Wednesday, February 19, 2025

இந்த பதிவு எதனை பற்றியது என்று கண்டுபிடியுங்கள் - 1


1. Neurocysticercosis - A parasitic infection caused by the pork tapeworm.

2. Subacute sclerosing panencephalitis - A rare, chronic, progressive encephalitis that affects children and young adults, caused by the measles virus.

3. Colchicine poisoning - Toxicity from colchicine, a medication used to treat gout.

4. Echovirus 11 - A virus that can cause a range of illnesses, including meningitis and myocarditis.

5. Allergic reaction to copper IUD - An immune response to a copper intrauterine device.

6. Vitamin K deficiency, liver cancer, Wilson's disease - Vitamin K deficiency affects blood clotting; liver cancer is a malignant tumor of the liver; Wilson's disease is a genetic disorder causing copper accumulation in tissues.

7. African trypanosomiasis - Also known as sleeping sickness, caused by the Trypanosoma parasite.

8. Organophosphate poisoning - Toxicity from organophosphate chemicals, often found in pesticides.

9. Arteriovenous malformation - An abnormal connection between arteries and veins, bypassing the capillary system.

10. Rabies - A viral disease that causes inflammation of the brain in humans and other mammals.

11. Naphthalene poisoning - Toxicity from naphthalene, a substance found in mothballs.

12. Cadmium poisoning - Toxicity from cadmium, a heavy metal.

13. Leprosy - A chronic infectious disease caused by Mycobacterium leprae.

14. Congestive heart failure due to drug abuse - Heart failure caused by the heart's inability to pump blood effectively, exacerbated by drug use.

15. Ornithine Transcarbamylase Deficiency - A genetic disorder affecting the urea cycle, leading to ammonia accumulation.

16. Cushing's disease - A condition caused by excess cortisol production.

17. Common variable immunodeficiency disease from interaction of Epstein-Barr virus with anti-seizure medication - A disorder characterized by low levels of serum immunoglobulins and an increased susceptibility to infections.

18. Small-cell lung cancer - A fast-growing type of lung cancer.

19. Thrombotic thrombocytopenic purpura - A rare blood disorder causing blood clots in small blood vessels.

20. Fulminating osteomyelitis - A severe, rapidly progressing infection of the bone.

21. Necrotizing fasciitis, cancerous adenoma, necrosis due to muscle death due to infarction due to clot due to aneurysm - Necrotizing fasciitis is a severe infection causing tissue death; cancerous adenoma is a benign tumor that can become cancerous; necrosis is tissue death due to lack of blood flow.

22. Acute intermittent porphyria - A genetic disorder affecting the production of heme, leading to a buildup of toxic substances.

Season 2

1. Acute Respiratory Distress Syndrome, Cystic Fibrosis - ARDS is a severe lung condition causing respiratory failure; Cystic Fibrosis is a genetic disorder affecting the lungs and digestive system.

2. Melioidosis, Alcoholic Cirrhosis - Melioidosis is a bacterial infection affecting various organs; Alcoholic Cirrhosis is severe liver damage due to long-term alcohol abuse.

3. Erdheim-Chester Disease - A rare form of non-Langerhans cell histiocytosis, causing abnormal growths in various tissues.

4. Wegener's Granulomatosis - An autoimmune disease causing inflammation of blood vessels, leading to damage in the respiratory tract and kidneys.

5. Aortic Dissection - A serious condition where the inner layer of the aorta tears, causing blood to flow between the layers of the artery wall.

6. Heavy Metal Poisoning - Toxicity due to exposure to heavy metals such as lead, mercury, or arsenic.

7. Celiac Disease - An autoimmune disorder where ingestion of gluten leads to damage in the small intestine.

8. Heat Stroke - A condition caused by the body overheating, typically as a result of prolonged exposure to high temperatures.

9. Acute Intermittent Porphyria - A genetic disorder affecting the production of heme, leading to a buildup of toxic substances.

10. Tuberous Sclerosis - A genetic disorder causing benign tumors to form in various organs, including the brain, heart, kidneys, and skin.

11. Amantadine Poisoning - Toxicity from amantadine, a medication used to treat Parkinson's disease and influenza.

12. Measles - A highly contagious viral infection causing a skin rash and flu-like symptoms.

13. Wilson's Disease - A genetic disorder causing copper accumulation in tissues, leading to liver and neurological damage.

14. Tumor Lysis Syndrome - A potentially fatal complication of cancer treatment, causing the release of cellular contents into the bloodstream.

15. Fabry Disease - A rare genetic disorder affecting the body's ability to break down a specific type of fat, leading to organ damage.

16. Fish Poisoning (Ciguatera) - A foodborne illness caused by consuming fish contaminated with ciguatoxins.

17. Mercury Poisoning - Toxicity from mercury exposure, leading to neurological and renal damage.

18. Radiation Poisoning - Illness caused by excessive exposure to ionizing radiation, affecting various organs and tissues.

19. Epilepsy, Mitochondrial Disease - Epilepsy is a neurological disorder causing recurrent seizures; Mitochondrial Disease affects the mitochondria, leading to energy production issues in cells.

20. Hypersensitivity Pneumonitis - An immune system disorder causing inflammation of the lungs due to inhalation of various environmental substances.

21. Pseudo Tumor Cerebri - A condition characterized by increased intracranial pressure without a detectable cause.

22. Capgras Syndrome - A psychiatric disorder where a person believes that a friend or family member has been replaced by an identical imposter.


இந்த பதிவு எதனை பற்றியது என்று கண்டுபிடியுங்கள் - 2

 Season 3

1. Cushing's syndrome - A condition caused by excess cortisol production.
2. Secondary syphilis, vasculitis - Syphilis is a sexually transmitted infection caused by the bacterium Treponema pallidum; vasculitis is inflammation of blood vessels.
3. Brain tumor (craniopharyngioma) - A type of benign brain tumor that can affect the pituitary gland.
4. Guillain-Barré syndrome - A rare neurological disorder in which the body's immune system attacks the peripheral nerves.
5. Leptospirosis - A bacterial infection that can lead to liver and kidney damage.
6. Lymphoma - A type of cancer that begins in the lymphatic system.
7. Cancer (mesothelioma) - A rare cancer that affects the lining of the lungs, chest, or abdomen.
8. Graft-versus-host disease - A complication following a bone marrow transplant where the donor's immune cells attack the recipient's tissues.
9. Acute eosinophilic pneumonia - A rare lung condition characterized by the accumulation of eosinophils (a type of white blood cell) in the lungs.
10. Multiple sclerosis - A chronic autoimmune disease that affects the central nervous system, leading to a range of neurological symptoms.
11. Hepatitis C, cryoglobulinemia - Hepatitis C is a viral infection that affects the liver; cryoglobulinemia is a condition where abnormal proteins in the blood become solid at low temperatures.
12. Copper deficiency - A condition caused by insufficient copper intake, affecting various bodily functions.
13. Subacute thyroiditis - An inflammation of the thyroid gland that can cause temporary hyperthyroidism or hypothyroidism.
14. Scleroderma - A group of autoimmune diseases that cause the skin and connective tissues to harden and tighten.
15. Primary biliary cirrhosis - A chronic liver disease caused by progressive destruction of the bile ducts.
16. Ameloblastoma - A rare, benign tumor of the jaw.
17. Mastocytosis - A condition characterized by an abnormal accumulation of mast cells in the skin and other organs.
18. Brucellosis - A bacterial infection transmitted from animals to humans, causing fever, joint pain, and fatigue.
19. Diabetes insipidus - A condition characterized by excessive thirst and excretion of large amounts of dilute urine.
20. Thiamine deficiency (beriberi) - A condition caused by a lack of vitamin B1, leading to neurological and cardiovascular problems.
21. Von Hippel-Lindau disease - A genetic disorder that causes tumors and cysts to develop in various organs.
22. TTP (thrombotic thrombocytopenic purpura) - A rare blood disorder causing blood clots in small blood vessels throughout the body.
23. Creutzfeldt-Jakob disease - A rare, degenerative brain disorder caused by prions.
24. Chagas disease - A parasitic infection transmitted by insects, causing heart and digestive system problems.

Season 4

1. Alone - Environmental poisoning (mold exposure): Toxicity resulting from inhaling mold spores, which can cause respiratory issues and other health problems.
2. The Right Stuff - Pseudocyesis (false pregnancy): A condition where a person believes they are pregnant, exhibiting pregnancy symptoms without being actually pregnant.
3. 97 Seconds - Tension pneumothorax, electrical injury: A life-threatening condition where air enters the pleural space, causing lung collapse; injury caused by electric shock.
4. Guardian Angels - Lymphoma, paraneoplastic syndrome: Cancer that begins in the lymphatic system; a group of rare disorders triggered by an abnormal immune response to a neoplasm.
5. Mirror Mirror - Bacterial infection (Streptococcus): An infection caused by Streptococcus bacteria, leading to various illnesses such as strep throat, impetigo, and cellulitis.
6. Whatever It Takes - Leptospirosis: A bacterial infection transmitted through contact with contaminated water or animal urine, affecting the kidneys and liver.
7. Ugly - Tuberous sclerosis: A genetic disorder that causes benign tumors to form in various organs, including the brain, heart, kidneys, and skin.
8. You Don't Want to Know - Von Hippel-Lindau disease: A genetic disorder that causes tumors and cysts to develop in various organs, including the brain, spinal cord, kidneys, and eyes.
9. Games - Cystic fibrosis, allergic reaction to medication: A genetic disorder affecting the lungs and digestive system; an immune response to a medication causing symptoms like rash, itching, and difficulty breathing.
10. It's a Wonderful Lie - Erythropoietic protoporphyria: A form of porphyria that affects the skin, causing sensitivity to sunlight and painful skin reactions.
11. Frozen - Cold agglutinin disease: A rare autoimmune disorder in which cold temperatures trigger the immune system to attack red blood cells.
12. Don't Ever Change - Lymphocytic choriomeningitis virus (LCMV): A rodent-borne viral infection that can cause meningitis, encephalitis, or mild flu-like symptoms.
13. No More Mr. Nice Guy - Chagas disease: A parasitic infection transmitted by insects, causing heart and digestive system problems.
14. Living the Dream - Heavy metal poisoning (thallium): Toxicity resulting from exposure to thallium, a heavy metal that can cause neurological and gastrointestinal symptoms.
15. House's Head - Amnesia, brain injury: Loss of memory due to brain injury, affecting the ability to recall information or events.
16. Wilson's Heart - Heart failure, brain death: The heart's inability to pump blood effectively, leading to organ failure; irreversible loss of all brain function.

Season 5

1. Dying Changes Everything - Eosinophilic pneumonia: A condition where eosinophils (a type of white blood cell) accumulate in the lungs, causing inflammation.
2. Not Cancer - Heavy metal poisoning (gold): Toxicity from exposure to gold particles, which can cause various health issues.
3. Adverse Events - Bisphosphonate poisoning: Adverse effects from medications used to treat osteoporosis and similar diseases.
4. Birthmarks - Malignant melanoma: A type of skin cancer that develops in the cells that produce melanin.
5. Lucky Thirteen - Huntington's disease: A genetic disorder causing the progressive breakdown of nerve cells in the brain.
6. Joy - Eclampsia: A severe complication of pregnancy characterized by high blood pressure and seizures.
7. The Itch - Tinea (ringworm): A fungal infection that affects the skin, scalp, or nails.
8. Emancipation - Paraneoplastic syndrome: A group of rare disorders triggered by an abnormal immune response to a neoplasm (cancer).
9. Last Resort - Melioidosis: A bacterial infection that can affect various organs and cause severe illness.
10. Let Them Eat Cake - Carnitine palmitoyltransferase II deficiency (CPT II deficiency): A metabolic disorder affecting muscle cells and causing muscle weakness and pain.
11. Joy to the World - Von Hippel-Lindau disease: A genetic disorder that causes tumors and cysts to develop in various organs.
12. Painless - Autoimmune polyendocrine syndrome type 1 (APS-1): A genetic disorder affecting multiple endocrine glands.
13. Big Baby - Erdheim-Chester disease: A rare form of non-Langerhans cell histiocytosis, causing abnormal growths in various tissues.
14. The Greater Good - Whipple's disease: A rare bacterial infection that can affect the intestines and other organs.
15. Unfaithful - Chagas disease: A parasitic infection transmitted by insects, causing heart and digestive system problems.
16. The Softer Side - Androgen insensitivity syndrome: A condition where a person is genetically male but has some or all physical traits of a female due to resistance to male hormones.
17. The Social Contract - Hurler syndrome (Mucopolysaccharidosis type I): A genetic disorder affecting the breakdown of glycosaminoglycans, leading to buildup and damage to organs and tissues.
18. Here Kitty - Fabry disease: A rare genetic disorder affecting the body's ability to break down a specific type of fat, leading to organ damage.
19. Locked In - Locked-in syndrome: A condition where a person is conscious and aware but cannot move or communicate verbally due to complete paralysis of nearly all voluntary muscles.
20. Simple Explanation - Amyloidosis: A condition where abnormal protein deposits called amyloids build up in organs and tissues, causing damage.
21. Saviors - Acromegaly: A hormonal disorder that results from excess growth hormone, leading to enlarged bones and tissues.
22. House Divided - Alice in Wonderland syndrome: A neurological condition that affects perception, causing size distortions and altered body image.
23. Under My Skin - Acute promyelocytic leukemia: A type of cancer affecting the blood and bone marrow, characterized by an overproduction of immature white blood cells.
24. Both Sides Now - Disulfiram reaction: An adverse reaction to disulfiram, a medication used to treat chronic alcoholism, causing severe nausea and other symptoms when alcohol is consumed.
1. Broken - Catatonia, Pelvic infection: Catatonia is a state of psycho-motor immobility and behavioral abnormality; a pelvic infection is an infection in the female reproductive organs.
2. Epic Fail - Meningoencephalitis: Inflammation of the brain and its surrounding protective membranes.
3. The Tyrant - Amyloidosis: A condition where abnormal protein deposits called amyloids build up in organs and tissues.
4. Instant Karma - Opioid-induced constipation, congenital adrenal hyperplasia: Constipation caused by opioid use; a genetic disorder affecting adrenal gland function.
5. Brave Heart - Ehrlichiosis: A tick-borne bacterial infection causing flu-like symptoms.
6. Known Unknowns - Systemic lupus erythematosus: An autoimmune disease where the immune system attacks its own tissues.
7. Teamwork - Amebic liver abscess: A pus-filled mass in the liver due to an intestinal parasite.
8. Ignorance Is Bliss - Sickle cell trait and poisoning from ephedrine: Sickle cell trait is a genetic condition where a person inherits one sickle cell gene; ephedrine poisoning is toxicity from a stimulant drug.
9. Wilson - Hypertension, Takayasu's arteritis: High blood pressure; a rare type of vasculitis that damages large arteries.
10. The Down Low - Superior vena cava syndrome: A group of symptoms caused by partial blockage of the superior vena cava.
11. Remorse - Lead poisoning: Toxicity due to lead exposure, affecting multiple body systems.
12. Moving the Chains - Trauma-induced rhabdomyolysis, compartment syndrome: Muscle breakdown leading to the release of muscle fibers into the bloodstream; a painful condition caused by pressure buildup within muscles.
13. 5 to 9 - Acromegaly: A hormonal disorder resulting from excess growth hormone, leading to enlarged bones and tissues.
14. Private Lives - Decompression sickness: A condition caused by dissolved gases coming out of solution into bubbles inside the body on depressurization.
15. Black Hole - Chromosome 6 translocation, Creutzfeldt-Jakob disease: A genetic abnormality; a rare, degenerative brain disorder caused by prions.
16. Lockdown - Locked-in syndrome: A condition where a person is conscious and aware but cannot move or communicate verbally due to complete paralysis of nearly all voluntary muscles.
17. Knight Fall - Hyper-IgM syndrome: A condition causing immune system problems due to abnormal levels of antibodies.
18. Open and Shut - Primary amoebic meningoencephalitis: A rare, usually fatal brain infection caused by Naegleria fowleri.
19. The Choice - Pseudo-Cushing's syndrome: A condition causing symptoms similar to Cushing's syndrome, without the excess cortisol production.
20. Baggage - Stiff-person syndrome: A rare neurological disorder causing muscle stiffness and spasms.
21. Help Me - Exertional heat stroke: A condition caused by strenuous physical activity in high temperatures, leading to overheating and potential organ damage.


இந்த பதிவு எதனை பற்றியது என்று கண்டுபிடியுங்கள் - 3

Season 7


1. Now What? - Post-traumatic stress disorder (PTSD): A mental health condition triggered by experiencing or witnessing a traumatic event, causing symptoms like flashbacks and anxiety.
2. Selfish - Cystic fibrosis, primary ciliary dyskinesia: Cystic fibrosis is a genetic disorder affecting the lungs and digestive system; primary ciliary dyskinesia is a genetic condition affecting the cilia's function, leading to respiratory issues.
3. Unwritten - Psychogenic non-epileptic seizures (PNES): Seizure-like episodes that are not caused by electrical disturbances in the brain, but by psychological factors.
4. Massage Therapy - Syphilis, renal cell carcinoma: Syphilis is a sexually transmitted infection caused by the bacterium Treponema pallidum; renal cell carcinoma is a type of kidney cancer.
5. Unplanned Parenthood - Herpes simplex encephalitis: A severe brain infection caused by the herpes simplex virus.
6. Office Politics - Hepatitis C: A viral infection that affects the liver.
7. A Pox on Our House - Smallpox, necrotizing fasciitis: Smallpox is a highly contagious and deadly viral disease eradicated by vaccination; necrotizing fasciitis is a severe infection causing tissue death.
8. Small Sacrifices - Paraneoplastic syndrome: A group of rare disorders triggered by an abnormal immune response to a neoplasm (cancer).
9. Larger Than Life - Mesenteric ischemia: A condition where blood flow to the intestines is restricted, causing tissue death and severe pain.
10. Carrot or Stick - Spinal epidural abscess: A collection of pus that forms in the epidural space around the spinal cord, causing pressure and inflammation.
11. Family Practice - Chromosomal translocation, leukemia: A genetic abnormality involving rearrangement of chromosomes, leading to leukemia (cancer of blood-forming tissues).
12. You Must Remember This - Hyperammonemia: Elevated levels of ammonia in the blood, which can cause neurological symptoms.
13. Two Stories - Gastrointestinal stromal tumor (GIST): A type of tumor that occurs in the digestive tract, most commonly in the stomach or small intestine.
14. Recession Proof - Celiac disease: An autoimmune disorder where ingestion of gluten leads to damage in the small intestine.
15. Bombshells - Systemic lupus erythematosus (SLE): An autoimmune disease where the immune system attacks healthy tissues, causing inflammation and damage to various organs.
16. Out of the Chute - Takotsubo cardiomyopathy: A temporary heart condition often triggered by stress, also known as "broken heart syndrome."
17. Fall from Grace - Tuberous sclerosis: A genetic disorder that causes benign tumors to form in various organs, including the brain, heart, kidneys, and skin.
18. The Dig - Coccidioidomycosis (Valley fever): A fungal infection caused by inhaling spores of the Coccidioides fungus, found in soil.
19. Last Temptation - Eosinophilic granulomatosis with polyangiitis (Churg-Strauss syndrome): A rare autoimmune disease causing inflammation of blood vessels and tissues, leading to organ damage.
20. Changes - Erdheim-Chester disease: A rare form of non-Langerhans cell histiocytosis, causing abnormal growths in various tissues.
21. The Fix - Black market silicone poisoning: Toxicity resulting from the use of non-medical-grade silicone, often used in illegal cosmetic procedures.
22. After Hours - Rhabdomyolysis: A condition where damaged muscle tissue releases proteins and electrolytes into the blood, potentially leading to kidney damage.
23. Moving On - Heroin overdose, schizophrenia: An overdose caused by excessive consumption of heroin, a highly addictive opioid; schizophrenia is a chronic mental disorder characterized by hallucinations, delusions, and cognitive issues.

Season 8

1. Twenty Vicodin - Eosinophilic granulomatosis with polyangiitis (Churg-Strauss syndrome): A rare autoimmune disease causing inflammation of blood vessels and tissues, leading to organ damage.
2. Transplant - Amyloidosis: A condition where abnormal protein deposits called amyloids build up in organs and tissues, causing damage.
3. Charity Case - Transverse myelitis: A neurological disorder caused by inflammation of the spinal cord, leading to pain, muscle weakness, and paralysis.
4. Risky Business - Hemophagocytic lymphohistiocytosis: A severe systemic inflammatory syndrome caused by excessive immune system activation.
5. The Confession - Ehlers-Danlos syndrome: A group of genetic disorders affecting connective tissues, causing hypermobility, skin elasticity, and tissue fragility.
6. Parents - Acid maltase deficiency (Pompe disease): A genetic disorder that affects the heart and skeletal muscles due to the buildup of glycogen.
7. Dead & Buried - Measles encephalitis: A severe brain infection caused by the measles virus.
8. Perils of Paranoia - Thymoma: A tumor originating from the thymus gland, which can cause various symptoms depending on its size and location.
9. Better Half - Anti-NMDA receptor encephalitis: An autoimmune disease where antibodies attack NMDA receptors in the brain, causing psychiatric and neurological symptoms.
10. Runaways - Paraneoplastic syndrome: A group of rare disorders triggered by an abnormal immune response to a neoplasm (cancer).
11. Nobody's Fault - Meningococcemia: A severe bloodstream infection caused by Neisseria meningitidis, which can lead to sepsis and meningitis.
12. Chase - Stiff-person syndrome: A rare neurological disorder characterized by muscle stiffness and spasms.
13. Man of the House - Hyperparathyroidism: An overactivity of one or more of the parathyroid glands, causing elevated levels of parathyroid hormone and calcium in the blood.
14. Love is Blind - Microscopic polyangiitis: A form of vasculitis affecting small blood vessels, leading to organ damage.
15. Blowing the Whistle - Small bowel bacterial overgrowth: A condition where excessive bacteria in the small intestine cause digestive symptoms.
16. Gut Check - Tinnitus: The perception of noise or ringing in the ears not caused by an external sound.
17. We Need the Eggs - Syphilis: A sexually transmitted infection caused by the bacterium Treponema pallidum.
18. Body & Soul - Neurosyphilis: A severe form of syphilis that affects the central nervous system.
19. The C Word - Leukemia: Cancer of blood-forming tissues, including the bone marrow and lymphatic system, causing abnormal white blood cell production.
20. Post Mortem - Bowel ischemia: A condition where reduced blood flow to the intestines causes tissue damage and necrosis.
21. Holding On - Multiple sclerosis: A chronic autoimmune disease that affects the central nervous system, leading to a range of neurological symptoms.
22. Everybody Dies - Methyl bromide poisoning: Toxicity resulting from exposure to methyl bromide, a chemical used as a pesticide and fumigant, causing respiratory and neurological symptoms.


பென் டென் - தொடரின் கடந்த கால ஏலியன்கள்




1. Heatblast - Pyronite: Can generate and control fire, absorb heat, and fly using fire propulsion.

2. Wildmutt - Vulpimancer: Enhanced senses, agility, and strength; can track scents and see in the dark.

3. Diamondhead - Petrosapien: Can generate and manipulate crystal, create weapons and shields, and regenerate damaged crystal.

4. XLR8 - Kineceleran: Super speed, agility, and reflexes; can create tornadoes by running in circles.

5. Grey Matter - Galvan: Super intelligence, can fit into small spaces, and has enhanced agility.

6. Four Arms - Tetramand: Super strength, durability, and can create shockwaves by clapping hands.

7. Stinkfly - Lepidopterran: Can fly, shoot slime, and has enhanced agility and strength.

8. Ripjaws - Piscciss Volann: Can breathe underwater, swim at high speeds, and has powerful jaws and claws.

9. Upgrade - Galvanic Mechamorph: Can merge with and upgrade technology, shoot energy beams, and shape-shift.

10. Ghostfreak - Ectonurite: Can become intangible, invisible, and possess other beings.

11. Cannonbolt - Arburian Pelarota: Can roll into a ball, has super strength and durability.

12. Wildvine - Florauna: Can stretch limbs, grow vines, and regenerate.

13. Spitter - Spheroid: Can spit slime that can trap enemies and create slippery surfaces.

14. Buzzshock - Nosedeenian: Can generate and control electricity, and travel through electrical currents.

15. Arctiguana - Polar Manzardill: Can generate and control ice, and has enhanced strength and durability.

16. Upchuck - Gourmand: Can eat and digest any material, and shoot explosive projectiles.

17. Way Big - To'kustar: Can grow to enormous size, has super strength, and can shoot cosmic rays.

18. Big Chill - Necrofriggian: Can become intangible, fly, and generate extreme cold.

19. Echo Echo - Sonorosian: Can create sonic blasts, duplicate himself, and merge duplicates.

20. Humungousaur - Vaxasaurian: Can grow in size, has super strength, and durability.

21. Jetray - Aerophibian: Can fly at high speeds, shoot neuroshock blasts, and breathe underwater.

22. Chromastone - Crystalsapien: Can absorb and redirect energy, and has enhanced strength and durability.

23. Brainstorm - Cerebrocrustacean: Super intelligence, can generate and control electricity, and has telekinesis.

24. Alien X - Celestialsapien: Can alter reality, has invulnerability, and can regenerate.

25. Clockwork - Chronosapien: Can control time, travel through time, and alter timelines.

26. Atomix - Unknown species: Can generate atomic energy, create nuclear blasts, and fly.


Additional Aliens

1. Swampfire - Methanosian: Can generate and control fire, regenerate, and has super strength.

2. Ultimate Humungousaur - Enhanced version of Humungousaur: Can grow bone-like armor and shoot missiles.

3. Shocksquatch - Gimlinopithecus: Can generate and control electricity.

4. Overflow - Cascan: Can shoot water jets and create water constructs.

5. Slapback - Ekoplektoid: Can duplicate himself and each duplicate becomes smaller and stronger.


கணிதம் உங்களுக்காக - 37 - கான்ஸெப்ட்கள்

 



1. General form of the equation of a circle: x² + y² + Dx + Ey + F = 0 (where D, E, and F are constants)
2. Distance between two points in a plane: d = √((x₂ - x₁)² + (y₂ - y₁)²)
3. Midpoint formula: M = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)
4. Slope of a line passing through points (x₁, y₁) and (x₂, y₂): m = (y₂ - y₁) / (x₂ - x₁)
5. Equation of a line in slope-intercept form: y = mx + c (where m is the slope and c is the y-intercept)
6. Equation of a line in point-slope form: y - y₁ = m(x - x₁)
7. General form of a line equation: Ax + By + C = 0
8. Distance from a point to a line: d = |Ax₁ + By₁ + C| / √(A² + B²) (where (x₁, y₁) is the point and Ax + By + C = 0 is the line)

9. Volume of a regular tetrahedron: V = (√2 / 12) a³ (where a is the side length)
10. Surface area of a regular tetrahedron: SA = √3 a² (where a is the side length)
11. Volume of an octahedron: V = (√2 / 3) a³ (where a is the side length)
12. Surface area of an octahedron: SA = 2√3 a² (where a is the side length)
13. Volume of a regular dodecahedron: V = (15 + 7√5) / 4 a³ (where a is the side length)
14. Surface area of a regular dodecahedron: SA = 3√25 + 10√5 a² (where a is the side length)
15. Volume of a regular icosahedron: V = 5(3 + √5) / 12 a³ (where a is the side length)
16. Surface area of a regular icosahedron: SA = 5√3 a² (where a is the side length)

17. Polar to Cartesian coordinates: x = r cos(θ), y = r sin(θ)
18. Cartesian to Polar coordinates: r = √(x² + y²), θ = tan⁻¹(y / x)
19. Polar form of the equation of a line: r = l / cos(θ - φ) (where l is the perpendicular distance from the origin and φ is the angle with the positive x-axis)
20. Polar form of the equation of a circle: r(θ) = R (where R is the radius)
21. Parametric equations for a circle in polar coordinates: x = R cos(θ), y = R sin(θ) (where R is the radius and θ is the parameter)

22. Magnitude of a vector in 3D: |A| = √(A₁² + A₂² + A₃²)
23. Scalar projection of vector A onto vector B: proj_B(A) = (A · B) / |B|
24. Vector projection of vector A onto vector B: Proj_B(A) = ((A · B) / |B|²) B
25. Angle between two vectors: cos(θ) = (A · B) / (|A||B|)
26. Cross product: A × B = (A₂B₃ - A₃B₂)i + (A₃B₁ - A₁B₃)j + (A₁B₂ - A₂B₁)k
27. Dot product: A · B = A₁B₁ + A₂B₂ + A₃B₃

28. Product-to-Sum Formulas:
    - sin(A) sin(B) = ½ [cos(A - B) - cos(A + B)]
    - cos(A) cos(B) = ½ [cos(A + B) + cos(A - B)]
    - sin(A) cos(B) = ½ [sin(A + B) + sin(A - B)]
29. Sum-to-Product Formulas:
    - sin(A) ± sin(B) = 2 sin((A ± B) / 2) cos((A ∓ B) / 2)
    - cos(A) + cos(B) = 2 cos((A + B) / 2) cos((A - B) / 2)
    - cos(A) - cos(B) = -2 sin((A + B) / 2) sin((A - B) / 2)
30. Half-Angle Formulas:
    - sin²(A/2) = (1 - cosA) / 2
    - cos²(A/2) = (1 + cosA) / 2
    - tan²(A/2) = (1 - cosA) / (1 + cosA)
31. Double Angle Formulas:
    - sin(2A) = 2 sinA cosA
    - cos(2A) = cos²A - sin²A = 2 cos²A - 1 = 1 - 2 sin²A
    - tan(2A) = 2 tanA / (1 - tan²A)
32. Triple Angle Formulas:
    - sin(3A) = 3 sinA - 4 sin³A
    - cos(3A) = 4 cos³A - 3 cosA
    - tan(3A) = (3 tanA - tan³A) / (1 - 3 tan²A)

கணிதம் உங்களுக்காக - 36 - கான்ஸெப்ட்கள்

 


1. Volume of a torus: V = (πr²) × (2πR) = 2π²Rr² (where r is the radius of the tube and R is the distance from the center of the tube to the center of the torus)
2. Surface area of a torus: SA = (2πr) × (2πR) = 4π²Rr
3. Volume of a truncated pyramid: V = (1/3)h(A₁ + A₂ + √(A₁A₂)) (where h is the height, A₁ is the area of the top base, and A₂ is the area of the bottom base)
4. Surface area of a truncated pyramid: SA = A₁ + A₂ + (1/2)Pℓ (where P is the perimeter of the base and ℓ is the slant height)
5. Volume of an ellipsoid: V = (4/3)πabc (where a, b, and c are the semi-axes)
6. Surface area of an ellipsoid (approximate): SA = 4π[(a²b^(p) + a²c^(p) + b²c^(p))/3]^(1/p) (where p ≈ 1.6075)

7. Scalar triple product: V = A · (B × C) (where A, B, and C are vectors)
8. Vector triple product: A × (B × C) = (A · C)B - (A · B)C
9. Volume of a parallelepiped: V = |A · (B × C)| (where A, B, and C are vectors)
10. Distance between two skew lines: d = |(A₁ - A₂) · (B₁ × B₂)| / |B₁ × B₂| (where A₁ and A₂ are points on the lines, and B₁ and B₂ are direction vectors)

11. Heron's formula for the area of a triangle: A = √(s(s - a)(s - b)(s - c)) (where s is the semi-perimeter and a, b, and c are the lengths of the sides)
12. Brahmagupta's formula (area of a cyclic quadrilateral): A = √((s - a)(s - b)(s - c)(s - d) - abcd cos²(½θ)) (where θ is the sum of the opposite angles)
13. Radius of the inscribed circle in a triangle: r = A / s (where A is the area of the triangle and s is the semi-perimeter)
14. Radius of the circumscribed circle in a triangle: R = (abc) / (4A) (where a, b, and c are the side lengths, and A is the area of the triangle)

19. Power of a point theorem: If a point P lies outside a circle and two secant lines PA and PB intersect the circle at A and B, then PA × PB = PC × PD (where C and D are points of intersection)
20. Length of an arc: L = rθ (where r is the radius and θ is the central angle in radians)
21. Area of a sector: A = 1/2r²θ (where r is the radius and θ is the central angle in radians)
22. Segment area: A = 1/2r²(θ - sinθ)

23. Rotation around a point (h, k) by θ degrees: (x', y') = ((x - h) cosθ - (y - k) sinθ + h, (x - h) sinθ + (y - k) cosθ + k)
24. Reflection over a line y = mx + c: (x', y') = ((x(1 - m²) + 2my - 2mc) / (1 + m²), (y(1 - m²) + 2mx + 2c) / (1 + m²))
25. Dilation with respect to a point (h, k): (x', y') = (kx + (1 - k)h, ky + (1 - k)k)
26. Horizontal shear transformation: (x', y') = (x + ky, y)
27. Vertical shear transformation: (x', y') = (x, y + kx)

கணிதம் உங்களுக்காக - 35 - கான்ஸெப்ட்கள்

 


1. Equation of an ellipse in standard form (centered at the origin): (x² / a²) + (y² / b²) = 1 (where a is the semi-major axis and b is the semi-minor axis)
2. Equation of a hyperbola in standard form (centered at the origin): (x² / a²) - (y² / b²) = 1 (horizontal) or (y² / a²) - (x² / b²) = 1 (vertical)
3. Asymptotes of a hyperbola: y = ±(b / a)x (horizontal) or y = ±(a / b)x (vertical)
4. Parametric equations of a circle: x = h + r cos(t), y = k + r sin(t) (where (h, k) is the center, r is the radius, and t is the parameter)
5. Parametric equations of an ellipse: x = h + a cos(t), y = k + b sin(t) (where (h, k) is the center, a is the semi-major axis, b is the semi-minor axis, and t is the parameter)
6. Polar form of the equation of a line: r = (l) / (cos(θ - φ)) (where l is the perpendicular distance from the origin and φ is the angle with the positive x-axis)
7. Polar form of the equation of a circle: r(θ) = R (where R is the radius)

8. Volume of a spherical cap: V = (1/6)πh(3a² + 3b² + h²) (where h is the height of the cap and a and b are the radii of the cap's bases)
9. Surface area of a spherical cap: SA = 2πRh (where h is the height of the cap and R is the radius of the sphere)
10. Volume of a spherical sector: V = (2/3)πR²h (where R is the radius of the sphere and h is the height of the spherical sector)
11. Volume of a spherical zone: V = (2/3)πR²(h₂ - h₁) (where R is the radius of the sphere, h₁ is the height of the lower zone, and h₂ is the height of the upper zone)
12. Surface area of a spherical zone: SA = 2πRh (where R is the radius of the sphere and h is the height of the zone)
13. Volume of a spherical wedge: V = (2/3)πR²θ (where R is the radius of the sphere and θ is the dihedral angle)
14. Surface area of a spherical wedge: SA = 2πRh (where R is the radius of the sphere and h is the height of the spherical wedge)

15. Scalar triple product: V = A · (B × C) (where A, B, and C are vectors)
16. Vector triple product: A × (B × C) = (A · C)B - (A · B)C
17. Distance between two skew lines: d = |(A₁ - A₂) · (B₁ × B₂)| / |B₁ × B₂| (where A₁ and A₂ are points on the lines, and B₁ and B₂ are direction vectors)
18. Equation of a line in vector form: r = r₀ + t(v) (where r is the position vector, r₀ is a point on the line, v is the direction vector, and t is a scalar)
19. Equation of a plane in vector form: r · n = d (where r is the position vector, n is the normal vector, and d is the distance from the origin)
20. Equation of a sphere in vector form: |r - r₀| = R (where r is the position vector, r₀ is the center, and R is the radius)

21. Heron's formula for the area of a triangle: A = √(s(s - a)(s - b)(s - c)) (where s is the semi-perimeter and a, b, and c are the lengths of the sides)
22. Radius of the inscribed circle in a triangle: r = A / s (where A is the area of the triangle and s is the semi-perimeter)
23. Radius of the circumscribed circle in a triangle: R = (abc) / (4A) (where a, b, and c are the side lengths, and A is the area of the triangle)
24. Length of the altitude of a right triangle: h = (a * b) / c (where a and b are the legs and c is the hypotenuse)
25. Length of the altitude of an equilateral triangle: h = (√3 / 2) * a (where a is the side length)
26. Length of the median of a trapezoid: m = (a + b) / 2 (where a and b are the lengths of the parallel sides)
27. Length of the diagonal of a rectangle: d = √(a² + b²) (where a and b are the side lengths)
28. Length of the diagonal of a parallelogram: d = √(a² + b² + 2ab cos(θ)) (where a and b are the side lengths and θ is the angle between the sides)
29. Length of the side of a regular polygon: s = 2R sin(π / n) (where R is the radius of the circumscribed circle and n is the number of sides)
30. Radius of the circumscribed circle of a regular polygon: R = (s / 2) * csc(π / n) (where s is the side length and n is the number of sides)
31. Radius of the inscribed circle of a regular polygon: r = (s / 2) * cot(π / n) (where s is the side length and n is the number of sides)

32. Product-to-Sum Formulas:
    - sin(A) sin(B) = ½ [cos(A - B) - cos(A + B)]
    - cos(A) cos(B) = ½ [cos(A + B) + cos(A - B)]
    - sin(A) cos(B) = ½ [sin(A + B) + sin(A - B)]
33. Sum-to-Product Formulas:
    - sin(A) ± sin(B) = 2 sin((A ± B) / 2) cos((A ∓ B) / 2)
    - cos(A) + cos(B) = 2 cos((A + B) / 2) cos((A - B) / 2)
    - cos(A) - cos(B) = -2 sin((A + B) / 2) sin((A - B) / 2)
34. Half-Angle Formulas:
    - sin²(A/2) = (1 - cosA) / 2
    - cos²(A/2) = (1 + cosA) / 2
    - tan²(A/2) = (1 - cosA) / (1 + cosA)
35. Double Angle Formulas:
    - sin(2A) = 2 sinA cosA
    - cos(2A) = cos²A - sin²A = 2 cos²A - 1 = 1 - 2 sin²A
    - tan(2A) = 2 tanA / (1 - tan²A)
36. Triple Angle Formulas:
    - sin(3A) = 3 sinA - 4 sin³A
    - cos(3A) = 4 cos³A - 3 cosA
    - tan(3A) = (3 tanA - tan³A) / (1 - 3 tan²A)

கணிதம் உங்களுக்காக - 34 - கான்ஸெப்ட்கள்

1. Volume of a right circular cone: V = (1/3)πr²h (where r is the radius of the base and h is the height)

2. Surface area of a right circular cone: SA = πr(r + √(r² + h²))
3. Volume of a right circular cylinder: V = πr²h (where r is the radius of the base and h is the height)
4. Surface area of a right circular cylinder: SA = 2πrh + 2πr²
5. Volume of a spherical segment: V = (1/6)πh(3a² + 3b² + h²) (where h is the height of the segment, a and b are the radii of the segment's bases)
6. Surface area of a spherical segment: SA = 2πRh (where R is the radius of the sphere and h is the height of the segment)

7. Length of the altitude of a right triangle: h = (a * b) / c (where a and b are the legs and c is the hypotenuse)
8. Length of the altitude of an equilateral triangle: h = (√3 / 2) * a (where a is the side length)
9. Radius of the circumscribed circle of a triangle: R = (abc) / (4A) (where a, b, and c are the side lengths and A is the area of the triangle)
10. Radius of the inscribed circle of a triangle: r = A / s (where A is the area of the triangle and s is the semi-perimeter)
11. Length of the median of a trapezoid: m = (a + b) / 2 (where a and b are the lengths of the parallel sides)
12. Length of the diagonal of a rectangle: d = √(a² + b²) (where a and b are the side lengths)
13. Length of the diagonal of a parallelogram: d = √(a² + b² + 2ab cos(θ)) (where a and b are the side lengths and θ is the angle between the sides)
14. Length of the side of a regular polygon: s = 2R sin(π / n) (where R is the radius of the circumscribed circle and n is the number of sides)
15. Radius of the circumscribed circle of a regular polygon: R = (s / 2) * csc(π / n) (where s is the side length and n is the number of sides)
16. Radius of the inscribed circle of a regular polygon: r = (s / 2) * cot(π / n) (where s is the side length and n is the number of sides)

17. Equation of the parabola (vertex form): y - k = a(x - h)² (where (h, k) is the vertex)
18. Equation of the ellipse (standard form): (x - h)² / a² + (y - k)² / b² = 1 (where (h, k) is the center, a is the semi-major axis, and b is the semi-minor axis)
19. Equation of the hyperbola (standard form): (x - h)² / a² - (y - k)² / b² = 1 (horizontal) or (y - k)² / a² - (x - h)² / b² = 1 (vertical)
20. Slopes of the asymptotes of a hyperbola: ±(b / a) (horizontal) or ±(a / b) (vertical)
21. Distance between two parallel lines: d = |c₂ - c₁| / √(a² + b²) (where the equations of the lines are Ax + By + C₁ = 0 and Ax + By + C₂ = 0)
22. Distance between a point and a plane: d = |Ax₁ + By₁ + Cz₁ + D| / √(A² + B² + C²)

23. Scalar triple product: V = A · (B × C) (where A, B, and C are vectors)
24. Vector triple product: A × (B × C) = (A · C)B - (A · B)C
25. Volume of a parallelepiped: V = |A · (B × C)| (where A, B, and C are vectors)
26. Distance between two skew lines: d = |(A₁ - A₂) · (B₁ × B₂)| / |B₁ × B₂| (where A₁ and A₂ are points on the lines, and B₁ and B₂ are direction vectors)

27. Product-to-Sum Formulas:
    - sin(A) sin(B) = ½ [cos(A - B) - cos(A + B)]
    - cos(A) cos(B) = ½ [cos(A + B) + cos(A - B)]
    - sin(A) cos(B) = ½ [sin(A + B) + sin(A - B)]
28. Sum-to-Product Formulas:
    - sin(A) ± sin(B) = 2 sin((A ± B) / 2) cos((A ∓ B) / 2)
    - cos(A) + cos(B) = 2 cos((A + B) / 2) cos((A - B) / 2)
    - cos(A) - cos(B) = -2 sin((A + B) / 2) sin((A - B) / 2)
29. Half-Angle Formulas:
    - sin²(A/2) = (1 - cosA) / 2
    - cos²(A/2) = (1 + cosA) / 2
    - tan²(A/2) = (1 - cosA) / (1 + cosA)
30. Double Angle Formulas:
    - sin(2A) = 2 sinA cosA
    - cos(2A) = cos²A - sin²A = 2 cos²A - 1 = 1 - 2 sin²A
    - tan(2A) = 2 tanA / (1 - tan²A)
31. Triple Angle Formulas:
    - sin(3A) = 3 sinA - 4 sin³A
    - cos(3A) = 4 cos³A - 3 cosA
    - tan(3A) = (3 tanA - tan³A) / (1 - 3 tan²A)

கணிதம் உங்களுக்காக - 33 - கான்ஸெப்ட்கள்

 1. Equation of a straight line in general form: Ax + By + C = 0

2. Equation of a line in slope-intercept form: y = mx + c (where m is the slope and c is the y-intercept)
3. Distance between two points (x₁, y₁) and (x₂, y₂): d = √((x₂ - x₁)² + (y₂ - y₁)²)
4. Midpoint formula: M = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)
5. Slope of a line through points (x₁, y₁) and (x₂, y₂): m = (y₂ - y₁) / (x₂ - x₁)
6. Distance from a point to a line Ax + By + C = 0: d = |Ax₁ + By₁ + C| / √(A² + B²)
7. Equation of a circle in standard form: (x - h)² + (y - k)² = r² (where (h, k) is the center and r is the radius)
8. Equation of a parabola in standard form: y = ax² + bx + c or (y - k) = a(x - h)² (where (h, k) is the vertex)

9. Volume of a frustum of a cone: V = (1/3)πh(R₁² + R₁R₂ + R₂²) (where h is the height, R₁ is the radius of the top base, and R₂ is the radius of the bottom base)
10. Surface area of a frustum of a cone: SA = π(R₁ + R₂)√((R₁ - R₂)² + h²) + πR₁² + πR₂²
11. Volume of an ellipsoid: V = (4/3)πabc (where a, b, and c are the semi-axes)
12. Surface area of an ellipsoid (approximate): SA = 4π[(a²b^(p) + a²c^(p) + b²c^(p))/3]^(1/p) (where p ≈ 1.6075)
13. Volume of a paraboloid: V = (1/2)πr²h
14. Volume of a truncated pyramid: V = (1/3)h(A₁ + A₂ + √(A₁A₂)) (where h is the height, A₁ is the area of the top base, and A₂ is the area of the bottom base)
15. Surface area of a truncated pyramid: SA = A₁ + A₂ + (1/2)Pℓ (where P is the perimeter of the base and ℓ is the slant height)

16. Law of Sines: a/sin(A) = b/sin(B) = c/sin(C)
17. Law of Cosines: c² = a² + b² - 2ab cos(C)
18. Law of Tangents: (a - b) / (a + b) = tan[(A - B)/2] / tan[(A + B)/2]
19. Half-Angle Formulas:
    - sin²(A/2) = (1 - cosA) / 2
    - cos²(A/2) = (1 + cosA) / 2
    - tan²(A/2) = (1 - cosA) / (1 + cosA)
20. Double Angle Formulas:
    - sin(2A) = 2 sinA cosA
    - cos(2A) = cos²A - sin²A = 2 cos²A - 1 = 1 - 2 sin²A
    - tan(2A) = 2 tanA / (1 - tan²A)
21. Triple Angle Formulas:
    - sin(3A) = 3 sinA - 4 sin³A
    - cos(3A) = 4 cos³A - 3 cosA
    - tan(3A) = (3 tanA - tan³A) / (1 - 3 tan²A)
22. Product-to-Sum Formulas:
    - sin(A) sin(B) = ½ [cos(A - B) - cos(A + B)]
    - cos(A) cos(B) = ½ [cos(A + B) + cos(A - B)]
    - sin(A) cos(B) = ½ [sin(A + B) + sin(A - B)]
23. Sum-to-Product Formulas:
    - sin(A) ± sin(B) = 2 sin((A ± B) / 2) cos((A ∓ B) / 2)
    - cos(A) + cos(B) = 2 cos((A + B) / 2) cos((A - B) / 2)
    - cos(A) - cos(B) = -2 sin((A + B) / 2) sin((A - B) / 2)

கணிதம் உங்களுக்காக - 32 - கான்ஸெப்ட்கள்

1. Length of a chord of a circle: c = 2r sin(θ/2) (where r is the radius and θ is the central angle in radians)

2. Equation of a circle in parametric form: x = h + r cos(t), y = k + r sin(t) (where (h, k) is the center, r is the radius, and t is the parameter)
3. Equation of an ellipse in parametric form: x = h + a cos(t), y = k + b sin(t) (where (h, k) is the center, a is the semi-major axis, b is the semi-minor axis, and t is the parameter)
4. Equation of a hyperbola in parametric form: x = h + a sec(t), y = k + b tan(t) (where (h, k) is the center, a is the semi-major axis, b is the semi-minor axis, and t is the parameter)
5. Locus of a point: The set of all points that satisfy a given condition.
6. Length of the arc of a sector: L = rθ (where r is the radius and θ is the central angle in radians)
7. Area of a sector: A = 1/2r²θ (where r is the radius and θ is the central angle in radians)

8. Volume of a frustum of a pyramid: V = (1/3)h(A₁ + A₂ + √(A₁A₂)) (where h is the height, A₁ is the area of the top base, and A₂ is the area of the bottom base)
9. Surface area of a frustum of a pyramid: SA = A₁ + A₂ + (1/2)Pℓ (where P is the perimeter of the base and ℓ is the slant height)
10. Volume of a parallelepiped: V = |a · (b × c)| (where a, b, and c are vectors representing the edges)
11. Surface area of a parallelepiped: SA = 2(ab + bc + ca) (where a, b, and c are the lengths of the edges)
12. Volume of an oblique cylinder: V = πr²h
13. Surface area of an oblique cylinder: SA = 2πrh + 2πr²
14. Volume of a cone: V = 1/3πr²h
15. Surface area of a cone: SA = πr(r + l) (where l is the slant height)

16. Length of the diagonal of a regular polygon: d = √(2r²(1 - cos(2π/n))) (where r is the radius of the circumscribed circle and n is the number of sides)
17. Radius of the circumscribed circle of a regular polygon: R = (s / 2) * csc(π / n) (where s is the side length and n is the number of sides)
18. Radius of the inscribed circle of a regular polygon: r = (s / 2) * cot(π / n) (where s is the side length and n is the number of sides)
19. Length of a median of a trapezoid: m = (a + b) / 2 (where a and b are the lengths of the parallel sides)
20. Length of the diagonal of a parallelogram: d = √(a² + b² + 2ab cos(θ)) (where a and b are the side lengths and θ is the angle between the sides)

21. Law of Tangents: (a - b) / (a + b) = tan[(A - B)/2] / tan[(A + B)/2]
22. Law of Cotangents: (a - b) / (a + b) = cot[(A - B)/2] / cot[(A + B)/2]
23. Half-Angle Formulas:
    - sin²(A/2) = (1 - cosA) / 2
    - cos²(A/2) = (1 + cosA) / 2
    - tan²(A/2) = (1 - cosA) / (1 + cosA)
24. Double Angle Formulas:
    - sin(2A) = 2 sinA cosA
    - cos(2A) = cos²A - sin²A = 2 cos²A - 1 = 1 - 2 sin²A
    - tan(2A) = 2 tanA / (1 - tan²A)
25. Triple Angle Formulas:
    - sin(3A) = 3 sinA - 4 sin³A
    - cos(3A) = 4 cos³A - 3 cosA
    - tan(3A) = (3 tanA - tan³A) / (1 - 3 tan²A)

26. Scalar triple product: V = A · (B × C) (where A, B, and C are vectors)
27. Vector triple product: A × (B × C) = (A · C)B - (A · B)C
28. Distance between two skew lines: d = |(A₁ - A₂) · (B₁ × B₂)| / |B₁ × B₂| (where A₁ and A₂ are points on the lines, and B₁ and B₂ are direction vectors)

பிரபலமான படங்கள் (ஸ்டான்ட் அலோன் கதைக்களம்)

 1. E.T. the Extra-Terrestrial (1982)

2. Forrest Gump (1994)

3. Close Encounters of the Third Kind (1977)

4. Beetlejuice (1988)

5. Edward Scissorhands (1990)

6. Misery (1990)

7. The Princess Bride (1987)

8. The Big Lebowski (1998)

9. The Shawshank Redemption (1994)

10. Fight Club (1999)

11. The Sixth Sense (1999)

12. The Matrix (1999)

13. The Lion King (1994)

14. Toy Story (1995)

15. Jurassic Park (1993)

16. Titanic (1997)

17. Schindler's List (1993)

18. The Fugitive (1993)

19. Braveheart (1995)

20. Apollo 13 (1995)

21. The Green Mile (1999)

22. The Truman Show (1998)

23. The Silence of the Lambs (1991)

24. Good Will Hunting (1997)

25. The Departed (2006)

26. The Pursuit of Happyness (2006)

27. The Curious Case of Benjamin Button (2008)

28. Avatar (2009)

29. Inception (2010)

30. The Dark Knight (2008)

31. Up (2009)

32. The Hangover (2009)

33. The Social Network (2010)

34. The Wolf of Wall Street (2013)

35. Gravity (2013)

36. Interstellar (2014)

37. Mad Max: Fury Road (2015)

38. Creed (2015)

39. Spotlight (2015)

40. The Revenant (2015)

41. La La Land (2016)

42. Moonlight (2016)

43. Arrival (2016)

44. Dunkirk (2017)

45. Get Out (2017)

46. The Shape of Water (2017)

47. Black Panther (2018)

48. Roma (2018)

49. Parasite (2019)

50. Joker (2019)

கணிதம் உங்களுக்காக - 31 - கான்ஸெப்ட்கள்

 1. Angle between two lines: tan(θ) = |(m₁ - m₂) / (1 + m₁m₂)| (where m₁ and m₂ are the slopes of the lines)

2. Area of a triangle (using coordinates): A = ½ |x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂)|
3. Centroid of a triangle (using coordinates): G = ((x₁ + x₂ + x₃) / 3, (y₁ + y₂ + y₃) / 3)
4. Circumcenter of a triangle (using coordinates): Intersection of perpendicular bisectors of the sides of the triangle
5. Incenter of a triangle (using coordinates): Intersection of angle bisectors of the triangle

6. Volume of a regular polyhedron: V = (1/6) a³√(2/3)[5n(3 + 2√5)] (where a is the side length and n is the number of faces)
7. Surface area of a regular polyhedron: SA = n a²√3 (where a is the side length and n is the number of faces)
8. Volume of a truncated cube: V = (a³ / 3) (where a is the side length of the original cube and b is the side length of the truncated portion)
9. Surface area of a truncated cube: SA = 3a² + 2√3a² (where a is the side length of the original cube)
10. Volume of a cylindrical shell: V = 2πRh (R - r) (where R is the outer radius, r is the inner radius, and h is the height)
11. Surface area of a cylindrical shell: SA = 2πh(R + r) (where R is the outer radius, r is the inner radius, and h is the height)

12. Rotation around the origin by θ degrees: (x', y') = (x cosθ - y sinθ, x sinθ + y cosθ)
13. Reflection over a line y = mx + c: (x', y') = ((x(1 - m²) + 2my - 2mc) / (1 + m²), (y(1 - m²) + 2mx + 2c) / (1 + m²))
14. Dilation with respect to the origin: (x, y) → (kx, ky) (where k is the scale factor)
15. Horizontal shear transformation: (x', y') = (x + ky, y)
16. Vertical shear transformation: (x', y') = (x, y + kx)

17. Length of an arc: L = rθ (where r is the radius and θ is the central angle in radians)
18. Area of a sector: A = ½r²θ (where r is the radius and θ is the central angle in radians)
19. Segment area: A = ½r²(θ - sinθ)
20. Length of a chord: c = 2r sin(θ/2) (where r is the radius and θ is the central angle in radians)
21. Power of a Point Theorem: If a point P lies outside a circle and two secant lines PA and PB intersect the circle at A and B, then PA × PB = PC × PD (where C and D are points of intersection)
22. Segment lengths in a circle: If two chords AB and CD intersect at point P inside the circle, then PA × PB = PC × PD.
23. Length of a tangent segment: If a tangent from an external point P touches the circle at T, then PT² = PA × PB (where A and B are points of intersection of a secant through P)

24. Law of Tangents: (a - b) / (a + b) = tan[(A - B)/2] / tan[(A + B)/2]
25. Half-Angle Formulas:
    - sin²(A/2) = (1 - cosA) / 2
    - cos²(A/2) = (1 + cosA) / 2
    - tan²(A/2) = (1 - cosA) / (1 + cosA)
26. Double Angle Formulas:
    - sin(2A) = 2 sinA cosA
    - cos(2A) = cos²A - sin²A = 2 cos²A - 1 = 1 - 2 sin²A
    - tan(2A) = 2 tanA / (1 - tan²A)
27. Triple Angle Formulas:
    - sin(3A) = 3 sinA - 4 sin³A
    - cos(3A) = 4 cos³A - 3 cosA
    - tan(3A) = (3 tanA - tan³A) / (1 - 3 tan²A)

28. Dot product: A · B = A₁B₁ + A₂B₂ + A₃B₃
29. Vector cross product: A × B = (A₂B₃ - A₃B₂)i + (A₃B₁ - A₁B₃)j + (A₁B₂ - A₂B₁)k
30. Magnitude of a vector in 3D: |A| = √(A₁² + A₂² + A₃²)
31. Scalar projection of vector A onto vector B: proj_B(A) = (A · B) / |B|
32. Vector projection of vector A onto vector B: Proj_B(A) = ((A · B) / |B|²) B
33. Angle between two vectors: cos(θ) = (A · B) / (|A||B|)
34. Distance between two skew lines: d = |(A₁ - A₂) · (B₁ × B₂)| / |B₁ × B₂| (where A₁ and A₂ are points on the lines, and B₁ and B₂ are direction vectors)
35. Volume of a parallelepiped: V = |A · (B × C)| (where A, B, and C are vectors)
36. Scalar triple product: V = A · (B × C) (where A, B, and C are vectors)
37. Vector triple product: A × (B × C) = (A · C)B - (A · B)C

கணிதம் உங்களுக்காக - 30 - கான்ஸெப்ட்கள்

 


1. Volume of a cylindrical shell: V = 2πrh × (R - r) (where R is the outer radius and r is the inner radius)
2. Surface area of a cylindrical shell: SA = 2πh(R + r) (where R is the outer radius and r is the inner radius)
3. Volume of a truncated cone (frustum of a cone): V = (1/3)πh(R₁² + R₁R₂ + R₂²) (where h is the height, R₁ is the radius of the top base, and R₂ is the radius of the bottom base)
4. Surface area of a truncated cone: SA = π(R₁ + R₂)√((R₁ - R₂)² + h²) + πR₁² + πR₂²
5. Volume of a prismoid: V = (h/6)(A₁ + 4Aₘ + A₂) (where A₁ and A₂ are the areas of the parallel bases, Aₘ is the area of the midsection, and h is the height)
6. Surface area of a prismoid: SA = 2Aₘ + hP (where Aₘ is the area of the midsection and P is the perimeter of the base)

7. Polar to Cartesian coordinates: x = r cos(θ), y = r sin(θ)
8. Cartesian to Polar coordinates: r = √(x² + y²), θ = tan⁻¹(y / x)
9. Polar form of the equation of a line: r = (l) / (cos(θ - φ)) (where l is the perpendicular distance from the origin and φ is the angle with the positive x-axis)
10. Polar form of the equation of a circle: r(θ) = R (where R is the radius)
11. Parametric equations for a circle in polar coordinates: x = R cos(θ), y = R sin(θ) (where R is the radius and θ is the parameter)

12. Product-to-Sum Formulas:
    - sin(A) sin(B) = ½ [cos(A - B) - cos(A + B)]
    - cos(A) cos(B) = ½ [cos(A + B) + cos(A - B)]
    - sin(A) cos(B) = ½ [sin(A + B) + sin(A - B)]
13. Sum-to-Product Formulas:
    - sin(A) ± sin(B) = 2 sin((A ± B) / 2) cos((A ∓ B) / 2)
    - cos(A) + cos(B) = 2 cos((A + B) / 2) cos((A - B) / 2)
    - cos(A) - cos(B) = -2 sin((A + B) / 2) sin((A - B) / 2)
14. Half-Angle Formulas:
    - sin²(A/2) = (1 - cosA) / 2
    - cos²(A/2) = (1 + cosA) / 2
    - tan²(A/2) = (1 - cosA) / (1 + cosA)
15. Double Angle Formulas:
    - sin(2A) = 2 sinA cosA
    - cos(2A) = cos²A - sin²A = 2 cos²A - 1 = 1 - 2 sin²A
    - tan(2A) = 2 tanA / (1 - tan²A)
16. Triple Angle Formulas:
    - sin(3A) = 3 sinA - 4 sin³A
    - cos(3A) = 4 cos³A - 3 cosA
    - tan(3A) = (3 tanA - tan³A) / (1 - 3 tan²A)

17. Equation of a line in vector form: r = r₀ + t(v) (where r is the position vector, r₀ is a point on the line, v is the direction vector, and t is a scalar)
18. Equation of a plane in vector form: r · n = d (where r is the position vector, n is the normal vector, and d is the distance from the origin)
19. Equation of a sphere in vector form: |r - r₀| = R (where r is the position vector, r₀ is the center, and R is the radius)
20. Distance between two parallel planes: d = |d₁ - d₂| / |n| (where d₁ and d₂ are the distances from the origin and n is the normal vector)

21. Length of a median of a triangle: m = ½ √(2b² + 2c² - a²) (where a, b, and c are the lengths of the sides of the triangle, and m is the median to side a)
22. Length of an altitude in a triangle: h = 2A / a (where A is the area of the triangle and a is the base)
23. Length of an angle bisector in a triangle: l = √(bc[1 - (a² / (b + c)²)]) (where a, b, and c are the lengths of the sides of the triangle, and l is the angle bisector)
24. Brahmagupta's formula (area of a cyclic quadrilateral): A = √((s - a)(s - b)(s - c)(s - d) - abcd cos²(½θ)) (where θ is the sum of the opposite angles)
25. Area of a cyclic quadrilateral: A = √((s - a)(s - b)(s - c)(s - d)) (where a, b, c, and d are the lengths of the sides, and s is the semi-perimeter)
26. Area of an inscribed circle in a triangle: A = r × s (where r is the radius of the inscribed circle and s is the semi-perimeter)

1. Volume of a spherical wedge: V = (2/3)πR²θ (where R is the radius of the sphere and θ is the dihedral angle)
2. Volume of a spherical sector: V = (2/3)πR²h (where R is the radius of the sphere and h is the height of the spherical sector)
3. Surface area of a spherical sector: SA = 2πRh (where R is the radius of the sphere and h is the height of the spherical sector)
4. Volume of a spherical lune: V = (1/3)πR²θ (where R is the radius of the sphere and θ is the dihedral angle)
5. Surface area of a spherical lune: SA = 2πRh (where R is the radius of the sphere and h is the height of the spherical lune)

6. Polar to Cartesian coordinates: x = r cos(θ), y = r sin(θ)
7. Cartesian to Polar coordinates: r = √(x² + y²), θ = tan⁻¹(y / x)
8. Polar form of the equation of a line: r = l / cos(θ - φ) (where l is the perpendicular distance from the origin and φ is the angle with the positive x-axis)
9. Polar form of the equation of a circle: r(θ) = R (where R is the radius)
10. Parametric equations for a circle in polar coordinates: x = R cos(θ), y = R sin(θ) (where R is the radius and θ is the parameter)

11. Product-to-Sum Formulas:
    - sin(A) sin(B) = ½ [cos(A - B) - cos(A + B)]
    - cos(A) cos(B) = ½ [cos(A + B) + cos(A - B)]
    - sin(A) cos(B) = ½ [sin(A + B) + sin(A - B)]
12. Sum-to-Product Formulas:
    - sin(A) ± sin(B) = 2 sin((A ± B) / 2) cos((A ∓ B) / 2)
    - cos(A) + cos(B) = 2 cos((A + B) / 2) cos((A - B) / 2)
    - cos(A) - cos(B) = -2 sin((A + B) / 2) sin((A - B) / 2)
13. Half-Angle Formulas:
    - sin²(A/2) = (1 - cosA) / 2
    - cos²(A/2) = (1 + cosA) / 2
    - tan²(A/2) = (1 - cosA) / (1 + cosA)
14. Double Angle Formulas:
    - sin(2A) = 2 sinA cosA
    - cos(2A) = cos²A - sin²A = 2 cos²A - 1 = 1 - 2 sin²A
    - tan(2A) = 2 tanA / (1 - tan²A)
15. Triple Angle Formulas:
    - sin(3A) = 3 sinA - 4 sin³A
    - cos(3A) = 4 cos³A - 3 cosA
    - tan(3A) = (3 tanA - tan³A) / (1 - 3 tan²A)

16. Dot product: A · B = A₁B₁ + A₂B₂ + A₃B₃
17. Vector cross product: A × B = (A₂B₃ - A₃B₂)i + (A₃B₁ - A₁B₃)j + (A₁B₂ - A₂B₁)k
18. Magnitude of a vector in 3D: |A| = √(A₁² + A₂² + A₃²)
19. Scalar projection of vector A onto vector B: proj_B(A) = (A · B) / |B|
20. Vector projection of vector A onto vector B: Proj_B(A) = ((A · B) / |B|²) B
21. Angle between two vectors: cos(θ) = (A · B) / (|A||B|)

22. Length of a median of a triangle: m = ½ √(2b² + 2c² - a²) (where a, b, and c are the lengths of the sides of the triangle, and m is the median to side a)
23. Length of an altitude in a triangle: h = 2A / a (where A is the area of the triangle and a is the base)
24. Length of an angle bisector in a triangle: l = √(bc[1 - (a² / (b + c)²)]) (where a, b, and c are the lengths of the sides of the triangle, and l is the angle bisector)
25. Brahmagupta's formula (area of a cyclic quadrilateral): A = √((s - a)(s - b)(s - c)(s - d) - abcd cos²(½θ)) (where θ is the sum of the opposite angles)
26. Area of a cyclic quadrilateral: A = √((s - a)(s - b)(s - c)(s - d)) (where a, b, c, and d are the lengths of the sides, and s is the semi-perimeter)
27. Area of an inscribed circle in a triangle: A = r × s (where r is the radius of the inscribed circle and s is the semi-perimeter)


1. Length of the altitude of a right triangle: h = (a * b) / c (where a and b are the legs and c is the hypotenuse)
2. Length of the altitude of an equilateral triangle: h = (√3 / 2) * a (where a is the side length)
3. Radius of the circumscribed circle of a triangle: R = (abc) / (4A) (where a, b, and c are the side lengths and A is the area of the triangle)
4. Radius of the inscribed circle of a triangle: r = A / s (where A is the area of the triangle and s is the semi-perimeter)
5. Length of the median of a trapezoid: m = (a + b) / 2 (where a and b are the lengths of the parallel sides)
6. Length of the diagonal of a rectangle: d = √(a² + b²) (where a and b are the side lengths)
7. Length of the diagonal of a parallelogram: d = √(a² + b² + 2ab cos(θ)) (where a and b are the side lengths and θ is the angle between the sides)
8. Length of the side of a regular polygon: s = 2R sin(π / n) (where R is the radius of the circumscribed circle and n is the number of sides)
9. Radius of the circumscribed circle of a regular polygon: R = (s / 2) * csc(π / n) (where s is the side length and n is the number of sides)
10. Radius of the inscribed circle of a regular polygon: r = (s / 2) * cot(π / n) (where s is the side length and n is the number of sides)

11. Equation of the parabola (vertex form): y - k = a(x - h)² (where (h, k) is the vertex)
12. Equation of the ellipse (standard form): (x - h)² / a² + (y - k)² / b² = 1 (where (h, k) is the center, a is the semi-major axis, and b is the semi-minor axis)
13. Equation of the hyperbola (standard form): (x - h)² / a² - (y - k)² / b² = 1 (horizontal) or (y - k)² / a² - (x - h)² / b² = 1 (vertical)
14. Slopes of the asymptotes of a hyperbola: ±(b / a) (horizontal) or ±(a / b) (vertical)
15. Distance between two parallel lines: d = |c₂ - c₁| / √(a² + b²) (where the equations of the lines are Ax + By + C₁ = 0 and Ax + By + C₂ = 0)
16. Distance between a point and a plane: d = |Ax₁ + By₁ + Cz₁ + D| / √(A² + B² + C²)

17. Volume of an oblique prism: V = B * h (where B is the area of the base and h is the height)
18. Surface area of an oblique prism: SA = 2B + P * h (where B is the area of the base, P is the perimeter of the base, and h is the height)
19. Volume of a truncated cylinder: V = πh(r₁² + r₁r₂ + r₂²) / 3 (where h is the height, r₁ is the radius of the top base, and r₂ is the radius of the bottom base)
20. Surface area of a truncated cylinder: SA = π(r₁ + r₂)√((r₂ - r₁)² + h²) + πr₁² + πr₂²
21. Volume of a spherical cap: V = (1/6)πh(3a² + 3b² + h²) (where h is the height of the cap and a and b are the radii of the cap's bases)
22. Surface area of a spherical cap: SA = 2πRh (where h is the height of the cap and R is the radius of the sphere)
23. Volume of a spherical wedge: V = (2/3)πR²θ (where R is the radius of the sphere and θ is the dihedral angle)
24. Surface area of a spherical wedge: SA = 2πRh (where R is the radius of the sphere and h is the height of the spherical wedge)

25. Rotation about the origin by θ degrees: (x', y') = (x cosθ - y sinθ, x sinθ + y cosθ)
26. Translation: (x, y) → (x + a, y + b)
27. Reflection over the x-axis: (x, y) → (x, -y)
28. Reflection over the y-axis: (x, y) → (-x, y)
29. Reflection over the line y = x: (x, y) → (y, x)
30. Reflection over the line y = -x: (x, y) → (-y, -x)
31. Dilation with respect to the origin: (x, y) → (kx, ky) (where k is the scale factor)
32. Dilation with respect to a point (h, k): (x', y') = (kx + (1 - k)h, ky + (1 - k)k)


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