Indian Army GD / Technical Recruitment Technical Subjects (Soldier Technical Posts) Syllabus

How does resistance depend on length and cross-sectional area of a wire?

R = ρL/A — resistance is directly proportional to length L and inversely proportional to cross-sectional area A; ρ is resistivity.

State the formula for capacitors in series and in parallel.

Series: 1/C = 1/C1 + 1/C2 + ... ; Parallel: C = C1 + C2 + ... (opposite to the rules for resistors).

What is the photoelectric effect?

The emission of electrons from a metal surface when light of sufficiently high frequency strikes it. Einstein explained it using photons: KE_max = hf − φ (work function).

State Einstein's mass–energy equivalence relation.

E = mc2, where c is the speed of light (≈ 3 x 10^8 m/s). Mass and energy are interconvertible.

What is the de Broglie wavelength formula?

λ = h/p = h/mv, where h is Planck's constant. It expresses the wave nature of matter.

Differentiate nuclear fission and nuclear fusion.

Fission splits a heavy nucleus into lighter ones (e.g. uranium in reactors); fusion combines light nuclei into a heavier one (e.g. hydrogen in the Sun). Both release energy.

State Avogadro's number and what it represents.

6.022 x 10^23 — the number of particles (atoms, molecules, ions) in one mole of a substance.

Define molarity.

Molarity (M) = moles of solute per litre of solution. Unit: mol/L.

State the ideal gas equation.

PV = nRT, where P is pressure, V is volume, n is moles, R is the gas constant (8.314 J/mol·K), and T is absolute temperature.

What is the pH scale and what does pH = 7 indicate?

pH = −log10[H+], measuring acidity/basicity from 0 to 14. pH = 7 is neutral; below 7 is acidic, above 7 is basic.

State Boyle's law and Charles's law.

Boyle's law: at constant temperature, P ∝ 1/V (PV = constant). Charles's law: at constant pressure, V ∝ T (V/T = constant).

What is the difference between an exothermic and an endothermic reaction?

Exothermic reactions release heat (ΔH negative); endothermic reactions absorb heat (ΔH positive).

How are elements arranged in the modern periodic table?

In order of increasing atomic number (number of protons), arranged in periods (rows) and groups (columns) based on recurring properties.

Name the most electronegative element and the lightest element.

Fluorine is the most electronegative element; hydrogen is the lightest element.

What is the difference between an ionic bond and a covalent bond?

An ionic bond forms by transfer of electrons (between metals and non-metals); a covalent bond forms by sharing of electrons (between non-metals).

What are isotopes?

Atoms of the same element with the same number of protons but different numbers of neutrons (same atomic number, different mass number).

Name the noble gases and state their key chemical property.

Helium, neon, argon, krypton, xenon, radon. They are chemically inert because they have completely filled outer electron shells.

What is catenation, and which element shows it most?

Catenation is the ability of an element's atoms to bond with one another forming chains/rings. Carbon shows it most strongly, enabling organic chemistry.

Differentiate saturated and unsaturated hydrocarbons.

Saturated hydrocarbons (alkanes) have only single C–C bonds; unsaturated hydrocarbons have double (alkenes) or triple (alkynes) bonds.

Give the general formula of alkanes, alkenes, and alkynes.

Alkanes: CnH2n+2; Alkenes: CnH2n; Alkynes: CnH2n−2.

What is a functional group? Give the group for alcohols and carboxylic acids.

A functional group is an atom or group that determines a molecule's chemical properties. Alcohols: −OH; carboxylic acids: −COOH.

State the quadratic formula.

For ax2 + bx + c = 0, x = [−b ± √(b2 − 4ac)] / 2a.

What does the discriminant of a quadratic tell you?

D = b2 − 4ac. If D > 0 roots are real and distinct; D = 0 real and equal; D < 0 complex (no real roots).

Define the union and intersection of two sets.

Union (A ∪ B) is the set of elements in A or B or both; intersection (A ∩ B) is the set of elements common to both A and B.

State De Morgan's laws for sets.

(A ∪ B)' = A' ∩ B' and (A ∩ B)' = A' ∪ B' — the complement of a union is the intersection of complements, and vice versa.

What is the derivative of x^n with respect to x?

d/dx (x^n) = n·x^(n−1) (the power rule).

State the integral of x^n (n ≠ −1).

∫ x^n dx = x^(n+1)/(n+1) + C, where C is the constant of integration.

Give the distance formula between two points in coordinate geometry.

d = √[(x2 − x1)2 + (y2 − y1)2].

State the values of sin, cos, and tan at 30°, 45°, and 60°.

sin: 1/2, 1/√2, √3/2; cos: √3/2, 1/√2, 1/2; tan: 1/√3, 1, √3 (at 30°, 45°, 60° respectively).

What is a determinant of a 2x2 matrix [[a, b],[c, d]]?

The determinant is ad − bc.

State the basic formula for the probability of an event.

P(E) = (number of favourable outcomes) / (total number of equally likely outcomes), where 0 ≤ P(E) ≤ 1.