$\ln(C_A/C_{A0}) = -kt$

Second Order: $1/C_A = 1/C_{A0} + kt$

Activation Energy (Arrhenius Equation): $k = A e^{-E_a/RT}$

Reactor Types:

Batch Reactor: Unsteady state, no inflow/outflow during reaction.
CSTR (Continuous Stirred Tank Reactor): Well-mixed, uniform composition, $V = \frac{F_{A0} - F_A}{-r_A}$.
PFR (Plug Flow Reactor): No radial mixing, composition varies axially, $V = F_{A0} \int_{X_{A0}}^{X_A} \frac{dX_A}{-r_A}$.
Comparison: For positive order reactions, PFR is generally smaller than CSTR for same conversion.

Cracking: Breaking down long-chain hydrocarbons into shorter, more valuable ones.
- Thermal Cracking: High temperature, pressure.
- Catalytic Cracking (FCC): Uses catalysts (zeolites) to enhance selectivity and yield.
Reforming: Converting low-octane naphtha into high-octane gasoline components (aromatics, branched paraffins). Catalytic reforming uses platinum catalyst.
Octane Number: Measure of a fuel's resistance to knocking/pre-ignition. Higher octane = more resistant. (Iso-octane = 100, n-heptane = 0)
Cetane Number: Measure of diesel fuel's ignition delay. Higher cetane = shorter delay, better ignition. (n-hexadecane = 100, alpha-methylnaphthalene = 0)
Hydrotreating: Removal of impurities (S, N, metals) from feedstocks using hydrogen and catalysts.
Delayed Coking: Severe thermal cracking process to convert heavy residues into lighter products and petroleum coke.

Time & Work: If A does a work in $x$ days, B in $y$ days, together in $\frac{xy}{x+y}$ days.
Percentage: $x\%$ of $y = \frac{x}{100} \times y$. Percentage change: $\frac{\text{New} - \text{Old}}{\text{Old}} \times 100$.
Ratio & Proportion: If $a:b$ and $b:c$, then $a:b:c$. Direct/Inverse proportionality.
Profit & Loss: Profit = SP - CP, Loss = CP - SP. Profit/Loss % based on CP.
Averages: Sum of quantities / Number of quantities.

Series Completion: Number series, Alphabet series, Mixed series (identifying pattern: arithmetic, geometric, squares, cubes, prime numbers, alternating patterns).
Coding-Decoding: Assigning codes to letters/words based on specific rules (shifting letters, reverse order, numerical values).
Blood Relations: Understanding family tree relationships.
Direction Sense: Problems involving movement in directions (North, South, East, West) and calculating final position/distance.
Syllogism: Drawing conclusions from given statements (All A are B, Some B are C).

Active Voice: Subject performs the action (e.g., "The student wrote the essay.").
Passive Voice: Action is performed on the subject (e.g., "The essay was written by the student."). (Focus on "be" verb + past participle)
Prepositions:
- Time: at (specific time), on (days), in (months, years, seasons).
- Place: at (specific point), on (surface), in (enclosed space).
- Movement: to (destination), into (entering), onto (moving to surface).
Subject-Verb Agreement:</