Gaurav Gupta sir

2021-12-17 07:23:27 Algebra - Revision Notes on Permutations

The concept of permutation is used for the arrangement of objects in a specific order i.e. whenever the order is important, permutation is used.

The total number of permutations on a set of n objects is given by n! and is denoted as nPn = n!

The total number of permutations on a set of n objects taken r at a time is given by nPr = n!/ (n-r)!

The number of ways of arranging n objects of which r are the same is given by n!/ r!

If we wish to arrange a total of n objects, out of which ‘p’ are of one type, q of second type are alike, and r of a third kind are same, then such a computation is done as n!/p!q!r!

Al most all permutation questions involve putting things in order from a line where the order matters. For example ABC is a different permutation to ACB.

The number of permutations of n distinct objects when a particular object is not to be considered in the arrangement is given by n-1Pr

The number of permutations of n distinct objects when a specific object is to be always included in the arrangement is given by r.n-1Pr-1.

If we need to compute the number of permutations of n different objects, out of which r have to be selected and each object has the probability of occurring once, twice or thrice… up to r times in any arrangement is given by (n)r.

Circular permutation is used when some arrangement is to be made in the form of a ring or circle.

When ‘n’ different or unlike objects are to be arranged in a ring in such a way that the clockwise and anticlockwise arrangements are different, then the number of such arrangements is given by (n – 1)!

If n persons are to be seated around a round table in such a way that no person has similar neighbor then it is given as ½ (n – 1)!

The number of necklaces formed with n beads of different colors = ½ (n – 1)!

nP0 =1

nP1 = n

nPn = n!/(n-n)! = n! /0! = n! /1= n! Open / Comment

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2021-12-16 15:00:02 Father of Biology : Aristole
Father of Modern Biology: Linnaeus
Father of Antibiotics fb: Alexander Fleming
Father of Taxonomy : Carolus Linnaeus
Father of Immunology : Edward Jenner
Father of Microbiology : Anton van Leenuwenhoek
Father of Modern Microbiology : Louis Pasteur
Father of Medical Microbiology : Robert Koch
Father of Pathology : Rudolph Virchow
Father of Bacteriology : Robert Koch
Father of Virology : W.M.Stanley
Father of Embryology : Aristotle
Father of Modern Embryology : Ernst Von Baer
Father of Physiology : Stephan Hales
Father of Modern experimental physiology : Calude Bernard
Father of Genetics : Rev. Gregor Mendel
Father of Modern Genetics : Bateson
Father of Human Genetics/ Biochemical genetics : Arachibald Garrod
Father of Experimental Genetics : T.H. Morgan
Father of Haploid Genetics / Neurospora Genetics : Dodge
Father of Ecology : Theophrastus
Father of Cloning : Ian Willmut
Father of Plant anatomy : Grew
Father of Histology (Microscopic anatomy) : Malpighi
Father of Cytology : Robert Hooke
Father of modern Cytology : Swanson
Father of Paleontology : Leonard da Vinci
Father of modern Paleontology : Cuvier
Father of Concept of Evolution: Empedocles
Father of Botany: Theophrastus
Father of Modern Botany : Bauhin
Father of Zoology : Aristotle
Father of Biochemistry : Liebig
Father of Epidemiology : John Snow
Father of Plant Pathology : de Bary
Father of Modern Pathology : Rudolf Virchow
Father of Genetic Engineering : Paul Berg
Father of Gene therapy : Anderson
Father of Ethology : Konard Lorentz
Father of Endocrinology : Thomas Addison
Father of Eugenics : Galton
Father of Gerantology : Korenchevsk
Father of Palynology : Erdtman
Father of Stress physiology : Hans Selye
Father of Electrocardiography : Einthoven
Father of DNA Fingerprinting : Alec Jeffery
Father of Mycology : Micheli
Father of Bryology : Hedwig
Father of Phycology:Father of ATP cycle: Lipmann
Father of Chemotherapy :Father of Anatomy : Herophilus
Father of Modern Anatomy : Andreas Vesalius
Father of actinobiology / radiation biology : HJVS Muller
Father of Homeopathy : Hahnemann
Father of Ayurveda : Charka
Father of Surgery and Plastic Surgery : Susruta
Father of Blood circulation : William Harvey
Father of Medicine : Hippocrates
Father of Blood Group : Landsteiner
Father of Polio Vaccine : Jonas Salk
Father of Green Revolution: Norman Borlaug Open / Comment

2021-12-16 13:39:27 Let’s aim for full marks in Biology Term 1 exam!!

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2021-12-16 10:14:38 Important Points For NEET

Evidences from comparative morphology and anatomy :-

Examples of homologous organs:

(i) Forelimbs of mammals
(ii) Thorn of Bougainvillea and tendril of Cucurbita both are modification of axillary bud.
(iii)Vertebrate hearts or brains
(iv)Mouth parts of insects :
Cockroach Honey bee Mosquito
(Biting & chewing) (Chewing & lapping) (Piercing & Sucking)
(v) Testes in male and ovaries in female
(vi) Potato and Ginger - both are modified shoot
(vii) Radish and Carrot - both are modified roots

Examples of Analogous organs :

(i) Wings of butterfly and birds
(ii) Eye of the octopus and of mammals
(iii) Flippers of Penguins and Dolphins
(iv) Sweet potato (root modification) and potato (stem modification)
(v) Sting of bee and scorpion
(vi) Chloragogen cells of earthworm and liver of vertebrates Open / Comment

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2021-12-16 08:40:23 Hello baccho

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2021-12-16 07:03:39 Revision Notes on Liquids at Rest


Force of cohesion:- It is force between two molecules of similar nature.

Force of adhesion:- It is the force between two molecules of different nature.

Molecular range:- The maximum distance between two molecules so that the force of attraction between them remains effective is called molecular range.

Sphere of influence:- Sphere of influence of any molecule is the sphere with molecule as its center and having a radius equal to molecular range (=10-7 cm).

Surface film:- Surface film of a liquid is defined as the portion of liquid lying on the surface and caught between two parallel planes situated molecular range apart.

Surface tension:-

Surface Tension

Surface tension is the property of a liquid by virtue of which its free surface behaves like a stretched membrane and supports, comparatively heavier objects placed over it. It is measured in terms of force of surface tension.

Force of surface tension:- It is defined as the amount of force acting per unit length on either side of an imaginary line drawn over the liquid surface.

(a) T = Force/length = F/l

(b) T = Surface energy/Surface area = W/A

Units:- S.I – Nm-1

C.G.S- dyn cm-1

Additional force:-
(a) For a cylindrical rod:- F = T×2πr (Here r is the radius of cylindrical rod)

(b) For a rectangular block:- F = T×2(l+d) (Here l is the length and d is the thickness of the rectangular block)

(c) For a ring:- F = T×2×2πr (Here r is the radius of cylindrical rod)

Surface energy:-
Potential energy per unit area of the surface is called surface energy.

(a) Expansion under isothermal condition:-

To do work against forces of surface tension:-

W= T×A (Here A is the total increase in surface area)

To supply energy for maintaining the temperature of the film:-

E = T+H

(b) Expansion under adiabatic conditions:-

E = T

Force of surface tension is numerically equal to the surface energy under adiabatic conditions.

Drops and Bubbles:-

(a) Drop:- Area of surface film of a spherical drop of radius R is given by, A = 4πR2

(b) Bubble:- The surface area of the surface films of a bubble of radius R is, A = 2×4πR2

Combination of n drops into one big drop:-

(a) R = n1/3r

(b) Ei = n (4πr2T), Ef =4πR2T

(c) Ef/ Ei = n -1/3

(d) ΔE/Ei = [1-(1/n1/3)]

(e) ΔE = 4πR2T (n1/3-1) = 4πR3T (1/r – 1/R)

Angle of contact:- Angle of contact, for a pair of solid and liquid, is defined as the angle between tangent to the liquid surface drawn at the point of contact and the solid surface inside the liquid.

(a) When θ < 90º (acute):-

Fa >Fc/√2

(i) Force of cohesion between two molecules of liquid is less than the force of adhesion between molecules of solid and liquid.

(ii) Liquid molecules will stick with the solid, thus making solid wet.

(iii) Such liquid is put in the solid tube; it will have meniscus concave upwards.

(b) When θ > 90º (obtuse):-Fa
(i) Force of cohesion between two molecules of liquid is less than the force of adhesion between molecules of solid and liquid.

(ii) In this case, liquids do not wet the solids.

(iii) Such liquids when put in the solid tube will have a meniscus convex upwards.

(c) When θ = 90º:-?

Fa=Fc/√2

The surface of liquid at the point of contact is plane. In this case force of cohesion and adhesion are comparable to each other.

(d) cosθc = Tsa – Tsl/Tla

Here, Tsa,Tsl and Tla represent solid-air, solid-liquid and liquid-air surface tension respectively). Here θc is acute if Tsl < Tsa while θc is obtuse if Tsl >Tsa.

Capillarity:-

?Rise of Liquid in a Capillary Tube?Capillarity is the phenomenon, by virtue of which the level of liquid in a capillary tube is different from that outside it, is called capillarity.

Weight of liquid, W = Vρg = πr2[h+(r/3)]ρg (Here r is the radius meniscus)

If weight of meniscus is taken into account, the force of surface tension will be,

T = [r(h+(r/3)) ρg]/2 cosθ

For fine capillary, force of surface tension, T = rhρg/2 cosθ

So height, h = 2T cosθ/ rρg Open / Comment