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:
- \[ \sin 2A + \sin 2B + \sin 2C = 4\sin A \sin B \sin C \]
- \[ \sin A + \sin B + \sin C = 4 \cos \frac{A}{2} \cos \frac{B}{2} \cos \frac{C}{2} \]
- \[ \cos 2A + \cos 2B + \cos 2C = -1-4\cos A \cos B \cos C \]
- \[ \cos A + \cos B + \cos C = 1 + 4 \sin \frac{A}{2} \sin \frac{B}{2} \sin \frac{C}{2} \]
- \[ \tan A + \tan B + \tan C = \tan A \tan B \tan C \]
- \[ \tan \frac{A}{2} \tan \frac{B}{2} + \tan \frac{B}{2} \tan \frac{C}{2} + \tan \frac{C}{2} \tan \frac{A}{2} = 1 \]
- \[ \cot \frac{A}{2} + \cot \frac{B}{2} + \cot \frac{C}{2} = \cot \frac{A}{2} \cot \frac{B}{2} \cot \frac{C}{2} \]
- \[ \cot A \cot B + \cot B \cot C + \cot C \cot A = 1 \]
- \[ \sin 2A + \sin 2B + \sin 2C = 4\sin A \sin B \sin C \]
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.
- Produced by rapid acceleration/deceleration of electrons.
[ ]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.
3.7. Others
4. Chemistry
[ ]Everything!
Sounds like a joke but actually isn’t :(
4.1. Organic
[X]Oxidation, Reduction, Hydrolysis (The bad boy of organic chemistry)[X]Nucleophilic attact on alpha, beta positions in conjugated carbonyls
Grignard reagant(\( \ce{RMgX} \) ) results in addition of nucleophile at carbonyl carbon, whereas Gillman’s reagant(\( \ce{R_2CuLi} \) ) results in addition at \( \beta \) carbon.[X]Named Reactions[X]Test of organic compounds- Biomolecules
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(\( x \)) = \( \det (A) \)