CDS 2027 Science! Notes

Comprehensive Science Cheat Sheet - Mechanics, Thermodynamics, Cell Biology & Electromagnetism - CDS 2027

Welcome to the ultimate revision module for the CDS 2027 General Science preparation. Designed in a LibreTexts structured chapter style, this comprehensive study guide aggregates high-yield core concepts, mathematical formulas, and foundational theoretical paradigms across Physics, Chemistry, and Biology as per the latest UPSC exam trend.

1. UPSC CDS Science PYQ Analysis & Chapter Weightage

General Science accounts for approximately 30% of the General Knowledge paper in the Combined Defence Services (CDS) examination. Analyzing previous years' question patterns (PYQ Analysis) reveals a balanced distribution across Physics, Chemistry, and Biology.

Subject Domain	Core Focus Areas	Average Weightage (Questions)	Difficulty Level
Physics	Mechanics, Newton's Laws, Work-Energy-Power, Electromagnetism	10 - 12 Questions	Moderate to High
Chemistry	Gas Laws, Thermodynamics, Stoichiometry, Equations	8 - 10 Questions	Moderate
Biology	Cell Biology, Organelles, Photosynthesis, Physiology	10 - 12 Questions	Easy to Moderate

2. Physics Chapter 1: Mechanics & Kinematics

Newton's Laws of Motion

Mechanics forms the backbone of physical dynamics. Newton's three laws describe the relationship between a body and the forces acting upon it:

• First Law (Inertia): \(F_{\text{net}} = 0 \implies \Delta v = 0\). A body remains at rest or in uniform motion unless acted upon by a net external force.
• Second Law (Momentum & Acceleration): \(F_{\text{net}} = m \cdot a = \frac{dp}{dt}\). Force is proportional to the rate of change of momentum.
• Third Law (Action & Reaction): \(F_{A \to B} = -F_{B \to A}\). Every action has an equal and opposite reaction.

Kinematic Equations (Constant Acceleration \(a\))

When acceleration \(a\) is uniform, motion is governed by three fundamental equations:

\[v = v_0 + at\]

\[\Delta x = v_0t + \frac{1}{2}at^2\]

\[v^2 = v_0^2 + 2a\Delta x\]

Work, Energy, and Power

• Work Done: \(W = \vec{F} \cdot \vec{d} = Fd \cos\theta\)
• Kinetic Energy: \(K = \frac{1}{2}mv^2\)
• Gravitational Potential Energy: \(U = mgh\)
• Power: \(P = \frac{dW}{dt} = \vec{F} \cdot \vec{v}\)

Free-Body Diagram Example

Below is a dynamic representation of a block sliding down an inclined plane under gravity and friction, a classic CDS Physics problem:

```tikz \begin{tikzpicture}[scale=1.2] \draw[thick] (0,0) -- (4,0) -- (4,2.3) -- cycle; \draw (0.8,0) arc (0:30:0.8) node[midway, right] {$\theta$}; \begin{scope}[rotate=30] \draw[fill=blue!20, thick] (2,0) rectangle (3,0.8); ode at (2.5,0.4) {$m$}; \draw[->, thick, red] (2.5,0.4) -- (2.5,-1) node[below] {$m g$}; \draw[->, thick, green!50!black] (2.5,0.4) -- (2.5,1.2) node[above] {$N$}; \draw[->, thick, orange] (2.5,0.4) -- (1.2,0.4) node[left] {$f_k$}; \end{scope} \end{tikzpicture} ```

3. Chemistry Chapter 1: Chemical Thermodynamics & Gas Laws

Ideal Gas Law

The state of an ideal gas is described by the equation linking pressure \(P\), volume \(V\), moles \(n\), and temperature \(T\):

\[PV = nRT\]

where the universal gas constant \(R \approx 8.314 \text{ J/(mol}\cdot\text{K)}\).

Enthalpy, Entropy, and Gibbs Free Energy

• Enthalpy Change: \(\Delta H = \Delta U + P\Delta V\), representing the total heat content change of a system.
• Gibbs Free Energy: \(\Delta G = \Delta H - T\Delta S\), where \(\Delta S\) is the change in entropy (disorder).
• Spontaneity Condition: A process occurs spontaneously if and only if \(\Delta G < 0\).

4. Biology Chapter 1: Cell Structure & Bioenergetics

Key Cellular Organelles

Understanding cellular hierarchy is critical for CDS Biology questions:

• Nucleus: Contains genetic code (DNA); regulates cell metabolism and reproduction.
• Mitochondria: The "powerhouse" of the cell; site of ATP synthesis via cellular respiration.
• Ribosomes: Non-membrane-bound sites for protein translation.
• Endoplasmic Reticulum (ER): Rough ER processes proteins; Smooth ER synthesizes lipids and detoxifies compounds.

Photosynthesis Equation

Photosynthesis transforms light energy into chemical potential energy in autotrophs:

\[6CO_2 + 6H_2O \xrightarrow{\text{Light}} C_6H_{12}O_6 + 6O_2\]

5. Physics Chapter 2: Electromagnetism & Maxwell's Equations

Maxwell's classical equations encapsulate electromagnetic phenomena into differential form:

• Gauss's Law for Electricity: \( abla \cdot \vec{E} = \frac{\varrho}{\varepsilon_0}\)
• Gauss's Law for Magnetism: \( abla \cdot \vec{B} = 0\) (Absence of magnetic monopoles)
• Faraday's Law of Induction: \( abla \times \vec{E} = -\frac{\partial \vec{B}}{\partial t}\)
• Ampère-Maxwell Law: \( abla \times \vec{B} = \mu_0\vec{J} + \mu_0\varepsilon_0\frac{\partial \vec{E}}{\partial t}\)

6. Frequently Asked Questions (People Also Ask)

What is the importance of Newton's Second Law in CDS Physics?

Newton's Second Law provides the quantitative definition of force (\(F=ma\)) and is fundamental for solving mechanics, impulse, and momentum-related PYQs in CDS exams.

Why is \(\Delta G < 0\) mandatory for spontaneous chemical reactions?

A negative Gibbs Free Energy (\(\Delta G < 0\)) indicates that a reaction decreases the total free energy of the system, making it thermodynamically favorable without external energy input.

What is the role of displacement current in Maxwell's Equations?

Displacement current (\(\mu_0\varepsilon_0\frac{\partial \vec{E}}{\partial t}\)) accounts for changing electric fields producing magnetic fields, completing the symmetry in Maxwell's Ampère law extension.