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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Tuesday, 21 February 2017

Mathematics

Topic-1 Boolean expressions

Boolean expressions is one of the easiest topic and also important for scoring marks in competitive exams . If we check out the last three question papers of  mains examination we can find questions . Questions are as follows..

Jee mains 2016 paper question:-





         ANS(2) p /\ q

 

    p   q   ~p   ~q    p /\ ~q   ~p /\ q       ( p /\ ~q )  V q V (~p /\ q)      p /\ q
   
    1    0    0      1        1             0                            1                                     1

   
    1    1    0      0        0             0                            1                                     1
   

    0   0     1      1        0             0                            0                                     0


    0    1    1      0        0             1                            1                                     1



Jee mains 2015 paper question:-



        ANS(4)  

  s   r    ~s   ~r   ( ~r /\ s )   ~s V  ( ~r /\ s )    ~( ~s V  ( ~r /\ s ) )        s/\ r

  0   0     1     1          1                    1                               0                             0


  0   1     1    0          0                     1                               0                             0
 
  1   0     0    1         1                      1                               0                             0

  1   1     0    0         0                      0                               1                             1

Tips and tricks for scoring marks in Jee mains

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Sunday, 19 February 2017

                                           Physics 



Topic-1 Electronic devices

Electronic devices is a very important chapter since it is the base of today's technology . Marks wise also it's a very important chapter . If we check out in the last three years papers questions appeared from this chapter . The questions are as follows.


Jee mains 2016 paper questions:-



           ANS(3) Linear increase for cu , exponential decrease for si .



     Copper



   Intrinsic semi conductor 


  • Thus when temperature goes up, resistance goes up. For some materials, resistivity is a linear function of temperature . The resistivity of a conductor increases with temperature . In the case of copper, the relationship between resistivity and temperature is approximately linear over a wide range of temperatures.
  • So its conductivity increases. But in metal, it decreases due to the decrease in mobility. Conductivity of metal decrease with increase in temperature. For intrinsic semiconductor , conductivity increases with increase in temperature.



          ANS(3) OR




             a   b   c   d   x(output)   

0   0    0   0      0


0   0    0   1      1


0   0    1   0      1


0   0    1   1      1


0   1    0    0     1


0   1    0    1     1


1   0    1    0     1


1   0    1    1     1




  • By observing the table when at least one input is high (logic one)  the output is high (logic one) so the gate is OR .





















         ANS(2)  and (4)
  • By cross multiplying the below equations you can get the above relations





               ANS(1)


Jee mains 2014 paper questions:-




             ANS(1)
  •  Higher voltage should be connected to the anode of the diode and lower voltage should be connected to the cathode of the diode .




Tips and tricks for scoring marks in Jee mains

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Saturday, 18 February 2017

                                          Chemistry



Topic-2 Chemistry in everyday life

There is a high probability of getting question from this chapter ... If we check out the last three years papers of mains a question appeared in three years papers from this chapter . The questions are as follows..

Jeemains 2016 paper question:-



                              
         ANS(2) Sodium lauryl sulphate
  • All other options are cationic detergent .


Jeemains 2015 paper question:-



       ANS(3) Phenelzine
  • Phenelzine is a anti depressant drug .
  • All other options are antacid .


Jeemains 2014 paper question:-




       ANS(1) Quinoline
  • Quinoline is a aromatic compound and doesnot present in DNA .
  • All other options are bases and also present in DNA .

Tips and tricks for scoring marks in jee mains

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Friday, 17 February 2017

Chemistry

   Topic-1 Polymers

There is a high probability of getting a question from this chapter . If we check out  the last three years papers a question appeared in all three years  from this chapter . The questions are as follows:-


Jeemains 2016  paper question:-



           ANS-(4) It is used in the manufacture of buckets , dustbins etc...

  •  It is is widely used for manufacturing various containers, dispensing bottles, wash bottles, tubing, plastic bags for computer components, and various molded laboratory equipment. Its most common use is in plastic bags

Jeemains 2015  paper question:-






            ANS-(2) Glyptal

  • BAKELITE used for its electrical non conductivity and heat-resistant properties in electrical insulators, radio and telephone casings and such diverse products as kitchenware, jewelry, pipe stems, children's toys, and firearms.


  • POLYPROPENE- is a thermoplastic polymer  used in a wide variety of applications including packaging and labeling, textiles (e.g., ropes, thermal underwear and carpets), stationery, plastic parts and reusable containers of various types, laboratory equipment, loudspeakers, automotive .

  • POLY VINYL CHLORIDE-Regular PVC (polyvinyl chloride) is a common, strong but lightweight plastic  used in construction. It is made softer and more flexible by the addition of plasticizers. If no plasticizers are added, it is known as uPVC (unplasticized polyvinyl chloride). Example PVC pipes , PVC cables etc..


Jeemains 2014 paper question:-




           ANS-(1) Dacron
  • Neoprene , Teflon and acrylonitrile are addition polymers.










Tips and tricks for scoring marks in jee mains

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