UPPCS Prelims 2025 CSAT PYQs with explanations

The answer is (c) 1, 2, 4, 6, 8, 9, 10. Step 1: The question lists ten items and asks which seven are the 'secrets' of good body language, meaning the visible signals we send. Step 2: The seven are: face (expressions and smiles), gestures (hand movements), head movement (nodding, tilting), eye contact, posture (how we stand or sit), territory (personal space), and mirroring (matching the other person's body language to build rapport). Step 3: 'Cultural' (3), 'comfortable' (5) and 'reflection' (7) are not body parts or actions. They describe context or feelings, not signals. Only option (c) includes all seven correct items and leaves out these three. Tip: in such lists, keep the items that are things you can actually see someone doing. Remove words that are general ideas or adjectives, such as 'comfortable'.

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The answer is (c) Goethe. Step 1: The quote 'To act is easy, to think is hard' is attributed to Johann Wolfgang von Goethe, the German poet and thinker who wrote Faust. Step 2: The full line is often given as 'To think is easy, to act is hard, but the hardest thing in the world is to act in accordance with your thinking',. In problem-solving, the point is that careful thinking before acting is the hard part. Step 3: E.M. Forster (a), the English novelist of A Passage to India, Jean Paul (b), a German writer, and Thompson (d) are not linked to this line. Note: the Hindi version of the paper prints 'गांधी' for option (c), which is a translation slip, so go by the English. Tip: when two language versions of a paper differ, the English version is usually treated as the authentic one.

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The answer is (d) Context. Step 1: Think of how the same words can mean different things in different situations. 'Well done' sounds like praise at a prize function but can be sarcasm after a mistake. Step 2: Context means the setting, the relationship between people, the culture, the time and the purpose of the message. It shapes how every type of communication, spoken, written or non-verbal, is sent and understood. Step 3: Reception (b) and transmission (c) are stages within the communication process, not factors that affect every type of it. Non-regulation (a) is not a standard idea in communication theory. Tip: in communication questions, context is the broadest and safest answer when the question says 'every type'. The basic model has sender, message, channel, receiver, feedback and noise, all set within a context.

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The answer is (d) Administrative power. Step 1: Interpersonal skills are the abilities we use to deal well with other people, such as listening, understanding feelings and behaving politely. Step 2: Empathy (a) is the ability to feel what others feel. Positive thinking (b) helps build hope and good relationships. Courtesy (c) means being polite and respectful. All three are interpersonal skills. Step 3: Administrative power is the authority that comes from holding a post, such as an officer's power to order or sanction. It is not a skill; someone can have power and still deal badly with people. Tip: in communication and interpersonal questions, separate skills (things you learn and practise, like listening, patience and teamwork) from positions or powers (things given by rules). A good civil servant uses interpersonal skills, not just authority.

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The answer is (a) Proximity, utility, loneliness. Step 1: Think about whom you talk to most in daily life. Usually it is people who live or work near you, people who can help you, and people you seek out when you feel alone. Step 2: These match the three factors: proximity (physical closeness, such as neighbours and colleagues), utility (usefulness, such as someone who can guide you), and loneliness (the need for company drives people to start conversations). Step 3: The other options list factors such as secrecy, dissonance (disagreement), deception, dissimilarity and deviance. These tend to push people apart or block communication, so they do not explain whom we choose to talk to. Tip: when options include negative words like deception and dissonance, check whether the question is about forming links or breaking them. Choosing partners is about forming links.

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The answer is (c), Pavlov with the stimulus-response bond theory, which is the wrong pair. Step 1: Match each psychologist with the learning theory they are known for. Step 2: Ivan Pavlov is known for classical conditioning: a dog learned to salivate at the sound of a bell because the bell had been paired with food. The stimulus-response bond theory, also called connectionism or trial-and-error learning, belongs to Edward Thorndike, who studied cats in puzzle boxes and gave the laws of effect, exercise and readiness. Step 3: The other pairs are correct. Kurt Lewin gave field theory, Skinner gave operant conditioning (learning through rewards and punishments), and Wolfgang Kohler gave insight theory from his experiments with chimpanzees. Tip: link each name to its animal: Pavlov's dog, Thorndike's cat, Skinner's rat and pigeon, Kohler's chimpanzee. This makes pairing questions easy.

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The answer is (d) Intellectual process. Step 1: Think about what happens when you make a decision. You gather information, list options, compare their pros and cons, and choose the best one using reason and judgement. Step 2: All of this is mental work done by thinking, which is why decision-making is described as an intellectual (cognitive) process. Step 3: A somatic process (a) relates to the body, such as digestion or reflexes. A social process (b) involves interaction among people, and while decisions can be taken in groups, the act of deciding itself is mental. A psychological process (c) is close, since decisions involve the mind, but the key treats the more specific term, intellectual, as the answer. Tip: when options overlap, as psychological and intellectual do here, pick the one that describes the activity most precisely. Weighing options is a thinking task, so intellectual fits best.

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The answer is (a) Ice-breaker. Step 1: Think about the start of a talk. The audience may be distracted, nervous or unsure about the speaker. Step 2: An ice-breaker is a light opening, such as a short story, a relevant fact, a simple question or a bit of humour. It relaxes the audience, builds a connection and gets their attention before the main content. Step 3: A complex question (b) at the very beginning may confuse or put off listeners. A repetitive phrase (c) makes the talk dull. A non-sequitur (d) is a statement that does not follow from what came before, which would confuse the audience. Tip: a good presentation has three parts: an opening that grabs attention (ice-breaker), a clear body with the main points, and a closing that sums up. This simple structure helps in interviews and group discussions too.

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The answer is (c): star bursting is a creative thinking and brainstorming technique. Step 1: Picture a six-pointed star with an idea or problem written in the centre. Step 2: At each point of the star, you write one question word: who, what, where, when, why and how. Then you think of questions under each, such as 'Who will use this product?' or 'Why would they need it?'. This helps you explore an idea fully before acting. Step 3: It is not a method of measurement (a). It can support good communication (b), but its purpose is generating questions and ideas. It has nothing to do with personal attraction (d). Tip: star bursting differs from normal brainstorming, which generates answers; star bursting generates questions. The six question words, the 5W1H, are also a handy checklist for writing essays and answering case studies.

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The answer is (b) Replying using 'Reply All' unnecessarily. Step 1: Picture an office email sent to 50 people. If everyone hits 'Reply All' just to say 'Thanks' or 'Noted', each person gets dozens of useless emails. Step 2: This clutters inboxes, wastes time and can make people miss important messages. So 'Reply All' should be used only when everyone on the list really needs to see your reply; otherwise reply only to the sender. Step 3: Spell-checking (a), filling in the subject line (c) and using a signature (d) are all good email habits, not things to avoid. Tip: good email etiquette means a clear subject line, short and polite text, careful use of CC and BCC, checking attachments, and thinking before using 'Reply All'. These points matter for officers too, as government work now runs largely on email and e-Office.

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The answer is (b) 'on'. Step 1: Look at the word right after the blank. It is 'Fridays', which is a day of the week. Step 2: Recall the simple time rule for prepositions. We use 'at' for an exact clock time (at 5 o'clock, at noon), 'on' for days and dates (on Monday, on 15 August, on Fridays), and 'in' for longer periods like months, years and seasons (in July, in 2025, in winter). Step 3: Since Fridays are days, the correct word is 'on': 'We usually finish work early on Fridays.' 'During' (a) is used for a stretch of time such as 'during the week', and 'in' (c) and 'at' (d) do not fit a day. Tip: remember the ladder AT-ON-IN, from small to big: at for a point of time, on for a day, in for anything longer.

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The answer is (a) 'of'. Step 1: Find the key word before the blank. It is the adjective 'suspicious', meaning not trusting someone. Step 2: Some adjectives always take a fixed preposition, and you simply have to know the pair. 'Suspicious' goes with 'of', so we say 'suspicious of someone'. Similar pairs are afraid of, jealous of, fond of, proud of and aware of. Step 3: So the sentence reads 'He is suspicious of all his neighbours.' 'Before' (b) and 'from' (c) do not go with suspicious, and 'none of the above' (d) is wrong because 'of' fits perfectly. Tip: learn adjective-preposition pairs in small groups: feelings about people often take 'of' (afraid of, jealous of, suspicious of), while 'good at', 'interested in' and 'angry with' follow other patterns. Reading the full phrase aloud usually tells you what sounds natural.

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The answer is (c) 'We saw them go out.' per the key. Step 1: The given sentence 'They were seen to go out' is passive and does not say who saw them. Step 2: To change it to active voice, we need a doer. When no doer is given, we use a general subject such as 'we', 'people' or 'someone'. The object 'them' comes from 'they'. Step 3: After the verb 'see' in active voice, we use the bare infinitive (go, without 'to'): 'saw them go out'. In passive, the 'to' returns: 'were seen to go out'. Option (a) just repeats the passive. Options (b) 'He' and (d) 'I' pick a specific person not hinted in the sentence, so 'We' is the safest general subject. Tip: see, hear, make and let drop 'to' in the active ('made him laugh') but take 'to' in the passive ('was made to laugh').

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The answer is (d) 'Reservoir'. Step 1: Say the word slowly: rez-er-vwahr. It comes from the French word réservoir, meaning a place where something is stored. Step 2: The tricky part is the ending, which is spelled '-oir', not '-our' or '-or'. So the correct spelling is r-e-s-e-r-v-o-i-r. Step 3: 'Reservoure' (a), 'Reservor' (b) and 'Reservour' (c) all get the ending wrong, because they write it the way it sounds in casual speech. A reservoir is a large natural or artificial lake used to store water, like the Gobind Sagar behind the Bhakra dam. Tip: many words borrowed from French keep the '-oir' ending, such as memoir, repertoire and boudoir. When a word ends with a 'wahr' sound, think of '-oir' first.

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The answer is (d) 'has'. Step 1: Notice the phrase 'Many a man'. Even though it means many men, grammar treats 'many a' as singular, because it is followed by a singular noun ('a man'). Step 2: A singular subject needs a singular verb. With 'died' we need a helping verb in the present perfect tense, so the singular form is 'has': 'Many a man has died for his country.' Step 3: 'Have' (c) is plural, so it is wrong. 'Was' (a) and 'is' (b) are singular, but 'was died' and 'is died' are not correct English; we need 'has died'. Tip: 'many a' + singular noun + singular verb is a fixed rule. Compare 'Many men have died' (plural) with 'Many a man has died' (singular). Examiners love this pair because the meaning feels plural.

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The answer is (b): a midshipman is an officer of the lowest rank in the navy. Step 1: In the passage, the wounded Nelson is carried down to the 'midshipmen's berth', which is the living area for junior officers. Step 2: A midshipman is a young officer under training, the lowest rank of commissioned or trainee officer in the old Royal Navy and many navies today. The name came from where they were stationed on the ship, amidships, in the middle. Step 3: The 'mid' in the name tempts people to choose 'middle rank' (a), but that is a trap. The rank is not non-commissioned (c), which means sailors such as petty officers, and certainly not the highest rank (d), which would be an admiral, like Nelson himself. Tip: do not guess a word's meaning only from its parts. 'Mid' here is about position on the ship, not seniority.

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The answer is (a) 'Panic'. Step 1: Understand the phrase 'presence of mind'. It means the ability to stay calm and think clearly and quickly in a sudden or dangerous situation, as Nelson does while badly wounded. Step 2: An antonym is a word with the opposite meaning. The opposite of staying calm and thinking clearly is losing control and acting out of fear, which is 'panic'. Step 3: 'Attentiveness' (b), 'alertness' (c) and 'quick thinking' (d) all describe a sharp, focused mind. They are close in meaning to presence of mind, so they are synonyms, not antonyms. Tip: when a question asks for an antonym, first find the three options that mean roughly the same as the word. Those are your traps. The one left that means the opposite is the answer.

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The answer is (c): he knew he was dying and wanted the surgeon to help others. Step 1: Find the part where Nelson talks to the surgeon. He says he felt a gush of blood in his breast and knew from the feeling in his back that no human care could save him. Step 2: So he told the surgeon to leave him and attend to those to whom he might be useful. He was sure of his death and cared more for his wounded men. Step 3: Option (a) is the opposite, since he knew the wound was fatal. Option (b), privacy, is not mentioned. Option (d) is wrong, since he did not expect to recover. Tip: for 'why' questions, look for reason words in the passage, such as 'for', 'because' or 'so', and pick the option that matches them.

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The answer is (b) 'Bravery, patriotism and humanity'. Step 1: List what Nelson does in the passage. He twice orders his men to stop firing at the Redoubtable because he thinks it has surrendered. He keeps asking about the battle while dying. He covers his face and medals so his crew will not lose heart. Step 2: Match actions to qualities. Sparing an enemy ship shows humanity. Thinking about the battle while mortally wounded shows bravery. Protecting the crew's morale and caring for the country's victory shows patriotism. Step 3: Option (a), cruelty and cunning, is the opposite of sparing the enemy. Option (c), greed and pride, is not shown. Option (d), confusion and detachment, is wrong because he stays clear-headed and deeply involved. Tip: character questions are answered by actions. Note two or three actions and name the quality each one shows.

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The answer is (c): the platform around the lower part of the mast nearest the stern. Step 1: Break the word down. The 'mizzen' is the mast nearest the stern, the back of a ship. A 'top' is a platform at the head of the lower part of a mast. Step 2: In the passage, a musket ball fired from the Redoubtable's mizzen-top hit Nelson, because sharpshooters stood on these platforms to fire down on the enemy's deck. Step 3: It is not a cabin roof (a), the captain's look-out post (b) or the highest point of the bow (d), the front of the ship. Note: 'most nearest' in the option is a printing slip for 'mast nearest'. Tip: when an option has an obvious typo, read what it means. On ships, bow = front, stern = back.

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The answer is (d) 'during'. Step 1: Look at the phrase after the blank: 'her holiday', which is a period of time. Step 2: 'During' is used for something that happens within a period of time, so 'She wrote this article during her holiday' means at some point while she was on holiday. Step 3: 'In' (a) works with some periods, but we would say 'in the holidays' rather than 'in her holiday'. 'On' (b) is used for days or for being 'on holiday' (without 'her'). 'By' (c) means 'not later than', as in 'by Monday', which changes the meaning. Tip: 'during' answers the question 'when, within what period?', while 'for' answers 'how long?'. For example, 'during the summer' versus 'for two weeks'. If the blank is followed by a named event or period, 'during' is usually right.

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The answer is (d) 'All the salaries have been cut by the company.' Step 1: Identify the tense. 'Has cut' is the present perfect tense in active voice. Step 2: In passive voice, the present perfect becomes 'has been' or 'have been' plus the past participle. The object 'all the salaries' becomes the subject, and it is plural, so we use 'have been cut'. The doer, 'the company', moves to the end with 'by'. Step 3: Option (a) 'are cut' is present simple, so the tense is wrong. Options (b) and (c) add 'should have been', which brings in a new meaning, that something ought to have happened. Option (c) also drops 'all'. Tip: in voice change, keep the tense the same. Present perfect active (has or have + V3) always becomes present perfect passive (has or have + been + V3).

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The answer is (c) 'Collective'. Step 1: Look at the noun 'crowd' in 'The crowd was very big.' Step 2: A crowd is many people, but here it is treated as one single group, which is why the verb is singular ('was'). A noun that names a group as a single unit is a collective noun. Other examples are team, army, family, jury, herd and flock. Step 3: An abstract noun (a) names an idea or feeling, like honesty or joy. A common noun (b) names a general person or thing, like boy or city; 'crowd' is common in a broad sense, but its special type is collective. A proper noun (d) is a particular name, like Delhi or Ganga. Tip: if a noun means 'a group of something', such as a bunch of grapes or a fleet of ships, it is collective. The singular verb is a strong clue.

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The answer is (a) 'Morally bad'. Step 1: 'Nefarious' is a strong word meaning wicked, evil or criminal. It is often used in news, as in 'nefarious activities' or 'nefarious designs'. Step 2: It comes from the Latin word nefas, meaning a crime or something against divine law. So its core meaning is morally bad. Step 3: 'Extremely wealthy' (b) has nothing to do with it. 'Very fearful' (c) may come from the sound of the word, but that is a trap. 'Honest' (d) is the opposite. Tip: when you are unsure of a hard word, think of where you have seen it. 'Nefarious' usually appears with crime, terror or smuggling, so the meaning must be negative. Build a small list of such words: nefarious, heinous, villainous and sinister all mean evil or wicked.

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The answer is (b) 'Entrepreneur'. Step 1: Say it slowly: on-truh-pruh-nur. It comes from the French verb entreprendre, meaning to undertake. Step 2: Break the spelling into parts: entre + pre + neur. So it is e-n-t-r-e-p-r-e-n-e-u-r. An entrepreneur is a person who starts and runs a business and takes the risk. Step 3: 'Enterpranore' (a), 'Entraprenure' (c) and 'Enterprenure' (d) all go wrong in the middle (writing 'enter' instead of 'entre') or at the end (writing '-ure' or '-ore' instead of '-eur'). Tip: two parts trip people up. Start with 'entre', not 'enter', and finish with '-eur', like amateur and connoisseur. Linking it to schemes such as Stand-Up India for entrepreneurs can help you remember the word.

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The answer is (b) 'Temporary'. Step 1: 'Ephemeral' means lasting for a very short time, short-lived. It comes from the Greek ephemeros, meaning lasting only a day. Step 2: For example, 'the ephemeral beauty of a rainbow' or 'ephemeral streams', which flow only after rain. So the closest meaning is temporary. Step 3: 'Mysterious' (a) and 'loud' (c) are unrelated. 'Permanent' (d) is the exact opposite, which makes it a trap for students who confuse the word with eternal. Tip: link 'ephemeral' to the mayfly, an insect that lives only about a day, and whose scientific order is Ephemeroptera. Opposites of ephemeral include permanent, lasting, enduring and perpetual. In geography too, ephemeral rivers flow only in the rainy season.

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The answer is (c) 'over'. Step 1: Recognise the idiom: 'cry over spilt milk'. It means to feel sad or complain about something that has already happened and cannot be changed. Step 2: The fixed preposition in this idiom is 'over', because we 'cry over' or 'grieve over' a loss. For example, 'You failed once, but there is no use crying over spilt milk; prepare again.' Step 3: 'At' (a), 'upon' (b) and 'on' (d) are not used in this idiom. Note: the paper prints 'split milk', but the correct word is 'spilt', the past participle of 'spill', so 'split' is a typo. Tip: idioms are fixed groups of words, so learn them whole. Similar ones include 'water under the bridge' and 'what is done is done', which carry the same message.

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The answer is (d) 'He said that he had been waiting for ages.' Step 1: The reporting verb 'said' is in the past tense, so the tense inside the quote shifts one step back. Step 2: 'Have been waiting' (present perfect continuous) becomes 'had been waiting' (past perfect continuous). The pronoun 'I' changes to 'he' to match the speaker. The inverted commas go, and we add 'that'. Step 3: Option (a) changes 'said' to 'says', which alters the reporting verb. Option (b) keeps 'has been', which is not shifted back. Option (c) 'is being waiting' is not correct English. Tip: learn the backshift chain: is to was, has to had, have been to had been, will to would, can to could. If the reporting verb is in the present (says), there is no backshift at all.

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The answer is (a) 'will have been working'. Step 1: Look at the time clues: 'By next July' and 'for ten years'. The action started in the past, continues now, and will still be going on up to a point in the future. Step 2: That pattern needs the future perfect continuous tense: will have been + verb-ing. So the sentence is 'By next July, I will have been working in this office for ten years.' Step 3: 'Worked' (b) is past simple and does not reach into the future. 'Will be worked' (c) is a wrong passive form. 'Will work' (d) is simple future and misses the 'for ten years up to then' idea. Tip: 'by + future time' plus 'for + duration' almost always signals the future perfect continuous. Without 'for', as in 'By July I will have finished', the future perfect is enough.

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The answer is (b) 'is'. Step 1: Find the real subject. It is 'Either', meaning one or the other of the two pens, not both. Step 2: 'Either', 'neither', 'each' and 'every' are singular, so they take a singular verb. With the adjective 'good' we need a linking verb, so the singular form is 'is': 'Either of these two pens is good.' Step 3: 'Are' (d) and 'have' (a) are plural forms. 'Has' (c) is singular, but 'has good' is not correct English, since we need 'is good'. Tip: do not be fooled by the plural noun 'pens' after 'of'. The verb agrees with 'either', not with 'pens'. Read the sentence as 'Either one is good' to check. The same rule applies to 'Neither of them is ready' and 'Each of the boys has a book'.

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सही उत्तर (c) है। चरण 1: हर वाक्य को धीरे से पढ़िए और देखिए कि कहाँ कोई शब्द खटकता है। चरण 2: (a) में 'धन के रहित' गलत है, 'रहित' के साथ 'से' आता है, इसलिए 'धन से रहित' या 'धनरहित जीवन' होना चाहिए। (b) में 'बहुत ही दुखपूर्ण' भारी और अटपटा है, 'अत्यन्त दुखद' ठीक रहता। (d) में 'केवल' और 'ही' दोनों एक ही बात कहते हैं, यह पुनरुक्ति दोष है, इसलिए 'मैं इतना ही चाहता हूँ' या 'मैं केवल इतना चाहता हूँ' लिखना चाहिए। चरण 3: (c) 'क्या विश्वविद्यालय समाज का नेतृत्व करने में सफल रहे हैं?' में कोई दोष नहीं है, कर्ता, क्रिया और वचन तीनों ठीक मेल खाते हैं। टिप: केवल-ही, सिर्फ़-मात्र, अनेकों जैसे जोड़े देखते ही सावधान हो जाइए, ये अक्सर पुनरुक्ति के जाल होते हैं।

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सही उत्तर (a) तद्भव है। चरण 1: शब्दों के चार स्रोत याद कीजिए: तत्सम, तद्भव, देशज और विदेशज। चरण 2: तत्सम का अर्थ है 'उसके समान', यानी संस्कृत का शब्द बिना बदले हिन्दी में आ गया, जैसे अग्नि, हस्त, सूर्य। तद्भव का अर्थ है 'उससे उत्पन्न', यानी संस्कृत या प्राकृत का शब्द घिसकर और रूप बदलकर आया, जैसे अग्नि से आग, हस्त से हाथ, दुग्ध से दूध। चरण 3: प्रश्न में 'विकृत होकर आए शब्द' कहा गया है, यानी रूप बदला है, इसलिए उत्तर तद्भव है। देशज शब्द लोक-बोली से बने होते हैं, जैसे लोटा, पगड़ी, और विदेशज दूसरी भाषाओं से आए, जैसे स्कूल, कुर्सी। टिप: 'विकृत' या 'बदलकर' पढ़ते ही तद्भव, और 'ज्यों का त्यों' पढ़ते ही तत्सम चुनिए।

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सही उत्तर (c) अपादान तत्पुरुष है। चरण 1: समास को खोलकर देखिए: दूरागत = दूर से आगत, यानी दूर से आया हुआ। चरण 2: बीच में छिपा कारक-चिह्न 'से' है। 'से' दो कारकों में आता है: करण (साधन का भाव, जैसे कलम से लिखा) और अपादान (अलग होने या कहीं से आने का भाव, जैसे पेड़ से गिरा)। चरण 3: यहाँ कोई चीज़ दूर से आई है, यानी अलग होने या स्थान से निकलने का भाव है, इसलिए अपादान तत्पुरुष। ऐसे ही उदाहरण हैं पथभ्रष्ट (पथ से भ्रष्ट), देशनिकाला (देश से निकाला), जन्मान्ध। करण तत्पुरुष के उदाहरण हैं तुलसीकृत, हस्तलिखित। अधिकरण में 'में/पर' और सम्प्रदान में 'के लिए' आता है। टिप: 'से' दिखे तो पूछिए, साधन है या अलगाव? साधन हो तो करण, अलगाव हो तो अपादान।

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सही उत्तर (c) 'चित्र का रूप-रंग' है। चरण 1: प्रश्न पूछता है कि अच्छी भाषा में क्या नहीं बताया गया, इसलिए गद्यांश में वह पंक्ति खोजिए जहाँ अच्छी भाषा के गुण गिनाए गए हैं। चरण 2: गद्यांश कहता है कि अच्छी भाषा में जादू का असर, संगीत का माधुर्य और तलवार की शक्ति होती है। इसलिए (a) संगीत का माधुर्य, (b) जादू का असर और (d) तलवार की शक्ति, तीनों गद्यांश में हैं। चरण 3: 'चित्र का रूप-रंग' गद्यांश में कहीं नहीं आया, इसलिए यही वह विकल्प है जो अच्छी भाषा में नहीं बताया गया। टिप: 'नहीं है' वाले प्रश्नों में हर विकल्प पर गद्यांश में टिक लगाइए। जो विकल्प गद्यांश में न मिले, वही उत्तर है। अपनी राय से नहीं, केवल गद्यांश के शब्दों से उत्तर दीजिए, क्योंकि चित्र भी सुन्दर होता है पर लेखक ने उसका ज़िक्र नहीं किया।

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सही उत्तर (d) कलम को है। चरण 1: गद्यांश की अन्तिम पंक्तियों पर ध्यान दीजिए, जहाँ लिखित भाषा की बात होती है। चरण 2: लेखक कहता है कि कलम लिखित भाषा का प्रतीक है और 'हम उसे सरस्वती देवी का रूप मानते हैं'। यहाँ 'उसे' सर्वनाम कलम के लिए आया है, क्योंकि ठीक पहले कलम की ही बात हो रही है। चरण 3: चित्र, मूर्ति और स्थापत्य कलाएँ हैं, पर गद्यांश उन्हें सरस्वती का रूप नहीं कहता, इसलिए (a), (b) और (c) गलत हैं। सरस्वती विद्या, वाणी और ज्ञान की देवी हैं, इसलिए लिखने के साधन कलम को उनका रूप मानना स्वाभाविक भी है। टिप: जब प्रश्न में 'किसे' पूछा जाए और गद्यांश में 'उसे', 'यह', 'वह' जैसे सर्वनाम आएँ, तो ठीक पिछले वाक्य की संज्ञा देखिए, सर्वनाम उसी की ओर इशारा करता है।

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सही उत्तर (b) 'अपरिमित और अमोघ' है। चरण 1: गद्यांश में 'भाषा की शक्ति' वाली पंक्ति खोजिए: 'भाषा की शक्ति अपरिमित और अमोघ है।' चरण 2: शब्दों का अर्थ समझिए। अपरिमित = जिसकी कोई सीमा या माप न हो (परिमित = सीमित, 'अ' लगाकर उल्टा)। अमोघ = जो कभी निष्फल न जाए (मोघ = व्यर्थ)। चरण 3: (c) 'परिमित और मोघ' ठीक उल्टा अर्थ है, यानी सीमित और व्यर्थ। (d) 'सीमित और क्षुद्र' भी उल्टा है। (a) 'सीमान्त और सीमेतर' गद्यांश में नहीं है और अर्थ भी नहीं बैठता। टिप: गद्यांश के प्रश्नों में अक्सर सही विकल्प गद्यांश के शब्दों को ज्यों का त्यों उठाता है, और गलत विकल्प उन्हीं शब्दों का उल्टा ('अ' हटाकर) बना देते हैं। इसलिए 'अ' उपसर्ग पर खास नज़र रखिए।

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सही उत्तर (a) कलम है। चरण 1: गद्यांश में तलवार और कलम की तुलना वाली पंक्ति देखिए। चरण 2: लेखक कहता है कि कलम तलवार से भी बढ़कर शक्तिशालिनी है। यह अंग्रेज़ी कहावत 'The pen is mightier than the sword' का ही भाव है, जिसे एडवर्ड बुलवर-लिटन ने 1839 में लोकप्रिय बनाया। मतलब यह कि विचार और लेखन लोगों का मन बदल देते हैं, जो हथियार से नहीं हो पाता। चरण 3: किताब (b) भी लिखी जाती है, पर गद्यांश ने तुलना कलम से की है। कोठी (c) और लता (d) का गद्यांश से कोई सम्बन्ध नहीं है। टिप: व्याकरण से भी संकेत मिलता है, 'शक्तिशालिनी' स्त्रीलिंग है, और कलम स्त्रीलिंग शब्द है। ऐसे लिंग-संकेत कई बार उत्तर पक्का करने में मदद करते हैं।

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सही उत्तर (c) 'भाषा के सहारे' है। चरण 1: गद्यांश की पहली ही पंक्ति पढ़िए: 'बड़े-बड़े उत्थान और बड़ी-बड़ी क्रान्तियाँ प्रायः भाषा के सहारे ही होती हैं।' चरण 2: पूरा गद्यांश इसी विचार पर टिका है कि भाषा लोगों को बहका भी सकती है और सन्मार्ग पर भी ला सकती है। यही इसका केन्द्रीय भाव है। चरण 3: धर्म (a), युद्ध (b) और मार-काट (d) सामान्य ज्ञान में क्रान्तियों से जुड़े लग सकते हैं, पर गद्यांश ऐसा नहीं कहता। उल्टे, लेखक कहता है कि भाषा तलवार से भी अधिक शक्तिशाली है। इसलिए ये विकल्प गलत हैं। टिप: गद्यांश का पहला और अन्तिम वाक्य अक्सर मुख्य विचार बताते हैं। सीधा तथ्य पूछने वाले प्रश्न का उत्तर ढूँढने से पहले वही दो वाक्य देख लीजिए, समय बचेगा।

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सही उत्तर (b) मिश्र वाक्य है। चरण 1: वाक्य को टुकड़ों में बाँटिए: 'विमला ने कहा' और 'कि गोविन्द अब स्वस्थ है'। चरण 2: पहला हिस्सा अपने आप पूरा है, यह प्रधान उपवाक्य है। दूसरा हिस्सा 'कि' से शुरू होता है और पहले पर निर्भर है, यानी बताता है कि विमला ने क्या कहा। यह आश्रित (संज्ञा) उपवाक्य है। चरण 3: जिस वाक्य में एक प्रधान और एक या अधिक आश्रित उपवाक्य हों, वह मिश्र वाक्य है। सरल वाक्य में एक ही क्रिया होती है। संयुक्त वाक्य में दो स्वतन्त्र वाक्य 'और', 'पर', 'या', 'इसलिए' से जुड़ते हैं, जैसे 'वह आया और बैठ गया'। टिप: कि, जो, जिसे, जब, क्योंकि, यदि जैसे शब्द दिखें तो मिश्र वाक्य की सम्भावना सबसे अधिक है, जबकि और, परन्तु, या दिखें तो संयुक्त।

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सही उत्तर (a) 'इतर–बुराई' है, यह गलत युग्म है। चरण 1: हर शब्द का सही अर्थ याद कीजिए। चरण 2: 'इतर' का अर्थ है दूसरा, अन्य या भिन्न, जैसे 'इतर जन' यानी दूसरे लोग, 'पाठ्येतर' यानी पाठ के अलावा। इसका अर्थ बुराई नहीं है। चरण 3: बाकी तीन युग्म सही हैं। द्विप = हाथी (जो दो बार पीता है, सूँड से और फिर मुँह से)। कृषाण = किसान (कृषि करने वाला)। कृती = निपुण, कुशल या पुण्यात्मा। इसलिए (b), (c) और (d) ठीक हैं। एक सावधानी: 'इत्र' (सुगन्ध) और 'इतर' अलग शब्द हैं, और 'इतराना' (घमण्ड करना) भी अलग है। टिप: मिलते-जुलते शब्दों के जाल से बचिए। 'इतर' सुनकर 'इतराना' या बुरा अर्थ न मान लीजिए, इसका सीधा अर्थ 'अन्य' है।

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सही उत्तर (d) ख, झ, फ, भ है। चरण 1: नियम याद कीजिए: हर वर्ग (क, च, ट, त, प) का दूसरा और चौथा वर्ण महाप्राण होता है, क्योंकि इन्हें बोलते समय मुँह से अधिक हवा (प्राण) निकलती है। चरण 2: महाप्राण वर्ण हैं ख, घ, छ, झ, ठ, ढ, थ, ध, फ, भ, और साथ में ह। ख (क वर्ग का दूसरा), झ (च वर्ग का चौथा), फ (प वर्ग का दूसरा) और भ (प वर्ग का चौथा), चारों महाप्राण हैं। चरण 3: (a) क, च, ब, म अल्पप्राण हैं (पहला, तीसरा, पाँचवाँ वर्ण)। (b) य, ल अन्तःस्थ हैं और क्ष, ज्ञ संयुक्त व्यंजन हैं। (c) त, द, न, प भी अल्पप्राण हैं। टिप: इसे हाथ पर हथेली रखकर जाँचिए। 'ख' बोलने पर हवा का झोंका लगेगा, 'क' बोलने पर नहीं। दूसरा और चौथा = महाप्राण, यही सबसे आसान सूत्र है।

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सही उत्तर (a) है, यही युग्म सुमेलित नहीं है। चरण 1: हर मुहावरे का सामान्य अर्थ याद कीजिए। चरण 2: 'शीशे में मुँह देखना' का अर्थ है अपनी योग्यता या हैसियत पहचानना, जैसे कोई बड़ी बात करे तो कहते हैं 'पहले शीशे में अपना मुँह देखो'। इसका अर्थ विरोध प्रकट करना नहीं है, इसलिए यह युग्म गलत है। चरण 3: बाकी युग्म सही हैं। 'विष की गाँठ' = झगड़े या उपद्रव की जड़, उपद्रवी व्यक्ति। 'लुटिया डुबोना' = बना-बनाया काम बिगाड़ देना। 'शान में बट्टा लगना' = इज़्ज़त या प्रतिष्ठा घटना। टिप: मुहावरों के प्रश्न में शब्दशः अर्थ नहीं, लोक-प्रयोग वाला अर्थ सोचिए। मन में एक छोटा वाक्य बनाइए, जैसे 'पहले शीशे में मुँह देखो', तो अर्थ अपने आप स्पष्ट हो जाता है।

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सही उत्तर (c) भोजपुरी है। चरण 1: हिन्दी की बोलियों के पाँच उपवर्ग याद कीजिए: पश्चिमी हिन्दी, पूर्वी हिन्दी, बिहारी, राजस्थानी और पहाड़ी। चरण 2: पूर्वी हिन्दी में तीन बोलियाँ आती हैं: अवधी (लखनऊ, अयोध्या), बघेली (रीवा, मध्य प्रदेश) और छत्तीसगढ़ी (रायपुर, छत्तीसगढ़)। इसलिए (a), (b) और (d) पूर्वी हिन्दी की हैं। चरण 3: भोजपुरी पूर्वी उत्तर प्रदेश और पश्चिमी बिहार में बोली जाती है, पर भाषा-वैज्ञानिक वर्गीकरण में यह बिहारी हिन्दी वर्ग में आती है, मगही और मैथिली के साथ। पश्चिमी हिन्दी में खड़ी बोली, ब्रज, बाँगरू, बुन्देली और कन्नौजी हैं। टिप: भूगोल से धोखा न खाइए। भोजपुरी 'पूरब' में बोली जाती है, पर वर्ग 'बिहारी' है। पूर्वी हिन्दी के लिए सूत्र 'अब छ' याद रखिए: अवधी, बघेली, छत्तीसगढ़ी।

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सही उत्तर (c) अम्बिका है। चरण 1: द्रौपदी के महाभारत में आए नाम याद कीजिए। चरण 2: पांचाली, क्योंकि वह पांचाल नरेश द्रुपद की पुत्री थीं। कृष्णा, क्योंकि उनका रंग साँवला था। याज्ञसेनी, क्योंकि उनका जन्म यज्ञ की अग्नि से हुआ था और द्रुपद का एक नाम यज्ञसेन था। इसलिए (a), (b) और (d) द्रौपदी के पर्याय हैं। उन्हें द्रुपदसुता और सैरन्ध्री भी कहा गया। चरण 3: अम्बिका देवी पार्वती या दुर्गा का नाम है। महाभारत में अम्बिका काशीराज की एक पुत्री भी थीं, जो धृतराष्ट्र की माता बनीं, पर वह द्रौपदी नहीं हैं। टिप: पर्यायवाची में नाम के पीछे की कहानी याद रखिए: पिता से (द्रुपदसुता), देश से (पांचाली), जन्म से (याज्ञसेनी)। जो नाम किसी कहानी से न जुड़े, वही बाहर का है।

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सही उत्तर (d) ब्रज है। चरण 1: बोली को उसके क्षेत्र से जोड़िए। चरण 2: ब्रजभाषा का केन्द्र मथुरा, आगरा और वृन्दावन का क्षेत्र है, जिसे ब्रजमण्डल कहते हैं। कृष्ण-भक्ति काव्य इसी भाषा में लिखा गया। सूरदास का सूरसागर, नन्ददास और बिहारी की रचनाएँ ब्रजभाषा में हैं। रीतिकाल की लगभग सारी कविता भी ब्रज में है। चरण 3: बाँगरू (a) हरियाणा की बोली है, जिसे हरियाणवी भी कहते हैं। अवधी (b) लखनऊ, अयोध्या और रायबरेली के क्षेत्र की है, जिसमें तुलसीदास ने रामचरितमानस लिखा। बुन्देली (c) झाँसी, ललितपुर और बुन्देलखण्ड की है। टिप: कवियों से याद कीजिए: सूरदास = ब्रज (कृष्ण), तुलसीदास = अवधी (राम), जायसी = अवधी (पद्मावत)। कृष्ण की लीला-भूमि मथुरा है, तो वहाँ की बोली ब्रज।

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सही उत्तर (d) सत्तू है। चरण 1: 'सक्तु' संस्कृत का तत्सम शब्द है, जिसका अर्थ है भुने हुए अन्न (जौ या चने) का आटा। चरण 2: बोलचाल में घिसते-घिसते संयुक्त 'क्त' बदलकर 'त्त' हो गया, और अन्त का 'उ' दीर्घ 'ऊ' बन गया। इस तरह सक्तु से सत्तू बना। ऐसे ही भक्त से भगत और रक्त से रत बनते हैं। चरण 3: शक्ति (a) अलग तत्सम शब्द है, जिसका अर्थ है बल। सात (b) 'सप्त' का तद्भव है। सकता (c) 'सकना' क्रिया का रूप है। इसलिए ये गलत हैं। पूर्वी उत्तर प्रदेश और बिहार में चने का सत्तू आज भी गर्मियों का लोकप्रिय भोजन है, और लिट्टी में भरा जाता है। टिप: तद्भव पहचानने के लिए अर्थ भी मिलाइए। 'सक्तु' का अर्थ भुना आटा है, और विकल्पों में केवल सत्तू का अर्थ वही है।

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सही उत्तर (d) 'चार बजा है' है, यही अशुद्ध वाक्य है। चरण 1: हर वाक्य में कर्ता और क्रिया का वचन मिलाइए। चरण 2: समय बताते समय 'एक बजा है' एकवचन है, पर दो या अधिक के लिए क्रिया बहुवचन होती है: 'दो बजे हैं', 'चार बजे हैं'। इसलिए 'चार बजा है' अशुद्ध है। चरण 3: बाकी वाक्य शुद्ध हैं। (a) 'वे लोग विविध विषयों से परिचित थे' में बहुवचन कर्ता के साथ 'थे' ठीक है। (b) 'लड़कियाँ जा रही थीं' में स्त्रीलिंग बहुवचन के साथ 'रही थीं' ठीक है। (c) 'अनेक प्रकार की विद्याएँ सीखीं' में स्त्रीलिंग बहुवचन कर्म के साथ 'सीखीं' ठीक है। टिप: समय वाले वाक्यों में सूत्र याद रखिए, एक के साथ 'बजा', बाकी सबके साथ 'बजे'। साढ़े एक के लिए 'डेढ़ बजा' कहते हैं, पर ढाई, चार, पाँच के साथ 'बजे'।

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सही उत्तर (a) पाठकगण है। चरण 1: समझिए कि कुछ शब्दों का बहुवचन उनके रूप में बदलाव से नहीं, बल्कि समूहवाचक शब्द जोड़कर बनता है। चरण 2: पुल्लिंग 'पाठक' के साथ 'गण' जोड़कर 'पाठकगण' बनता है, जिसका अर्थ है बहुत से पाठक। इसी तरह छात्रगण, अध्यापकवृन्द, गुरुजन, मित्रवर्ग और आप लोग बनते हैं। चरण 3: पाठिकाएँ (b) स्त्रीलिंग 'पाठिका' का बहुवचन है, 'पाठक' का नहीं। पाठक (c) वही एकवचन है, जो अकेले बहुवचन का भाव नहीं देता। पाठिका (d) स्त्रीलिंग एकवचन है। ध्यान रहे, 'पाठक' आकारान्त नहीं है, इसलिए 'लड़का से लड़के' जैसा बदलाव नहीं होता। टिप: प्रश्न में लिंग बदलने वाले विकल्पों से बचिए। पुल्लिंग शब्द का बहुवचन पुल्लिंग ही रहेगा, और गण, वृन्द, जन, वर्ग जोड़ना सबसे पक्का तरीका है।

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सही उत्तर (b) चिड़िया है। चरण 1: देशज शब्द वे होते हैं जो लोक-बोलचाल से अपने आप बने, और जिनका स्रोत संस्कृत या किसी विदेशी भाषा में नहीं मिलता। चरण 2: चिड़िया इसी तरह का शब्द माना जाता है, जैसे लोटा, पगड़ी, खिड़की, डिबिया, झोला और तेंदुआ। चरण 3: पलंग (a) फ़ारसी 'पलंग' से आया विदेशज शब्द माना जाता है, जबकि कुछ इसे संस्कृत 'पर्यंक' से भी जोड़ते हैं। भात (c) संस्कृत 'भक्त' (पका चावल) का तद्भव है। बच्चा (d) फ़ारसी 'बच्चः' से आया है। इसलिए ये तीनों देशज नहीं हैं। टिप: देशज पहचानने के लिए उलटा सोचिए: क्या शब्द किसी संस्कृत शब्द से घिसकर बना लगता है (तद्भव) या फ़ारसी, अरबी, अंग्रेज़ी से आया (विदेशज)? यदि दोनों में न बैठे, तो वह देशज है।

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सही उत्तर (a) चरम + उत्कर्ष है। चरण 1: शब्द को देखिए, 'चरमोत्कर्ष' में 'मो' पर 'ओ' की मात्रा है, जो सन्धि का संकेत देती है। चरण 2: गुण सन्धि का नियम है कि अ या आ के बाद उ या ऊ आए, तो दोनों मिलकर ओ बन जाते हैं। यहाँ चरम का अन्तिम 'अ' और उत्कर्ष का पहला 'उ' मिलकर 'ओ' बने: चरम + उत्कर्ष = चरमोत्कर्ष। इसका अर्थ है उन्नति या ऊँचाई की अन्तिम सीमा। ऐसे ही सूर्य + उदय = सूर्योदय, महा + उत्सव = महोत्सव। चरण 3: (b) 'चरमो' कोई शब्द नहीं है। (c) 'चरम + कर्ष' में 'उत्' गायब है। (d) 'चर + मोत्कर्ष' अर्थहीन है। टिप: सन्धि-विच्छेद के बाद दोनों हिस्से सार्थक शब्द होने चाहिए। अ + उ = ओ, अ + इ = ए, यही गुण सन्धि के दो मुख्य सूत्र हैं।

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सही उत्तर (a) 'निसंदेह' है, यही अशुद्ध वर्तनी है। चरण 1: हर शब्द को उसके मूल से जाँचिए। चरण 2: शुद्ध रूप 'निःसन्देह' है, जो निः + सन्देह से बना है, और इसमें विसर्ग (ः) ज़रूरी है। इसका अर्थ है बिना सन्देह के, यानी निश्चित रूप से। विसर्ग छोड़कर 'निसंदेह' लिखना आम गलती है। चरण 3: बाकी तीनों शब्द शुद्ध हैं। सत्त्व (b) में दो 'त' और 'व' हैं, क्योंकि यह सत् + त्व से बना है। उज्ज्वल (c) में दो 'ज' हैं, क्योंकि यह उत् + ज्वल है। महत्त्व (d) भी महत् + त्व से बना है, इसलिए दो 'त' आते हैं। टिप: 'त्व' प्रत्यय वाले शब्दों (महत्त्व, सत्त्व, तत्त्व) में दोहरा 'त्त' होता है, और 'निः' उपसर्ग वाले शब्दों (निःसन्देह, निःस्वार्थ, निःशुल्क) में विसर्ग। ये दोनों जगहें परीक्षा में सबसे अधिक पूछी जाती हैं।

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सही उत्तर (b) पहाड़ी है। चरण 1: उत्तर प्रदेश की बोलियों की सूची याद कीजिए: खड़ी बोली (मेरठ), ब्रज (मथुरा, आगरा), कन्नौजी (कन्नौज, फ़र्रुख़ाबाद), बुन्देली (झाँसी), अवधी (लखनऊ, अयोध्या) और भोजपुरी (वाराणसी, बलिया)। चरण 2: कन्नौजी (a), अवधी (c) और ब्रजभाषा (d), तीनों उत्तर प्रदेश में बोली जाती हैं, इसलिए ये गलत विकल्प हैं। चरण 3: पहाड़ी बोलियाँ, जैसे गढ़वाली और कुमाऊँनी, उत्तराखण्ड और हिमाचल प्रदेश में बोली जाती हैं। 9 नवम्बर 2000 को उत्तराखण्ड अलग राज्य बना, उसके बाद ये क्षेत्र उत्तर प्रदेश में नहीं रहे। इसलिए आज उत्तर प्रदेश में पहाड़ी बोली का क्षेत्र नहीं है। टिप: पुरानी किताबों में पहाड़ी को उत्तर प्रदेश से जोड़ा मिलेगा, क्योंकि पहले उत्तराखण्ड उसी का हिस्सा था। प्रश्न 'आज' के उत्तर प्रदेश के बारे में है, इसलिए 2000 का विभाजन ध्यान रखिए।

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सही उत्तर (b) बुन्देली है। चरण 1: झाँसी किस क्षेत्र में है, यह सोचिए: झाँसी बुन्देलखण्ड का प्रमुख नगर है। चरण 2: बुन्देलखण्ड में झाँसी, ललितपुर, जालौन, हमीरपुर, महोबा, बाँदा और चित्रकूट ज़िले आते हैं, और मध्य प्रदेश के सागर, छतरपुर, टीकमगढ़ भी। इस पूरे क्षेत्र की बोली बुन्देली है, जो पश्चिमी हिन्दी वर्ग की है। आल्हा-ऊदल की वीर गाथाएँ और ईसुरी की फागें बुन्देली में प्रसिद्ध हैं। चरण 3: भोजपुरी (a) पूर्वी उत्तर प्रदेश और बिहार की है। कन्नौजी (c) कन्नौज और फ़र्रुख़ाबाद की है। छत्तीसगढ़ी (d) छत्तीसगढ़ की है। इसलिए ये गलत हैं। टिप: बोली का नाम अक्सर क्षेत्र के नाम से बनता है: बुन्देलखण्ड से बुन्देली, कन्नौज से कन्नौजी, अवध से अवधी, ब्रज से ब्रजभाषा, बघेलखण्ड से बघेली। पहले क्षेत्र पहचानिए, बोली अपने आप मिल जाएगी।

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सही उत्तर (b) 'विमुख–प्रमुख' है, यही गलत विलोम युग्म है। चरण 1: विलोम का अर्थ है ठीक उल्टा अर्थ देने वाला शब्द। चरण 2: 'विमुख' का अर्थ है मुँह फेरे हुए या विरुद्ध। इसका विलोम 'सम्मुख' (सामने) या 'उन्मुख' (की ओर झुका) होता है। 'प्रमुख' का अर्थ है मुख्य या प्रधान, जो विमुख का उल्टा नहीं है। इसलिए यह युग्म गलत है। चरण 3: बाकी युग्म सही हैं। स्वाधीन (अपने अधीन) का विलोम पराधीन (दूसरे के अधीन) है। विधवा का विलोम सधवा (जिसका पति जीवित हो) है। निष्काम (बिना इच्छा के) का विलोम सकाम है। टिप: उपसर्ग बदलकर बने विलोम पर ध्यान दीजिए: स्व-पर, वि-स, निः-स। पर सिर्फ़ उपसर्ग बदलने से हमेशा विलोम नहीं बनता। 'प्रमुख' दिखने में मिलता-जुलता है, पर अर्थ नहीं।

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सही उत्तर (c) भोजपुरी है। चरण 1: वाक्य के शब्द-रूपों पर ध्यान दीजिए: 'ऊ' (वह), 'हमरा के' (मुझको), 'खेलही' (खेलने ही) और 'देत रहे' (देता था)। चरण 2: 'के' का कर्म-चिह्न के रूप में प्रयोग (हमरा के, तोहरा के) और 'रहे' से भूतकाल बनाना भोजपुरी की खास पहचान है। वाराणसी, गाज़ीपुर, बलिया, देवरिया और पश्चिमी बिहार में ऐसे वाक्य सुनाई देते हैं। चरण 3: बुन्देली (a) में 'हमें' या 'मोय' जैसे रूप आते हैं, और ब्रज (d) में 'मोकूँ' या 'मोहि', जैसे 'मोकूँ खेलन न दियो'। अवधी (b) में 'हमका' या 'मोका' रूप आता है। इसलिए ये गलत हैं। टिप: कर्म-चिह्न से बोली पहचानिए: खड़ी बोली में 'मुझको', ब्रज में 'मोकूँ', अवधी में 'हमका', भोजपुरी में 'हमरा के'। यह एक छोटा संकेत अक्सर सही बोली तक पहुँचा देता है।

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The answer is (d) 13. Step 1: Write down the gaps between the numbers: 3 to 5 is +2, 5 to 8 is +3, 8 to 10 is +2. So the gaps alternate +2, +3, +2, +3. Step 2: Continue the pattern. After 10 the next gap should be +3, so 10 + 3 = 13. Step 3: Check with the rest of the series: 13 + 2 = 15, 15 + 3 = 18, 18 + 2 = 20. These match the given numbers exactly, so 13 is right. 11 (a), 14 (b) and 12 (c) break the pattern. Tip: for any number series, first find the difference between neighbouring numbers. If the differences look irregular, check whether they alternate (as here), go up steadily (+1, +2, +3) or double. Always confirm your answer against the numbers after the blank.

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The answer is (b) 11. Step 1: The hour and minute hands make a right angle (90°) about twice every hour. Step 2: List them from 4 p.m. to 10 p.m.: about 4:05, 4:38, 5:11, 5:44, 6:16, 6:49, 7:22, 7:55, 8:27, exactly 9:00, and 9:33. The next one, about 10:05, is after 10 p.m. Step 3: That makes 11, not 12, because between 8 and 10 o'clock the single 9:00 right angle takes the place of two. Options (a) 6, (c) 10 and (d) 9 undercount. Tip: in 12 hours the hands are at right angles 22 times, not 24, because the 3:00 and 9:00 cases each serve two hours. If 3:00 or 9:00 falls inside your interval, subtract one from the 'two per hour' count.

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The answer is (a) 2 units. Step 1: Write the two formulas. The perimeter (circumference) of a circle is 2πr, and the area is πr². Step 2: The question says they are numerically equal, so set 2πr = πr². Divide both sides by πr (r cannot be zero). This gives 2 = r. Step 3: So the radius is 2 units. Check: with r = 2, perimeter = 4π and area = π × 4 = 4π, so they are equal. Options (b) 4, (c) π and (d) 7 do not satisfy the equation. Tip: whenever two formulas share a common factor like π or r, cancel it first; the answer then appears in one step. A similar quick result: for a square, perimeter equals area when the side is 4 (4a = a²).

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The answer is (a) 30 seconds. Step 1: When a train crosses a tunnel, it must cover its own length plus the tunnel's length, because the whole train has to come out. So distance = 280 + 220 = 500 metres. Step 2: Convert the speed to metres per second. Multiply km/h by 5/18: 60 × 5/18 = 50/3 m/s, or about 16.67 m/s. Step 3: Time = distance ÷ speed = 500 ÷ (50/3) = 500 × 3/50 = 30 seconds. Options (b) 20, (c) 25 and (d) 15 come from using the wrong distance or skipping the unit change; for example, using only 280 m gives about 17 seconds. Tip: to cross a pole or a person, the train covers only its own length. To cross a bridge, platform or tunnel, add both lengths. Always change km/h to m/s by multiplying by 5/18.

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The answer is (b) 55. Step 1: A handshake always involves two people, so we are counting how many different pairs can be made from 11 friends. Step 2: Each person shakes hands with the other 10, giving 11 × 10 = 110. But this counts every handshake twice, since A shaking B's hand is the same as B shaking A's. So divide by 2: 110 ÷ 2 = 55. Step 3: In formula form, this is 11C2 = 11 × 10 / 2 = 55. Option (a) 22 is just 11 × 2. Option (c) 56 and option (d) 65 are near-miss figures that do not follow the method. Tip: for n people, handshakes = n(n − 1)/2. The same formula counts the matches in a round-robin tournament or the lines joining n points.

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The answer is (c) 54. Step 1: Look at how each number turns into the next: 48 to 24 is halving (÷2), 24 to 72 is tripling (×3), 72 to 36 is ÷2, and 36 to 108 is ×3. Step 2: So the pattern alternates: ÷2, ×3, ÷2, ×3. The next step must be ÷2. Step 3: 108 ÷ 2 = 54. Option (b) 72 and option (d) 36 repeat earlier numbers in the series, and (a) 64 does not fit the pattern at all. Tip: when numbers jump up and down instead of rising steadily, check for two alternating operations, such as ÷2 and ×3, or +5 and −2. Write the operation above each gap; the pattern usually becomes clear within three steps.

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The answer is (d) Mother. Step 1: Read the clue slowly from the end: 'my mother's father' is the woman's maternal grandfather. Step 2: 'The only daughter of my mother's father' is the only daughter of that grandfather. Since the woman's mother is his daughter, and he has only one daughter, that daughter must be the woman's mother. Step 3: So the person in the photograph is her mother, and the woman is the daughter of that person. Note that the question asks how the woman is related to the person in the photo, so the strict answer would be 'daughter' (c), but the key gives (d), reading the question as who is in the photograph. Tip: in blood-relation puzzles, start from the far end of the sentence ('my mother's father') and work back step by step. Draw a tiny family tree if needed.

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The answer is (c) B. Step 1: Turn each clue into a comparison. 'A is taller than B' gives A > B. 'But not taller than C' gives C > A. 'D is taller than C' gives D > C. 'But not taller than E' gives E > D. Step 2: Join them in one chain: E > D > C > A > B. So E is the tallest, and B is the shortest. Step 3: In increasing order of height, from shortest to tallest, the line is B, A, C, D, E. The first place goes to B. Tip: always write clues as symbols (>, <) and join them into one line. Then read carefully whether the question wants increasing order (shortest first) or decreasing order (tallest first); this is where most mistakes happen.

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The answer is (a) 180. Step 1: Look for a formula tied to the position of each term. Take n as 1, 2, 3, 4, 5. Step 2: Try n² × (n − 1). For n = 1: 1 × 0 = 0. For n = 2: 4 × 1 = 4. For n = 3: 9 × 2 = 18. For n = 4: 16 × 3 = 48. For n = 5: 25 × 4 = 100. All five terms fit. Step 3: So the next term, for n = 6, is 36 × 5 = 180. Options (b) 160, (c) 170 and (d) 120 do not fit the rule. Tip: when the differences (4, 14, 30, 52) do not form an easy pattern, try squares and cubes of the position number.

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The answer is (b) (5, 0). Step 1: Any point on the x-axis has a y-coordinate of 0. Step 2: Put y = 0 in the equation 2x + 5y = 10. This gives 2x = 10, so x = 5. The point is (5, 0). Step 3: Check the other options. (0, 2) (d) is where the line meets the y-axis, found by putting x = 0, which gives 5y = 10 and y = 2. (2, 1) (a) does not satisfy the equation, since 4 + 5 = 9. (1/2, 2) (c) gives 1 + 10 = 11, so it is also wrong. Tip: to find where a line cuts the x-axis, set y = 0. To find where it cuts the y-axis, set x = 0.

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The answer is (a) 3600. Step 1: First find the LCM of 3, 4, 5, 6 and 8. Break them into primes: 4 = 2², 6 = 2 × 3, 8 = 2³. The LCM takes the highest powers: 2³ × 3 × 5 = 120. Step 2: A perfect square needs every prime factor to have an even power. In 120 = 2³ × 3¹ × 5¹, all three powers are odd. Multiply by one more 2, one more 3 and one more 5, which is 2 × 3 × 5 = 30. Step 3: 120 × 30 = 3600 = 2⁴ × 3² × 5², which is 60². So 3600 is the least perfect square divisible by all the numbers. 900 (d) and 2500 (c) are squares, but 900 is not divisible by 8, and 2500 is not divisible by 3. 1200 (b) is not a perfect square.

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The answer is (c) 15 and 25. Step 1: Let the numbers be 3x and 5x, since they are in the ratio 3 : 5. Step 2: After adding 10 to each, the new ratio is 5 : 7, so (3x + 10)/(5x + 10) = 5/7. Cross-multiply: 7(3x + 10) = 5(5x + 10), which gives 21x + 70 = 25x + 50. So 4x = 20 and x = 5. Step 3: The numbers are 3 × 5 = 15 and 5 × 5 = 25. Check: 25 and 35 are in the ratio 5 : 7. Tip: in ratio questions with options, the fastest method is often to test each option directly. Add 10 to both numbers and see which gives 5 : 7.

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The answer is (b) 10, as per the provisional key. Step 1: Look at the first two triangles to find a rule linking the corner numbers to the centre. In triangle 1, 7 × 5 = 35, which uses the two bottom numbers. In triangle 2, 4 × 5 = 20, which uses the top and bottom-left numbers. Step 2: These two triangles seem to follow different pairings, and no single rule fits both cleanly. One rule that gives 10 for triangle 3 is (6 × 15) ÷ (3 × 3) = 10, but it does not fit the first two triangles. Step 3: So the answer depends on the key. Note: this key is doubtful, as no consistent rule fits all three triangles, so check the final key. Tip: in figure puzzles, test the same operation on every figure before choosing an answer.

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The answer is (d) 8:45. Step 1: A mirror flips a clock left to right. To find the real time from a mirror image, subtract the shown time from 11:60, which is the same as 12:00. Step 2: 11:60 − 3:15 = 8:45. Step 3: Check: at 8:45, the hour hand is near 9 and the minute hand on 9; in a mirror, 9 appears where 3 is, so the clock looks like 3:15. Option (a) 3:15 is the image itself, (b) 9:45 adds the wrong way, and (c) 7:45 is off by an hour. Tip: for times between 1:00 and 11:00, subtract from 11:60. If the shown time is between 11:00 and 12:59, subtract from 23:60 instead. Also, 12:00 and 6:00 look the same in a mirror.

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The answer is (a) 96. Step 1: Look at how the numbers grow: 1, 2, 4, 8, 16, 32, 64. Each number is double the one before (×2). These are the powers of 2, from 2⁰ to 2⁶. Step 2: Following the pattern, the number after 64 should be 64 × 2 = 128. Step 3: But the series shows 96, which breaks the doubling rule (64 × 1.5 = 96). So 96 is the odd one out. The numbers 4 (b), 64 (c) and 32 (d) all fit the pattern, so they are not odd. Tip: in odd-one-out series, find the rule using the first few numbers, then check each later number against it. Know the powers of 2 by heart: 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024. They appear often in reasoning papers.

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The answer is (d) 40 minutes. Step 1: Find the distance first. Time = 2 hours 45 minutes = 2.75 hours. Distance = speed × time = 4 × 2.75 = 11 km. Step 2: Now find the time at the new speed. Time = distance ÷ speed = 11 ÷ 16.5 hours. Since 16.5 = 33/2, this is 11 × 2/33 = 2/3 hours. Step 3: 2/3 of an hour is 2/3 × 60 = 40 minutes. Options (a) 55 min 15 s, (b) 45 min and (c) 50 min 15 s come from wrong conversions, such as treating 2 hours 45 minutes as 2.45 hours. Tip: always convert minutes to hours as a fraction (45 minutes = 3/4 hour = 0.75), never as a decimal like .45.

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The answer is (d) Rs. 1,261. Step 1: Use the simple interest to find the principal. SI = P × R × T / 100, so 1,200 = P × 5 × 3 / 100. This gives P = 1,200 × 100 / 15 = 8,000. Step 2: Compound interest for 3 years at 5% = P × (1.05³ − 1). Here 1.05³ = 1.157625, so CI = 8,000 × 0.157625 = 1,261. Step 3: Another way: year 1 interest = 400, year 2 = 400 + 20 = 420, year 3 = 400 + 40 + 1 = 441. Total = 400 + 420 + 441 = 1,261. Tip: compound interest is always a little more than simple interest for more than one year. For 3 years at 5%, CI is about 5.1% more than SI, so the answer must be just above 1,200.

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The answer is (b) 50°, per the key. Step 1: Since AB is parallel to CD, the angle that CD makes with the extended line CE (100°) is linked to the angles at A and E in the triangle formed. Step 2: The exterior angle at C, made by the parallel line, equals the sum of the two interior opposite angles, the angle at A (50°) and the angle at E (x). So 50 + x = 100. Step 3: Solving gives x = 50°. Options (a) 100° repeats the exterior angle, (c) 80° and (d) 60° do not satisfy the equation. Tip: with parallel lines, look for corresponding and alternate angles first, then use the rule that an exterior angle of a triangle equals the sum of the two opposite interior angles. Marking equal angles on the figure saves time.

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The answer is (d) His son's. Step 1: The man has no brother or sister, so 'the son of my father' can only be the man himself. Step 2: So the sentence becomes: the father of that man (in the photo) is me. In other words, the man in the photograph is someone whose father is the speaker. Step 3: That makes the person in the photograph the speaker's son. Option (a), his own photo, would need him to be his own father. Option (b), his father's, would need the photo person's father to be his grandfather. Option (c), his nephew, is impossible because he has no siblings. Tip: in 'son of my father' type puzzles, always check first whether the speaker has brothers. If not, 'son of my father' means the speaker. Replace that phrase with 'me' and the puzzle becomes simple.

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The answer is (a) 7185514. Step 1: Find how BLINK becomes 21291411. Write the alphabet positions: B = 2, L = 12, I = 9, N = 14, K = 11. Put them side by side: 2-12-9-14-11 = 21291411. So each letter is replaced by its position in the alphabet. Step 2: Apply the same rule to GREEN: G = 7, R = 18, E = 5, E = 5, N = 14. Step 3: Joined together, that is 7-18-5-5-14 = 7185514. Option (b) 29121411 is just a jumbled form of BLINK's code, (c) 8175514 shifts G and R, and (d) 1455178 reverses the order. Tip: learn the EJOTY trick for letter positions: E = 5, J = 10, O = 15, T = 20, Y = 25. From these markers you can count quickly to any letter, for example R = T − 2 = 18.

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The answer is (b) Brother. Step 1: Break the long phrase into small pieces. 'My father's wife' is Deepak's mother. 'The daughter of my father's wife' is Deepak's sister. Step 2: 'The two brothers of the daughter' are the two brothers of Deepak's sister. These are Deepak himself and one other boy. Step 3: The boy playing football is 'the younger of the two brothers', so he is Deepak's younger brother (Deepak being the elder). Options (a) nephew, (c) cousin and (d) son would need a new generation or a different branch of the family, which the clues do not show. Tip: replace phrases step by step with simpler words: father's wife = mother, mother's daughter = sister, sister's brothers = me and my brother. Remember that the speaker himself is often one of the people described.

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The answer is (a) JNR. Step 1: Find the pattern in each group of letters by counting the steps between them. Step 2: CGF: C to G is +4, G to F is −1. HLK: H to L is +4, L to K is −1. DHG: D to H is +4, H to G is −1. These three follow the same rule, +4 then −1. Step 3: JNR: J to N is +4, but N to R is +4 again, not −1. So JNR breaks the pattern and is the odd one out. Tip: write the position numbers above the letters (J = 10, N = 14, R = 18) to see the gaps clearly. In odd-one-out letter groups, check the gap between the first and second letter, then between the second and third.

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The answer is (d) 'Some non-philosophers are not non-scientists.' Step 1: Start with the fact: 'No scientists are philosophers.' This means every scientist is a non-philosopher. Step 2: If every scientist is a non-philosopher, then at least some non-philosophers are scientists. 'Some non-philosophers are not non-scientists' says exactly this, because 'not non-scientists' means scientists (two negatives cancel). Step 3: Option (a), 'Some philosophers are scientists', directly contradicts the given fact. Option (c), 'All scientists are philosophers', is the opposite. Option (b), 'No non-philosophers are scientists', is false because all scientists are non-philosophers. Tip: when you see double negatives such as 'not non-scientists', cancel them first to get 'are scientists'. Then the statement becomes simple: 'Some non-philosophers are scientists', which clearly follows from the fact.

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The answer is (b) Rs. 92. Step 1: Payment is shared in proportion to the work done. A and C together do 19/23 of the work. Step 2: The whole work is 1, or 23/23. So B does 23/23 − 19/23 = 4/23 of the work. Step 3: B's share = 4/23 × 529 = 4 × 23 = 92 rupees, since 529 = 23 × 23. Option (a) Rs. 437 is the share of A and C together (19 × 23 = 437). Options (c) 300 and (d) 82 do not follow from the fractions. Tip: in work-and-wages questions, money is always split in the ratio of work done, not time spent. Notice that 529 is 23², which is a strong hint that the denominator 23 will cancel neatly; examiners often choose numbers this way.

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The answer is (a) 12 years. Step 1: Let the daughter's present age be x. Then the mother's age is 3x, since she is three times as old. Step 2: After 12 years, the daughter will be x + 12 and the mother 3x + 12. At that time the mother will be twice the daughter's age, so 3x + 12 = 2(x + 12). Step 3: Open the bracket: 3x + 12 = 2x + 24. So x = 12. The daughter is 12 and the mother 36. Check: in 12 years they will be 24 and 48, and 48 is twice 24. Options (b) 16, (c) 14 and (d) 18 do not pass this check. Tip: in age problems, add the same number of years to both people. Testing each option directly is often faster than forming the equation.

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The answer is (c) 80°. Step 1: In a rhombus, angles next to each other (adjacent angles, like ∠A and ∠B) add up to 180°, just as in any parallelogram. Step 2: The ratio ∠A : ∠B is 4 : 5, so 4k + 5k = 180°, which gives 9k = 180° and k = 20°. So ∠A = 80° and ∠B = 100°. Step 3: Opposite angles of a rhombus are equal, and ∠C is opposite ∠A. So ∠C = ∠A = 80°. Option (a) 95° and (d) 50° do not come from the ratio, and (b) 45° would be half of a right angle, which does not fit. The words 'non-square' just tell us the angles are not all 90°. Tip: in any parallelogram, rhombus or rectangle, opposite angles are equal and adjacent angles add up to 180°. With a ratio, divide 180 into the given parts first.

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The answer is (c) 75°. Step 1: Use the clock angle formula: angle = |30H − 5.5M|, where H is the hour and M the minutes. Step 2: At half past 8, H = 8 and M = 30. So 30 × 8 = 240 and 5.5 × 30 = 165. Step 3: 240 − 165 = 75°. Option (a) 60° is the gap between the 6 and the 8 alone, which forgets that the hour hand has moved halfway towards 9. Options (b) 80° and (d) 70° are near misses. Tip: the hour hand moves 0.5° every minute, so it never stays exactly on the number. Using 30H − 5.5M takes care of this automatically and avoids the most common mistake.

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The answer is (d) 18 years. Step 1: Let Ravish's age be 3x and Shikha's age 8x, since their ages are in the ratio 3 : 8. Step 2: In six years, they will be 3x + 6 and 8x + 6, in the ratio 4 : 9. So (3x + 6)/(8x + 6) = 4/9. Cross-multiply: 9(3x + 6) = 4(8x + 6), which gives 27x + 54 = 32x + 24. So 5x = 30 and x = 6. Step 3: Ravish's present age is 3 × 6 = 18 years, and Shikha is 48. Check: in six years they will be 24 and 54, and 24 : 54 = 4 : 9. Options (a) 21, (b) 15 and (c) 12 fail this check. Tip: with options, just add 6 to each and test the ratio.

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The answer is (b) 25%. Step 1: The real cost includes all money spent to get the radio ready for sale. Cost price = purchase price + overhead expenses = 225 + 15 = 240 rupees. Step 2: Profit = selling price − cost price = 300 − 240 = 60 rupees. Step 3: Profit % = (profit ÷ cost price) × 100 = (60 ÷ 240) × 100 = 25%. Option (c) 50% forgets the overheads and divides 75 by 150, a wrong base. Option (a) 52% and (d) 10% come from other mistakes; for example, dividing 75 by 225 gives about 33%. Tip: always add overheads, transport and repair costs to the cost price before finding profit. And always calculate profit percentage on the cost price, never on the selling price, unless the question says otherwise.

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The answer is (b) 561. Step 1: Look closely at the digits of each number: 143, 275, 495. Step 2: In each, the middle digit equals the sum of the first and last digits: 1 + 3 = 4, 2 + 5 = 7, 4 + 5 = 9. Step 3: Check the options. 561: 5 + 1 = 6, and the middle digit is 6, so it fits. 683: 6 + 3 = 9, but the middle is 8. 927: 9 + 7 = 16, which does not match 2. 243: 2 + 3 = 5, but the middle is 4. So only 561 fits. Tip: a quick trick for multiplying a two-digit number by 11: put the sum of its digits in the middle. For example, 11 × 51 = 5 (5 + 1) 1 = 561.

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The answer is (c) A ∩ B. Step 1: Understand A − B: it means all elements of A that are not in B. In other words, A with the common part removed. Step 2: Now take A − (A − B). This means: start with A and remove everything that is only in A. What is left is the part of A that is also in B. Step 3: That common part is A ∩ B, the intersection. For example, if A = {1, 2, 3} and B = {2, 3, 4}, then A − B = {1}, and A − {1} = {2, 3}, which is A ∩ B. Tip: for set questions, test with small example sets like {1, 2, 3} and {2, 3, 4}. A Venn diagram also makes such problems quick.

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The answer is (c) FLOWER. Step 1: Compare SIMPLE with ISPMEL. Split SIMPLE into pairs: SI, MP, LE. Swap the letters in each pair: IS, PM, EL. Join them: ISPMEL. Step 2: Check with CHAPTER: CH, AP, TE, R. Swapping gives HC, PA, ET, R = HCPAETR. The printed code is HCPARET, which changes the order at the end, but the pair-swap idea is clear from SIMPLE. Step 3: Now reverse the rule for LFWORE. Split it into pairs: LF, WO, RE. Swap each pair: FL, OW, ER. Joined, this gives FLOWER. Options (a) WORFEL, (b) FLOREW and (d) LOWFER do not come from swapping pairs. Tip: in coding questions, first check simple patterns such as reversing the word, swapping pairs or shifting each letter by a fixed number. Then decode by applying the same rule backwards. A meaningful English word among the options is a good confirmation.

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The answer is (d) 24 hours. Step 1: Think in terms of work done in one hour. Together, A and B finish the trench in 8 hours, so in one hour they do 1/8 of it. A alone takes 12 hours, so A does 1/12 of it in one hour. Step 2: B's one-hour work = their combined work − A's work = 1/8 − 1/12. Using a common denominator of 24, this is 3/24 − 2/24 = 1/24. Step 3: So B does 1/24 of the trench every hour and needs 24 hours alone. Options (a) 30, (b) 26 and (c) 28 do not match. Check: in 8 hours A does 8/12 = 2/3 and B does 8/24 = 1/3, which adds to 1 whole trench. Tip: convert times into one-hour work (1/time), add or subtract, then flip the answer back.

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The answer is (b) Swastik. Step 1: Find the common link among most of the options. The pyramids, the mummy and the sphinx are all famous features of ancient Egypt. Step 2: The pyramids of Giza were tombs for the pharaohs, mummies are preserved bodies prepared for the afterlife, and the Great Sphinx is a huge statue with a lion's body and a human head near the pyramids. Step 3: The swastik is an ancient symbol of good luck and well-being in Indian traditions, used in Hinduism, Jainism and Buddhism. It is not linked to Egypt, so it is the odd one out. Tip: in odd-one-out questions with words, look for a category that fits three options: place, era, use, shape or field. Here the category is ancient Egypt. If one option belongs to a different culture or country, that is usually the answer.

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The answer is (a) 894. Step 1: Look for something common in 957, 777 and 876. Add the digits of each: 9 + 5 + 7 = 21, 7 + 7 + 7 = 21, 8 + 7 + 6 = 21. All three have a digit sum of 21. Step 2: Now check the options. 894: 8 + 9 + 4 = 21, so it matches. 697: 6 + 9 + 7 = 22. 979: 9 + 7 + 9 = 25. 999: 9 + 9 + 9 = 27. Step 3: Only 894 has the same property, a digit sum of 21. Tip: for 'same property' number questions, try the simplest checks first: sum of digits, product of digits, odd or even, divisibility by 3, 9 or 11, and whether the number is a square. The digit sum is the most common rule in such questions.

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The answer is (c) 4, as per the provisional key. Step 1: Look at the table row by row: 8, 5, 7, 6; 9, 7, 8, 2; 3, 4, 7, 12; and 6, 10, X, 6. Step 2: Try the usual rules: sums of rows, products, or the first two numbers compared with the last two. In the first row, 8 + 5 = 13 and 7 + 6 = 13, which looks promising, but the second row gives 16 and 10, so that rule fails. Step 3: So the printed table does not show a clear rule, and the answer rests on the key. Note: this key is doubtful because no consistent rule fits the table as printed; check the final key. Tip: in the exam, if a puzzle eats time without a clear rule, mark your best guess and move on.

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The answer is (a) Friday. Step 1: Three days after Sunday is Wednesday (Sunday + 3 = Monday, Tuesday, Wednesday). So the 8th of the month is a Wednesday. Step 2: From the 8th to the 17th is 9 days. Days of the week repeat every 7 days, so 9 days later is the same as 9 − 7 = 2 days later. Step 3: Wednesday + 2 days = Friday. So the 17th is a Friday. Check: the 15th is Wednesday (8 + 7), the 16th Thursday and the 17th Friday. Tip: in calendar questions, find the gap in days, divide by 7, and use only the remainder (odd days). Adding 7 to a date always gives the same weekday, so 8, 15, 22 and 29 are all Wednesdays here.

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The provisional key marks (a) 31, but the working gives 30. Step 1: If Sunday is the 3rd, then Monday is the 4th, Tuesday the 5th and Wednesday the 6th. Step 2: The Wednesdays of the month are the 6th, 13th, 20th and 27th. So the fourth Wednesday is the 27th. Step 3: Three days after the 27th is the 30th, which is option (d). The key's 31 would be four days after, or would count the first Wednesday differently. Options (b) 27 is the fourth Wednesday itself, and (c) 29 is only two days after. Note: the key looks doubtful; by straightforward counting the answer should be 30, so check the final key before relying on it. Tip: list all the dates of the required weekday by adding 7 each time (6, 13, 20, 27), then count forward carefully. 'After three days' means add 3 to the date.

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The answer is (c) infinitely many solutions. Step 1: The equation 3x − 5y = 15 has two unknowns, x and y, but only one equation. Step 2: For any value of x you choose, you can find a matching y. For example, x = 0 gives y = −3, x = 5 gives y = 0, and x = 10 gives y = 3. Each pair is a solution. Step 3: Since x can take endless values, there are infinitely many solutions. On a graph, the equation is a straight line, and every point on the line is a solution. Option (d), a unique solution, needs two equations whose lines cross at one point. Tip: one linear equation in two variables always has infinitely many solutions. You need two independent equations to get a unique answer.

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The answer is (b) 6. Step 1: Look at the first column: 12, 16, 5 and 197 at the bottom. Try multiplying the first two and adding the third: 12 × 16 = 192, and 192 + 5 = 197. It matches. Step 2: Check the second column: 12 × 12 = 144, and 144 + 12 = 156. It matches again, so the rule is: first × second + third = bottom number. Step 3: Apply it to the third column: 18 × 20 = 360, and 360 + ? = 366. So ? = 6. Option (c) 8 and the negative options (a) −8 and (d) −6 do not fit. Tip: when the bottom number is much bigger than the others, try multiplying two numbers and then adding or subtracting the third. Always confirm the rule on at least two columns before using it on the unknown one.

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The answer is (a) Square. Step 1: Start with a parallelogram, a four-sided shape with opposite sides parallel and equal. Step 2: If all four sides are equal, the parallelogram becomes a rhombus. If one angle of a parallelogram is a right angle, all four angles become right angles, since opposite angles are equal and adjacent angles add up to 180°. Step 3: A shape with all sides equal and all angles 90° is a square. A rectangle (d) has right angles but its sides need not all be equal. A rhombus (c) has equal sides but not right angles. A trapezium (b) has only one pair of parallel sides. Tip: remember the family: parallelogram + equal sides = rhombus; parallelogram + right angle = rectangle; both together = square. So every square is a rhombus and a rectangle, but not the other way around.

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The answer is (c) 529. Step 1: Look at the first pair: 17 and 18 give 1225. Add them: 17 + 18 = 35, and 35 × 35 = 1225. So the rule might be the square of the sum. Step 2: Check the second pair: 13 + 14 = 27, and 27 × 27 = 729. The rule works again. Step 3: Apply it to 19 and 4: 19 + 4 = 23, and 23 × 23 = 529. So the missing number is 529. Tip: when the answer numbers look like perfect squares (1225, 729), check whether they are the square of a sum, difference or product of the given numbers. Knowing squares up to 35 by heart (such as 23² = 529, 27² = 729, 35² = 1225) makes these puzzles fast.

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The answer is (b) 1. Step 1: Write the number in a general form: N = 84k + 37, where k is the quotient when N is divided by 84. Step 2: 84 is exactly divisible by 12 (84 = 12 × 7). So the part 84k leaves no remainder when divided by 12. The remainder depends only on 37. Step 3: 37 ÷ 12 = 3 with a remainder of 1 (since 12 × 3 = 36). So the remainder is 1. Check with an example: take k = 1, so N = 121. Then 121 ÷ 12 = 10 with remainder 1. Tip: if the first divisor (84) is a multiple of the second (12), just divide the first remainder (37) by the second divisor. This trick works only when the first divisor is a multiple of the second.

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The answer is (a) WXUV. Step 1: Write the alphabet positions for each option. RQPO is R(18), Q(17), P(16), O(15): four letters in a row going backwards. UTSR is U(21), T(20), S(19), R(18): also four letters backwards. NMLK is N(14), M(13), L(12), K(11): again four letters backwards. Step 2: WXUV is W(23), X(24), U(21), V(22). It goes forward by 1, then back by 3, then forward by 1. It does not follow the backward sequence. Step 3: So WXUV is different from the other three. Tip: for letter groups, check whether the letters run forwards or backwards in order, and whether the gaps are equal. Use the EJOTY markers (E5, J10, O15, T20, Y25) to find positions quickly. A group that breaks the direction or the gap is the odd one out.

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The answer is (c) 471. Step 1: Add the digits of each given number. 363: 3 + 6 + 3 = 12. 489: 4 + 8 + 9 = 21. 579: 5 + 7 + 9 = 21. Step 2: The digit sums are 12 and 21, which are reverses of each other, and both are multiples of 3. Step 3: Check the options. 471: 4 + 7 + 1 = 12, which matches. 562: 5 + 6 + 2 = 13. 382: 3 + 8 + 2 = 13. 281: 2 + 8 + 1 = 11. Only 471 has a digit sum of 12 or 21. Tip: the digit sum is also the quick test for divisibility by 3 and 9. If the digit sum is divisible by 3, the number is too. That makes such 'same property' questions very quick to check.

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