Pre Mains Checklist

Table of Contents

This is just a checklist to ensure that I haven’t left any topics before mains.

1. General

  • [ ] Anki cards

2. Maths

  • [ ] Numerically Greatest term in binomial.
  • [ ] Descartes rule of signs.
  • [ ] Geometric applications of complex numbers.
  • [X] Condition of conics
  • [ ] Reduction formulae for integration (can be ignored because of mostly impractical)
  • [ ] Expansion formulae (limits)
  • [X] Angle between two circles.
    Can be calculated manually by finding the intersection points and angle between the tangents at that point.
  • [ ] Important highlights of conics.
  • [ ] Solutions of triangles
  • [ ] Angle bisector of line (coordinate geometry)
  • [X] Trigonometry formulae for \( A + B + C = \pi \)
    If \( A + B + C = \pi \) then:
    1. \[ \sin 2A + \sin 2B + \sin 2C = 4\sin A \sin B \sin C \]
    2. \[ \sin A + \sin B + \sin C = 4 \cos \frac{A}{2} \cos \frac{B}{2} \cos \frac{C}{2} \]
    3. \[ \cos 2A + \cos 2B + \cos 2C = -1-4\cos A \cos B \cos C \]
    4. \[ \cos A + \cos B + \cos C = 1 + 4 \sin \frac{A}{2} \sin \frac{B}{2} \sin \frac{C}{2} \]
    5. \[ \tan A + \tan B + \tan C = \tan A \tan B \tan C \]
    6. \[ \tan \frac{A}{2} \tan \frac{B}{2} + \tan \frac{B}{2} \tan \frac{C}{2} + \tan \frac{C}{2} \tan \frac{A}{2} = 1 \]
    7. \[ \cot \frac{A}{2} + \cot \frac{B}{2} + \cot \frac{C}{2} = \cot \frac{A}{2} \cot \frac{B}{2} \cot \frac{C}{2} \]
    8. \[ \cot A \cot B + \cot B \cot C + \cot C \cot A = 1 \]

3. Physics

3.1. Mechanics

  • [X] Elasticity formulae (such as modulus of rigidity, young’s modulus, bulk modulus and their interconversions)
  • [X] Center of mass, moment of inertia of various arrangements (anki)

3.2. Thermodynamics

  • [X] Thermodynamics process formulae (polytropic in general and also most important)
  • [X] Calorimetry - Law of Mixture
  • [X] Thermal expansion/stress/strain
  • [X] Change in time-period of pendulum due to thermal expansion.
    \[ \text{Fractional change} = \frac{T' - T}{T} = \frac{1}{2}\alpha \ \Delta \theta \]
  • [X] Variation of density with temperature
    \[ \rho = \frac{\rho_0}{1 + \gamma \ \Delta T} \]
  • [X] Bimetallic strip

\[ R = \frac{d}{(\alpha_2 - \alpha_1) \ \Delta T} \]
Here, \( d \) is the width of bimetallic strip(combined).

3.3. Electrodynamics

  • [X]

    Field and Potential due to configuration of masses and charges of various arrangements and symmetries

    Potential energy of chared solid sphere
    \[ U = \frac{3}{5} \frac{KQ^2}{R} \]

    Potential energy of thin layered sphere
    \[ U = \frac{1}{2} \frac{KQ^2}{R} \]

  • [ ] Senstivity of galvanometer

3.4. Waves and Sound

  • [X] Organ pipe (the most annoying)

3.5. Optics

  • [X]

    EM Waves, wavelength range, production and uses.
    Radio Waves

    • Produced by rapid acceleration/deceleration of electrons.
    • Used in communication devices.

    Microwaves

    • Used in speed guns, RADAR like devices.
    • Produced by klystron/magnetron valves.

    Infrared

    • Used in physical therapy.
    • Produced by hot bodies.
    • Responsible for greenhouse effect.

    UV

    • Used in LASIK eye surgery, causes excess growth of melanin in skin.

    X-rays

    • Produced when electrons strike metals.
    • Used in Cancer treatement.
  • [ ] Optical instruments

3.6. Modern Physics

  • [X] Alpha particle trajectory deviation formula
    \[ \tan \frac{\theta}{2} = \frac{K Z e^2}{mv_0^2 b} \]
    Where, \( b \) is the aiming parameter.

4. Chemistry

  • [ ] Everything!
    Sounds like a joke but actually isn’t :(

4.1. Organic

4.2. Physical

  • [X] V.S. of \( \ce{H_2O_2} \) , Molarity, Normality, Percent free oleum and other basic physical chemistry stuffs.
  • [ ] Electrolysis Product
  • [X] Thermodynamics processes
  • [X] Atomic structure
    \[ \text{Orbital angular} = \sqrt{l(l+1)} \ \hbar \]
    \[ \text{Spin angular momentum} = \sqrt{s(s+1)} \ \hbar \]
    \[ \text{Spin-only magnetic moment} = \sqrt{n(n+2)} \text{ B.M.} \]

4.3. Inorganic

  • [ ] Trends, chemical properties, compounds of d-block.
  • [ ] Structures of various compounds.
  • [X] Coordination Chemistry (tetrahedral and octahedral complexes)
  • [X] CFT and Hybridization theory
  • [ ] Qualitative Analysis(colors of salts)
  • [X] Synergic bonded compounds structures
  • [X] Synergic bonding properties
    \[ \text{Synergic bonding} \propto \text{Number of lone pairs on metal} \]
    If lone pairs on metal are same:
    \[ \text{Synergic bonding} \propto \text{Electronic Charge density on metal } \]
    Note: Greater the synerginc bonding between metal and carbon, lower the bond order of carbon oxygen bond will be.

5. Miscellaneous

  • The phenomenon of perfect diamagnetism(\( \chi = -1 \) ) in superconductors is called Meissner effect.
  • For a characteristic equation,
    \[ \det (A - \lambda x) = 0 \]
    Sum of roots(\( x \)) = Trace(A)
    Product of roots(\( x \)) = \( \det (A) \)

Author: Prashant Tiwari

Created: 2024-02-08 Thu 02:11