CIL MT cheat sheet

The Constitution of India was adopted on 26 November 1949 and came into force on 26 January 1950.

Part III (Articles 12–35) contains Fundamental Rights; Article 32, the right to constitutional remedies, was called the 'heart and soul' of the Constitution by Dr. B. R. Ambedkar.

The President is elected indirectly by an electoral college of elected MPs and elected MLAs of States and Union Territories with legislatures (Article 54); removal is by impeachment under Article 61.

A Money Bill is defined in Article 110 and may be introduced only in the Lok Sabha with the President's recommendation; the Rajya Sabha can only recommend changes within 14 days.

The Reserve Bank of India was established in 1935 and nationalised in 1949; the repo rate is the rate at which RBI lends short-term funds to banks against government securities.

Census 2011 recorded an effective literacy rate of 74.04% (male 82.14%, female 65.46%) and a sex ratio of 943 females per 1000 males.

India is the world's largest producer of milk and pulses.

Stratospheric ozone absorbs most ultraviolet-B radiation; its depletion is driven mainly by chlorofluorocarbons and halons, controlled under the Montreal Protocol.

The Battle of Plassey (1757) was won by Robert Clive against Siraj-ud-Daulah; the Battle of Buxar followed in 1764.

Alphabet positions run A = 1 to Z = 26; the reverse position equals 27 minus the forward position, so A is 26 and Z is 1.

EJOTY is the mnemonic for positions 5, 10, 15, 20, 25: E, J, O, T, Y.

Clock: minute hand moves 6° per minute, hour hand 0.5° per minute, so the minute hand gains 5.5° per minute; the hands coincide every 65 5/11 minutes.

Odd days: 100 years give 5 odd days, 200 years give 3, 300 years give 1 and 400 years give 0.

A cube of side cut into n³ unit cubes gives 8 cubes with 3 painted faces, 12(n−2) with 2 faces, 6(n−2)² with 1 face and (n−2)³ with none.

Ranking: total persons in a row = rank from left + rank from right − 1, when the same person is counted in both.

Syllogism: 'All A are B' does not imply 'All B are A'; a conclusion is valid only if it holds in every possible Venn diagram of the premises.

Direction sense: net displacement is found by resolving north–south and east–west components, then applying Pythagoras' theorem.

Sum of the first n natural numbers = n(n+1)/2; their average = (n+1)/2; sum of squares = n(n+1)(2n+1)/6.

Simple interest = PRT/100; compound amount = P(1 + R/100)^T, with compound interest = amount − principal.

Unit conversion: 1 km/h = 5/18 m/s; to convert km/h to m/s multiply by 5/18.

Work: if A alone takes x days and B alone takes y days, together they take xy/(x+y) days.

Train problems: time to cross a pole = train length ÷ speed; time to cross a platform = (train length + platform length) ÷ speed.

Profit% and loss% are always calculated on cost price: SP = CP(1 + profit%/100); profit% = (SP − CP)/CP × 100.

For two positive integers, HCF × LCM = product of the numbers; this relation does not extend to three or more numbers.

Area formulas: circle = πr²; triangle = ½ × base × height; equilateral triangle = (√3/4)a²; trapezium = ½(a + b)h.

Alligation rule gives the ratio of mixing quantities as the difference of the given values from the mean value, taken crosswise.

Subject–verb agreement: in 'one of + plural noun', the verb agrees with 'one' (singular), as in 'One of the boys is absent'.

Use 'since' with a point of time and 'for' with a duration, both with the present perfect tense (has/have + past participle).

Passive voice is formed as object + be + past participle + by + subject, keeping the original tense unchanged.

'The' is used before superlatives, unique objects, rivers, mountain ranges and newspapers; it is generally omitted before most country names.

'A' precedes a consonant sound and 'an' a vowel sound, decided by pronunciation, not spelling - 'an hour', 'a university'.

In reported speech, present tenses shift to past, and 'this/today/tomorrow' change to 'that/that day/the next day'.

Common idiom: 'to bite the bullet' means to endure a painful or unavoidable situation with courage.

Frequently tested pairs: affect (verb) vs effect (noun); principal (head) vs principle (rule); stationary (fixed) vs stationery (paper).

Ohm's law: V = IR at constant temperature; DC power P = VI = I²R = V²/R.

Balanced three-phase power = √3 × line voltage × line current × power factor; for a star connection line voltage = √3 × phase voltage.

Ideal transformer relations: V1/V2 = N1/N2 and I1/I2 = N2/N1, with input power equal to output power.

Mohs hardness scale (increasing): talc 1, gypsum 2, calcite 3, fluorite 4, apatite 5, orthoclase 6, quartz 7, topaz 8, corundum 9, diamond 10.

Mechanical stress = force/area, strain = change in length/original length, and Young's modulus E = stress/strain within the elastic limit.

Concrete grade M20 denotes characteristic compressive strength of 20 N/mm² measured on 150 mm cubes at 28 days.

Carnot efficiency = 1 − Tc/Th, with both reservoir temperatures in kelvin; no heat engine between the same reservoirs can exceed it.

Bernoulli's equation for steady, incompressible, frictionless flow: P + ½ρv² + ρgh = constant along a streamline.

In coal mining, bord-and-pillar is the dominant Indian method; the Directorate General of Mines Safety (DGMS) regulates mine safety under the Ministry of Labour and Employment.

Liquidity and leverage: current ratio = current assets/current liabilities; debt–equity ratio = total debt/shareholders' funds.