JEE NEET PDF STUDY MATERIALS

Trigonometry Cheatsheet @pdfstudymaterialss

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📚 HALIDES - [CHEMISTRY] 📝 SHORT HANDWRITTEN NOTES @pdfstudymaterialss

1: Number of Bones 206😗 2: Number of Muscles 639 3: Number of Kidneys 2😍 4: Number of Milk Teeth 20 5: Number of Ribs 24 (12 pair) 6: Number of Heart Chamber 4 7: Largest artery Aorta 😉 8: Normal blood pressure 120/80mmHg 9: Ph of Blood 7.4 10: Number of vertebrae in the Spine 33😅 11: Number of vertebrae in the Neck 7 12: Number of Bones in Middle Ear 6😅 13: Number of Bones in Face 14 14: Number of Bones in Skull 22 15: Number of Bones in Chest 25🙊 16: Number of Bones in Arms 6 17: Number of Muscles in Human Arm 72 18: Number of Pumps in Heart 2🔥 19: Largest Organ Skin 20: Largest gland Liver🤟 21: Biggest cell female Ovum 22: Smallest cell male Sperm💦 23: Smallest Bone Stapes 24: First transplanted Organ Heart 😏 25: Average length of Small Intestine 7m 26: Average length of 🤧Large Intestine 1.5m 27: Average weight of new Born baby 2.6kg🔥 28: Pulse rate in One Minute 72 times 29: Normal body temperature 37 C° (98.4 F°)😎 30: Average Blood Volume 4 to 5 liters 31: Life Span of RBC 120 days 32: Life Span of WBC 10 to 15 days😊 33: Pregnancy Period 280 days (40 week) 34: Number of Bones in Human Foot 33 35: Number of Bones in Each wrist 8🙄 36: Number of Bones in Hand 27 37: Largest Endocrine gland Thyroid 🤗 38: Largest Lymphatic Organ Spleen 39: Largest part of Brain Cerebrum 40: Largest & Strongest Bone Femur 💋 41: Smallest Muscle Stapedius (Middle Ear) 41: Number of Chromosome 46 (23 pair)🙈 42: Number of Bones in new Born baby 306😘 43: Viscosity of Blood 4.5 to 5.5 44: Universal Donor Blood Group O 45: Universal Recipient Blood Group AB🧐 46: Largest WBC Monocyte 47: Smallest WBC Lymphocyte 48: Increase RBC count called🎲 Polycethemia 49: Blood Bank in the Body is Spleen 😜 50: Non Nucleated Blood cell is RBC 51: RBC produced in the Bone Marrow 🤔 52: River of Life is Called Blood 53: Normal Blood Cholesterol level 250mg/dl 54: Fluid part of Blood is Plasma🥺 55: Normal Blood Sugar 100mg/dl😍 @pdfstudymaterialss

Hormones

(c) Distance of closest approach, r0 = 2Ze2/(4πε0)E Here E = ½ mv2 = KE of the α particle. Bohr’s atomic model:- (a) The central part of the atom called nucleus, contains whole of positive charge and almost whole of the mass of atom. Electrons revolve round the nucleus in fixed circular orbits. (b) Electrons are capable of revolving only in certain fixed orbits, called stationary orbits or permitted orbits. In such orbits they do not radiate any energy. (c) While revolving permitted orbit an electron possesses angular momentum L (= mvr) which is an integral multiple of h/2π. L=mvr =n (h/2π) Here n is an integer and h is the Planck’s constant. (d) Electrons are capable of changing the orbits. On absorbing energy they move to a higher orbit while emission of energy takes place when electrons move to a lower orbit. If f is the frequency of radiant energy, hf= W2-W1 Here W2 is the energy of electron in lower orbit and W1 is the energy of electron in higher orbit. (e) All the laws of mechanics can be applied to electron revolving in a stable orbit while they are not applicable to an electron in transition. Bohr’s Theory of Atom:- (a) Orbital velocity of electron:- vn= 2πkZe2/nh For a particular orbit (n= constant), orbital velocity of electron varies directly as the atomic number of the substance. vn∝Z (b) For a particular element (Z= constant), orbital velocity of the electron varies inversely as the order of the orbit. vn∝1/n (c) v = nh/2πmr Relation between vn and v1:-vn = v1/n Radius of electron:- r= n2h2/4π2kmZe2 So, r∝n2 For, C.G.S system (k = 1), r = n2h2/4π2mZe2 S.I (k = 1/4πε0), r =(ε0/π) (n2h2/mZe2) Kinetic energy of the electron:- It is the energy possessed by the electron by virtue of its motion in the orbit. K.E = ½ mv2 = ½ k (Ze2/r) Potential energy:- It is the energypossessed by the electronby virtue of its position near the nucleus. P.E = -k (Ze2/r ) Total energy:- W= K.E + P.E W=- ½ k (Ze2/r) = -k2 2π2Z2me4/n2h2 For, C.G.S (k = 1), W = - [2π2Z2me4/n2h2] For, S.I. ( k = 1/4πε0), W = - (1/8ε02) [Z2me4/n2h2] Since, W∝1/n2, a higher orbit electron possesses a lesser negative energy (greater energy) than that of a lower orbit electron. Frequency, wavelength and wave number of radiation:- Frequency, f = k2[2π2Z2me4/h3] [1/n12 – 1/n22] Wave number of radiation, Here R is the Rydberg’s constant and its value is, R= k2 [2π2Z2me4/ch3] Bohr’s theory of hydrogen atom (Z=1):- (a) Radius of orbit:- r= n2h4/4π2me2 (C.G.S) r= (ε0/π) (n2h2/me2) (S.I) (b) Energy of electron:- W= 2π2me4/n2h2 (C.G.S) W =(1/8ε0)[me4/n2h2] (c) Frequency, wavelength and wave number of radiation:- C.G.S:- k =1 and Z=1 Frequency= f=2π2me4/h3 [1/n12 – 1/n22] Wave number = 1/λ = 2π2me4/ch3 [1/n12 – 1/n22] S.I:- k =1/4πε0 and Z=1 Frequency= f = (1/8ε0) (me4/h3)[1/n12 – 1/n22] Wave number = 1/λ = (1/8ε02) (me4/ch3)[1/n12 – 1/n22] Rydberg’s constant:- R=k2 =2π2z2 me4/ch3 For hydrogen atom, Z = 1, R = RH = k2 (2π2 me4/ch3). For C.G.S system (k=1), RH = 2π2 me4/ch3 For S.I system (k=1/4πε0), RH = (1/8ε02) (me4/ch3) Wave number, 1/λ = RH [1/n12 – 1/n22] Hydrogen Spectrum:- (a) For Lyman series:- 1/λ = R [1– 1/n2], n = 2,3,4…..∞ (b) For Balmer series:- 1/λ = R [1/22 – 1/n2], n =3,4,5…..∞ (c) For Paschen series:-1/λ = R [1/32 – 1/n2], n =4,5,6…..∞ (d) For Brackett series:-1/λ = R [1/42 – 1/n2], n =5,6,7…..∞ (e) P-fund series:-1/λ = R [1/52 – 1/n2], n =6,7,8…..∞ Series limits (λmin):- (a) Lyman:- λmin = 912 Å (b) Balmer:-λmin = 3645 Å (c) Paschen:- λmin = 8201 Å Energy levels of hydrogen atom:- W = -k22π2me4/n2h2 For, n=1, W1 = -13.6 eV For the first excited state, n=2, W2 =W1/4 = (-13.6/4) eV = -3.4 eV For the second excited state, n=3, W3 =W1/9 = (-13.6/9) eV = -1.51 eV Similarly, for other excited states, W4 = -0.85 eV and W5 = -0.54 eV Number of emission lines from excited state:-n = n(n-1)/2 Ionization energy:- - E1 = +(13.6Z2)eV (a) For H-atom, I.E = 13.6 eV (b) For He+ ion, I.E = 54.4 eV (c) For Li++ ion, I.E = 122.4 eV @pdfstudymaterialss

📚 POLYMERS 📝 SHORT HANDWRITTEN NOTES @pdfstudymaterialss

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🔥🔥 Thermodynamics🔥🔥 ™✓✓✓✓✓✓✓✓✓✓✓✓ At a Glance...... ,🔥Basic Terminology🔥 ⭐System- Part of the universe under investigation. ⭐Open System- A system which can exchange both energy and matter with its surroundings. ⭐Closed System- A system which permits passage of energy but not mass, across its boundary. ⭐Isolated system- A system which can neither exchange energy nor matter with its surrounding. ⭐Surroundings- Part of the universe other than system, which can interact with it. ⭐Boundary- Anything which separates system from surrounding. ⭐State variables- The variables which are required to be defined in order to define state of any system i.e. pressure, volume, mass, temperature, surface area, etc. ⭐State Functions- Property of system which depend only on the state of the system and not on the path. Example: Pressure, volume, temperature, internal energy, enthalpy, entropy etc. ⭐Intensive properties- Properties of a system which do not depend on mass of the system i.e. temperature, pressure, density, concentration, ⭐Extensive properties- Properties of a system which depend on mass of the system i.e. volume, energy, enthalpy, entropy etc. ⭐Process- Path along which state of a system changes. ⭐Isothermal process- Process which takes place at constant temperature ⭐Isobaric process- Process which takes place at constant pressure ⭐Isochoric process- Process which takes place at constant volume. ⭐Adiabatic process- Process during which transfer of heat cannot take place between system and surrounding. ⭐Cyclic process- Process in which system comes back to its initial state after undergoing series of changes. ⭐Reversible process- Process during which the system always departs infinitesimally from the state of equilibrium i.e. its direction can be reversed at any moment. ⭐Irriversible Process- This type of process is fast and gets completed in a single step. This process cannot be reversed. All the natural processes are of this type. @pdfstudymaterialss

Surface Chemistry Short Notes @pdfstudymaterialss

Female Reproductive System @pdfstudymaterialss

📚Notes on Trigonometric Equations and Identities📚 A function f(x) is said to be periodic if there exists some T > 0 such that f(x+T) = f(x) for all x in the domain of f(x). In case, the T in the definition of period of f(x) is the smallest positive real number then this ‘T’ is called the period of f(x). Periods of various trigonometric functions are listed below: 1) sin x has period 2π 2) cos x has period 2π 3) tan x has period π 4) sin(ax+b), cos (ax+b), sec(ax+b), cosec (ax+b) all are of period 2π/a 5) tan (ax+b) and cot (ax+b) have π/a as their period 6) |sin (ax+b)|, |cos (ax+b)|, |sec(ax+b)|, |cosec (ax+b)| all are of period π/a 7) |tan (ax+b)| and |cot (ax+b)| have π/2a as their period ➖Sum and Difference Formulae of Trigonometric Ratios 1) sin(a + ß) = sin(a)cos(ß) + cos(a)sin(ß) 2) sin(a – ß) = sin(a)cos(ß) – cos(a)sin(ß) 3) cos(a + ß) = cos(a)cos(ß) – sin(a)sin(ß) 4) cos(a – ß) = cos(a)cos(ß) + sin(a)sin(ß) 5) tan(a + ß) = [tan(a) + tan (ß)]/ [1 - tan(a)tan (ß)] 6)tan(a - ß) = [tan(a) - tan (ß)]/ [1 + tan (a) tan (ß)] 7) tan (π/4 + θ) = (1 + tan θ)/(1 - tan θ) 8) tan (π/4 - θ) = (1 - tan θ)/(1 + tan θ) 9) cot (a + ß) = [cot(a) . cot (ß) - 1]/ [cot (a) +cot (ß)] 10) cot (a - ß) = [cot(a) . cot (ß) + 1]/ [cot (ß) - cot (a)] ➖Double or Triple -Angle Identities 1) sin 2x = 2sin x cos x 2) cos2x = cos2x – sin2x = 1 – 2sin2x = 2cos2x – 1 3) tan 2x = 2 tan x / (1-tan 2x) 4) sin 3x = 3 sin x – 4 sin3x 5) cos3x = 4 cos3x – 3 cosx 6) tan 3x = (3 tan x - tan3x) / (1- 3tan 2x) ➖For angles A, B and C, we have 1) sin (A + B +C) = sinAcosBcosC + cosAsinBcosC + cosAcosBsinC - sinAsinBsinC 2) cos (A + B +C) = cosAcosBcosC- cosAsinBsinC - sinAcosBsinC - sinAsinBcosC 3) tan (A + B +C) = [tan A + tan B + tan C –tan A tan B tan C]/ [1- tan Atan B - tan B tan C –tan A tan C 4) cot (A + B +C) = [cot A cot B cot C – cotA - cot B - cot C]/ [cot A cot B + cot Bcot C + cot A cotC–1] ➖List of some other trigonometric formulas: 1) 2sinAcosB = sin(A + B) + sin (A - B) 2) 2cosAsinB = sin(A + B) - sin (A - B) 3) 2cosAcosB = cos(A + B) + cos(A - B) 4) 2sinAsinB = cos(A - B) - cos (A + B) 5) sin A + sin B = 2 sin [(A+B)/2] cos [(A-B)/2] 6) sin A - sin B = 2 sin [(A-B)/2] cos [(A+B)/2] 7) cosA + cos B = 2 cos [(A+B)/2] cos [(A-B)/2] 8) cosA - cos B = 2 sin [(A+B)/2] sin [(B-A)/2] 9) tanA ± tanB = sin (A ± B)/ cos A cos B 10)cot A ± cot B = sin (B ± A)/ sin A sin B ➖Method of solving a trigonometric equation: 1) If possible, reduce the equation in terms of any one variable, preferably x. Then solve the equation as you used to in case of a single variable. 2) Try to derive the linear/algebraic simultaneous equations from the given trigonometric equations and solve them as algebraic simultaneous equations. 3) At times, you might be required to make certain substitutions. It would be beneficial when the system has only two trigonometric functions. ➖Some results which are useful for solving trigonometric equations: 1) sin θ = sina and cosθ = cosa ⇒ θ = 2nπ + a 2) sin θ = 0 ⇒ θ = nπ 3) cosθ = 0 ⇒ θ = (2n + 1)π/2 4) tan θ = 0 ⇒ θ = nπ 5) sinθ = sina⇒ θ = nπ + (-1)na where a ∈ [–π/2, π/2] 6) cosθ= cos a ⇒ θ = 2nπ ± a, where a ∈[0,π] 7) tanθ = tana⇒ θ = nπ+ a, where a ∈[–π/2, π/2] 8) sinθ = 1 ⇒ θ= (4n + 1)π/2 9) sin θ = -1 ⇒ θ = (4n - 1) π /2 10) sin θ = -1 ⇒ θ = (2n +1) π /2 11) |sinθ| = 1⇒ θ =2nπ 12) cosθ = 1 ⇒ θ =(2n + 1) 13) |cosθ| = 1⇒ θ =nπ ❣️ FOR MORE JOIN❣️ @pdfstudymaterialss

Environmental Issues Important lines highlights @pdfstudymaterialss

Hydrogen Short Notes @pdfstudymaterialss

How do Organisms Reproduce Handwritten Notes @pdfstudymaterialss

📚 PHYSICAL CONSTANTS 📝 ONE SHOT - NOTES @pdfstudymaterialss

*#Some_Important_Questions#* *⭕️CELL⭕️* ⭕️The word cell came from the latin word. *⭕️Ans: Cellula* ⭕️All living organisms are made up of *⭕️Ans: Cell* ⭕️Study of cell - *Cytology* ⭕️Study of tissue - *Histology* ⭕️The physical unit of life *⭕️Ans: Protoplasm* ⭕️Who invented the cell? *⭕️Ans: Robert Hook in 1665* ⭕️Cell theory was proposed by? *⭕️Ans: M.J. Schleiden and Theodor Schwann (1839)* ⭕️Scientist who observed cork cells under a microscope? *⭕️Ans: Robert Hook* ⭕️Plant cell was discovered by? *⭕️Ans: Robert Hook* ⭕️The term protoplasm was coined by 3.E. Purkinje Scientist who called protoplasm as the physical basis of life T.H. Huxley Largest cell *⭕️Ans: Ostrich's egg* ⭕️Smallest cell? *⭕️Ans: Mycoplasma* ⭕️Organisms known as pleuro pneumonia like organism (PPLO)? *⭕️Ans: Mycoplasma* ⭕️Smallest cell in the human body? *⭕️Ans: Sperm* ⭕️Largest cell in human body? *⭕️Ans: Ovum* ⭕️Longest cell in human body? *⭕️Ans: Neuron* ⭕️Power house of a cell? *⭕️Ans: Mitochondria* ⭕️Brain of the cell? *⭕️Ans: Nucleus* ⭕️Kitchen of the cell? *⭕️Ans: Chloroplast* ⭕️Energy Currency of the cell? *⭕️Ans: ATP* ⭕️Suicidal bag? *⭕️Ans: Lysosomes* ⭕️Traffic Police of the cell? *⭕️Ans: Golgibodies* ⭕️Skeletal system of the cell? *⭕️Ans: Endoplasmic reticulum* ⭕️The cell having most life span in human body? *⭕️Ans: RBC* ⭕️Cytoplasm and Nucleus are included in? *⭕️Ans: Protoplasm* ⭕️The cell organelle known as protein factory? *⭕️Ans: Ribosome* ⭕️The organelle in the site of protein synthesis? *⭕️Ans: Ribosome* ⭕️Ribosome has its own? *⭕️Ans: RNA* ⭕️Two types of acids present in cell? *⭕️Ans: DNA and RNA* ⭕️The basic unit of chromosome? *⭕️Ans: DNA* ⭕️The functional unit of DNA? *⭕️Ans: Genes* ⭕️Function of DNA? *⭕️Ans: Transmission of hereditary traits* ⭕️Function of RNA? *⭕️Ans: Protein synthesis* ⭕️Each chromosome has? *⭕️Ans: A pair of DNA* ⭕️DNA sugar is called? *⭕️Ans: Deoxyribose* ⭕️The nitrogen bases in DNA? *⭕️Ans: Adenine, Guanine, Thymine, Cytosine* ⭕️The RNA sugar? *⭕️Ans: Ribose* ⭕️The nitrogen bases in RNA? *⭕️Ans : Adenine, Uracil, Cytosine and Guanine* ⭕️The double helical model of DNA was discovered by? *⭕️Ans: James Watson and Francis Crick* ⭕️The enzyme present in lysosome? *⭕️Ans: Hydrolytic enzyme* ⭕️Lysosome was discovered by? *⭕️Ans: Christion de Duve (1955)* ⭕️Compounds enter the cell through? *⭕️Ans: Endoplasmic reticulum* ⭕️The cell organelle which is the sites of energy transfer in living cell? *⭕️Ans: Mitochondria* ⭕️The functions of mitochondria? *⭕️Ans: Cellular respiration, ATP production* ⭕️The stage of cellular respiration which does not need oxygen? *⭕️Ans: Glycolysis* ⭕️The term Mitochondria was coined by? *⭕️Ans: Carl Benda (1898)* ⭕️Name the process in which the main product is energy? *⭕️Ans: Cellular respiration* ⭕️In mitochondria the energy is formed in the form of? *⭕️Ans: ATP molecules* ⭕️Which molecule is known as the energy currency? *⭕️Ans : ATP molecule* ⭕️ATP? *⭕️Ans: Adenosine Triphosphate* ⭕️The cell that lacks mitochondria and nucleus? *⭕️Ans: RBC* ⭕️Number of ATP molecule that will get from one molecule of glucose? *⭕️Ans: 38ATP* ⭕️The elements in the component of ATP? *⭕️Ans: Nitrogen and phosphorus* ⭕️Kerb's cycle is related to? *⭕️Ans: Cellular respiration* ⭕️Cell respiration was discovered by? *⭕️Ans: Adolf Krebs* ⭕️The whole process of a cell is controlled by? *⭕️Ans: Nucleus* ⭕️The cell without nucleus? *⭕️Ans: Prokaryotic cell* ⭕️The cell with nucleus? *⭕️Ans : Eukaryotic cell* ⭕️Nucleus was discovered by? *⭕️Ans : Robert Brown* ⭕️Name the process in which lysosome digest its own cell organelles? *⭕️Ans: Autoplagy* ⭕️A network like structure inside the nucleus is called? *⭕️Ans: Chromatin Reticulum* ⭕️The structure of cell is first explained in the book of? *⭕️Ans: Micrographia* ⭕️The living thing which do not obey cell theory? *⭕️Ans: Virus* ⭕️The scientist first studied about all structure and cell reaction? *⭕️Ans: Theodor Schwaan* ⭕️Schwaan cell are seen in? *⭕️Ans: Nerve cell* @pdfstudymaterialss