UP Police SI cheat sheet

Static GK anchors: Article 1 names India as a Union of States; the Constitution was adopted 26 November 1949 and came into force 26 January 1950.

National symbols: national bird Indian peacock, national animal Bengal tiger, national flower lotus, national fruit mango, national river Ganga, national aquatic animal Ganges river dolphin.

Reasoning rule - syllogism: in 'All A are B' and 'All B are C', the valid conclusion is 'All A are C'; a particular conclusion cannot follow from two universal premises alone.

Reasoning rule - blood relations: draw a fixed symbol set (square = male, circle = female, horizontal line = sibling, vertical line = parent-child) before answering.

Direction sense: net displacement uses Pythagoras when two moves are perpendicular, e.g. 3 m north then 4 m east gives 5 m from start.

Number series checks in order: differences, then ratios, then alternating/prime/square/cube patterns, then two interleaved series.

Coding-decoding: test letter-shift (+n/-n), reversal, and position-sum rules in that order; A=1 to Z=26 is the standard alphabet index.

Calendar rule: a normal year shifts the day of week by 1, a leap year by 2; a century leap year such as 2000 is divisible by 400.

संधि: स्वर संधि में दो स्वर मिलते हैं; 'विद्या + आलय = विद्यालय' दीर्घ संधि का उदाहरण है, जहाँ अ + आ = आ होता है।

समास: 'राजपुत्र' में राजा और पुत्र का संबंध है - यह तत्पुरुष (षष्ठी) समास है; 'चौराहा' द्वंद्व नहीं, द्विगु समास है।

उपसर्ग और प्रत्यय: 'अनुशासन' में उपसर्ग 'अनु' है; 'लेखक' में प्रत्यय 'क' जोड़कर संज्ञा बनी है।

विलोम शब्द युग्म: उत्कर्ष–अपकर्ष, सदाचार–दुराचार, आस्तिक–नास्तिक, जय–पराजय - परीक्षा में युग्म के रूप में पूछे जाते हैं।

मुहावरा अर्थ: 'नौ-दो ग्यारह होना' = भाग जाना; 'आँख का तारा' = बहुत प्यारा; 'लोहे के चने चबाना' = कठिन कार्य करना।

वाक्य शुद्धि: 'मैंने भोजन खाया' सही है; 'मुझे भोजन खाया' अनुपयुक्त है क्योंकि कर्ता कारक का चिह्न 'ने' कर्मवाच्य में बदलता है।

Legal awareness: भारतीय नागरिक सुरक्षा संहिता (BNSS) ने दंड प्रक्रिया संहिता (CrPC) का स्थान लिया और भारतीय न्याय संहिता (BNS) ने भारतीय दंड संहिता (IPC) का, जुलाई 2024 से प्रभावी।

FIR: संज्ञेय अपराध की सूचना थाने में लिखित या मौखिक दी जा सकती है, जिसे लिखकर पढ़कर सुनाया जाता है और सूचनाकर्ता के हस्ताक्षर लिए जाते हैं।

Percentage change of two successive changes a% then b%: net = a + b + (ab/100); a 20% rise then 20% fall gives a net 4% fall.

Profit and loss: SP = CP × (100 + profit%)/100; if an article is sold at a loss of 10%, SP = 0.9 × CP.

Simple interest SI = P × R × T / 100; compound interest CI = P[(1 + R/100)^T − 1]; for 2 years CI − SI = P(R/100)².

Time-speed-distance: distance = speed × time; to convert km/h to m/s multiply by 5/18, and m/s to km/h multiply by 18/5.

Average: new average after adding a value x to n items = (n·old average + x)/(n + 1); total = average × count.

Ratio and mixture: in an alloy of A and B in ratio m:n, quantity of A = total × m/(m + n); repeated replacement uses final = initial × (1 − replaced/total)^k.

Work: if A alone takes x days and B alone y days, together they take xy/(x + y) days; work rate is the reciprocal of days.

Number system: divisibility by 3 or 9 checked by digit sum, by 4 by last two digits, by 8 by last three digits, by 11 by alternating digit-sum difference.

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

Article 21A (86th Amendment, 2002) makes free and compulsory education a fundamental right for children aged 6 to 14; the RTE Act followed in 2009.

Directive Principles are in Part IV (Articles 36–51) and are non-justiciable; Article 40 covers organisation of village panchayats and Article 44 a uniform civil code.

Fundamental Duties are in Part IVA, Article 51A, added by the 42nd Amendment (1976) on the recommendation of the Swaran Singh Committee.

Emergency provisions: national emergency under Article 352, President's rule under Article 356, financial emergency under Article 360.

Amendment procedure under Article 368 requires a special majority; federal provisions such as Article 368 itself also need ratification by half the states.

Key officeholders: the Chief Election Commissioner is appointed by the President; the Comptroller and Auditor General's reports go to Parliament via the President (Article 151).

Current affairs anchor: the Bharatiya Nyaya Sanhita, Bharatiya Nagarik Suraksha Sanhita and Bharatiya Sakshya Adhiniyam replaced the IPC, CrPC and Indian Evidence Act with effect from 1 July 2024.

Analogy rule: identify the relation class first (worker–tool, cause–effect, part–whole, synonym), then apply the same class to the pair given in the options.

Ranking puzzles: if A is 7th from the left and 12th from the right, total = 7 + 12 − 1 = 18 persons.

Clocks: the minute hand gains 5.5° per minute on the hour hand; hands coincide 11 times in 12 hours.

Venn diagram questions on 'some/many' statements: a possibility conclusion is valid unless the premises make it impossible.

Indian polity quick list: President is elected by an electoral college; the Vice President is the ex-officio Chairman of the Rajya Sabha.

Geography anchor: Tropic of Cancer passes through 8 Indian states including Gujarat, Rajasthan, Madhya Pradesh, Chhattisgarh, Jharkhand, West Bengal, Tripura and Mizoram.

Mirror and water image: a mirror reverses left and right while a water image reverses top and bottom; letters with vertical symmetry look unchanged in a mirror.

Statement–assumption: an assumption is what the speaker must have taken for granted; a restatement of the statement is not an assumption.

कारक चिह्न: कर्ता 'ने', कर्म 'को', करण 'से/के द्वारा', संप्रदान 'के लिए', अपादान 'से', संबंध 'का/की/के', अधिकरण 'में/पर'।

वाच्य: कर्मवाच्य में क्रिया कर्म के लिंग-वचन के अनुसार बदलती है; भाववाच्य में अकर्मक क्रिया 'जाना' रूप में आती है।

काल पहचान: 'रहा है' अपूर्ण वर्तमान, 'चुका है' पूर्ण वर्तमान, 'रहा था' अपूर्ण भूत, 'चुका था' पूर्ण भूत दर्शाता है।

अलंकार: अनुप्रास में वर्ण की आवृत्ति, यमक में एक शब्द का भिन्न अर्थ में दोहराव, उपमा में 'सा/सम/तुल्य' वाचक शब्द होता है।

Legal awareness: गिरफ्तार व्यक्ति को संविधान के अनुच्छेद 22 के अंतर्गत 24 घंटे के भीतर मजिस्ट्रेट के समक्ष प्रस्तुत किया जाता है।

Zero FIR किसी भी थाने में दर्ज हो सकती है, भले ही अपराध क्षेत्राधिकार से बाहर हुआ हो; बाद में संबंधित थाने को स्थानांतरित की जाती है।

साक्ष्य: भारतीय साक्ष्य अधिनियम, 2023 के अंतर्गत इलेक्ट्रॉनिक अभिलेख भी साक्ष्य के रूप में स्वीकार्य हैं, जिनके प्रमाणीकरण की शर्तें हैं।

शब्द-शुद्धि: 'पर्यावरण' सही है, 'पर्यावरण' में 'र्य' का प्रयोग; 'आवश्यक' सही, 'आवश्यकता' संज्ञा रूप है।

Ages: if the present age ratio is a:b and after n years it is c:d, solve a·x + n over b·x + n = c/d for x.

Boats and streams: downstream speed = u + v, upstream speed = u − v; speed in still water u = (down + up)/2.

Pipes and cisterns: a filling pipe's work is positive, a draining pipe's is negative; combined rate = sum of reciprocals with signs.

Simple interest doubling rule: a sum doubles in 100/R years at simple interest; at 12.5% it doubles in 8 years.

Permutation and combination: arrangements of n distinct items = n!; selections of r from n = nCr = n!/[r!(n − r)!].

Probability of an event = favourable outcomes / total equally likely outcomes; P(A or B) = P(A) + P(B) − P(A and B).

Mensuration: area of circle = πr², circumference = 2πr; volume of cylinder = πr²h; surface area of sphere = 4πr².

Data interpretation: percentage share = part/whole × 100; read the axis units and whether figures are in thousands or lakhs before computing.

Writs under Articles 32 and 226: habeas corpus (produce the person), mandamus (command a public duty), prohibition (stop lower court), certiorari (quash order), quo warranto (question authority to hold office).

The Supreme Court's advisory jurisdiction is under Article 143; its appellate jurisdiction in constitutional matters is under Article 132.

Money Bill is defined in Article 110 and can be introduced only in the Lok Sabha with the President's recommendation; the Speaker certifies it.

Panchayati Raj: the 73rd Amendment (1992) added Part IX and the Eleventh Schedule with 29 subjects; the 74th Amendment dealt with municipalities.

President's pardoning power under Article 72 covers death sentences; the Governor's power under Article 161 does not extend to death sentences or court-martial cases.

Current affairs anchor: the Women's Reservation (106th Amendment) Act, 2023 reserves one-third of seats in the Lok Sabha and state assemblies for women.

Current affairs anchor: Chandrayaan-3's Vikram lander touched down near the lunar south pole on 23 August 2023, making India the first country to land there.

Current affairs anchor: India hosted the G20 summit in New Delhi in September 2023, where the African Union was admitted as a permanent member.

Seating arrangement: fix the most constrained person first, then place others relative to that anchor; for circular arrangements facing the centre, left is clockwise.

Cube cutting: a cube cut into n³ small cubes has 8 corner cubes with 3 painted faces, 12(n − 2) with 2 painted faces, and 6(n − 2)² with 1 painted face.

Odd one out in letter clusters: convert letters to numbers and check whether differences follow a constant or alternating pattern.

Indian history anchor: the Indian National Congress was founded in 1885; the Rowlatt Act was passed in 1919 and the Jallianwala Bagh massacre occurred on 13 April 1919.

Science anchor: the SI unit of force is the newton, of pressure the pascal, of power the watt, and of electric charge the coulomb.

Syllogism with 'No A is B': the valid conversion is 'No B is A'; a conclusion 'Some A are not B' does not follow from 'No A is B' alone in all cases.

Input-output and machine puzzles: track the transformation step by step on the given input rather than guessing the rule from the output alone.

तत्सम-तद्भव: दुग्ध–दूध, अग्नि–आग, हस्त–हाथ, कर्म–काम; तत्सम संस्कृत से सीधे आए शब्द हैं और तद्भव उनके परिवर्तित रूप।

वर्तनी: 'क्ष', 'त्र', 'ज्ञ' संयुक्त व्यंजन हैं; 'कवि' में 'व' हल्का और 'कवी' गलत प्रयोग है जब तक अर्थ 'कवयित्री' न हो।

वाक्य के भेद अर्थ के आधार पर: विधानवाचक, निषेधवाचक, प्रश्नवाचक, आज्ञावाचक, विस्मयादिबोधक, संदेहवाचक, इच्छावाचक।

Legal awareness: संविधान का अनुच्छेद 39A गरीबों को मुफ्त कानूनी सहायता का निर्देश देता है, जिससे विधिक सेवा प्राधिकरण अधिनियम, 1987 बना।

Legal awareness: लोक अदालत का गठन विधिक सेवा प्राधिकरण अधिनियम, 1987 के अंतर्गत होता है और इसका निर्णय अंतिम तथा बंधनकारक होता है।

Legal awareness: बाल अपराधों की सुनवाई किशोर न्याय अधिनियम, 2015 के अंतर्गत होती है, जिसमें 16 वर्ष से अधिक आयु के गंभीर अपराध में वयस्क के रूप में विचारण संभव है।

पत्र लेखन: औपचारिक पत्र में प्रेषक का पता, दिनांक, प्राप्तकर्ता का पदनाम, विषय, संबोधन और हस्ताक्षर का क्रम रहता है।

Partnership: profit share is proportional to capital × time; if capitals are in ratio a:b and periods in ratio x:y, shares are in ratio ax:by.

Successive discount: two discounts of a% and b% give a single equivalent discount of a + b − ab/100.

Simple and compound interest relation: for 2 years at rate R, the difference between CI and SI equals SI × R/200.

Trains: time to cross a platform = (length of train + length of platform)/speed; time to cross a pole = length of train/speed.

Ratio comparison: to compare a/b and c/d, cross-multiply; ad > bc means a/b > c/d when b and d are positive.

Square roots and cubes to memorise: squares 1–30 and cubes 1–15 speed up simplification; √2 ≈ 1.414, √3 ≈ 1.732, √5 ≈ 2.236.

Approximation strategy in objective papers: round to the nearest convenient value, compute, then check which option lies closest rather than doing exact long division.

Calendar and clock combined: to find the day of the week for a date, count odd days from a known reference year and add the day-of-year offset.

Citizenship is in Part II, Articles 5–11; Parliament has power under Article 11 to regulate citizenship, and the Citizenship Act, 1955 governs it.

The Election Commission is a constitutional body under Article 324; the Finance Commission under Article 280; the UPSC under Article 315.

The Attorney General of India is appointed under Article 76 and is the first law officer; the Advocate General is the state counterpart under Article 165.

Anti-defection is governed by the Tenth Schedule, added by the 52nd Amendment (1985); the presiding officer decides disqualification.

Criminal law anchor: under the Bharatiya Nyaya Sanhita, 2023, murder is punishable under Section 103, and the definition of theft appears in Section 303.

Current affairs anchor: the Ram Mandir pran pratishtha at Ayodhya took place on 22 January 2024.

Current affairs anchor: India's Aditya-L1 solar mission was inserted into a halo orbit around the Sun–Earth L1 point in January 2024.

Current affairs anchor: the 2024 Lok Sabha elections were held in seven phases from April to June 2024, with results declared on 4 June 2024.

Alphabet position pairs that sum to 27: A–Z, B–Y, C–X; useful for opposite-letter coding questions.

Series with squares and cubes: check n² ± 1, n³ ± 1, and alternating prime/square patterns before assuming a simple difference series.

Cause and effect questions: a statement pair is accepted as cause-effect only when one event plausibly produces the other, not merely when both occur together.

Indian economy anchor: the Reserve Bank of India was established on 1 April 1935 and nationalised in 1949; it is the monetary authority under the RBI Act, 1934.

Awards anchor: the Bharat Ratna is India's highest civilian award; the Param Vir Chakra is the highest wartime military decoration.

Sports anchor: the Ranji Trophy is for cricket, the Santosh Trophy for football, the Duleep Trophy for cricket, and the Thomas Cup for badminton (men).

Sitting arrangement with two rows facing each other: in one row facing south, a person's left is the observer's right, so mirror the directions before placing.

रस के स्थायी भाव: श्रृंगार–रति, हास्य–हास, करुण–शोक, रौद्र–क्रोध, वीर–उत्साह, भयानक–भय, वीभत्स–जुगुप्सा, अद्भुत–विस्मय, शांत–निर्वेद।

अनेकार्थी शब्द: 'कनक' का अर्थ सोना और धतूरा दोनों है; 'हरि' का अर्थ विष्णु, इंद्र, सूर्य आदि हो सकता है।

Legal awareness: संविधान के अनुच्छेद 20 में अपराधों के लिए दोषसिद्धि के संबंध में संरक्षण है - दोहरी सजा नहीं, आत्म-अभियोजन नहीं, और पूर्वव्यापी दंड नहीं।

Legal awareness: अनुच्छेद 22 में निवारक निरोध के विशेष प्रावधान हैं, जिसमें 3 माह से अधिक निरोध पर सलाहकार बोर्ड की आवश्यकता होती है।

Legal awareness: अनुच्छेद 23 मानव तस्करी और बलात् श्रम का निषेध करता है तथा अनुच्छेद 24 में 14 वर्ष से कम बच्चों के कारखानों में काम का निषेध है।

अनुवाद शुद्धता: अंग्रेजी 'reasonable' का हिंदी में 'विवेकपूर्ण/तर्कसंगत' प्रयोग होता है, 'उचित' प्रसंग के अनुसार; तकनीकी शब्दों को कोष्ठक में मूल रूप में रखना उपयुक्त है।

Mixture replacement: after removing x litres from V litres of pure liquid and refilling with water k times, pure liquid left = V(1 − x/V)^k.

Average speed over equal distances: average = 2ab/(a + b) for speeds a and b; for equal times, average is the simple mean.

Number of factors: if N = a^p × b^q, the number of divisors is (p + 1)(q + 1); the number of ways to express N as a product of two factors is half the divisor count.

LCM and HCF relation: LCM × HCF = product of the two numbers; HCF divides both numbers and LCM is a multiple of both.

Simple interest instalments and CI half-yearly: when interest is compounded half-yearly, the rate is halved and the time doubled.

Mensuration of a cone: volume = (1/3)πr²h, curved surface area = πrl where l = √(r² + h²).

Speed of a train crossing another moving train in the same direction = relative speed = difference of speeds; opposite direction = sum of speeds.

Percentage of a percentage: x% of y% of z = (x/100)(y/100)z; keep units consistent when the base changes between steps.

The Preamble was amended by the 42nd Amendment (1976), which added 'socialist', 'secular' and 'integrity'; the words 'sovereign democratic republic' were already present.

Article 14 guarantees equality before the law and equal protection of laws; Article 15 prohibits discrimination on grounds of religion, race, caste, sex or place of birth.

Article 25 guarantees freedom of conscience and free profession, practice and propagation of religion, subject to public order, morality and health.

The Supreme Court's Basic Structure doctrine comes from the Kesavananda Bharati case (1973); Parliament cannot amend the Constitution so as to destroy its basic structure.

Current affairs anchor: the new criminal codes - BNS, BNSS and BSA - came into force on 1 July 2024, replacing the IPC, CrPC and Evidence Act respectively.

Current affairs anchor: India's Goods and Services Tax Council is a constitutional body under Article 279A, created by the 101st Amendment (2016).

Current affairs anchor: the National Green Hydrogen Mission was approved in January 2023 with a target of 5 million metric tonnes of green hydrogen capacity by 2030.

Statement–conclusion: a conclusion must follow from the statement alone; outside knowledge or a mere possibility is not sufficient unless the question says 'probably'.

Letter series with reversals: when the alphabet is reversed, position of a letter = 27 − its normal position.

Indian geography anchor: the Deccan Plateau is bounded by the Western Ghats and Eastern Ghats; the Narmada flows west into the Arabian Sea between the Vindhyas and Satpuras.

Polity anchor: the Rajya Sabha has a maximum strength of 250 members, of whom 12 are nominated by the President for special knowledge in specified fields.

History anchor: the Battle of Plassey (1757) and the Battle of Buxar (1764) established British power in Bengal; the Permanent Settlement followed in 1793.

Science anchor: photosynthesis converts CO2 and water into glucose and oxygen in the presence of chlorophyll and sunlight; the light reaction occurs in the thylakoid membranes.

Odd-even and classification: group items by a shared attribute such as state capital, currency, or sport, then pick the item lacking that attribute.

संज्ञा के भेद: व्यक्तिवाचक, जातिवाचक, भाववाचक, समूहवाचक, द्रव्यवाचक; 'सेना' समूहवाचक और 'सुंदरता' भाववाचक संज्ञा है।

सर्वनाम के भेद: निजवाचक ('स्वयं', 'आप'), निश्चयवाचक ('यह', 'वह'), अनिश्चयवाचक ('कोई', 'कुछ'), प्रश्नवाचक ('कौन', 'क्या'), संबंधवाचक ('जो', 'जिसका')।

क्रिया विशेषण के भेद: कालवाचक ('आज'), स्थानवाचक ('यहाँ'), परिमाणवाचक ('बहुत'), रीतिवाचक ('धीरे')।

Legal awareness: भारतीय नागरिक सुरक्षा संहिता के अंतर्गत गिरफ्तार व्यक्ति को गिरफ्तारी के कारणों की सूचना और अपने अधिवक्ता से मिलने का अधिकार है।

Legal awareness: संविधान के अनुच्छेद 21 में 'विधि की उचित प्रक्रिया' के स्थान पर 'विधि द्वारा स्थापित प्रक्रिया' का प्रयोग है, जिसे मेनका गांधी मामले (1978) में विस्तारित किया गया।

Legal awareness: सूचना का अधिकार अधिनियम, 2005 के अंतर्गत सार्वजनिक प्राधिकरण को 30 दिनों के भीतर सूचना देने की बाध्यता है।

शब्द-भेद: 'अधिकार' (right) और 'अधिकारी' (officer) भिन्न अर्थ देते हैं; 'अनुचित' और 'अनुचितता' में प्रत्यय से भाववाचक संज्ञा बनती है।

Ratio of ages or quantities after a fixed interval: set up equations with a common multiplier x and solve; avoid assuming the difference changes.

Simple interest with changing rates: total SI = P(R1T1 + R2T2 + …)/100 when the rate changes over successive periods.

Compound interest with different yearly rates: amount = P(1 + R1/100)(1 + R2/100)… for successive years.

Probability with replacement vs without: with replacement the total stays the same; without replacement the denominator decreases by one after each draw.

Number of handshakes or matches in a round robin: n(n − 1)/2; in a knockout with n players, n − 1 matches are needed.

Area of a triangle with sides a, b, c: Heron's formula, area = √[s(s − a)(s − b)(s − c)] where s = (a + b + c)/2.

Discount and marked price: SP = MP(1 − d/100); if profit is made after discount, CP = SP × 100/(100 + profit%).

Ratio of work and wages: wages are shared in the ratio of work done, so if A and B work together their shares are proportional to their one-day work rates.

The President is elected by an electoral college of elected members of both Houses of Parliament and elected members of state legislative assemblies, using the single transferable vote system.

Article 356 (President's rule) was first invoked in Punjab in 1951; the Supreme Court's S. R. Bommai judgment (1994) laid down judicial review standards for it.

The Governor is appointed by the President under Article 155 and holds office during the President's pleasure; the Governor's legislative powers include Article 200 (assent to Bills).

The Finance Commission is constituted every five years under Article 280; the first commission was chaired by K. C. Neogy.

Current affairs anchor: the 16th Finance Commission, chaired by Arvind Panagariya, was constituted in December 2023 for the period from 2026–27.

Current affairs anchor: India assumed the G20 presidency in December 2022 and hosted the leaders' summit in New Delhi on 9–10 September 2023.

Current affairs anchor: the National Education Policy 2020 replaced the 1986 policy and introduced a 5+3+3+4 school structure.

Current affairs anchor: the Ayushman Bharat health insurance scheme provides cover of ₹5 lakh per family per year for secondary and tertiary hospitalisation.

Syllogism with possibility: 'All A are B' permits 'Some B are A' and 'Some A are B'; it does not permit 'All B are A'.

Number analogy: check whether the relation is square, cube, product of digits, or sum of digits before choosing an option.

Direction with turns: track the facing direction after each turn; a right turn from north faces east, and a left turn from east faces north.

Indian art and culture anchor: Kathakali is from Kerala, Bharatanatyam from Tamil Nadu, Odissi from Odisha, Kuchipudi from Andhra Pradesh, Manipuri from Manipur, and Kathak from Uttar Pradesh.

Static GK anchor: the Tropic of Capricorn passes through Australia, Africa and South America; the Equator passes through 13 countries including Kenya, Indonesia and Brazil.

Science anchor: the pH scale runs 0–14; a pH below 7 is acidic, above 7 is basic, and 7 is neutral at 25°C.

Classification: pick the odd item by checking whether it is a state, a capital, a river, or a country - the odd one differs in category, not merely in name.

काल के भेद: वर्तमान, भूत, भविष्यत्; प्रत्येक के सामान्य, अपूर्ण, पूर्ण और संदिग्ध रूप होते हैं।

वाच्य के भेद: कर्तृवाच्य, कर्मवाच्य, भाववाच्य; 'राम ने पत्र लिखा' कर्तृवाच्य और 'राम से पत्र लिखा गया' कर्मवाच्य है।

मुहावरे और लोकोक्तियाँ: 'अंधे की लाठी' = एकमात्र सहारा; 'नाच न जाने आँगन टेढ़ा' = अपनी अयोग्यता छिपाने के लिए बहाना बनाना।

Legal awareness: अनुच्छेद 21A और शिक्षा का अधिकार अधिनियम, 2009 के अंतर्गत 6 से 14 वर्ष के बच्चों को निःशुल्क और अनिवार्य शिक्षा का अधिकार है।

Legal awareness: उपभोक्ता संरक्षण अधिनियम, 2019 में उपभोक्ता आयोगों की तीन स्तरीय व्यवस्था है - जिला, राज्य और राष्ट्रीय आयोग।

Legal awareness: संविधान की उद्देशिका में 'हम भारत के लोग' वाक्यांश संविधान की सर्वोच्चता और जनता की संप्रभुता दर्शाता है।

अशुद्धि सुधार: 'दर्शन' सही, 'दर्शन' में 'श' नहीं; 'विद्यार्थी' सही, 'विद्यार्थी' में 'द्' संयुक्त व्यंजन के रूप में आता है।

Percentage error: error% = (approximate − exact)/exact × 100; a 5% error in a length used in an area calculation becomes about 10% in the area.

Simple interest on instalments: for equal annual instalments, the total principal is the sum of instalments discounted by the interest periods.

Ratio of speeds and time: if the ratio of speeds is a:b, the ratio of times for the same distance is b:a.

Mensuration of a rectangle and path: area of a path of uniform width w around a rectangle l × b is (l + 2w)(b + 2w) − lb.

Coding of numbers: check whether the code uses digit reversal, digit sum, or a fixed arithmetic operation such as multiply by 2 and add 1.

Probability of at least one: P(at least one) = 1 − P(none); use this when the event is easier to complement.

Data sufficiency: a question is answerable only if the data yields a unique value; if two statements give different valid values, the answer is 'cannot be determined'.

Ratio and proportion: if a:b = c:d then ad = bc; to divide a sum S in ratio a:b:c, parts are S·a/(a+b+c), S·b/(a+b+c), S·c/(a+b+c).

The Constitution originally had 395 Articles in 22 Parts and 8 Schedules; it now has 12 Schedules, the latest added by the 101st Amendment for GST.

Article 370, which gave special status to Jammu and Kashmir, was abrogated in August 2019, and the Jammu and Kashmir Reorganisation Act, 2019 created two Union Territories.

The Right to Information, the Right to Education and the National Food Security Act are statutory rights, distinct from the fundamental rights in Part III.

The Supreme Court has original jurisdiction in disputes between the Centre and states under Article 131; writ jurisdiction is under Article 32.

Current affairs anchor: the Election Commission of India announced the 2024 Lok Sabha poll schedule in March 2024; the National Democratic Alliance formed the government after the results.

Current affairs anchor: India's Unified Pension Scheme was approved in August 2024 and takes effect from 1 April 2025 for central government employees.

Current affairs anchor: the Bharatiya Sakshya Adhiniyam, 2023 allows electronic records as primary evidence, with Section 63 covering the admissibility of electronic evidence.

Current affairs anchor: the 2023 G20 New Delhi Declaration included the India–Middle East–Europe Economic Corridor and the Global Biofuels Alliance.

Statement–course of action: a course of action must be practical, within the authority of the actor, and directly address the problem stated.

Ordering and ranking: when people are arranged by height, the middle position in a group of n is (n + 1)/2 when n is odd.

Indian economy anchor: the First Five-Year Plan (1951–56) focused on agriculture; the Second (1956–61) focused on industry under the Mahalanobis model.

Static GK anchor: the National Physical Laboratory is in New Delhi; the Indian Institute of Science is in Bengaluru; Bhabha Atomic Research Centre is in Mumbai.

Science anchor: sound travels faster in solids than in liquids and faster in liquids than in gases; its speed in air at 0°C is about 331 m/s.

Polity anchor: the Speaker of the Lok Sabha decides whether a Bill is a Money Bill; the Rajya Sabha can only recommend changes and must return it within 14 days.

Blood relation with coded symbols: decode the symbol table first, then draw the family tree; never infer gender from names alone.

समास के भेद: अव्ययीभाव, तत्पुरुष, कर्मधारय, द्विगु, द्वंद्व, बहुव्रीहि; 'चतुर्भुज' द्विगु और 'दशानन' बहुव्रीहि समास है।

उपसर्ग के भेद: संस्कृत ('अ', 'अनु', 'प्र', 'वि'), हिंदी ('अन', 'उन', 'बिन'), उर्दू ('बे', 'ना', 'खुश') और अंग्रेजी ('रि', 'सब')।

प्रत्यय के भेद: कृत् प्रत्यय क्रिया से शब्द बनाते हैं ('पढ़ाई', 'लेखक'), तद्धित प्रत्यय संज्ञा-विशेषण से ('मानवता', 'भारतीय')।

Legal awareness: संविधान के अनुच्छेद 21 के अंतर्गत निजता का अधिकार के. एस. पुट्टस्वामी मामले (2017) में मूल अधिकार के रूप में मान्य हुआ।

Legal awareness: भारतीय न्याय संहिता, 2023 में 'भ्रष्टाचार' और 'रिश्वत' से संबंधित प्रावधान भ्रष्टाचार निवारण अधिनियम, 1988 से भिन्न रूप में समाहित हैं।

Legal awareness: लोकपाल और लोकायुक्त अधिनियम, 2013 के अंतर्गत लोकपाल केंद्र स्तर पर और लोकायुक्त राज्य स्तर पर भ्रष्टाचार की जाँच करते हैं।

वाक्य-संश्लेषण: दो सरल वाक्यों को 'और', 'किंतु', 'इसलिए' जैसे संयोजकों से जोड़कर संयुक्त वाक्य बनता है; 'जो', 'क्योंकि' से मिश्र वाक्य बनता है।

Ratio of areas of similar figures = square of the ratio of corresponding sides; ratio of volumes of similar solids = cube of the ratio of sides.

Simple interest: to find the rate when a sum becomes n times in T years, R = 100(n − 1)/T.

Average of consecutive numbers: the average of n consecutive integers is the middle term, so the average of 1 to 100 is 50.5.

Boats: if the time taken downstream equals the time upstream for different distances, use distance/speed equality to solve for the stream speed.

Clocks: the angle between the hands at H hours and M minutes = |30H − 5.5M|, taken modulo 360 and adjusted to the smaller angle.

Calendar: the number of odd days in 100 years is 5, in 200 years is 3, in 300 years is 1, and in 400 years is 0.

Number of zeros at the end of n!: count factors of 5 as ⌊n/5⌋ + ⌊n/25⌋ + ⌊n/125⌋ + …, since factors of 2 are more plentiful.

Profit and loss with two articles: if one is sold at a gain of x% and another at a loss of x% for the same selling price, the net result is always a loss of (x/10)²%.

The Constitution's Article 1 describes India as a 'Union of States', and Articles 2 and 3 deal with admission of new states and alteration of boundaries.

The 42nd Amendment (1976) is called the 'Mini Constitution' for adding Fundamental Duties, the words 'socialist' and 'secular', and altering the amendment procedure.

The 44th Amendment (1978) reversed several 42nd Amendment changes, including restoring the right to property as a legal right under Article 300A.

Current affairs anchor: the Supreme Court in 2024 delivered judgments on the electoral bonds scheme (struck down in February 2024) and on the scope of Article 39(b).

Current affairs anchor: India's Chandrayaan-3 mission launched on 14 July 2023 and landed on 23 August 2023; the lander was named Vikram and the rover Pragyan.

Current affairs anchor: the 2023 Women's Reservation Act (106th Amendment) will take effect after a census and delimitation exercise.

Current affairs anchor: India's UPI and digital public infrastructure were highlighted at the 2023 G20 summit; the New Delhi Declaration was adopted unanimously.

Current affairs anchor: the National Quantum Mission was approved in April 2023 with a budget of over ₹6,000 crore for 2023–2031.

Statement–argument: a strong argument must be relevant to the statement, substantive, and not merely a restatement or an emotional appeal.

Matrix and figure counting: count squares in an n × n grid as 1² + 2² + … + n²; count triangles by combining smaller regions systematically.

Static GK anchor: the headquarters of the World Trade Organization is in Geneva, of the International Monetary Fund in Washington DC, and of UNESCO in Paris.

Indian polity anchor: the Vice President is elected by members of both Houses of Parliament, not by state legislatures, using proportional representation by single transferable vote.

History anchor: the Quit India Movement was launched in August 1942; the Cabinet Mission came in 1946 and the Mountbatten Plan in June 1947.

Science anchor: the SI unit of electric current is the ampere, of resistance the ohm, of potential difference the volt, and of capacitance the farad.

Coding with mixed letters and digits: convert letters to positions and digits to their values, then look for a single formula covering both parts.

रस के अंग: विभाव, अनुभाव, संचारी भाव और स्थायी भाव; रस निष्पत्ति के लिए स्थायी भाव का उदय आवश्यक है।

अलंकार के भेद: अनुप्रास, यमक, श्लेष (शब्दालंकार); उपमा, रूपक, उत्प्रेक्षा, अतिशयोक्ति (अर्थालंकार)।

छंद: चौपाई में 16 मात्राएँ प्रति चरण, दोहा में 13 और 11 मात्राएँ, सोरठा दोहे का उल्टा रूप है।

Legal awareness: संविधान के अनुच्छेद 20(3) में आत्म-अभियोजन से संरक्षण है, जिसका अर्थ है कि अभियुक्त को स्वयं के विरुद्ध साक्षी होने के लिए बाध्य नहीं किया जा सकता।

Legal awareness: अनुच्छेद 30 अल्पसंख्यकों को अपनी शिक्षण संस्थाओं की स्थापना और प्रशासन का अधिकार देता है।

Legal awareness: भारतीय नागरिक सुरक्षा संहिता में जमानत के प्रावधानों के अंतर्गत कुछ अपराधों में जमानत का अधिकार है, जबकि कुछ में न्यायालय की अनुमति आवश्यक है।

पारिभाषिक शब्दावली: 'अभियुक्त' (accused), 'अभियोजन' (prosecution), 'साक्षी' (witness), 'न्यायनिर्णय' (judgment), 'अपील' (appeal) - इनका प्रयोग सटीक संदर्भ में करें।

Simple interest: if a sum becomes 3 times in 10 years at simple interest, the rate is 20% per annum because interest equals twice the principal.

Average with change: if the average of n items increases by d when one item is replaced, the new item exceeds the old by n × d.

Mensuration of a cylinder: total surface area = 2πr(r + h); volume = πr²h. For a hemisphere, TSA = 3πr².

Speed and distance with stoppages: if a bus travels at speed v with stoppage time, effective speed = total distance/total time including stops.

Ratio and percentage: to express a ratio a:b as a percentage of the total, a/(a+b) × 100; a 3:2 ratio gives 60% and 40%.

Permutation with repetition: arrangements of n items with p, q identical items = n!/(p! q!).

Probability of a sum with two dice: total outcomes 36; sums 7 and 8 are most likely with 6 and 5 favourable outcomes respectively.

Simplification order: brackets first, then orders/powers, then division and multiplication left to right, then addition and subtraction left to right.

The Election Commission of India is a three-member body when the Chief Election Commissioner is joined by two Election Commissioners; the CEC can be removed only like a Supreme Court judge.

The National Human Rights Commission is a statutory body under the Protection of Human Rights Act, 1993; it cannot investigate matters older than one year.

The Central Bureau of Investigation derives its powers from the Delhi Special Police Establishment Act, 1946, and is not a constitutional body.

Article 148 establishes the Comptroller and Auditor General; Article 324 the Election Commission; Article 315 the Public Service Commissions.

Current affairs anchor: the Bharatiya Nyaya Sanhita, 2023 contains 358 sections, the BNSS has 531 sections, and the Bharatiya Sakshya Adhiniyam has 170 sections.

Current affairs anchor: India won the ICC Men's T20 World Cup in June 2024, defeating South Africa in the final in Barbados.

Current affairs anchor: the Paris Olympics were held in July–August 2024; India won six medals, including a silver in javelin throw by Neeraj Chopra.

Current affairs anchor: the Union Budget 2024–25 was presented in July 2024 and focused on employment, skilling and agriculture under the Viksit Bharat framework.