Rajasthan BSTC / Pre D.El.Ed cheat sheet

Series rule: check differences between consecutive terms first; if differences grow by a constant amount, the series is quadratic (second difference constant).

Alphabet position values: A=1 through Z=26; for reverse values use 27 minus the forward value (A=26, Z=1).

Odd one out: test each option against the same property (divisibility, perfect square, prime, vowel pattern); the answer is the only one failing it.

Blood relations: draw a small family tree; vertical line = parent-child, horizontal line = spouse, and mark gender with symbols before answering.

Direction sense: use a coordinate grid, north = +y, east = +x; final displacement uses Pythagoras, direction uses the sign of both coordinates.

Clock problems: angle between hands = |30H − 5.5M| degrees; hands coincide 11 times in 12 hours, so every 65 5/11 minutes.

Calendar: an ordinary year shifts the weekday by 1, a leap year by 2; the 100-year shift is 5, the 400-year shift is 0.

Coding-decoding: convert letters to numbers, then look for a fixed shift, reversal, or position-wise sum between the word and its code.

Rajasthan borders Pakistan on the west (Jaisalmer, Barmer, Bikaner, Sriganganagar) and five Indian states: Punjab, Haryana, Uttar Pradesh, Madhya Pradesh, Gujarat.

Thar Desert covers about 61% of the state; the Aravalli range divides Rajasthan into arid west (Marusthali) and relatively fertile east.

Longest river fully within Rajasthan is the Banas (origin Khamnor hills, Aravalli); the Chambal is a major border river with Madhya Pradesh.

Sambhar Lake is India's largest inland salt lake; Keoladeo Ghana National Park (Bharatpur) is a UNESCO World Heritage wetland.

Mount Abu (Sirohi district) is the highest peak area of the Aravallis; Guru Shikhar is the highest point at about 1,722 m.

Forts of Rajasthan: Chittorgarh, Kumbhalgarh, Ranthambore, Amber, Jaisalmer, and Gagron are UNESCO Hill Forts of Rajasthan.

Rajasthan's folk deities include Pabuji, Gogaji, Tejaji, and Ramdevji; Pabuji is associated with the Phad painting tradition.

State symbols: tree Khejri, flower Rohida, animal Chinkara (and Camel as state animal), bird Godawan (Great Indian Bustard).

Piaget's stages: sensorimotor (0-2), preoperational (2-7), concrete operational (7-11), formal operational (11+); formal thought allows abstract and hypothetical reasoning.

Vygotsky's ZPD is the gap between what a learner can do alone and what they can do with guidance; scaffolding is temporary support within that gap.

Kohlberg's moral levels: preconventional (punishment/obedience, self-interest), conventional (approval, law and order), postconventional (social contract, universal ethics).

Bloom's revised taxonomy order: Remember, Understand, Apply, Analyze, Evaluate, Create; lower three are LOTS, upper three are HOTS.

Maslow's hierarchy order: physiological, safety, belonging, esteem, self-actualization; lower needs generally precede higher ones.

Formative assessment is ongoing and diagnostic; summative assessment is terminal and certifying. Continuous and Comprehensive Evaluation (CCE) mixes both.

Classical conditioning (Pavlov) pairs a neutral stimulus with an unconditioned one; operant conditioning (Skinner) shapes behaviour through reinforcement and punishment.

Inclusive education adapts curriculum and assessment to the learner; it is not merely placing a child with special needs in a regular class.

वर्णमाला में स्वर 11 और व्यंजन 33 होते हैं; अयोगवाह अनुस्वार, अनुनासिक, विसर्ग तथा उपध्मानीय-जिह्वामूलीय हैं।

संधि: स्वर संधि (दो स्वर), व्यंजन संधि (व्यंजन+स्वर/व्यंजन), विसर्ग संधि। उदाहरण: विद्या+आलय = विद्यालय (दीर्घ संधि)।

समास: तत्पुरुष में उत्तरपद प्रधान, द्वंद्व में दोनों पद प्रधान, बहुव्रीहि में कोई भी पद प्रधान नहीं, अव्ययीभाव में पूर्व पद अव्यय होता है।

उपसर्ग अर्थ बदलते हैं: अनु (पीछे/समान), अप (बुरा), प्र (अधिक), वि (विशेष/विपरीत)। प्रत्यय दो प्रकार: कृत् (क्रिया से) और तद्धित (संज्ञा/विशेषण से)।

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

अलंकार: अनुप्रास (व्यंजन आवृत्ति), यमक (एक शब्द भिन्न अर्थ में दो बार), उपमा (सा/सम/तुल्य), रूपक (अभेद आरोप), उत्प्रेक्षा (मानो/जनु)।

रस के नौ भेद: शृंगार, हास्य, करुण, रौद्र, वीर, भयानक, बीभत्स, अद्भुत, शांत; शांत रस का स्थायी भाव शम है।

वाक्य शुद्धि: लिंग, वचन, काल तथा पदक्रम की संगति जाँचें; 'सभी लड़के आए हैं' में सर्वनाम-क्रिया का लिंग-वचन मेल आवश्यक है।

Subject-verb agreement: singular subject takes singular verb; 'each, every, either, neither, everyone' are singular; 'news, mathematics' are singular despite the -s.

Article rules: 'a' before consonant sounds, 'an' before vowel sounds (an hour, a university); 'the' for unique or already specified nouns.

Tenses: present perfect (has/have + V3) links past to present; past perfect (had + V3) marks the earlier of two past actions.

Active to passive: object becomes subject, verb becomes be + past participle, agent takes 'by'; tense of the original is preserved.

Direct to indirect speech: present tense shifts to past, 'said to' becomes 'told', question word order becomes statement order, and 'this/here/today' shift to 'that/there/that day'.

Prepositions: 'since' with a point of time, 'for' with duration; 'in' with months/years, 'on' with days and dates, 'at' with clock times.

Conditional forms: zero (present + present), first (if + present, will), second (if + past, would), third (if + had + V3, would have + V3).

Common confusables: 'affect' (verb) vs 'effect' (noun), 'principal' (main/head) vs 'principle' (rule), 'advice' (noun) vs 'advise' (verb).

विभक्ति: प्रथमा कर्ता, द्वितीया कर्म, तृतीया करण, चतुर्थी संप्रदान, पंचमी अपादान, षष्ठी संबंध, सप्तमी अधिकरण; संबोधन प्रथमा के समान।

पुल्लिंग 'राम' शब्द: रामः, रामौ, रामाः (प्रथमा); रामम्, रामौ, रामान् (द्वितीया); रामेण, रामाभ्याम्, रामैः (तृतीया)।

स्त्रीलिंग 'लता': लता, लते, लताः; लताम्, लते, लताः; लतया, लताभ्याम्, लताभिः।

नपुंसक 'फल': फलम्, फले, फलानि; द्वितीया में भी फलम्, फले, फलानि।

लकार: लट् (वर्तमान), लिट् (परोक्ष भूत), लृट् (भविष्य), लङ् (अनद्यतन भूत), लोट् (आज्ञा), विधिलिङ् (विधि)।

धातु रूप 'पठ्' लट् प्रथम पुरुष: पठति, पठतः, पठन्ति; मध्यम: पठसि, पठथः, पठथ; उत्तम: पठामि, पठावः, पठामः।

संधि: सवर्ण दीर्घ (अ+अ=आ), गुण (अ+इ=ए), वृद्धि (अ+ए=ऐ), यण (इ+अ=य), अयादि। उदाहरण: सूर्य+उदयः = सूर्योदयः।

समास: तत्पुरुष में उत्तरपद प्रधान, बहुव्रीहि में अन्य पद प्रधान, द्वंद्व में उभय पद प्रधान, अव्ययीभाव में पूर्वपद अव्यय।

Average = sum of terms / number of terms; average speed for equal distances = 2xy/(x+y), not the plain mean of speeds.

Profit and loss: profit% = (SP − CP)/CP × 100; successive discounts of a% and b% equal a + b − ab/100 percent off.

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

Percentage change and ratio: increase by x% then decrease by x% gives a net loss of x²/100 percent.

Time and work: if A takes a days and B takes b days, together they take ab/(a+b) days; work rate is the reciprocal of time.

Area formulas: triangle ½ × base × height, circle πr², trapezium ½(a + b)h; volume of cylinder πr²h, cone ⅓πr²h, sphere 4/3πr³.

Pythagorean triples: 3-4-5, 5-12-13, 7-24-25, 8-15-17, 9-40-41; multiples of these are also triples.

LCM × HCF = product of the two numbers; HCF divides both numbers, LCM is divisible by both.

Divisibility: 3 and 9 by digit sum, 4 by last two digits, 8 by last three digits, 11 by alternating digit-sum difference.