Monday, 13 March 2017




Definition:

A conic section is said to be a hyperbola if its eccentricity is greater than 1


Four standard forms of hyperbola:

Eccentricity of four standard form of hyperbola is same and given below.

Content           I                    II                        III                         IV


1.  Equation            x2/a2-y2/b2=1            x2/a2-y2/b2=-1                 (x-α)2/a2-(y-β)2/b2=1       (x-α)2/a2-(y-β)2/b2=-1   
                                 where b2=a2(e2-1)      where a2=b2(e2-1)          where b2=a2(e2-1)            where a2=b2(e2-1)      



2.  Centre(C)             (0,0)                      (0,0)                                (α,β)                                   (α,β)


3.  Vertices                 A,A’=(±a,0 )                      B,B’=(0,±b)                     (α±a, β)                           (α,b± β)


4 .  Foci(S,S’)               (±ae,0)                           (0,±be)                              (α±ae,β)                         (α,β±be)


 5.    Z,Z’                       (±a/e,0)                          (0,±b/e)                            (α±a/e,β)                       (α,β±b/e)  


6.  Ends of LR           (±ae, ±b2/a)                   (±a2/b,±be)                     (α±ae, β±b2/a)              (α±a2/b, β±be)


7.  Eqn’s. of Trans-           y=0                                     x=0                            y=β                                    x=α
    verse axis


8.  Eqn’s. of Conjugate    x=0                                 y=0                                x=α                                    y=β
     axis


9.  Eqn’s.Latas rectas       x=±ae                              y=±be                         x=α±be                              y= β±be


10. Eqn’s of Directrices    x=±a/e                            y=±b/e                      x= α±a/e                          y= β±b/e


11. Length of Transverse      2a                          2b                                  2a                                         2b
     axis


12.  Length of Conjugate       2b                          2a                                  2b                                        2a
               axis



13. Length of Latus Rectum   2 b2/a                      2 a2/b                        2 b2/a                               2 a2/b


14. Differences of                |S’P-SP|=2a              |S’P-SP|=2b              |S’P-SP|=2a                 |S’P-SP|=2b
    focal distance(focal radii)
    of a point P on the Hyperbola



15. Distance between the foci         SS’=2ae              SS’=2be                       SS’=2ae                        SS’=2be


16. Distance  b/w the vertices  AA’=2a            BB’=2b                     AA’=2a                            BB’=2b 
     

17. Distance b/w directrices   ZZ’=2a/e              ZZ’=2b/e              ZZ’=2a/e              ZZ’=2b/e



...........................................................................................................................................................................................




II. The hyperbola     x2/a2-y2/b2=1 and  x2/a2-y2/b2=-1 are called conjugate hyperbolas to each other .


III. If e1,e2  are the two eccentricities of two  conjugate hyperbolas then e12+ e22= e12 e22


IV. A hyperbola is said to be a rectangular hyperbola if the length of its transverse axis  is equal to             length of its conjugate axis


V. x2-y2=a2,xy=c2  represents a rectangular hyperbola


VI. The eccentricity of a rectangular hyperbola is


VII. We use the following notation in this chapter
        S= x2/a2-y2/b2-1,  S’= xx1/a2-yy1/b2-1, S11=x12/a2-y12/b2-1,  S12=xx1/ a2-yy1/ b2-1


IX.A point is said  (x1,y1) is said to be 0:-an external point to the hyperbola S=0   if  S11<0.
    ii) An internal point to the hyperbola S=0 if S11>0
    iii) Lies on the hyperbola S=0 if S11=0


X. Two tangents can be drawn to a hyperbola from an external point.


XI. The equation of the tangent to a hyperbola S=0 at P(x1,y1) is S1=0


XII. The equation of the normal to the hyperbola  x2/a2-y2/b2=1    at   P(x1,y1) is a2x/x1 + b2y/b1=a2+b2


XIV. The condition that the line y=mx+c may be a tangent to the hyperbola x2/a2-y2/b2=1 is                        c2=a2m2-b2 and the point of contact is (-a2m/c , -b2/c)


XV. The condition that the line lx+my+n=0 may be a tangent to the hyperbola x2/a2-y2/b2=1 is (-a2l/n,-b2m/n).


XVI. The equation of a tangent to the hyperbola x2/a2-y2/b2=1 may be taken as y=mx±


XVII. If m1,m2 are the slopes of the tangents through P to the hyperbola x2/a2-y2/b2=1 then                          m1+m2=2x1y1/x12-a; m1m2=y12+ b2/ x12-a


XVII. if  is the angle between the tangents  drawn from a point (x1,y1) to the hyperbola S= x2/a2-y2/b2-1=0 then  



XIX. The equation to the director circle x2/a2-y2/b2=1 is x2+y2=a2-b2


XX. The equation to the auxiliary circle of  x2/a2-y2/b2=1 is x2+y2=a2


XXI. The equation to the chord of contact  of P(x1,y1) with respect to the hyperbola S=0 is S1=0


XXII. The qquation to the chord of the hyperbola S=0 having P(x1,y1)  as its midpoint is S1=S12


XXIV. The midpoint of the chord lx+my+n=0 of the hyperbola  x2/a2-y2/b2=1 is (-a2ln/ a2l2-b2 m2,b2mn/ a2l2-b2 m2  )


 XXV. The equation to the pair of tangents to the hyperbola S=0 from    P(x1,y1)   is S12=SS11


XXVI.  The equation x=asec   ; y=b tan  are called parametric equations of the hyperbola x2/a-y2/b2=1                           and the point (asec  b tan ) is called parametric point it is denoted by p.


XXVII. If  P(x1,y1) =(asec  b tan ) is a point on hyperbola x2/a2-y2/b2=1 and its foci are S,S’ then
             SP=|ex1-a|=|asec and S’P=|ex1+a|=|asec


XXVII. The equation of the chord joining two points a and b on the hyperbola x2/a2-y2/b2=1 is x/a cos(α-β/2)-y/bsin(α+ β/2)=Cos (α+ β/2)


XXX. If a and b are the ends of a focal chord of a hyperbola S=0   then e cos(α- β/2)= Cos (α+ β/2)


XXXI. The equation of tangent at p( ) on the hyperbola S=0 is x/asec  - y/btan =1


XXXII.  The equation of normal at  p( ) on the hyperbola S=0 is ax/sec +by /btan =1


XXXIII. The condition that the line lx+my+n=0 to be a normal to the hyperbola x2/a2-y2/b2=1  is  a2/                l2-b2/m2=( a2+ b2)2/n2



XXXIV. Atmost four normals can be drawn from a point to a hyperbola


XXXV. The parametric equation of xy=c2 are x=ct;y=c/t

Properties of Asymptotes:

i). The equation of the asymptotes  of the hyperbola S=0 are x/a±y/b=0 (or)  y=±b/ax

ii). The equation to the pair of asymptotes of x2/a2-y2/b2=1   is x2/a2-y2/b2=0

iii). Equation of hyperbola and equation of its pair of   asymptotes   are differ in their constant terms          only.

iv). Asymptotes  of the hyperbola passes through the centre of the hyperbola and they are equally inclined to the axes of the hyperbola

v). The angle between the asymptotes of the hyperbola S=0 is 2  or 2

vi). The angle between the asymptotes of a rectangular  hyperbola is

vii). The equation of a rectangular hyperbola whose asymptotes are the coordinate axes is xy=c2

viii). The product of perpendiculars from any point on hyperbola S=0 to its asymptotes is a2b2/a2+b2

ix). Asymptotes of a hyperbola and its conjugate hyperbola are same.

x). If H,C and A are the equation of a hyperbola and its pair of asymptotes respectively then H+C=2A

xi).  Equation of pair of asymptotes of hyperbola ax2+2hxy+by2+2gx+2fy+c=0 is                                        ax2+2hxy+by2+2gx+2fy+c- =0
                             



Hyperbola synopsis points

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Friday, 3 March 2017

Mathematics


Topic-2 Quadratic equations

One of the  easiest chapter in mathematics and  also important for scoring marks in competitive exams [formula based chapter] .  This chapter includes ,
  • The main concept in this chapter is how to find roots of given quadratic equation both in real and complex equations .
  • relationship between roots , nature of roots etc..
  • Formation of equations using given roots etc...
Questions that appeared in the recent three years main papers from this chapter are as follows :-



Jee mains 2015 paper questions:-







  Hint

For a given quadratic equation ax2 + bx + c = 0 . Let p and q be roots of the equation then the sum of roots[p+q] is -b/a and  product[pxq] of roots is c/a .

  Ans(3) -3



Jee mains 2014 paper questions:-


   Hint

For a given quadratic equation ax2 + bx + c = 0 . Let p and q be roots of the equation then the sum of roots[p+q] is -b/a and  product[pxq] of roots is c/a . The other conditions given are A.P i.e, 1/p + 1/q = 4 and  p + r = 2q . By using these conditions we can find the answer for above problem . 

  Ans(2)  




Tips and tricks for scoring marks in jee mains

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JEE MAINS CHEMISTRY CHAPTERWISE WEIGHTAGE:



These are the following Chapter Weightages for Chemistry for JEE MAINS:

1)Most Important Chapters.  62%
2)Important Chapters.  20%
3)Less Important Chapters.  15%

Miscellaneous 3%


1)Most Important Chapters:

  • Organic Compounds-10%
  • Equilibrium-8%
  • Chemical Kinetics-7%
  • Transition Elements (d and f block)-6%
  • s-block Elements-6%
  • Chemical Bonding And Molecular Structure-6%
  • Some Basic Principles Of Organic Chemistry-6%
  • p-block Elements-5%
  • Coordination Compounds-4%
  • Chemical Thermodynamics-4%

2)Important Chapters:

  • Redox Reactions-3%
  • Biomolecules-3%
  • Electrochemistry-2.1%
  • Atomic Structure-2%
  • Polymers-2%
  • Solutions-2%
  • Solid State-2%
  • Some Basic Concepts In Chemistry-2%
  • Classification Of Elements And Periodicity In Properties-2%

3)Less Important:

  • States Of Matter-2
  • Hydrogen-2
  • Hydrocarbons-2
  • General Principles And Processes Of Isolation Of Metals-2
  • Organic Compounds Containing Halogens-2
  • Surface Chemistry-1
  • Purification Characterization Organic Compounds-1
  • Chemistry In Everyday Life-1
  • Principles Related To Practical Chemistry-1
  • Environmental Chemistry-1

JEE Mains Chemistry Chapter wise Weightage

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JEE MAINS MATHEMATICS CHAPTERWISE WEIGHTAGE:

These are the following Chapter Weightages for Mathematics for JEE MAINS:

1)Most Important Chapters.  60%
2)Important Chapters.  30%
3)Less Important Chapters.  8%
Miscellaneous-2%



1)Most Important Chapters:

  • Integrals-8.8%
  • Probability-7% 
  • Three Dimensional Geometry-7% 
  • Trigonometry-7%
  • Vector Algebra-7%
  • Conic Sections-7%
  • Straight Lines-6%
  • Sets, Relations and Functions-5%
  • Matrices And Determinants-5%

2)Important Chapters:

  • Limits And Continuity-5%
  • Quadratic Equations-5%
  • Derivatives-4.5%
  • Permutation and Combination-4%
  • Complex Numbers-4%
  • Circles-3%
  • Binomial Theorem-3%
  • Sequences and Series-3%
  • Differential Equations-3%

3)Less Important:

  • Inverse Trigonometry-2%
  • Heights and Distances-1
  • Application of Derivatives-1
  • Statistics-1
  • Mathematical Induction-1
  • Mathematical Reasoning-1
  • Application Of Integrals-1

JEE Mains Maths Chapter wise Weightage

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JEE MAINS PHYSICS CHAPTERWISE WEIGHTAGE:



These are the following Chapter Weightages for Physics for JEE MAINS:

1)Most Important Chapters.  53%
2)Important Chapters.  35%
3)Less Important Chapters.  12%

1)Most Important Chapters:

  • Oscillations And Waves--10%
  • Rotational Motion---8%
  • Electrostatics---8%
  • Atoms And Nuclei--- 7.9%
  • Current Electricity---7%
  • Laws of Motion---6%
  • Magnetic effect of Current and Magnetism---6%

2)Important Chapters:

  • Kinematics---6%
  • Thermodynamics--6%
  • Work Energy Power--5%
  • Optics--5%
  • Electronic Devices--5%
  • Properties Of Solids And Liquids--4%
  • Electromagnetic Waves--4%

3)Less Important Chapters:

  • Electromagnetic Induction-3%
  • Alternating Current--2%
  • Physics And Measurement--2%
  • Dual Nature Of Matter And Radiation-2%
  • Communication Systems--%2
  • Gravitation--1%
  • Kinetic Theory of Gases-1%

JEE Mains Physics Chapter Wise Weightage

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Friday, 26 June 2015

JoSAA 2015 CHOICE FILLING


Joint Seat Allocation Authority 2015 conducts the allocation of seats into IITs, NITs, IIITs, and other GFTIs for the academic session 2015-2016. The online registration and choice filling begins on 29th June ,2015 at 10 AM and ends on 3rd July, 2015 at 5 PM. 

Click here to know the full schedule of JoSAA 2015 activities.

The guidelines for registration and choice filling are given below



Step : 1

Click on “Online Registering and Choice Filling” in JoSAA Website: http://josaa.nic.in/


Enter your JEE (MAIN) 2015 Roll Number and Password to login to the portal.


Step : 2

Go to Candidate’s Profile and ensure that all the personal details shown are correct. During
Registration process, all the candidates, if they desired to update their Gender and State of
Eligibility, they can do so. Rest of the information in Registration Form is in Read only mode.


Click CHANGE PASSWORD to change your password and it is compulsory.


To modify contact details, go to Contact Details and click “EDIT CONTACT DETAILS


After editing, click on “SUBMIT CHANGES


Step : 3

Click “Choices Available” to view the various programs available for you to choose


For those qualified in both JEE (MAIN) 2015 and JEE (ADVANCED) 2015, all choices are
available (Few courses have certain restrictions).

For those qualified only in JEE (MAIN) 2015, Choices are restricted to programs available in
NITs, IIITs and Other-GFTIs.

You can choose to view the available programs Institute-wise or discipline-wise.

You can also take a printout.

Step : 4

Next go to (Click) Choice Filling & Locking


Click the academic programs available in the left panel and it will appear automatically in
Filled Choices” on right side column. This way, fill as many choices as possible to enhance
your chances of getting a seat.

JEE (ADVANCED) 2015 qualified candidates can fill all choices (~600)* and only JEE (MAIN)
2015 qualified candidates can also fill all choices* except those of IITs and ISM. *Some
restrictions do apply for some programs based on candidature. Such programs may not be
listed among the available choices.

Click on Arrange Filled Choices to modify the order of preference. For example: to change
the first option to second just click “MOVE DOWN” arrow or vice versa. This way, you can
reshuffle the order of preference of choices.


Step : 5

Click on Choices InterChange to modify the order of preference. For example choice number
100 is changed to choice 111. Automatically 111 will become 100.


Click on Choice Rearrange to change the preference of more than one choice. For example:
Choice Numbers given in the extreme right column can be rearranged as shown below:


Changed sequences can be seen below: Choices 1, 2, 3 and 4 are renumbered as 5, 6, 7 and
8. Similarly 5, 6, 7 and 8 are renumbered 1, 2, 3 and 4. By clicking SAVE, modified sequence
will appear on the screen. Please make sure that the same number is not typed twice.


After saving, updated right order appears on the screen.

After clicking SAVE, the choices filled are updated as shown below WITH A MESSAGE.


Close the box to see new preference list (see below):


Click Multiple Deletion to delete more than one filled choices


You can check all or check only the selected choices to delete from the list



These options will be deleted from your choices list and the remaining choices will be
automatically reordered as shown below:


Click YES to delete or say NO to go back again to modify the deleting list or lock choice. After
saying YES, the choices appear as shown below which do not contain the deleted ones.


Step : 6

Now Click LOCK CHOICE


After completing choice filling, you can either click on I agree to lock my choices, complete
the choice filling process and take the printout or if you want to do modification of choices
filled later, click on I will lock my choices later.


After clicking I agree to lock my choices, the screen will appear as shown below: Once again
it will ask your final consent if it is final. In order to protect your choices filled, you have to
enter your password again to complete the choice filling option.



Click “Click here to take a printout of Locked Choices” which will appear as shown below. It
may run into few pages depending on the number choices filled by the candidate


Candidate should read the above terms and conditions carefully and sign at the specified
place and present it at the reporting center along other relevant documents.

JoSAA 2015 -Guidelines and procedures for online choice filling

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Thursday, 25 June 2015




JEE Main 2015 rank list for admission into NITs, IIITs, etc. was published on 1st July,2015.. The rank list based on your JEE Main 2015 marks and your performance in board. The list will be prepared giving 60% weightage to your JEE Main 2015 marks and 40% weightage to your board performance. Check the page frequently for updates about JEE Main 2015 rank list.



As the supreme court ordered, this the counseling for IITs and NITs,IIITs will be conducted by Joint Seat Allocation Authority (JoSAA).

Intially the rank list was rumoured to be released on 24th June,2015 as the filling of choices for JoSAA was scheduled on 25th June,2015. But CBSE released a notice on 24th June,2015 asking the students to ensure their marks have been submitted to CBSE in prescribed format.


The revised JoSAA schedule for filling in of choices and seat allocation was released on 25th June,2015.

Update

JEE MAIN 2015 RANK LIST RELEASED




JEE Main rank list 2015

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Sunday, 10 May 2015

jee advanced 2015 syllabus

JEE Advanced 2015 is conducted by IIT - Bombay for admissions into IITs and ISM Dhanbad. Students who have cleared JEE Main cut off marks can write the examination on 24th May, 2015.






JEE Advanced 2015 syllabi

Physics

General

Units and dimensions, dimensional analysis; least count, significant figures; Methods of measurement and error analysis for physical quantities pertaining to the following experiments: Experiments based on using Verniercalipers and screw gauge (micrometer), Determination of g using simple pendulum, Young’s modulus by Searle’s method, Specific heat of a liquid using calorimeter, focal length of a concave mirror and a convex lens using u-v method, Speed of sound using resonance column, Verification of Ohm’s law using voltmeter and ammeter, and specific resistance of the material of a wire using meter bridge and post office box.

Mechanics

Kinematics in one and two dimensions (Cartesian coordinates only), projectiles; Uniform Circular motion; Relative velocity.

Newton’s laws of motion; Inertial and uniformly accelerated frames of reference; Static and dynamic friction; Kinetic and potential energy; Work and power; Conservation of linear momentum and mechanical energy.

Systems of particles; Centre of mass and its motion; Impulse; Elastic and inelastic collisions.

Law of gravitation; Gravitational potential and field; Acceleration due to gravity; Motion of planets and satellites in circular orbits; Escape velocity.

Rigid body, moment of inertia, parallel and perpendicular axes theorems, moment of inertia of uniform bodies with simple geometrical shapes; Angular momentum; Torque; Conservation of angular momentum; Dynamics of rigid bodies with fixed axis of rotation; Rolling without slipping of rings, cylinders and spheres; Equilibrium of rigid bodies; Collision of point masses with rigid bodies.

Linear and angular simple harmonic motions.

Hooke’s law, Young’s modulus.

Pressure in a fluid; Pascal’s law; Buoyancy; Surface energy and surface tension, capillary rise; Viscosity (Poiseuille’s equation excluded), Stoke’s law; Terminal velocity, Streamline flow, equation of continuity, Bernoulli’s theorem and its applications.

Wave motion (plane waves only), longitudinal and transverse waves, superposition of waves; Progressive and stationary waves; Vibration of strings and air columns; Resonance; Beats; Speed of sound in gases; Doppler effect (in sound).

Thermal Physics

Thermal expansion of solids, liquids and gases; Calorimetry, latent heat; Heat conduction in one dimension; Elementary concepts of convection and radiation; Newton’s law of cooling; Ideal gas laws; Specific heats (Cv and Cp for monoatomic and diatomic gases); Isothermal and adiabatic processes, bulk modulus of gases; Equivalence of heat and work; First law of thermodynamics and its applications (only for ideal gases); Blackbody radiation: absorptive and emissive powers; Kirchhoff’s law; Wien’s displacement law, Stefan’s law.

Electricity and Magnetism

Coulomb’s law; Electric field and potential; Electrical potential energy of a system of point charges and of electrical dipoles in a uniform electrostatic field; Electric field lines; Flux of electric field; Gauss’s law and its application in simple cases, such as, to find field due to infinitely long straight wire, uniformly charged infinite plane sheet and uniformly charged thin spherical shell.

Capacitance; Parallel plate capacitor with and without dielectrics; Capacitors in series and parallel; Energy stored in a capacitor.

Electric current; Ohm’s law; Series and parallel arrangements of resistances and cells; Kirchhoff’s laws and simple applications; Heating effect of current.

Biot–Savart’s law and Ampere’s law; Magnetic field near a current-carrying straight wire, along the axis of a circular coil and inside a long straight solenoid; Force on a moving charge and on a current-carrying wire in a uniform magnetic field.

Magnetic moment of a current loop; Effect of a uniform magnetic field on a current loop; Moving coil galvanometer, voltmeter, ammeter and their conversions.

Electromagnetic induction: Faraday’s law, Lenz’s law; Self and mutual inductance; RC, LR and LC circuits with d.c. and a.c. sources.

Optics

Rectilinear propagation of light; Reflection and refraction at plane and spherical surfaces; Total internal reflection; Deviation and dispersion of light by a prism; Thin lenses; Combinations of mirrors and thin lenses; Magnification.

Wave nature of light: Huygen’s principle, interference limited to Young’s double-slit experiment.

Modern physics

Atomic nucleus; α, β and γ radiations; Law of radioactive decay;  Decay constant; Half-life and mean life; Binding energy and its calculation; Fission and fusion processes; Energy calculation in these processes.

Photoelectric effect; Bohr’s theory of hydrogen-like atoms; Characteristic and continuous X-rays, Moseley’s law; de Broglie wavelength of matter waves

Chemistry

Physical chemistry

General topics: Concept of atoms and molecules; Dalton’s atomic theory; Mole concept; Chemical formulae; Balanced chemical equations; Calculations (based on mole concept) involving common oxidation-reduction, neutralisation, and displacement reactions; Concentration in terms of mole fraction, molarity, molality and normality.

Gaseous and liquid states: Absolute scale of temperature, ideal gas equation; Deviation from ideality, van der Waals equation; Kinetic theory of gases, average, root mean square and most probable velocities and their relation with temperature; Law of partial pressures; Vapour pressure; Diffusion of gases.

Atomic structure and chemical bonding:  Bohr model, spectrum of hydrogen atom, quantum numbers; Wave-particle duality, de Broglie hypothesis; Uncertainty principle; Qualitative quantum mechanical picture of hydrogen atom, shapes of s, p and d orbitals; Electronic configurations of elements (up to atomic number 36); Aufbau principle; Pauli’s exclusion principle and Hund’s rule; Orbital overlap and covalent bond; Hybridisation involving s, p and d orbitals only; Orbital energy diagrams for homonuclear diatomic species;  Hydrogen bond; Polarity in molecules, dipole moment (qualitative aspects only); VSEPR model and shapes of molecules (linear, angular, triangular, square planar, pyramidal, square pyramidal, trigonalbipyramidal, tetrahedral and octahedral).

Energetics: First law of thermodynamics; Internal energy, work and heat, pressure-volume work; Enthalpy, Hess’s law; Heat of reaction, fusion and vapourization; Second law of thermodynamics; Entropy; Free energy; Criterion of spontaneity.

Chemical equilibrium:Law of mass action; Equilibrium constant, Le Chatelier’s principle (effect of concentration, temperature and pressure); Significance of ΔG and ΔG0 in chemical equilibrium; Solubility product, common ion effect, pH and buffer solutions;  Acids and bases (Bronsted and Lewis concepts); Hydrolysis of salts.

Electrochemistry: Electrochemical cells and cell reactions; Standard electrode potentials; Nernst equation and its relation to ΔG; Electrochemical series, emf of galvanic cells; Faraday’s laws of electrolysis; Electrolytic conductance, specific, equivalent and molar conductivity, Kohlrausch’s law; Concentration cells.

Chemical kinetics:  Rates of chemical reactions; Order of reactions; Rate constant; First order reactions; Temperature dependence of rate constant (Arrhenius equation).

Solid state: Classification of solids, crystalline state, seven crystal systems (cell parameters a, b, c, α, β, γ), close packed structure of solids (cubic), packing in fcc, bcc and hcp lattices; Nearest neighbours, ionic radii, simple ionic compounds, point defects.

Solutions:  Raoult’s law; Molecular weight determination from lowering of vapour pressure, elevation of boiling point and depression of freezing point.

Surface chemistry:  Elementary concepts of adsorption (excluding adsorption isotherms); Colloids: types, methods of preparation and general properties; Elementary ideas of emulsions, surfactants and micelles (only definitions and examples).

Nuclear chemistry:  Radioactivity: isotopes and isobars; Properties of α, β and γ rays; Kinetics of radioactive decay (decay series excluded), carbon dating; Stability of nuclei with respect to proton-neutron ratio; Brief discussion on fission and fusion reactions.

Inorganic chemistry

Isolation/preparation and properties of the following non-metals: Boron, silicon, nitrogen, phosphorus, oxygen, sulphur and halogens; Properties of allotropes of carbon (only diamond and graphite), phosphorus and sulphur.

Preparation and properties of the following compounds: Oxides, peroxides, hydroxides, carbonates, bicarbonates, chlorides and sulphates of sodium, potassium, magnesium and calcium; Boron: diborane, boric acid and borax; Aluminium: alumina, aluminium chloride and alums; Carbon: oxides and oxyacid (carbonic acid); Silicon: silicones, silicates and silicon carbide;  Nitrogen: oxides, oxyacids and ammonia; Phosphorus: oxides, oxyacids (phosphorus acid, phosphoric acid) and phosphine; Oxygen: ozone and hydrogen peroxide; Sulphur: hydrogen sulphide, oxides, sulphurous acid, sulphuric acid and sodium thiosulphate; Halogens: hydrohalic acids, oxides and oxyacids of chlorine, bleaching powder; Xenon fluorides.

Transition elements (3d series): Definition, general characteristics, oxidation states and their stabilities, colour (excluding the details of electronic transitions) and calculation of spin-only magnetic moment; Coordination compounds: nomenclature of mononuclear coordination compounds, cis-trans and ionisation isomerisms, hybridization and geometries of mononuclear coordination compounds (linear, tetrahedral, square planar and octahedral).

Preparation and properties of the following compounds: Oxides and chlorides of tin and lead; Oxides, chlorides and sulphates of Fe2+, Cu2+ and Zn2+; Potassium permanganate, potassium dichromate, silver oxide, silver nitrate, silver thiosulphate.

Ores and minerals: Commonly occurring ores and minerals of iron, copper, tin, lead, magnesium, aluminium, zinc and silver.

Extractive metallurgy: Chemical principles and reactions only (industrial details excluded); Carbon reduction method (iron and tin); Self reduction method (copper and lead); Electrolytic reduction method (magnesium and aluminium); Cyanide process (silver and gold).


Principles of qualitative analysis: Groups I to V (only Ag+, Hg2+, Cu2+, Pb2+, Bi3+, Fe3+, Cr3+,  Al3+, Ca2+, Ba2+, Zn2+, Mn2+ and Mg2+); Nitrate, halides (excluding fluoride), sulphate and sulphide.

Organic chemistry

Concepts: Hybridisation of carbon; σ and π-bonds; Shapes of simple organic molecules; Structural and geometrical isomerism;  Optical isomerism of compounds containing up to two asymmetric centres, (R,S and E,Z nomenclature excluded); IUPAC nomenclature of simple organic compounds (only hydrocarbons, mono-functional and bi-functional compounds); Conformations of ethane and butane (Newman projections); Resonance and hyperconjugation; Keto-enoltautomerism; Determination of empirical and molecular formulae of simple compounds (only combustion method); Hydrogen bonds: definition and their effects on physical properties of alcohols and carboxylic acids; Inductive and resonance effects on acidity and basicity of organic acids and bases; Polarity and inductive effects in alkyl halides; Reactive intermediates produced during homolytic and heterolytic bond cleavage;  Formation, structure and stability of carbocations, carbanions and free radicals.    

Preparation, properties and reactions of alkanes: Homologous series, physical properties of alkanes (melting points, boiling points and density); Combustion and halogenation of alkanes; Preparation of alkanes by Wurtz reaction and decarboxylation reactions.

Preparation, properties and reactions of alkenes and alkynes: Physical properties of alkenes and alkynes (boiling points, density and dipole moments); Acidity of alkynes; Acid catalysed hydration of alkenes and alkynes (excluding the stereochemistry of addition and elimination); Reactions of alkenes with KMnO4 and ozone; Reduction of alkenes and alkynes; Preparation of alkenes and alkynes by elimination reactions; Electrophilic addition reactions of alkenes with X2, HX, HOX and H2O (X=halogen);  Addition reactions of alkynes; Metal acetylides.

Reactions of benzene: Structure and aromaticity; Electrophilic substitution reactions: halogenation, nitration, sulphonation, Friedel-Crafts alkylation and acylation; Effect of o-, m- and p-directing groups in monosubstituted benzenes.

Phenols: Acidity, electrophilic substitution reactions (halogenation, nitration and sulphonation); Reimer-Tieman reaction, Kolbe reaction.

Characteristic reactions of the following (including those mentioned above): Alkyl halides: rearrangement reactions of alkyl carbocation, Grignard reactions,  nucleophilic substitution reactions;  Alcohols: esterification, dehydration and oxidation, reaction with sodium, phosphorus halides, ZnCl2/concentrated HCl, conversion of alcohols into aldehydes and ketones; Ethers: Preparation by Williamson’s  Synthesis; Aldehydes and Ketones: oxidation, reduction, oxime and hydrazone formation; aldol condensation, Perkin reaction; Cannizzaro reaction; haloform reaction and nucleophilic addition reactions (Grignard addition);  Carboxylic acids: formation of esters, acid chlorides and amides, ester hydrolysis; Amines: basicity of substituted anilines and aliphatic amines, preparation from nitro compounds, reaction with nitrous acid, azo coupling reaction of diazonium salts of aromatic amines, Sandmeyer and related reactions of diazonium salts; carbylamine reaction; Haloarenes: nucleophilic aromatic substitution in haloarenes and substituted haloarenes (excluding Benzyne mechanism and Cine substitution).

Carbohydrates: Classification; mono- and di-saccharides (glucose and sucrose); Oxidation, reduction, glycoside formation and hydrolysis of sucrose.

Amino acids and peptides: General structure (only primary structure for peptides) and physical properties.

Properties and uses of some important polymers: Natural rubber, cellulose, nylon, teflon and PVC.

Practical organic chemistry: Detection of elements (N, S, halogens); Detection and identification of the following functional groups: hydroxyl (alcoholic and phenolic), carbonyl (aldehyde and ketone), carboxyl, amino and nitro; Chemical methods of separation of mono-functional organic compounds from binary mixtures.

Mathematics

Algebra

Algebra of complex numbers, addition, multiplication, conjugation, polar representation, properties of modulus and principal argument, triangle inequality, cube roots of unity, geometric interpretations.

Quadratic equations with real coefficients, relations between roots and coefficients, formation of quadratic equations with given roots, symmetric functions of roots.

Arithmetic, geometric and harmonic progressions, arithmetic, geometric  and harmonic means, sums of finite arithmetic and geometric progressions, infinite geometric series, sums of squares and cubes of the first n natural numbers.

Logarithms and their properties.

Permutations and combinations, Binomial theorem for a positive integral index, properties of binomial coefficients.

Matrices as a rectangular array of real numbers, equality of matrices, addition, multiplication by a scalar and product of matrices, transpose of a matrix, determinant of a square matrix of order up to three, inverse of a square matrix of order up to three, properties of these matrix operations, diagonal, symmetric and skew-symmetric matrices and their properties, solutions of simultaneous linear equations in two or three variables.

Addition and multiplication rules of probability, conditional probability, Bayes Theorem, independence of events, computation of probability of events using permutations and combinations.

Trigonometry


Trigonometric functions, their periodicity and graphs, addition and subtraction formulae, formulae involving multiple and sub-multiple angles, general solution of trigonometric equations.

Relations between sides and angles of a triangle, sine rule, cosine rule, half-angle formula and the area of a triangle, inverse trigonometric functions (principal value only).

Analytical Geometry


Two dimensions: Cartesian coordinates, distance between two points, section formulae, shift of origin.

Equation of a straight line in various forms, angle between two lines, distance of a point from a line; Lines through the point of intersection of two given lines, equation of the bisector of the angle between two lines, concurrency of lines;  Centroid, orthocentre, incentre and circumcentre of a triangle.

Equation of a circle in various forms, equations of tangent, normal and chord.

Parametric equations of a circle, intersection of a circle with a straight line or a circle, equation of a circle through the points  of  intersection of two circles and those of a circle and a straight line.

Equations of a parabola, ellipse and hyperbola in standard form, their foci, directrices and eccentricity, parametric equations, equations of tangent and normal.

Locus Problems.


Three dimensions: Direction cosines and direction ratios, equation of a straight line in space, equation of a plane, distance of a point from a plane.

Differential calculus

Real valued functions of a real variable, into, onto and one-to-one functions, sum, difference, product and quotient of two functions, composite functions, absolute value, polynomial, rational, trigonometric, exponential and logarithmic functions.

Limit and continuity of a function, limit and continuity of the sum, difference, product and quotient of two functions, L’Hospital rule of evaluation of limits of functions.

Even and odd functions, inverse of a function, continuity of composite functions, intermediate value property of continuous functions.

Derivative of a function, derivative of the sum, difference, product and quotient of two functions, chain rule, derivatives of polynomial, rational, trigonometric, inverse trigonometric, exponential and logarithmic functions.

Derivatives of implicit functions, derivatives up to order two, geometrical interpretation of the derivative, tangents and normals, increasing and decreasing functions, maximum and minimum values of a function, Rolle’s Theorem and Lagrange’s Mean Value Theorem.

Integral calculus

Integration as the inverse process of differentiation, indefinite integrals of standard functions, definite integrals and their properties, Fundamental Theorem of Integral Calculus.

Integration by parts, integration by the methods of substitution and partial fractions, application of definite integrals to the determination of areas involving simple curves.

Formation of ordinary differential equations, solution of homogeneous differential equations, separation of variables method, linear first order differential equations.

Vectors

Addition of vectors, scalar multiplication, dot and cross products, scalar triple products and their geometrical interpretations.

Source : http://www.jeeadv.iitb.ac.in


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