The correct answer is 'Pejorative.'

Key Points

• Pejorative means expressing disapproval or belittling the importance of something.​
• In the first sentence, filling the blank with 'pejorative' would imply that the reason for separation between two groups is a disapproving statement.
• In the second sentence, filling the blank with 'pejorative' would imply that the statement of the writer has been taken in a disapproving way.
• Therefore, the most appropriate word to be filled in the blank is 'pejorative'.

Hence, the correct answer is option 5.

Complete Sentences:

1. Her pejorative statement created a division between the two groups.
2. Although the writer meant to be kind, his words implied a pejorative point of view.

Additional Information

• Let us explore the other options:
• Warm means having or showing enthusiasm, affection, or kindness.
• Sympathetic means feeling, showing or expressing sympathy.
• Laudative means expressing praise and commendation.
• Complimentary means praising or approving.

The correct answer is 'Disparate.'

Key Points

• Disparate means very different from each other.​
• In the first sentence, filling the blank with 'disparate' would imply that different tapes or CDs are being played at the same time.
• In the second sentence, filling the blank with 'disparate' would imply bringing different ideas for producing new things.
• Therefore, the most appropriate word to be filled in the blank is 'disparate'.

Hence, the correct answer is option 1.

Complete Sentences:

1. It sounded like three disparate tapes or CDs being played simultaneously.
2. They are excellent at bringing disparate ideas together in creative ways.

Additional Information

• Let us explore the other options:
• Patriot means a person who loves his or her country and is ready to defend it against an enemy.
• Ruthless means having or showing no pity or compassion for others.
• Urbane means (of a person) courteous and refined in manner.
• Deter means discourage someone from doing something by instilling doubt or fear of the consequences.

The correct answer is 'Inveterate.'

Key Points

• Inveterate means to have a particular interest or habit that is unlikely to change.​
• In the first sentence, filling the blank with 'inveterate' would imply reading books very often.
• In the second sentence, filling the blank with 'inveterate' would imply the habit of enjoyment in helping others.
• Therefore, the most appropriate word to be filled in the blank is 'inveterate'.

Hence, the correct answer is option 3.

Complete Sentences:

1. Komal is an inveterate reader who always has a book in her hands.
2. As a nurse, Sheela has an inveterate desire to help others.

Additional Information

• Let us explore the other options:
• Intermittent means occurring at irregular intervals; not continuous or steady.
• Occasional means occurring, appearing, or done infrequently and irregularly.
• Transient means lasting only for a short time; impermanent.
• Interim means not final or lasting; temporary until somebody/something more permanent is found.

The correct answer is 'quickly reach'.

Key Points

• The error is in the usage of 'quick' in the underlined part.
• The sentence talks about how reaching the other part of the earth has become easy, thanks to advancing technology.
• The correct word for the underlined part must be 'quickly' which means at a fast speed; rapidly. The adverb form of 'quick' must be used as it describes the verb 'reach'.
• 'quick' must be replaced with 'quickly'. 

Thus the correct sentence is - We can quickly reach the other part of the earth within hours, all thanks to advancing technology.

Important Points

• 'quickness' is the noun form of the word 'quick'.
• 'quicker' is the comparative degree of the word 'quick'.

The correct answer is 'younger individuals'.

Key Points

• The error is in the usage of 'young' in the underlined part.
• The sentence talks about how diabetes and hypertension are rising among young people.
• The correct word for the underlined part must be 'younger' which means an inferior in age or junior. In the sentence, the word 'more' is used which suggests comparative degree. ''younger' is the comparative degree of 'young'.
• 'young' must be replaced with 'younger'. 

Thus the correct sentence is - Diseases like diabetes and hypertension are repeatedly on the rise and affecting more and more younger individuals.

Important Points

• ​Degrees of comparison relate to adjectives and adverbs. Every adjective and adverb can be written in one of three degrees: The positive degree, the comparative degree, superlative degree.
• The positive degree offers no comparison. It just tells us about the existence of a quality.
• ​For example, Lee is hungry.
• The comparative degree compares two things to show which has the lesser or greater degree of the quality.
• ​​For example, Lee is hungrier than Mark.
• The superlative degree compares more than two things to show which has the least or greatest degree of quality.
• ​​​For example, Lee is the hungriest of all.

The correct answer is 'is required​​'.

Key Points

• The error is in the usage of 'are' in the underlined part.
• The sentence talks about protein and how it helps our body.
• The correct word for the underlined part must be 'is' which is used for present tense and singular nouns. In the sentence, 'protein' is mentioned which is singular so the verb used must also be singular.
• 'are' must be replaced with 'is'. 

Thus the correct sentence is - Protein is required to build, maintain, and restore blood, muscle, bones, skin, and organs in the body.

Important Points

• 'are' is used for present tense and plural nouns.
• 'required' is used for past tense.
• 'required by body' is in passive form but the sentence is in active form.

The correct answer is Option 2.

Key Points

• Mr. Verma and Meera embraced organic techniques to restore their farmland.
• They replaced synthetic chemicals with natural compost.
• They also implemented crop rotation to allow essential nutrients to percolate into the soil.

Therefore, the correct answer is Option 2.

Explanation: To restore the health of their farmland's soil, Mr. Verma and Meera used natural compost and implemented crop rotation, avoiding synthetic chemicals and embracing sustainable farming practices.

Additional Information

• 1: Used synthetic chemicals – This is incorrect as they avoided synthetic chemicals and used natural compost instead.
• 3: Adopted mechanized farming techniques – This is incorrect as the passage does not mention mechanized farming techniques being used.
• 4: Introduced genetically modified crops – This option is incorrect because the passage highlights organic farming, not genetically modified crops.
• 5: Sought external funding from the government – This is incorrect as there is no mention of seeking external funding; the focus was on sustainable farming practices.

The correct answer is Option 3.

Key Points

• Mr. Verma and Meera's approach to farming included meticulously analysing the soil and local climate, embracing organic techniques, replacing synthetic chemicals, and implementing crop rotation.
• Promoting monoculture practices was not mentioned as part of their approach.
• Their farming practices focused on sustainable and eco-friendly methods, unlike monoculture which often depletes soil nutrients.
• This omission highlights their commitment to biodiversity and ecological balance.

Therefore, the correct answer is Option 3.

Additional Information

• Soil Analysis: Understanding the soil composition helped them in deciding the best organic practices to use, ensuring a healthier yield.
• Organic Techniques: Using natural compost and avoiding synthetic chemicals promoted long-term soil health.
• Crop Rotation: This practice prevented nutrient depletion and reduced soil erosion.
• Sustainable Practices: Their farming practices aimed at achieving ecological balance and enhancing biodiversity.

The correct answer is Option 2.

Key Points

• The passage mentions that the villagers gave cautious advice to avoid farming initially.
• This suggests that the villagers were not initially enthusiastic or supportive of the farming initiatives.
• They were sceptical about the success of Mr. Verma and Meera's approach to farming.

Therefore, the correct answer is Option 2.

Explanation: The villagers' initial reaction was cautious and sceptical, as they advised Mr. Verma and Meera to avoid farming. However, this scepticism eventually turned into admiration as they witnessed the success and quality of the produce.

Additional Information

• 1: Enthusiastic and supportive – This is incorrect since the passage indicates the villagers were cautious and gave advice to avoid farming.
• 3: Indifferent and neutral – This option is incorrect as the villagers were not indifferent; they were actively advising against the farming initiatives.
• 4: Hostile and obstructive – This is incorrect as the passage does not suggest any hostility or obstruction from the villagers.
• 5: Encouraging and helpful – This is incorrect because the villagers were initially cautious and sceptical, not encouraging.

The correct answer is Option 4.

Key Points

• Mr. Verma and Meera embraced sustainable and organic farming practices, transforming their once-depleted farmland into a thriving bed of life.
• Their innovative methods not only enhanced soil fertility and productivity but also cultivated a harmonious ecological balance.
• The entire community benefitted from their sustainable practices, and the villagers were inspired by the remarkable quality of their produce.
• Their success was recognized with a prestigious award, which inspired other local farmers to explore environmentally friendly cultivation practices.

Therefore, the correct answer is Option 4.

Additional Information

• 1: Increased dependency on external assistance – This option does not align with the passage, which emphasizes self-sufficiency through sustainable practices.
• 2: Decreased agricultural productivity – This option is incorrect as the passage highlights increased productivity.
• 3: Decline in ecological balance – This option is incorrect as the passage mentions the restoration of ecological balance.
• 5: Led to conflicts among local farmers – There is no mention of conflicts in the passage; instead, the community was inspired by their success.

The correct answer is Option 1.

Key Points

• Statement A: The villagers remained sceptical even after the success of Mr. Verma and Meera's farming methods.
• This statement is incorrect because the passage indicates that the villagers’ scepticism was replaced by amazement and acceptance after seeing the success of Mr. Verma and Meera's farming methods.
• Statement B: The agricultural committee awarded Mr. Verma and Meera for their work.
• This statement is correct as it accurately reflects the context provided in the passage.
• Statement C: The renewed soil fertility created a harmonious ecological balance.
• This statement is correct as it aligns with the information provided in the passage.
• Hence, the statement A is identified as incorrect in the context of the passage.

Therefore, the correct answer is: ‘Only A’.

The correct answer is 'revitalized'.

Key Points

• The word "revitalized" means to imbue something with new life and vitality. (नवजीवन प्रदान करना)
• In the context of the passage, "revitalized" appropriately describes transforming the once-depleted earth into a thriving bed of life.
• The other options: "diminished," "eroded," "displaced," and "contaminated" do not fit the context as appropriately as they imply negative outcomes.

​Therefore, the correct answer is 'Option 2'.

Complete Sentence: This persistent and dedicated approach revitalized the once-depleted earth into a thriving bed of life.

Additional Information

• Diminished (घटाया हुआ): means to make or become less.
• Eroded (क्षीण): means gradually worn away.
• Displaced (विस्थापित): means moved from the usual or proper place.
• Contaminated (प्रदूषित): means made impure or unclean.

The correct answer is: Option 2 i.e., 'Endure'.

Key Points

• The word "persist" means to continue firmly or obstinately in an opinion or a course of action despite difficulty or opposition. (अवस्थित रहना)
• Example: Despite the obstacles, he persisted in his studies and eventually graduated with honors.
• "Endure" refers to suffering something painful or difficult patiently or remaining in existence. (सहन करना)
• Example: Soldiers had to endure long hours and harsh conditions during the battle.
• Hence, 'endure' is similar in meaning to 'persist'.

Therefore, the correct answer is: Option 2 i.e., 'Endure'.

Additional Information

Here are the other options explained along with their Hindi meanings and example sentences:

• Cease (रोकना): To bring or come to an end.
• Example: The factory had to cease operations due to the severe storm.
• Terminate (समाप्त करना): To bring to a conclusion or end.
• Example: The contract was terminated due to a breach of terms.
• Conclude (समाप्त करना): To bring to an end.
• Example: The conference will conclude with a keynote speech.
• Surrender (आत्मसमर्पण करना): To give up or yield to the power, control, or possession of another.
• Example: The enemy was forced to surrender after a long battle.

The correct answer is: Option 2 i.e., 'Seep'.

Key Points

• The word "percolate" means gradually filter through a porous surface or substance. (रिसना)
• Example: The coffee slowly percolated through the filter.
• "Seep" means to flow or pass slowly through small openings. (रिसना)
• Example: Water began to seep through the cracks in the basement wall.
• Hence, the word "percolate" is closest in meaning to "seep."

Therefore, the correct answer is: Option 2 i.e., 'Seep'.

Additional Information

Here are the other options explained along with their Hindi meanings and example sentences:

• Block (अवरोधित करना): To prevent movement through something.
• Example: The road was blocked due to the fallen tree.
• Halt (रोकना): To stop or cause to stop.
• Example: The guard called to halt the progress of the vehicle.
• Contain (समाहित करना): To hold or include within.
• Example: The bottle contains water.
• Accumulate (संचय करना): To gather or collect, often in gradual degrees.
• Example: Dust accumulated on the shelves over time.

The correct answer is 'DACB'.

Key Points

• Part D will be the first sentence of the sequence because it introduces the topic of India's defining geological processes that began 75 million years ago.
• Part A will come after D as it gives information about the Indian Plate, then part of the southern supercontinent Gondwana 75 million years ago.
• Part C will come after A as it gives information about the Indian Plate that it began a north-eastward drift caused by seafloor spreading.
• Part 'B' is the concluding or last part as it concludes by giving information about the directions of the drift that is to its southwest, and later, south and south-east.

Hence, the correct answer is option 3.

Correct Sentence: India's defining geological processes began 75 million years ago when the Indian Plate, then part of the southern supercontinent Gondwana, began a north-eastward drift caused by seafloor spreading to its south-west, and later, south and south-east.

Important Points

• Important Rules to Solve the Sentence Jumbles:
• Read the sentences attentively and try to comprehend the idea or theme of the sentences.
• Try to identify the opening and closing sentences.
• Try to identify the mandatory pairs. Two sentences can be connected through various connectors and other determinants.

The correct answer is 'CBDA'.

Key Points

• Part C will be the first sentence of the sequence because it introduces the topic of the Sudanese Army saying it was attacked by the RSF.
• Part B will come after C as it gives information about where the Sudanese Army is being attacked by the RSF.
• Part D will come after B as it gives information about how the Sudanese Army reacted to the attack i.e. they had repelled the attack inflicting "heavy losses" on the RSF.
• Part 'A' is the concluding or last part as it concludes by giving information about the ''heavy losses'' of the RSF i.e. the RSF abandoned 24 vehicles.

Hence, the correct answer is option 2.

Correct Sentence: The Sudanese Army said it was attacked by the RSF at its general command headquarters, but had repelled the attack, inflicting "heavy losses" on the RSF, which had reportedly abandoned 24 vehicles.

Important Points

• Important Rules to Solve the Sentence Jumbles:
• Read the sentences attentively and try to comprehend the idea or theme of the sentences.
• Try to identify the opening and closing sentences.
• Try to identify the mandatory pairs. Two sentences can be connected through various connectors and other determinants.

The correct answer is 'E' i.e. this part of the sentence has no error.

Key Points

• The sentence is errorless.
• We make the third conditional by using the past perfect after 'if' and then 'would have' and the past participle in the second part of the sentence:
• If + past perfect, ...would + have + past participle.
• It talks about the past. It's used to describe a situation that didn't happen, and to imagine the result of this situation.
• Ex: If she had studied, she would have passed the exam. (but, really we know she didn't study and so she didn't pass)

Additional Information

Conditional sentence type:

The correct answer is 'C' i.e. this part of the sentence has an error.

Key Points

• In the third part of the sentence, 'would have' is the mistake.
• We need to omit 'have' from Part C.
• The second conditional uses the past simple after if, then 'would' and the infinitive:
• if + past simple, ...would + infinitive
• E×: If I won the lottery, I would buy a big house.
• Hence, the correct answer is Option 3.

The correct sentence is: If I met the Queen of England, I would say hello.

Additional Information

Conditional sentence type:

The correct answer is 'D' i.e. this part of the sentence has an error.

Key Points

• We need to replace 'whom' with 'who' to correct the sentence.
• We use Who as a relative pronoun to introduce a relative clause about people.
• Ex: The police officer who came was a friend of my father’s.
• Whom is the object form of 'who'. We use whom to refer to people in formal styles or in writing when the person is the object of the verb.
• Ex: Whom did he marry?
• Hence, option 4 is the correct answer.

​Thus the correct sentence is: At the porch, he met two of the landed gentry, one of whom he knew.

Additional Information 

• 'Who' should be used to refer to the subject of a sentence.
• 'Whom' should be used to refer to the object of a verb or preposition.
• When in doubt, try this simple trick: If you can replace the word with “he”’ or “she,” use who. If you can replace it with “him” or “her,” use whom. (Here we can say, She saw her at the store)

The correct answer is option B.

Key Points

To answer this question, let's first understand the context of the sentence containing the blank labelled as (1):

The Amazon Rainforest is referred to as the "lungs of the Earth" because it produces a significant portion of the world's oxygen.

• This sentence conveys the idea that the rainforest plays a crucial role in generating oxygen.
• Blank (1) should be filled with a word conveying the idea of an essential element produced by the rainforest, which is "oxygen."
• Now, let's understand the meanings of the given words as options:
• Water - a transparent, odorless, tasteless liquid that forms the seas, lakes, rivers, and rain and is the basis of the fluids of living organisms.
• Oxygen - a chemical element with symbol O and atomic number 8, essential for respiration.
• Food - any nutritious substance that people or animals eat or drink or that plants absorb to maintain life and growth.
• Oil - a viscous liquid derived from petroleum, especially for use as a fuel or lubricant.
• Minerals - solid, naturally occurring inorganic substances.
• Given the context and the meanings of the words, the most appropriate option to fill in the blank labelled as (1) is "oxygen."
• Therefore, the correct answer is "oxygen."
• The complete sentence would be: "The Amazon Rainforest is often referred to as the "lungs of the Earth" because it produces a significant portion of the world's oxygen."

The correct answer is option B.

Key Points

To answer this question, let's first understand the context of the sentence containing the blank labelled as (2):

Rainforests play a crucial role in capturing carbon dioxide from the atmosphere, which helps mitigate climate change.

• This sentence conveys the idea that rainforests help in reducing carbon dioxide levels.
• Blank (2) should be filled with a word conveying the idea of taking in or absorbing carbon dioxide, which is "capturing."
• Now, let's understand the meanings of the given words as options:
• Emitting - producing and discharging something, especially gas or radiation.
• Capturing - taking into one's possession or control by force.
• Generating - producing or creating something.
• Releasing - allowing or enabling to escape from confinement; setting free.
• Producing - making or manufacturing from components or raw materials.
• Given the context and the meanings of the words, the most appropriate option to fill in the blank labelled as (2) is "capturing."
• Therefore, the correct answer is "capturing."
• The complete sentence would be: "Rainforests are also vital for capturing carbon dioxide from the atmosphere, which helps mitigate the effects of climate change."

The correct answer is option C.

Key Points

To answer this question, let's first understand the context of the sentence containing the blank labelled as (3):

Rainforests are under threat due to human activities such as logging, agriculture, and mining.

• This sentence conveys the idea that human activities are the main cause of deforestation.
• Blank (3) should be filled with a word conveying the idea of actions done by people, which is "human."
• Now, let's understand the meanings of the given words as options:
• Natural - existing in or caused by nature; not made or caused by humankind.
• Renewable - not depleted when used, such as solar energy.
• Human - relating to or characteristic of people or human beings.
• Wildlife - wild animals collectively; the native fauna (and sometimes flora) of a region.
• Seasonal - relating to or characteristic of a particular season of the year.
• Given the context and the meanings of the words, the most appropriate option to fill in the blank labelled as (3) is "human."
• Therefore, the correct answer is "human."
• The complete sentence would be: "However, these ecosystems are under threat due to human activities such as logging, agriculture, and mining."

The correct answer is option C.

Key Points

To answer this question, let's first understand the context of the sentence containing the blank labelled as (4):

Conservation efforts are essential to protect these vital ecosystems and ensure the survival of the planet's biodiversity.

• This sentence conveys the idea that conservation is necessary to keep the planet's biodiversity alive.
• Blank (4) should be filled with a word conveying the idea of continued existence, which is "survival."
• Now, let's understand the meanings of the given words as options:
• Destruction - the action or process of causing so much damage to something that it no longer exists or cannot be repaired.
• Expansion - the action of becoming larger or more extensive.
• Survival - the state or fact of continuing to live or exist, typically in spite of an accident, ordeal, or difficult circumstances.
• Reduction - the action or fact of making something smaller or less in amount, degree, or size.
• Extinction - the state or process of a species, family, or larger group being or becoming extinct.
• Given the context and the meanings of the words, the most appropriate option to fill in the blank labelled as (4) is "survival."
• Therefore, the correct answer is "survival."
• The complete sentence would be: "Conservation efforts are essential to protect these vital ecosystems and ensure the survival of the planet's biodiversity."

The correct answer is option D.

Key Points

To answer this question, let's first understand the context of the sentence containing the blank labelled as (5):

Sustainable practices and policies can help reduce the impact of human activities and promote the preservation of rainforests for future generations.

• This sentence conveys the idea that sustainable practices aim to protect rainforests.
• Blank (5) should be filled with a word conveying the idea of maintaining and protecting, which is "preservation."
• Now, let's understand the meanings of the given words as options:
• Depletion - reduction in the number or quantity of something.
• Exploitation - the action or fact of treating someone unfairly in order to benefit from their work.
• Deforestation - the action of clearing a wide area of trees.
• Preservation - the action of preserving something, especially the environment.
• Pollution - the presence in or introduction into the environment of a substance which has harmful or poisonous effects.
• Given the context and the meanings of the words, the most appropriate option to fill in the blank labelled as (5) is "preservation."
• Therefore, the correct answer is "preservation."
• The complete sentence would be: "Sustainable practices and policies can help reduce the impact of human activities and promote the preservation of rainforests for future generations."

The correct answer is 'C-D.'

Key Points

• The given sentence talks about Albert Einstein whose learning has left behind a long-lasting impact that changed physics and how we understand gravity.
• Let us explore the meaning of the highlighted words:
• Intelligence - The ability to understand, learn and think. (समझने, सीखने और सोचने की क्षमता; बुद्धि, समझ, प्रज्ञा)
• Legacy - The long-lasting impact of particular events, actions, etc. that took place in the past, or of a person’s life. (परंपरा)
• Understand - To know or realize the meaning of something. (किसी बात का अर्थ समझना उसे जानना या महसूस करना)
• Changed - To make somebody or something different. (बदलना, परिवर्तन करना)
• Thus, (C) and (D) must be interchanged.

Hence, the correct answer is option 1.

Correct Sentence: Albert Einstein’s intelligence left behind a legacy of knowledge that changed physics and how we understand gravity.

The correct answer is 'A-D.'

Key Points

• The given sentence talks about Rakhi who tried to tackle her financial problems by filing for bankruptcy, but that effort failed when her petition was rejected.
• Let us explore the meaning of the highlighted words:
• Denied - To refuse to admit or accept something. (किसी बात से इनकार करना; किसी बात को नकारना)
• Bankruptcy - The state of being bankrupt. (दिवालियापन, दिवाला)
• Failed - To not be successful in something. (असफल होना)
• Tackle - To make an effort to deal with a difficult situation or problem. (कठिन स्थिति या समस्‍या का हल निकालने का प्रयास करना)
• Thus, (A) and (D) must be interchanged.

Hence, the correct answer is option 2.

Correct Sentence: Rakhi tried to tackle her financial problems by filing for bankruptcy, but that effort failed when her petition was denied.

The correct answer is 'A-B.'

Key Points

• The given sentence talks about a patient who believed that the doctor knew what he was doing and agreed to undergo a risky surgery.
• Let us explore the meaning of the highlighted words:
• Knew - To have knowledge or information in your mind. (किसी बात या व्‍यक्ति की जानकारी होना)
• Trusted - To believe that somebody is good, sincere, honest, etc, and that he or she will not trick you or try to harm you. (किसी पर विश्‍वास या भरोसा करना)
• Undergo - To have a difficult or unpleasant experience. (कठिन या अप्रिय स्थिति में से गुज़रना, कठिन या अप्रिय स्थिति को झेलना)
• Risky - Involving the possibility of something bad happening; dangerous. (जोखिम की संभावना वाला, जोखिम भरा; ख़तरनाक)
• Thus, (A) and (B) must be interchanged.

Hence, the correct answer is option 3.

Correct Sentence: The patient trusted that the doctor knew what he was doing and agreed to undergo the risky surgery.

The correct answer is option 2.

Key Points

• To answer this question, let's first understand the meaning of the word given in the question:
• Incendiary:
• Causing or designed to cause fires.
• Tending to stir up conflict; inflammatory.

(आग लगाने वाला, उत्तेजक)

• Now, let's examine the given sentences:
• Sentence A: The politician’s incendiary remarks caused uproar among the public.
• This sentence correctly uses the word "incendiary" in the sense of causing conflict or stirring up strong emotions.
• Sentence B: The new song by the pop star was described as incendiary by the critics.
• This sentence also correctly uses the word "incendiary" in the figurative sense, suggesting the song stirred up strong reactions or controversy.
• Sentence C: They used incendiary materials to start the campfire.
• This sentence accurately uses the word "incendiary" in the literal sense, referring to materials that cause fire.
• So, all three sentences correctly use the word "incendiary" to illustrate different contexts of its meanings.

Therefore, the correct answer is "All A, B, and C."

The correct answer is option 4, 'Both A & B'.

Key Points

• To answer this question, let's first understand the meaning of "venerable":
• Venerable - accorded a great deal of respect, especially because of age, wisdom, or character.
• Now, let's examine the given sentences:
• Sentence A: The old, venerable building was a town landmark.
• This sentence correctly uses "venerable" to describe an old building that is respected and valued as a landmark, which aligns well with the definition.
• Sentence B: She was considered venerable for her wisdom and kindness.
• "Venerable" is appropriately used here to describe a person who is deeply respected due to her wisdom and kindness, matching the definition perfectly.
• Sentence C: His venerable driving skills were appreciated by all passengers.
• This sentence misuses "venerable" because it incorrectly applies it to describe driving skills, which are typically not described in terms of respect or reverence due to age, wisdom, or character.
• Only sentences A and B correctly use "venerable" to describe subjects respected for their age, wisdom, or character.
• Therefore, the correct answer is "Both A & B."

The correct answer is option 2, 'Both A & B'.

Key Points

• To answer this question, let's first understand the meaning of "convoluted":
• Convoluted - (especially of an argument, story, or sentence) extremely complex and difficult to follow.
• Now, let's examine the given sentences:
• Sentence A: The directions he gave were so convoluted that we got lost.
• This sentence correctly uses "convoluted" to describe directions that were complex and confusing, aligning perfectly with the definition.
• Sentence B: The novel’s plot was too convoluted to follow.
• "Convoluted" is used appropriately here to describe a plot that is overly complex and challenging to understand, which is a correct use of the word.
• Sentence C: His convoluted appearance made him stand out at the formal party.
• This sentence misuses "convoluted" because the term does not apply to physical appearances in the sense intended by the definition focused on complexity in narrative or argumentative structures.
• Only sentences A and B use "convoluted" correctly to describe situations that are complex and difficult to follow.
• Therefore, the correct answer is "Both A & B."

Shortcut Trick

John salary = ₹12000. Rahul salary = 80% of 12000 = ₹9600.

Spent on Food (20%) + Furniture (25%) + Rent (30%) = 75%.

Remaining for Books = 100% − 75% = 25%.

Total for Books + Furniture = 25% + 25% = 50%.

Required Amount = 50% of ₹9600 = ₹4800.

∴ The correct answer is ₹4800.

Alternate Method

Given: John salary = ₹12000, Rahul salary = 20% less than John, Expenses: Food = 20%, Furniture = 25%, Rent = 30%.

Calculations:

⇒ Rahul salary = 12000 − (20% of 12000)

⇒ Rahul salary = 12000 − 2400 = ₹9600

⇒ Percentage spent on Books = 100 − (20 + 25 + 30) = 25%

⇒ Total % for Books and Furniture = 25% + 25% = 50%

⇒ Required Amount = 50% of 9600 = 9600 ÷ 2 = ₹4800

∴ The correct answer is ₹4800.

Additional Information

Percentage Change

To find a value x% less than a base B, use the formula: B × (100 − x)/100.

Successive Percentage Expenditure

If expenses are given as a % of the 'total' salary, they are additive. If given as % of 'remaining', they are multiplicative.

Base Value Concept

Always identify the correct base (Rahul's salary vs John's salary) before applying percentage calculations.

Shortcut Trick

Total Work (LCM of 15, 18, 10) = 90 units.

Efficiency of (A+B+C) = 90 ÷ 10 = 9 units/day.

Efficiency of (B+C) = 90 ÷ 18 = 5 units/day ⇒ Efficiency of A = 9 − 5 = 4 units.

Efficiency of (A+B) = 90 ÷ 15 = 6 units/day ⇒ Efficiency of B = 6 − 4 = 2 units.

Wage ratio = Efficiency ratio ⇒ A : B = 4 : 2 = 2 : 1.

If 2 units = ₹600, then 1 unit (B’s wage) = ₹300.

∴ The correct answer is ₹300.

Alternate Method

Given: Time taken by (A+B) = 15 days, (B+C) = 18 days, (A+B+C) = 10 days. A’s wage = ₹600.

Formula: Efficiency = Total Work ÷ Time; Wage ∝ Efficiency.

⇒ Efficiency of A = Efficiency(A+B+C) − Efficiency(B+C) = 9 − 5 = 4

⇒ Efficiency of B = Efficiency(A+B) − Efficiency(A) = 6 − 4 = 2

⇒ Wage is distributed in the ratio of efficiencies of A : B = 4 : 2 = 2 : 1

⇒ Since A’s wage (2 units) = ₹600

⇒ B’s wage (1 unit) = 600 ÷ 2 = ₹300

∴ The correct answer is ₹300.

Additional Information

Work and Wages Relationship

Wages are always distributed in the ratio of work done. If all persons work for the same duration, the wage ratio is identical to their efficiency ratio.

LCM Method for Total Work

Total work is assumed as the Least Common Multiple (LCM) of the individual days to ensure efficiencies are whole numbers, simplifying calculations.

Efficiency of Individual in a Group

Efficiency of one person can be found by subtracting the combined efficiency of others from the total combined efficiency: Eff(A) = Eff(A+B+C) − Eff(B+C).

Shortcut Trick

Initial average = 56.2 kg.

Calculate deviations of new weights from 56.2: (62.3 − 56.2) + (59.7 − 56.2) + (59.5 − 56.2) = 6.1 + 3.5 + 3.3 = 12.9 kg.

Net change in average = Total Deviation ÷ Total children = 12.9 ÷ 63 ≈ 0.20 kg.

New average = 56.2 + 0.20 = 56.40 kg.

∴ The correct answer is 56.40 kg.

Alternate Method

Given: Initial average weight of 60 children = 56.2 kg. Weights of 3 new children = 62.3 kg, 59.7 kg, and 59.5 kg.

Formula Used: Average = (Sum of all observations) ÷ (Total number of observations)

⇒ Total weight of 60 children = 60 × 56.2 = 3372 kg.

⇒ Total weight of 63 children = 3372 + 62.3 + 59.7 + 59.5

⇒ Total weight of 63 children = 3372 + 181.5 = 3553.5 kg.

⇒ New Average = 3553.5 ÷ 63

⇒ New Average = 56.408... ≈ 56.40 kg.

∴ The correct answer is 56.40 kg.

Additional Information

Deviation Method for Average

New Average = Old Average + (Sum of deviations ÷ New total count). This avoids large multiplications.

Weighted Average

When two groups are combined, Combined Average = (n₁x₁ + n₂x₂) ÷ (n₁ + n₂), where n is the count and x is the average.

Shortcut Trick

Total Interest = ₹640

Interest from First Sum = 600 × 12% × 6 = ₹432

Interest from Second Sum = 640 − 432 = ₹208

Second Sum = (208 × 100) ÷ (10 × 6) = 2080 ÷ 6 = ₹346.66

∴ The correct answer is ₹346.66.

Alternate Method

Given:

Principal 1 (P₁) = ₹600, Rate 1 (R₁) = 12%, Time (T) = 6 years

Rate 2 (R₂) = 10%, Total Simple Interest (SI_total) = ₹640

Formula Used:

Simple Interest (SI) = (P × R × T) ÷ 100

⇒ SI₁ = (600 × 12 × 6) ÷ 100

⇒ SI₁ = 6 × 12 × 6 = ₹432

⇒ SI₂ = SI_total − SI₁

⇒ SI₂ = 640 − 432 = ₹208

⇒ SI₂ = (P₂ × 10 × 6) ÷ 100

⇒ 208 = (P₂ × 60) ÷ 100

⇒ P₂ = (208 × 100) ÷ 60

⇒ P₂ = 2080 ÷ 6 = ₹346.66

∴ The correct answer is ₹346.66.

Additional Information

Simple Interest Property

Simple interest remains constant every year because it is always calculated on the original Principal amount.

Amount Formula

Total Amount (A) = Principal (P) + Simple Interest (SI). In this question, the interest was additive.

Shortcut Trick

Ratio of Ankit : Son now is 3 : 1 (Difference = 2 units).

Ratio 4 years ago was 13 : 3 (Difference = 10 units).

Equating differences: Multiply present ratio by 5 → 15 : 5.

Change in units: 15 − 13 = 2 units → 4 years. So, 1 unit = 2 years.

Ankit's present age = 15 × 2 = 30 years.

∴ The correct answer is 30 years.

Alternate Method

Given: Present age ratio is 3 : 1. Ratio 4 years ago was 13 : 3.

Let the present age of the son be x and Ankit be 3x.

⇒ (3x − 4) / (x − 4) = 13 / 3

⇒ 3 × (3x − 4) = 13 × (x − 4)

⇒ 9x − 12 = 13x − 52

⇒ 13x − 9x = 52 − 12

⇒ 4x = 40

⇒ x = 10

⇒ Ankit's present age = 3x = 3 × 10 = 30 years.

∴ The correct answer is 30 years.

Additional Information

Concept of Age Difference

The difference between the ages of two people always remains constant regardless of the number of years passed.

Ratio Balancing Method

To solve age ratio problems quickly, multiply the ratios such that the difference between the parts (e.g., 15−5=10 and 13−3=10) becomes equal.

Calculations:

Total number of items brought by A in 2016 = 140 

Number of plastic items brought by A = 140 × 2 /7 = 40

Calculations:

Total number of items brought by A and B in 2015 = 120 + 130 = 250

Total number of items brought by A and B in 2016 = 140 + 160 = 300

Required ratio = 250 : 300 = 5:6

Calculations:

Total number of items brought by A and B in 2016 = 140 + 160 = 300

Average number of items brought by A and B in 2016 = 300/2 = 150

Number of items brought by C in the year 2016:

= 150 + 45 = 195

Calculations:

Number of items brought by A in 2017 = 180

Number of items brought by B in 2017 = 150

Total item brought by A and B together in the year 2018 is:

[180 × 125/100] + [150 ×120/100] = 225 + 180 = 405

Calculations:

Total number of items brought by A in the year 2015 and 2016 together = 120 + 140 = 260

Total number of items brought by B in the year 2015 and 2016 together = 130 + 160 = 290

So, required difference is 290 – 260 = 30

Calculations:

Total number of items brought by A in the year 2015 = 120

Total number of items brought by B in the year 2015 = 130

Difference between number items brought by B and A is 130 - 120 = 10

So, x – 5 = 10 ⇒  x = 15.

Solution:

125 ÷ 5 ×  171 ÷ 27 ÷ 249 ×  9 = x ÷ 83

25 ×  (171/27) ×  (1/249) ×  9 = x/83

25 ×  (19/3) ×  (3/83) = x/83

x = 25 ×  19

x = 475

Solution:

42 ÷ 6 ×  3 + 5 – (8 + 7) + 123 = x

7 ×  3 + 5 – (15) + 123 = x

21 + 5 – 15 + 123 = x

x = 134

Concept used:

Follow BODMAS rule to solve this question, as per the order given below.

Step - 1: Parts of an equation enclosed in 'Brackets' must be solved second, and following BODMAS rule in the bracket

Step - 2: Any mathematical 'Of' or 'Exponent' must be solved next.

Step - 3: Next, the parts of the equation that contain 'Division' and 'Multiplication' are calculated.

Step - 4: Last but not least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.

Calculations:

5265 ÷ 117 + 67 × 85 - 1172 + 289 + 263 - 120 = (?)

⇒ 45 + 5695 - 1172 + 289 + 263 - 120 = (?)

⇒  45 + 5695 - 1172 + 289 + 263 - 120 = (?)

⇒ 6292 - 1292 = (?)

⇒ ? = 5000

Hence, the correct answer is 5000.

Concept used:

Follow BODMAS rule to solve this question, as per the order given below.

Step - 1: Parts of an equation enclosed in 'Brackets' must be solved second, and following BODMAS rule in the bracket

Step - 2: Any mathematical 'Of' or 'Exponent' must be solved next.

Step - 3: Next, the parts of the equation that contain 'Division' and 'Multiplication' are calculated.

Step - 4: Last but not least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.

Calculations:

(159 + 321) ÷ 4 + (7250/50) + (4130 – 1270) ÷ 110 + 33 = ?2

⇒ 480 ÷ 4 + 145 + 2860 ÷ 110 + 33 = ?2

⇒ 120 + 145 + 26 + 33 = ?2

⇒ 324 = ?2

⇒ √324 = ?

⇒ 18 = ?

Hence, the correct answer is 18.

Given:

18 + 27 - 14 = ? + 10 + 20

Concept used:

Follow the BODMAS rule according to the table given below:

Calculation:

18 + 27 - 14 = ? + 10 + 20

⇒ 45 - 14 = ? + 30

⇒ 31 = ? + 30

⇒ ? = 31 - 30 = 1

∴ The value of ? is 1

Given:

(√1024 + 19 × 12) ÷ √676 - 4 + 4680 ÷ ? = 474

Concept Used:

​

Calculation:

(√1024 + 19 × 12) ÷ √676 - 4 + 4680 ÷ ? = 474

⇒ (32 + 228) ÷ 26 - 4 + 4680 ÷ ? = 474

⇒ 10 - 4 + 4680 ÷ ? = 474

⇒ 4680 ÷ ? = 468

⇒ 4680 ÷ 468 = ?

⇒ ? = 10

∴ The value of (?) is 10.

Given:  

(14)2 × 10 ÷ 4 - (15)2 + 16 = ?2 + 52

Concept Used:

Follow the BODMAS rule according to the table given below:

Calculation:

(14)2 × 10 ÷ 4 - (15)2 + 16 = ?2 + 52

⇒ 196 × 10 × 1/4 - 225 + 16 = ?² + 25

⇒ 98 × 5 - 225 + 16 = ?2 + 25

⇒ 490 - 225 + 16 = ?2 + 25

⇒ 490 - 225 + 16 - 25 = ?2 

⇒  ?² = 506 - 250 = 256

⇒ ? = √256 = 16

∴ 16 will come in place of the question mark '?'.

Concept used:

Follow the BODMAS rule according to the table given below:

Calculation:

⇒ (72 × 6 - 36 × 6) ÷ 12 = 288 ÷ ?

⇒ (432 - 216) ÷ 12 = 288 ÷ ?

⇒ 216 ÷ 12 = 288 ÷ ?

⇒ ? = 288 ÷ 18 = 16

∴ The value of ? is 16.

Given:

53 × 3 + 85 ÷ 5 - √(?) × 6 = 356

Concept used:

Follow the BODMAS rule according to the table given below:

Calculation:

53 × 3 + 85 ÷ 5 - √(?) × 6 = 356

⇒ 125 × 3 + 17 - √(?) × 6 = 356

⇒ 375 + 17 - √(?) × 6 = 356

⇒ √(?) × 6 = 36

⇒ √(?) = 6

⇒ ? = 6²

⇒ ? = 36

∴ 36 should come in place of the question mark (?).

Given:

328 ÷ 8 + 25 × 2.4 + ? = (11)2

Concept used:

Follow the BODMAS rule according to the table given below:

Calculation:

328 ÷ 8 + 25 × 2.4 + ? = (11)²

⇒ 41 + 60 + ? = 121

⇒ 101 + ? = 121

⇒ ? = 20

∴ 20 should come in place of the question mark (?).

Given:

15 × 678 - 10 × 802 + 60 ÷ 6 = ? × 50 ÷ 5

Concept Used:

Calculation:

15 × 678 - 10 × 802 + 60 ÷ 6 = ? × 50 ÷ 5

⇒ 10170 - 8020 + 10 = ? × 10

⇒ 2160 = ? × 10

⇒ 2160/10 = ?

⇒ ? = 216

∴ The value of ? is 216

Calculation:

We use the BODMAS rule as follows:

According to the rule ‘division’ should be solved first

⇒ 549 ÷ 3 × 54 - 25 × 321 + 31 = ?

⇒ 183 × 54 - 25 × 321 + 31 = ?

⇒ 9882 - 8025 + 31 = ?

⇒ 9913 - 8025 = ?

⇒ ? = 1888

∴ required answer is 1888.

Shortcut Trick

Ratio of Boat Speed (u) : Stream Speed (v) = 16 : 5

Upstream Speed (u−v) = 11 units | Downstream Speed (u+v) = 21 units

Upstream Speed = 33 km ÷ 1.5 hours = 22 kmph ⇒ 1 unit = 2 kmph

Downstream Speed = 21 × 2 = 42 kmph

Time Downstream = (35 ÷ 42) × 60 = 50 min

∴ The correct answer is 50 min.

Alternate Method

Given: Ratio of stream speed (v) to boat speed (u) = 5 : 16. Upstream distance = 33 km, Upstream time = 90 min (1.5 hours).

Formula Used: Speed = Distance ÷ Time; Upstream Speed (S_up) = u − v; Downstream Speed (S_down) = u + v.

⇒ Let Boat speed = 16x and Stream speed = 5x

⇒ Upstream speed = 16x − 5x = 11x

⇒ 11x = 33 km ÷ 1.5 hr = 22 kmph

⇒ x = 2 kmph

⇒ Downstream speed = 16x + 5x = 21x = 21 × 2 = 42 kmph

⇒ Time taken for 35 km downstream = (35 ÷ 42) hours

⇒ Time in minutes = (35 ÷ 42) × 60 = 5 × 10 = 50 min

∴ The correct answer is 50 min.

Additional Information

Relative Speed in Water

Downstream speed is the sum (u + v) and Upstream speed is the difference (u − v) of boat and stream speeds.

Boat Speed Calculation

Speed of boat in still water (u) = (Downstream Speed + Upstream Speed) ÷ 2.

Stream Speed Calculation

Speed of stream (v) = (Downstream Speed − Upstream Speed) ÷ 2.

Shortcut Trick

Profit Ratio = (Capital₁ × Time₁) : (Capital₂ × Time₂)

Ratio of Capitals = 32000 : 20000 = 8 : 5.

Time for Vaibhav = x, Time for Ashish = (x − 6).

Ratio = (8 × x) : (5 × (x − 6)) = 12 : 5.

Solving 8x ÷ (5x − 30) = 12 ÷ 5 ⇒ 40x = 60x − 360 ⇒ 20x = 360 ⇒ x = 18.

∴ The correct answer is 18 months.

Alternate Method

Given: Vaibhav Investment = Rs. 32000, Ashish Investment = Rs. 20000, Profit Ratio = 12 : 5, Ashish joined after 6 months.

Formula: Profit = Investment × Time period

⇒ Let Vaibhav invested for x months.

⇒ Ashish joined 6 months later, so his time = (x − 6) months.

⇒ (32000 × x) ÷ (20000 × (x − 6)) = 12 ÷ 5

⇒ (32 × x) ÷ (20 × (x − 6)) = 12 ÷ 5

⇒ (8x) ÷ (5 × (x − 6)) = 12 ÷ 5

⇒ 8x ÷ (x − 6) = 12

⇒ 8x = 12x − 72

⇒ 4x = 72 ⇒ x = 18 months.

∴ The correct answer is 18 months.

Additional Information

Partnership Principle

In a partnership, the profit is distributed among partners in the ratio of the product of their investment and time duration.

Time Calculation

If a person joins 'n' months after the start, their investment duration is (Total Time − n).

Shortcut Trick

Assume Marked Price (MP) is 100.

Given Discount = 20%, so Selling Price (SP) = 100 − 20 = 80.

Difference (MP − CP) = 50% of SP = 0.5 × 80 = 40.

Since MP − CP = 40, then 100 − CP = 40 ⇒ Cost Price (CP) = 60.

Ratio MP : CP = 100 : 60 = 5 : 3.

∴ The correct answer is 5 : 3.

Alternate Method

Given: MP − CP = 0.5 × SP and Discount% = 20%

Formulas: SP = MP × (100 − D%) ÷ 100

⇒ Let Marked Price be M and Cost Price be C.

⇒ Selling Price (S) = M − 0.20M = 0.8M.

⇒ According to the question: M − C = 0.5 × S.

⇒ M − C = 0.5 × (0.8M) = 0.4M.

⇒ M − 0.4M = C ⇒ 0.6M = C.

⇒ M ÷ C = 1 ÷ 0.6 = 10 ÷ 6 = 5 ÷ 3.

∴ The correct answer is 5 : 3.

Additional Information

Marked Price and Discount

Marked Price (MP) is the price printed on an item. Discount is always calculated on the MP. SP = MP − Discount.

Relationship between CP, SP, and MP

Profit is SP − CP, whereas Discount is MP − SP. To find the ratio between MP and CP, we can use the formula MP ÷ CP = (100 + P%) ÷ (100 − D%) if profit percentage is known.

Shortcut Trick

Initial Ratio (Water : Milk) = 6 : 7

Final Ratio (Water : Milk) = 3 : 5. To make Water constant, multiply final ratio by 2 → 6 : 10.

Increase in Milk = 10 − 7 = 3 units. Given, 3 units = 15 litres → 1 unit = 5 litres.

Initial mixture x = (6 + 7) units = 13 units = 13 × 5 = 65 litres.

∴ The correct answer is 65 litres.

Alternate Method

Given: Initial ratio 6:7, added 15 litres milk, final ratio 3:5.

Formula Used: Ratio × constant = Quantity; Initial Value x = Sum of initial components.

⇒ Let water = 6k and milk = 7k. Total volume x = 13k.

⇒ 6k / (7k + 15) = 3 / 5

⇒ 5 × 6k = 3 × (7k + 15)

⇒ 30k = 21k + 45

⇒ 9k = 45 ⇒ k = 5

⇒ x = 13 × 5 = 65 litres.

∴ The correct answer is 65 litres.

Additional Information

Constant Variable Concept

When only one component is added or removed from a mixture, the quantity of the other component remains constant. Always equate its ratio units first.

Alligation Rule

Used to find the ratio in which two quantities are mixed to get a final concentration: (Higher value − Mean) / (Mean − Lower value).

Replacement Method

Final Quantity = Initial Quantity × (1 − amount replaced/total)ⁿ, where n is the number of times the process is repeated.

Calculations:

Total number of books issued to A in all library together

⇒ 18 + 30 + 24 = 72

Total number of books issued to C in all library together

⇒ 25 + 10 + 32 = 67

So, required difference 72 – 67 = 5

Calculations:

Number of books issued to A in library Q = 30

Number of books issued to B in library Q = 35

Required ratio 30 : 35 = 6: 7

So, x = 7 ⇒  9x = 9 × 7 = 63

Calculations:

Total number of books issued to C in library R = 32

Number of books issued to D in library R:

⇒ 32 × 25/100 + 12

⇒ 8 + 12 = 20

Calculations:

Total Number of books issued to A = 18 + 30 + 24 = 72

Total Number of fiction books issued to A = 72 × (25 /100)

Total Number of fiction books issued to A = 18

Calculations:

Total number of book issue in library P to all three people together = [18 + 20 + 25] = 63

Total number of book issue in library Q to all three people together = [30 + 35 +10] = 75

So, Total number of book issue in library P to all three people together is 75 – 63 = 12 less than the number of book issue in library Q to all three people together.

Shortcut Trick

Assume Total Population = 100 units.

Literates = 80 units, Illiterates = 20 units (Ratio 4 : 1).

Literate Females = 30% of 80 = 24 units | Illiterate Females = 20% of 20 = 4 units.

Total Females = 24 + 4 = 28 units → 56 (Given).

1 unit = 2 | Total population = 100 × 2 = 200.

∴ The correct answer is 200.

Alternate Method

Given: Ratio of Literate to Illiterate = 4 : 1. Total Females = 56.

Let Literate = 400x and Illiterate = 100x. Total Population = 500x.

⇒ Literate Females = 30% of 400x = 0.30 × 400x = 120x.

⇒ Illiterate Females = 20% of 100x = 0.20 × 100x = 20x.

⇒ Total Females = 120x + 20x = 140x.

⇒ 140x = 56

⇒ x = 56 ÷ 140 = 0.4

⇒ Total Population = 500 × 0.4 = 200.

∴ The correct answer is 200.

Additional Information

Ratio Distribution

To divide a quantity N in ratio a : b, the parts are [a/(a+b)] × N and [b/(a+b)] × N.

Percentage of a Group

If x% are males, then (100 − x)% are females, provided there are only two categories.

Unitary Method

Finding the value of a single unit (140 units = 56 → 1 unit = 0.4) to calculate the total required value.

Shortcut Trick

Circumference of Circle = π × d = (22/7) × 56 = 176 cm.

Perimeter of Rectangle = 2 × (L + B). Given L + B = diameter = 56 cm.

⇒ Perimeter = 2 × 56 = 112 cm.

Ratio = 176 : 112 = 11 : 7 (dividing both by 16).

∴ The correct answer is 11 : 7.

Alternate Method

Given:

Diameter (d) of circle = 56 cm.

Sum of length (L) and breadth (B) of rectangle (L + B) = 56 cm.

Formula Used:

⇒ Circumference of circle (C) = π × d

⇒ Perimeter of rectangle (P) = 2 × (L + B)

Calculations:

⇒ C = (22/7) × 56

⇒ C = 22 × 8 = 176 cm

⇒ P = 2 × 56 = 112 cm

⇒ Ratio = C / P = 176 / 112

⇒ Ratio = (16 × 11) / (16 × 7) = 11 / 7

∴ The correct answer is 11 : 7.

Additional Information

Circle Properties

Area of circle = πr² or (πd²)/4. Circumference = 2πr or πd.

Rectangle Mensuration

Area of rectangle = L × B. Diagonal = √(L² + B²).

Standard π Values

For calculations involving 7 or its multiples, use π ≈ 22/7 for easier cancellation.

Shortcut Trick

When distance is constant, time is inversely proportional to speed (T ∝ 1/S).

Initial speed = 100% → New speed = 100% + 100% = 200%.

Speed ratio = 1 : 2 ∴ Time ratio = 2 : 1.

2 units = 10 hours ⇒ 1 unit = 5 hours.

∴ The correct answer is 5 hr.

Alternate Method

Given: Initial Speed (S₁) = 25 km/h, Initial Time (T₁) = 10 hours.

Formula Used: Distance = Speed × Time

⇒ Total Distance = S₁ × T₁ = 25 × 10 = 250 km.

⇒ New Speed (S₂) = 25 + (100% of 25) = 25 + 25 = 50 km/h.

⇒ New Time (T₂) = Distance ÷ S₂

⇒ T₂ = 250 ÷ 50 = 5 hours.

∴ The correct answer is 5 hr.

Additional Information

Inverse Proportion Rule

If distance is constant, S₁ × T₁ = S₂ × T₂. This allows for quick calculation without finding the actual distance.

Percentage Increase in Speed

A 100% increase means the value doubles (New = Old × 2). Similarly, a 200% increase means the value triples.

Average Speed

For two equal distances covered at speeds x and y, Average Speed = (2 × x × y) ÷ (x + y).

From the given instructions:

Eight people P, Q, R, S, T, U, V and W, they have different designation as General Manager, Deputy General Manager, Assistant General Manager, Manager, Assistant Manager, Sectional Officer, Cashier and Clerk. The order of seniority is same as given above i.e. General manager is the senior-most and the Clerk is the junior-most. So, we can a draw a structure as:

1. Only five people have their designations between S and V. Sectional Officer is senior to V. So, we have two cases:

2. More than two people are senior to Q. Q is immediately junior to W. U is senior to at least three designations. U is junior to W. Only three people have their designation between P and U.

So, from above conditions we can say that U can only be placed at Assistant Manager. So, we can say,

So, here we can clearly see that Case 1 is invalid, as there is no space to place P. So, Case 1 gets cancelled out.

3. S is senior to R, who is senior to T.

So, Final Arrangement:

R is the Sectional Officer.

From the given instructions:

Eight people P, Q, R, S, T, U, V and W, they have different designation as General Manager, Deputy General Manager, Assistant General Manager, Manager, Assistant Manager, Sectional Officer, Cashier and Clerk. The order of seniority is same as given above i.e. General manager is the senior-most and the Clerk is the junior-most. So, we can a draw a structure as:

1. Only five people have their designations between S and V. Sectional Officer is senior to V. So, we have two cases:

2. More than two people are senior to Q. Q is immediately junior to W. U is senior to at least three designations. U is junior to W. Only three people have their designation between P and U.

So, from above conditions we can say that U can only be placed at Assistant Manager. So, we can say,

So, here we can clearly see that Case 1 is invalid, as there is no space to place P. So, Case 1 gets cancelled out.

3. S is senior to R, who is senior to T.

So, Final Arrangement:

Three designations are there between W and T.

From the given instructions:

Eight people P, Q, R, S, T, U, V and W, they have different designation as General Manager, Deputy General Manager, Assistant General Manager, Manager, Assistant Manager, Sectional Officer, Cashier and Clerk. The order of seniority is same as given above i.e. General manager is the senior-most and the Clerk is the junior-most. So, we can a draw a structure as:

1. Only five people have their designations between S and V. Sectional Officer is senior to V. So, we have two cases:

2. More than two people are senior to Q. Q is immediately junior to W. U is senior to at least three designations. U is junior to W. Only three people have their designation between P and U.

So, from above conditions we can say that U can only be placed at Assistant Manager. So, we can say,

So, here we can clearly see that Case 1 is invalid, as there is no space to place P. So, Case 1 gets cancelled out.

3. S is senior to R, who is senior to T.

So, Final Arrangement:

W is just junior to Deputy General Manager.

From the given instructions:

Eight people P, Q, R, S, T, U, V and W, they have different designation as General Manager, Deputy General Manager, Assistant General Manager, Manager, Assistant Manager, Sectional Officer, Cashier and Clerk. The order of seniority is same as given above i.e. General manager is the senior-most and the Clerk is the junior-most. So, we can a draw a structure as:

1. Only five people have their designations between S and V. Sectional Officer is senior to V. So, we have two cases:

2. More than two people are senior to Q. Q is immediately junior to W. U is senior to at least three designations. U is junior to W. Only three people have their designation between P and U.

So, from above conditions we can say that U can only be placed at Assistant Manager. So, we can say,

So, here we can clearly see that Case 1 is invalid, as there is no space to place P. So, Case 1 gets cancelled out.

3. S is senior to R, who is senior to T.

So, Final Arrangement:

Q is the Manager.

From the given instructions:

Eight people P, Q, R, S, T, U, V and W, they have different designation as General Manager, Deputy General Manager, Assistant General Manager, Manager, Assistant Manager, Sectional Officer, Cashier and Clerk. The order of seniority is same as given above i.e. General manager is the senior-most and the Clerk is the junior-most. So, we can a draw a structure as:

1. Only five people have their designations between S and V. Sectional Officer is senior to V. So, we have two cases:

2. More than two people are senior to Q. Q is immediately junior to W. U is senior to at least three designations. U is junior to W. Only three people have their designation between P and U.

So, from above conditions we can say that U can only be placed at Assistant Manager. So, we can say,

So, here we can clearly see that Case 1 is invalid, as there is no space to place P. So, Case 1 gets cancelled out.

3. S is senior to R, who is senior to T.

So, Final Arrangement:

No designations is there below V. V is having junior most designation.

The least possible Venn diagram for the given statements is as follows

Conclusions:

I. All wood can be ant → False ( as the only drum is wood, which means all wood is drum, and wood can form only positive relation with drum, not with other elements. Hence, All wood can be ant is false).

II. All ant can be drum → True ( as there is no relation between ant and drum. so, it is possible. Hence, all ant can be drum is true).

Hence, Only II follows is the correct answer.

The least possible Venn Diagram for the given data:

Conclusions:

I. All graphite being marble is a possibility → True (it is possible for all graphites to be marble as it does not violate any statement.)

II. Some stones being tiles is a possibility → True (it is possible for some stones to be tiles as it does not violate any statement.)

Hence, "both conclusions follow."

Solution:

The least possible diagram for the given statements is as follows

Conclusions:

I. At least some dog are cat → False (It is possible but not definite, as no direct relation between the two is given).

II. Some cat is definitely not dog →  False (It is possible but not definite,  as no direct relation between the two is given).

Here, both conclusions are not complementary conclusions as shown in the below possible diagram,

Here, both conclusion I and II is false so it is not "either or" case.

Hence, Neither I nor II follows.

The logic follows here is :-

Given series :

Left side E 4 W 2 G 6 @ S 5 8 X A ! I M 9 & Q ^ J L # 7 * C $ G V % K Right side

 8^th to the right of 14^th from the left end → 14^th from left end + 8^th to right of 14^th → 22^nd from left end 

Clearly, 22^nd from left end is '#'.

Thus, the correct answer is "#"$.

The logic follows here is :-

Given series :

Left side E 4 W 2 G 6 @ S 5 8 X A ! I M 9 & Q ^ J L # 7 * C $ G V % K Right side

Vowels that are which is immediately preceded by a symbol and immediately followed by a consonant is :

E 4 W 2 G 6 @ S 5 8 X A ! I M 9 & Q ^ J L # 7 * C $ G V % K