UPPSC AE Mechanical cheat sheet

Carnot efficiency of any heat engine between reservoirs T_H and T_L is 1 − T_L/T_H; no real cycle between the same reservoirs can exceed it.

For an ideal gas, Cp − Cv = R and γ = Cp/Cv; air at room temperature has γ ≈ 1.4, so Cp ≈ 1.005 kJ/kg·K and Cv ≈ 0.718 kJ/kg·K.

Otto cycle efficiency = 1 − r^(1−γ) where r is compression ratio; Diesel cycle efficiency = 1 − [ρ^γ − 1] / [γ·r^(γ−1)·(ρ − 1)] with cut-off ratio ρ.

Beam bending: σ/y = M/I = E/R; maximum shear stress for a rectangular section is 1.5·V/A and for a circular section is 4·V/3A.

Torsion of a solid circular shaft: τ_max = 16T/(πd³); angle of twist θ = TL/(GJ) with polar moment J = πd⁴/32.

Euler buckling load P_cr = π²EI/L_e²; effective length L_e equals L for pinned-pinned, 0.5L for fixed-fixed, 0.7L for fixed-pinned, and 2L for fixed-free columns.

Reynolds number Re = ρVD/μ distinguishes laminar (Re < 2000 in pipes) from turbulent flow; Darcy–Weisbach head loss h_f = fLV²/(2gD).

In a Pelton wheel the bucket speed for maximum efficiency is half the jet velocity (u = V/2); specific speed identifies turbine type - low for Pelton, high for Kaplan.

For a single-stage reciprocating compressor, volumetric efficiency falls as clearance ratio and pressure ratio rise; ideal work = (n/(n−1))·P₁V₁[(P₂/P₁)^((n−1)/n) − 1].

The Constitution of India was adopted by the Constituent Assembly on 26 November 1949 and came into force on 26 January 1950; Dr B. R. Ambedkar chaired the Drafting Committee.

Fundamental Rights occupy Part III (Articles 12–35); the Right to Constitutional Remedies (Article 32) was called the 'heart and soul' of the Constitution by Ambedkar.

The Directive Principles of State Policy are in Part IV (Articles 36–51) and are non-justiciable; the Fundamental Duties were added by the 42nd Amendment (1976) in Part IVA.

Uttar Pradesh is India's most populous state; its capital is Lucknow, and the state borders eight other states plus Nepal, with the Ganga and Yamuna as major rivers.

The Tropic of Cancer passes through eight Indian states, including Rajasthan, Madhya Pradesh, Chhattisgarh, Jharkhand, West Bengal, Tripura, Mizoram and Gujarat.

Basic SI and physical constants worth memorising: g ≈ 9.81 m/s², speed of light c ≈ 3 × 10⁸ m/s, 1 kWh = 3.6 × 10⁶ J, and atmospheric pressure ≈ 101.325 kPa.

In Indian polity, a Money Bill can be introduced only in the Lok Sabha with the President's recommendation, and the Rajya Sabha must return it within 14 days.

India's Five-Year Plans began in 1951; NITI Aayog replaced the Planning Commission on 1 January 2015 and publishes the SDG India Index.

संधि: दो वर्णों के मेल से उत्पन्न परिवर्तन; स्वर संधि के भेद - दीर्घ, गुण, वृद्धि, यण और अयादि। उदाहरण: विद्या + आलय = विद्यालय (दीर्घ संधि)।

समास के छह प्रमुख भेद: तत्पुरुष, कर्मधारय, द्विगु, द्वंद्व, बहुव्रीहि और अव्ययीभाव; 'चौराहा' द्विगु समास तथा 'दशानन' बहुव्रीहि समास का उदाहरण है।

उपसर्ग अर्थ बदलते हैं - 'अनु' का अर्थ पीछे/समान (अनुकरण), 'अप' का अर्थ बुरा (अपमान); प्रत्यय दो प्रकार के: कृत् (करने वाला, जैसे -आई) और तद्धित (नाम से नाम, जैसे -ता)।

कारक के आठ भेद हैं और उनके विभक्ति चिह्न: कर्ता 'ने', कर्म 'को', करण 'से/के द्वारा', संप्रदान 'के लिए', अपादान 'से' (अलग होना), अधिकरण 'में/पर'।

रस के नौ भेद: शृंगार, हास्य, करुण, रौद्र, वीर, भयानक, बीभत्स, अद्भुत और शांत; शांत रस को 'रसराज' कहा जाता है।

अलंकार: अनुप्रास में वर्णों की आवृत्ति, यमक में भिन्न अर्थ वाले समान शब्द की आवृत्ति, उपमा में 'सा/सी/सम' वाचक शब्द, और रूपक में अभेद आरोप होता है।

मुहावरे अर्थ सहित: 'अंधे की लाठी' = एकमात्र सहारा; 'नौ दो ग्यारह होना' = भाग जाना; 'आँख का तारा' = अत्यंत प्रिय; 'ईंट से ईंट बजाना' = पूर्ण नाश करना।

विलोम शब्द: उत्कर्ष–अपकर्ष, सदाचार–दुराचार, आस्तिक–नास्तिक; पर्यायवाची: जल - पानी, वारि, नीर, अंबु, तोय।

Subject–verb agreement: a singular subject takes a singular verb, but 'each, either, neither, everyone, nobody' are singular, while 'both, few, several, many' take plural verbs.

Articles: 'a' before consonant sounds (a university, a one-rupee coin), 'an' before vowel sounds (an hour, an MLA); 'the' is used for unique nouns and superlatives.

Tenses: present perfect (has/have + past participle) is used for past actions with present relevance; past perfect (had + past participle) marks the earlier of two past actions.

Prepositions: 'since' with a point of time, 'for' with a duration; 'between' for two items, 'among' for more than two; 'discuss' and 'reach' take no preposition after them.

Active to passive: object becomes subject, verb becomes be + past participle, agent follows 'by'; only transitive verbs can be made passive.

Direct to indirect speech: present tense in the reporting verb keeps the reported tense unchanged; past reporting verb shifts present to past, and 'this/here/tomorrow' become 'that/there/the next day'.

Idioms: 'a blessing in disguise' = an apparent misfortune that turns out well; 'to beat about the bush' = to avoid the main point; 'once in a blue moon' = very rarely.

One-word substitutions: 'altruist' (one who lives for others), 'optimist' (one who looks at the bright side), 'philanthropist' (one who loves mankind), 'misanthrope' (one who hates mankind).

Common error traps: 'one of my friends is' (not are), 'the number of students is' versus 'a number of students are', and 'neither of the two boys was present'.