, (Signature) Amit Sharma
📄 Example 2 — Letter to the Principal (PYQ: CBSE 2019)
Q. Write a letter to your Principal requesting permission to organise a cleanliness drive in and around the school.
45, Model Town Ludhiana, Punjab – 141002 Date: 10 April 2024 The Principal DAV Public School Ludhiana, Punjab – 141001 Subject: Request for Permission to Organise a Cleanliness Drive Madam, I am Priya Mehta, a student of Class X-B of your school. I am writing this letter to seek your kind permission to organise a cleanliness drive in and around our school premises. As part of the Swachh Bharat Mission, our class wishes to take initiative by cleaning the school garden, corridors, and the nearby streets on the coming Saturday. We plan to involve nearly 40 students under the supervision of our class teacher. All necessary equipment such as gloves, brooms, and dustbins will be arranged by us. I humbly request you to grant us permission for this activity. Your support and encouragement will motivate us greatly. Yours faithfully, (Signature) Priya Mehta Class X-B, Roll No. 15
📄 Example 3 — Complaint Letter (PYQ: CBSE 2022)
Q. Write a letter to the Municipal Commissioner complaining about the poor condition of roads in your locality.
78, Shastri Nagar Jaipur, Rajasthan – 302016 Date: 5 May 2024 The Municipal Commissioner Jaipur Municipal Corporation Jaipur, Rajasthan – 302001 Subject: Poor Condition of Roads in Shastri Nagar Sir, I am a resident of Shastri Nagar and am writing to bring to your notice the deplorable condition of roads in our locality, which has been causing great inconvenience to the residents. The roads are riddled with deep potholes, and the situation worsens during the monsoon season when they get waterlogged. Two-wheeler riders have suffered injuries due to these potholes. Despite repeated complaints to the ward office, no corrective action has been taken for the past six months. I sincerely urge you to direct the concerned department to repair these roads on a priority basis. Prompt action on your part will be greatly appreciated by all the residents of our area. Yours faithfully, (Signature) Rakesh Gupta
📄 Example 4 — Letter Applying for a Job (PYQ: CBSE 2023)
Q. Write a letter to the Manager of a publishing house applying for the post of a part-time proofreader advertised in a newspaper.
23, Civil Lines Allahabad, Uttar Pradesh – 211001 Date: 20 June 2024 The Manager Oxford Publications Pvt. Ltd. Hazratganj, Lucknow – 226001 Subject: Application for the Post of Part-Time Proofreader Sir/Madam, With reference to your advertisement published in The Times of India dated 18 June 2024, I wish to apply for the post of part-time Proofreader in your esteemed organisation. I am a student of Class XII with English as my main subject. I have a keen interest in reading and possess a strong command over grammar, punctuation, and vocabulary. I have been editing my school magazine for the past two years, which has given me practical proofreading experience. I am hardworking, detail- oriented, and available on all weekends and after school hours. I assure you that I shall perform my duties with sincerity and dedication. I request you to give me an opportunity to prove my capabilities. My resume is enclosed herewith for your reference. Yours faithfully, (Signature) Sneha Joshi
📄 Example 5 — Letter to the Editor on Environment (PYQ: CBSE 2021)
Q. Write a letter to the Editor about the need to conserve water in your city.
9, Green Park Colony Bhopal, Madhya Pradesh – 462001 Date: 22 July 2024 The Editor The Times of India Bhopal, Madhya Pradesh – 462001 Subject: Urgent Need to Conserve Water in the City Sir, I am writing to express my deep concern over the reckless wastage of water in our city, which is fast approaching a water crisis. Taps left running, leaking pipelines left unrepaired for months, and water wasted during festivals and weddings are a common sight. Meanwhile, many areas of our city face severe water shortage for hours every day. The groundwater level has fallen drastically over the past decade. This situation demands immediate attention. I urge the authorities to launch public awareness campaigns, fix leaking pipelines on a war footing, and impose penalties on those who waste water. Citizens too must take individual responsibility. I hope your newspaper will help awaken public conscience on this critical issue. Yours faithfully, (Signature) Kavya Singh—
💌 INFORMAL LETTERS
📝 Example 1 — Letter to Friend About Summer Vacation (PYQ: CBSE 2020)
Q. Write a letter to your friend describing how you spent your summer vacation.
34, Vasant Vihar New Delhi – 110057 Date: 15 June 2024 Dear Rohan, Hope you are doing well! I had been meaning to write to you ever since my summer vacation began and now that I finally have some free time, here I am! This year, my family and I visited Manali for ten wonderful days. The snow-capped mountains and lush valleys were simply breathtaking. We went on a trek to Solang Valley, and I even tried skiing for the first time — I fell at least a dozen times but it was the most fun I have had in years! We also visited Hadimba Temple and enjoyed the local cuisine. In the evenings, we would sit by the Beas river and just watch the sun go down — something I will never forget. I also spent the last week at home reading novels and practising guitar. All in all, it was the most refreshing vacation ever. I cannot wait to hear about your vacation too — do write back soon! Yours lovingly, Arjun
📝 Example 2 — Letter to Friend Congratulating on Achievement (PYQ: CBSE 2019)
Q. Write a letter to your friend congratulating him/her on winning the district-level science quiz competition.
56, Anand Nagar Pune, Maharashtra – 411009 Date: 3 March 2024 Dear Meera, Congratulations! I was absolutely thrilled when I heard the news that you won the district-level science quiz. Honestly, I always knew you would do it someday! Your dedication to studies and your love for science has always inspired me. I remember how you would spend hours reading science journals and solving tricky questions — all that hard work has truly paid off. Your school must be so proud of you, and rightly so! I am sure this is just the beginning of many more achievements to come. Please do tell me all the details of the competition when we meet. Also, your parents must be over the moon! Celebrate well, you deserve it. I hope to match your dedication in my own studies as well. Once again, heartiest congratulations, Meera! Yours affectionately, Nandini
📝 Example 3 — Letter Inviting Friend to Birthday Party (PYQ: CBSE 2022)
Q. Write a letter to your friend inviting him/her to your birthday party.
12, Tagore Lane Kolkata, West Bengal – 700006 Date: 25 November 2024 Dear Aditya, How are you? It feels like ages since we last met! I have some exciting news — my birthday is on 5 December and my parents have agreed to throw a small party at our home. You simply have to come! The party will begin at 6 PM and we plan to have games, music, and a delicious dinner. Mum is making her famous biryani, which I know you love! A few of our old school friends will also be there, so it will be a wonderful reunion. Please do bring an overnight bag if you can — it would be great if you could stay over. I really hope nothing comes in the way and you can make it. Your presence would make the evening truly special for me. Let me know as soon as possible so I can confirm the arrangements. Waiting eagerly to see you! Yours lovingly, Souvik
📝 Example 4 — Letter to Elder Sister Seeking Career Advice (PYQ: CBSE 2023)
Q. Write a letter to your elder sister who is in college, asking for advice on choosing a career after Class 10.
8, Lajpat Nagar Amritsar, Punjab – 143001 Date: 18 August 2024 Dear Didi, I hope you are doing well and that college life is treating you kindly. I am writing to you because I am in a bit of a dilemma and there is no one whose advice I trust more than yours. My Class 10 board exams are approaching, and everyone around me keeps asking what stream I want to take up — Science, Commerce, or Arts. To be honest, I am quite confused. I enjoy both Mathematics and History equally and do not know which direction to go in. A few of my friends are choosing Science simply because of peer pressure, but I do not want to make such an important decision without thinking it through. Could you please share how you made your decision? Did you face a similar confusion? I would love any guidance you can offer. Maybe you could also suggest some resources or websites where I can learn more about different career paths. I look forward to your reply, Didi. Give my love to everyone there. Yours lovingly, Simran
📝 Example 5 — Letter to Friend Describing a Book (PYQ: CBSE 2021)
Q. Write a letter to your friend recommending a book you recently read and explaining why he/she should read it.
67, Rajendra Nagar Hyderabad, Telangana – 500030 Date: 9 September 2024 Dear Karthik, How are you doing? I hope your preparations for the upcoming exams are going well! I am writing with great excitement because I just finished reading a book that I simply must tell you about. The book is "The Alchemist" by Paulo Coelho. I picked it up on a whim from the school library and I finished it in just two days! The story follows a young shepherd named Santiago who travels from Spain to Egypt in search of treasure. But the real treasure, as you will discover, is the wisdom hidden in every page. The book beautifully talks about following your dreams, listening to your heart, and how the universe conspires to help you when you truly want something. Every chapter left me thinking for hours! I feel this book will resonate deeply with you, especially at this stage of our lives where we are figuring out our futures. Please do get a copy and read it — we can then discuss it when we meet next. I promise you will not be disappointed! Write back soon. Yours affectionately, Vikram
🏆 Quick Exam Tips
Tip Why It Matters Always write the date in full (15 March 2024) Avoids mark deduction Keep each paragraph focused on one idea Improves expression marks Never exceed 150–200 words Saves time, stays on point Underline the Subject line in formal letters Neat presentation Revise for spelling & grammar in last 2 mins Easy marks to protect -
Chapter 1: Complete Solutions
Exercise Set 1.1
(i) From the figure, $D_1$ lies on the x-axis at $x = 8$.
Distance from left wall (y-axis) = 8 ft
Distance from x-axis = 0 ft
(ii)
$$D_1 = (8, 0)$$
(iii)
$$\text{Width of door} = 11.5 – 8 = 3.5 \text{ ft}$$
A standard room door is about 3 ft wide, so 3.5 ft is comfortable. A wheelchair user can enter easily.
(iv)
$$\text{Bathroom door width} = 4 – 1.5 = 2.5 \text{ ft}$$
Since $2.5 < 3.5$, the bathroom door is narrower than the room door.
Exercise Set 1.2
Question 1 — Study table with feet at $(8,9)$, $(11,9)$, $(11,7)$
(i) The table is a rectangle. The fourth foot completes the rectangle:
$$\text{Fourth foot} = (8, 7)$$
(ii) The point $(8,7)$ is in the bedroom, clear of the wardrobe. It is a reasonable spot.
(iii)
$$\text{Width} = 11 – 8 = 3 \text{ ft}$$
$$\text{Length} = 9 – 7 = 2 \text{ ft}$$
Height cannot be found from a 2D floor map.
Question 2 — Bathroom door
The door is 2.5 ft wide. When it swings 90 degrees into the bedroom, the tip reaches up to $x = 2.5$. The wardrobe left edge is at $x = 3$. Since $2.5 < 3$, the door will not hit the wardrobe. If the door is made wider, a sliding door or outward opening door should be used.
Question 3 — Reiaan’s bathroom
(i) Four corners of the bathroom:
$$O = (0, 0), \quad F = (0, 10), \quad R = (-6, 10), \quad P = (-6, 0)$$
(ii) The showering area SHWR is a rectangle. Coordinates:
$$S = (-6, 6), \quad H = (-6, 9), \quad W = (-3, 9), \quad R = (-3, 6)$$
(iii) Washbasin $3 \times 2$ ft, one possible placement:
$$(-3, 8), \quad (-3, 10), \quad (0, 10), \quad (0, 8)$$
Toilet $2 \times 3$ ft, one possible placement:
$$(-6, 0), \quad (-6, 3), \quad (-4, 3), \quad (-4, 0)$$
Question 4 — Other rooms
(i) Dining room corners:
$$P(-6, 0), \quad A(12, 0), \quad (12, -15), \quad (-6, -15)$$
(ii) Centre of dining room:
$$x_c = \frac{-6 + 12}{2} = 3$$
$$y_c = \frac{0 + (-15)}{2} = -7.5$$
Dining table $5 \times 3$ ft centred at $(3, -7.5)$, feet at:
$$(0.5, -6), \quad (5.5, -6), \quad (5.5, -9), \quad (0.5, -9)$$
Section 1.4 — Distance Formula Worked Examples
For $A(3,4)$, $D(7,1)$, $M(9,6)$:
$$AD = \sqrt{(7-3)^2 + (1-4)^2} = \sqrt{16 + 9} = \sqrt{25} = 5 \text{ units}$$
$$DM = \sqrt{(9-7)^2 + (6-1)^2} = \sqrt{4 + 25} = \sqrt{29} \text{ units}$$
$$MA = \sqrt{(3-9)^2 + (4-6)^2} = \sqrt{36 + 4} = \sqrt{40} = 2\sqrt{10} \text{ units}$$
End of Chapter Exercises
Question 1
The axes intersect at the origin:
$$x\text{-coordinate} = 0, \quad y\text{-coordinate} = 0$$
Question 2
Point $H$ on the vertical line through $W(-5, y)$:
$$H = (-5, y) \text{ for any value of } y$$
If $y > 0$, H is in Quadrant II. If $y < 0$, H is in Quadrant III. If $y = 0$, H is on the x-axis.
Question 3
Points $R(3,0)$, $A(0,-2)$, $M(-5,-2)$, $P(-5,2)$
(i) Side $AM$ is horizontal. Side $MP$ is vertical. Therefore:
$$AM \perp MP$$
(ii) Side $AM$ from $(0,-2)$ to $(-5,-2)$ is parallel to the x-axis.
(iii) $M(-5,-2)$ and $P(-5,2)$ have the same x-coordinate and opposite y-values. They are mirror images in the x-axis.
Question 4
Triangle with $I(0,0)$, $N(5,0)$, $Z(5,-6)$:
$$IZ = \sqrt{(5-0)^2 + (-6-0)^2} = \sqrt{25 + 36} = \sqrt{61} \text{ units}$$
$$ZN = \sqrt{(5-5)^2 + (0+6)^2} = \sqrt{0 + 36} = 6 \text{ units}$$
$$IN = \sqrt{(5-0)^2 + (0-0)^2} = \sqrt{25} = 5 \text{ units}$$
Verification using Pythagoras:
$$IN^2 + ZN^2 = 25 + 36 = 61 = IZ^2$$
Question 5
Without negative numbers, only Quadrant I (where $x \geq 0$ and $y \geq 0$) can be used. Points in Quadrants II, III and IV cannot be located. So the system cannot locate all points on a 2D plane.
Question 6
Check if $M(-3,-4)$, $A(0,0)$, $G(6,8)$ are collinear by comparing slopes:
$$\text{Slope of } MA = \frac{0-(-4)}{0-(-3)} = \frac{4}{3}$$
$$\text{Slope of } AG = \frac{8-0}{6-0} = \frac{8}{6} = \frac{4}{3}$$
Both slopes are equal. The three points are collinear.
Question 7
Check if $R(-5,-1)$, $B(-2,-5)$, $C(4,-12)$ are collinear:
$$\text{Slope of } RB = \frac{-5-(-1)}{-2-(-5)} = \frac{-4}{3}$$
$$\text{Slope of } BC = \frac{-12-(-5)}{4-(-2)} = \frac{-7}{6}$$
$$\frac{-4}{3} \neq \frac{-7}{6}$$
The points are not collinear.
Question 8
(i) Right-angled isosceles triangle using $O(0,0)$, $A(4,0)$, $B(0,4)$:
$$OA = 4, \quad OB = 4, \quad AB = \sqrt{4^2 + 4^2} = 4\sqrt{2}$$
Right angle is at $O$ and $OA = OB$, so this is a right-angled isosceles triangle.
(ii) Using $O(0,0)$, $C(-3,-4)$ in Quadrant III, $D(3,-4)$ in Quadrant IV:
$$OC = \sqrt{9 + 16} = 5, \quad OD = \sqrt{9 + 16} = 5$$
Since $OC = OD$, triangle $OCD$ is isosceles.
Question 9 — Midpoint Table
For $S(-3,0)$, $M(0,0)$, $T(3,0)$:
$$\frac{-3+3}{2} = 0 \quad \text{and} \quad \frac{0+0}{2} = 0$$
M is the midpoint. Yes.
For $S(2,3)$, $M(3,4)$, $T(4,5)$:
$$\frac{2+4}{2} = 3 \quad \text{and} \quad \frac{3+5}{2} = 4$$
M is the midpoint. Yes.
For $S(0,0)$, $M(0,5)$, $T(0,-10)$:
$$\frac{0+(-10)}{2} = -5 \neq 5$$
M is not the midpoint. No.
For $S(-8,7)$, $M(0,-2)$, $T(6,-3)$:
$$\frac{-8+6}{2} = -1 \neq 0$$
M is not the midpoint. No.
The midpoint formula is:
$$M = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)$$
Question 10
$M(-7,1)$ is midpoint of $A(3,-4)$ and $B(x,y)$:
$$\frac{3 + x}{2} = -7 \implies 3 + x = -14 \implies x = -17$$
$$\frac{-4 + y}{2} = 1 \implies -4 + y = 2 \implies y = 6$$
$$B = (-17, 6)$$
Question 11
$A(4,7)$ and $B(16,-2)$. Point $P$ divides $AB$ in ratio $1:2$ from $A$:
$$P = \left(\frac{2 \times 4 + 1 \times 16}{3}, \frac{2 \times 7 + 1 \times (-2)}{3}\right) = \left(\frac{24}{3}, \frac{12}{3}\right) = (8, 4)$$
Point $Q$ divides $AB$ in ratio $2:1$ from $A$:
$$Q = \left(\frac{1 \times 4 + 2 \times 16}{3}, \frac{1 \times 7 + 2 \times (-2)}{3}\right) = \left(\frac{36}{3}, \frac{3}{3}\right) = (12, 1)$$
$$P = (8, 4), \quad Q = (12, 1)$$
Question 12
(i) Distance from origin to each point:
$$OA = \sqrt{1^2 + (-8)^2} = \sqrt{1 + 64} = \sqrt{65}$$
$$OB = \sqrt{(-4)^2 + 7^2} = \sqrt{16 + 49} = \sqrt{65}$$
$$OC = \sqrt{(-7)^2 + (-4)^2} = \sqrt{49 + 16} = \sqrt{65}$$
All three equal $\sqrt{65}$, so A, B, C lie on circle $K$ with centre $O$ and:
$$\text{Radius} = \sqrt{65} \approx 8.06 \text{ units}$$
(ii)
$$OD = \sqrt{(-5)^2 + 6^2} = \sqrt{25 + 36} = \sqrt{61}$$
Since $\sqrt{61} < \sqrt{65}$, point $D$ lies inside circle $K$.
$$OE = \sqrt{0^2 + 9^2} = 9$$
Since $9 > \sqrt{65} \approx 8.06$, point $E$ lies outside circle $K$.
Question 13
Midpoints $D(5,1)$, $E(6,5)$, $F(0,3)$ of sides $BC$, $CA$, $AB$:
$$A = E + F – D = (6+0-5, 5+3-1) = (1, 7)$$
$$B = D + F – E = (5+0-6, 1+3-5) = (-1, -1)$$
$$C = D + E – F = (5+6-0, 1+5-3) = (11, 3)$$
$$A = (1, 7), \quad B = (-1, -1), \quad C = (11, 3)$$
Question 14
(i) Draw a $10 \times 10$ grid with scale $1 \text{ cm} = 200 \text{ m}$. The two main roads are the axes. Streets are numbered 1 to 5 on each side in both directions.
(ii)
(a) Street intersection $(4,3)$ — exactly 1 such intersection.
(b) Street intersection $(3,4)$ — exactly 1 such intersection.
Note: $(4,3)$ and $(3,4)$ are different intersections, just as coordinates are ordered pairs.
Question 15
(i) Check Circle A, centre $A(100,150)$, radius $= 80$:
$$100 – 80 = 20 > 0, \quad 100 + 80 = 180 < 800$$
$$150 – 80 = 70 > 0, \quad 150 + 80 = 230 < 600$$
Circle A lies entirely inside the screen.
Check Circle B, centre $B(250,230)$, radius $= 100$:
$$250 – 100 = 150 > 0, \quad 250 + 100 = 350 < 800$$
$$230 – 100 = 130 > 0, \quad 230 + 100 = 330 < 600$$
Circle B lies entirely inside the screen. Neither circle lies outside.
(ii) Distance between centres:
$$AB = \sqrt{(250-100)^2 + (230-150)^2} = \sqrt{150^2 + 80^2} = \sqrt{22500 + 6400} = \sqrt{28900} = 170 \text{ px}$$
Sum of radii $= 80 + 100 = 180$ px
Difference of radii $= 100 – 80 = 20$ px
Since $20 < 170 < 180$, that is $|r_1 – r_2| < AB < r_1 + r_2$, the two circles intersect at two points.
Question 16
Points $A(2,1)$, $B(-1,2)$, $C(-2,-1)$, $D(1,-2)$
Step 1 — Side lengths:
$$AB = \sqrt{(-1-2)^2 + (2-1)^2} = \sqrt{9+1} = \sqrt{10}$$
$$BC = \sqrt{(-2+1)^2 + (-1-2)^2} = \sqrt{1+9} = \sqrt{10}$$
$$CD = \sqrt{(1+2)^2 + (-2+1)^2} = \sqrt{9+1} = \sqrt{10}$$
$$DA = \sqrt{(2-1)^2 + (1+2)^2} = \sqrt{1+9} = \sqrt{10}$$
All four sides are equal.
Step 2 — Diagonals:
$$AC = \sqrt{(-2-2)^2 + (-1-1)^2} = \sqrt{16+4} = \sqrt{20}$$
$$BD = \sqrt{(1+1)^2 + (-2-2)^2} = \sqrt{4+16} = \sqrt{20}$$
Both diagonals are equal.
Step 3 — Midpoints of diagonals:
$$\text{Midpoint of } AC = \left(\frac{2+(-2)}{2}, \frac{1+(-1)}{2}\right) = (0, 0)$$
$$\text{Midpoint of } BD = \left(\frac{-1+1}{2}, \frac{2+(-2)}{2}\right) = (0, 0)$$
The diagonals bisect each other at the origin. Since all sides are equal, diagonals are equal, and they bisect each other, ABCD is a square.
$$\text{Area} = (\sqrt{10})^2 = 10 \text{ square units}$$
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Chapter 5: Exploring Mixtures and Their Separation
Class 9 Science Chapter 5 – Exploring Mixtures and Their Separation Chapter 5: Exploring Mixtures and Their Separation
Introduction:
Mixtures are combinations of two or more substances. Separation of mixtures is important in daily life, industries, and medical fields such as sugar production and blood testing.5.1 Classification of Mixtures
Homogeneous Mixture: Uniform composition throughout.
Examples: Sugar solution, vinegar, soda.
Heterogeneous Mixture: Non-uniform composition.
Examples: Sand + water, oil + water.Key Activity (Laser Test)
• Salt + water → No visible particles → Solution
• Chalk + water → Particles visible → Suspension
• Milk + water → Appears uniform but scatters light → Colloid5.2 Solutions
Solution: Homogeneous mixture of solute and solvent.
• Solute → Substance dissolved
• Solvent → Substance that dissolves solute5.2.1 Concentration of Solution
Concentration = Amount of solute in a given amount of solvent/solution.5.2.2 Methods to Express Concentration
1. Mass by Mass (% m/m)
Formula:
% m/m = (Mass of solute / Mass of solution) × 100
Example:
10g salt + 90g water = 100g solution
% m/m = (10/100) × 100 = 10%2. Mass by Volume (% m/v)
Formula:
% m/v = (Mass of solute / Volume of solution) × 100
Example:
5g glucose in 100 mL → 5%3. Volume by Volume (% v/v)
Formula:
% v/v = (Volume of solute / Volume of solution) × 100
Example:
1 mL pesticide in 100 mL → 1%5.2.3 Solubility
Solubility = Maximum solute dissolved in 100g/100mL solvent at a given temperature.
• Increases with temperature (solids)
• Decreases with temperature (gases)
Saturated Solution: Cannot dissolve more solute.5.3 Separation of Homogeneous Mixtures
1. Crystallization
Formation of pure crystals from saturated solution.
Principle: Solubility changes with temperature.
Steps:
• Prepare saturated solution
• Filter impurities
• Cool slowly → crystals form2. Distillation
Used to separate miscible liquids based on boiling points.
Principle:
Lower boiling liquid vaporises first → condenses → collected.
Example:
Acetone (56°C) + Water (100°C)Fractional Distillation
Used when boiling point difference is small (<25°C).
Example: Petroleum refining3. Paper Chromatography
Separates substances based on movement rate on paper.
Principle:
Different substances move at different speeds.5.4 Separation of Heterogeneous Mixtures
1. Separating Funnel
Used for immiscible liquids (oil + water).
Based on density difference.2. Sublimation
Solid → Vapour (without liquid stage)
Examples:
Camphor, naphthalene, dry ice3. Suspensions
• Heterogeneous
• Particles visible
• Settle on standing
Example: Muddy water4. Centrifugation
Spinning separates heavier particles.
Example:
Blood separation5. Coagulation
Small particles combine into larger ones.
Example:
Alum purifies water5.4.4 Colloids
• Intermediate particle size (1–1000 nm)
• Do not settle
• Show Tyndall effect
Examples:
Milk, blood, ice cream5.5 Tyndall Effect
Scattering of light by particles.
Observed in:
• Fog
• Smoke
• Sunlight through treesComparison Table
Property Solution Suspension Colloid Nature Homogeneous Heterogeneous Heterogeneous (appears uniform) Particle Size < 1 nm > 1000 nm 1–1000 nm Visibility Not visible Visible Not visible Settling No Yes No Tyndall Effect No Yes Yes Important Points
• Mixtures can be homogeneous or heterogeneous.
• Crystallization purifies solids.
• Distillation separates liquids.
• Chromatography separates colours.
• Sublimation separates special solids.
• Centrifugation separates heavy particles.
• Tyndall effect distinguishes colloids.