Jharkhand Polytechnic (PECE) flashcards

32 cards. Read the term and the definition here. The deck at the top of this page is optional.

Newton's Second Law

The net force on a body equals mass times acceleration (F = ma). It links force, mass and acceleration and is used to find unknown forces or motion.

Ohm's Law

At constant temperature, current through a conductor is directly proportional to potential difference: V = IR. Resistance R is measured in ohms.

Work-Energy Theorem

The net work done on an object equals its change in kinetic energy. Useful when force varies or when speed changes are known but time is not.

Total Internal Reflection

When light travels from denser to rarer medium beyond the critical angle, it reflects back inside. Critical angle satisfies sin θc = n₂/n₁.

Lens Power

Power of a lens is the reciprocal of focal length in metres, P = 1/f, measured in dioptres. Converging lenses have positive power.

Half-Life

The time in which half the radioactive nuclei in a sample decay. After n half-lives, the fraction remaining is (1/2)^n.

Mole Concept

One mole contains 6.022 × 10²³ particles and equals the molar mass in grams. One mole of gas occupies 22.4 L at STP.

Molarity

Molarity is moles of solute per litre of solution (M = n/V). It changes with temperature because solution volume expands or contracts.

pH Scale

pH = −log[H⁺]. Values below 7 are acidic, 7 neutral and above 7 basic at 25 °C, where pH + pOH = 14.

Le Chatelier's Principle

When a system at equilibrium is disturbed by concentration, pressure or temperature change, it shifts to oppose the change and restore equilibrium.

Oxidation Number

A number showing an atom's electron gain or loss. Free elements are 0; oxygen is usually −2; the sum equals the ion's overall charge.

Ideal Gas Equation

PV = nRT relates pressure, volume, moles and absolute temperature of an ideal gas, with R = 8.314 J mol⁻¹ K⁻¹.

Quadratic Formula

For ax² + bx + c = 0, x = [−b ± √(b² − 4ac)]/2a. The discriminant b² − 4ac tells whether roots are real, equal or complex.

Arithmetic Progression Sum

For first term a and common difference d, the sum of n terms is Sₙ = n/2[2a + (n − 1)d]. The nth term is a + (n − 1)d.

Geometric Progression Sum

Sₙ = a(rⁿ − 1)/(r − 1) for r ≠ 1. If |r| < 1, the infinite sum converges to a/(1 − r).

Sum and Product of Roots

For ax² + bx + c = 0 with roots α and β, α + β = −b/a and αβ = c/a. Used to build equations from known roots.

Distance and Midpoint Formula

Distance between two points is √[(x₂−x₁)² + (y₂−y₁)²]; midpoint is the average of the coordinates. Both follow from coordinate geometry.

Derivative of xⁿ

d/dx(xⁿ) = nx^(n−1) for any real n. Standard derivatives also include d/dx(sin x) = cos x and d/dx(eˣ) = eˣ.

nCr Formula

Number of ways to choose r items from n is nCr = n!/[r!(n − r)!]. Order does not matter, unlike nPr.

Jharkhand State Formation

Jharkhand became India's 28th state on 15 November 2000, separated from Bihar, on the birth anniversary of tribal leader Birsa Munda.

Birsa Munda

A tribal leader from the Chotanagpur region who led the Munda rebellion (Ulgulan) against British rule in the 1890s; honoured as Bhagwan Birsa Munda.

Jharkhand Capital and Borders

Ranchi is the capital of Jharkhand. The state borders Bihar, Uttar Pradesh, Chhattisgarh, Odisha and West Bengal and is rich in minerals.

Article 32

The Right to Constitutional Remedies lets citizens approach the Supreme Court for enforcement of Fundamental Rights; Ambedkar called it the heart and soul of the Constitution.

National Symbols of India

National bird is the Indian peacock, national animal the Bengal tiger, national flower the lotus and national fruit the mango.

Alphabet Position Trick

Letters A to Z have positions 1 to 26. Reverse position equals 27 minus forward position, so A is 26 and Z is 1 from the other end.

Clock Angle Formula

Angle between clock hands = |30H − 5.5M| degrees, where H is the hour and M the minutes. The hands coincide 11 times in 12 hours.

Syllogism Validity Rule

A conclusion follows only if it is true in every diagram consistent with the statements. 'Some A are B' never implies 'All A are B'.

Direction Sense Pythagoras

Perpendicular movements give net displacement by Pythagoras; opposite movements cancel. Draw a rough compass diagram before computing the final distance.

Subject-Verb Agreement

Singular subjects take singular verbs. Words like each, every, either, neither and everyone are grammatically singular even when they refer to many people.

Active to Passive Voice

The object becomes the subject, the verb becomes be + past participle, and the original subject follows 'by' or is dropped.

Prepositions of Time

Use 'in' for months and years, 'on' for days and dates, and 'at' for clock times and festivals considered as points in time.

Direct to Indirect Speech

When reporting, present tense shifts to past and time words change: now becomes then, today becomes that day, tomorrow becomes the next day.