SSC CHSL Tier-1 2024: Official Paper (Held On: 09 Jul, 2024 Shift 1) (Previous Year Paper)

The correct answer is Option 4)

Key Points

• The segment "inside Germany, France, Austria, and Italy" is incorrect.
• The correct preposition to use here is "between" or "among" rather than "inside".
• Switzerland is not located inside these countries but is bordered by them.
• Therefore, the sentence should correctly state: "Switzerland lies between Germany, France, Austria, and Italy."

Hence, the correct answer is 'option 4.'

The correct answer is Option 1)

Key Points

• In the first part of the given sentence, the article 'a' is incorrect.
• The correct article to use before the word 'Earth' is 'the' because Earth is a unique object.
• Example: The Earth is the third planet from the Sun.
• Therefore, the article 'a' should be replaced with the article 'the'.

Hence, the correct statement is: There are eight planets in our solar system and the Earth is the third planet from the Sun.

Additional Information

• If a noun is unique or one of a kind, the definite article 'the' is used before it.
• Example: The Sun rises in the east.
• When referring to planets or celestial bodies by name, the definite article 'the' is usually used.
• Example: The Mars rover is sending back data.

The correct answer is Option 4)

Key Points

• In the given sentence, the phrase 'agree to you' is incorrect. The correct phrase should be 'agree with you'.
• The verb 'agree' is typically followed by the preposition 'with' when referring to a person.
• Example: I cannot agree with your opinion.
• Therefore, the correct form should be 'agree with you' instead of 'agree to you'.

Hence, the correct answer is: You expressed your opinion very clearly, but I am sorry, I cannot agree with you.

The correct answer is Option 3)

Key Points

• The sentence is in the present perfect continuous tense because it describes an action that started in the past and is still continuing.
• The correct form of the verb to use in this case is "has been suffering".
• This tense is used to talk about actions that began in the past and are still continuing at the present moment.
• Example: She has been living in London since 1995.

Hence, the correct statement is: Serena has been suffering from fever since the 5^th of this month.

Additional Information

• The present perfect continuous tense is often used with time expressions such as "since" and "for".
• "Since" is used to indicate the starting point of the action, while "for" is used to indicate the duration.
• Example with "for": He has been working here for three years.

The correct answer is Option 4)

Key Points

• The word "during" is used to indicate the entire time something happens or the period of time something occurs.
• In the context of the sentence, the filming of a scene is a process that takes some duration, hence "during" accurately captures the timeframe when the action (harming animals) is to be considered.
• The phrase "no animals were harmed during the filming" is a standardized declaration typically used in film productions.
• Other options like "from," "around," and "for" do not effectively convey the intended continuity of time associated with the filming process.
• "During" provides a clear, time-bound reference, making it the most appropriate choice for the context of ensuring no animals were harmed while the film was being made.

Therefore, the correct answer is 'Option 4'.

Additional Information

• "From" suggests a starting point but does not fit the idea of the timeframe of filming.
• "Around" refers to something being near or surrounding, which doesn't apply to the timing of filming.
• "For" typically indicates purpose or duration but does not appropriately fit the context here.

The correct answer is Option 1)

Key Points

• "To" is used to indicate the place, person, or thing that someone or something moves toward, or the direction of something.
• In the context of this sentence, the lipstick is applied "to" the heroines lips, denoting the target or end point where the lipstick is placed.
• The phrase "applied to" is a common collocation, meaning it is a standard and correct usage in the English language.
• Using "to" ensures clarity in meaning, directly stating the action and the destination of the application.
• Prepositions like "on," "upon," and "over" either imply a different type of placement or are not commonly used with the verb "applied" in this context.
• "To" seamlessly fits into the sentence structure, maintaining grammatical correctness and ease of understanding.

Therefore, the correct answer is 'Option 1'.

Additional Information

• "On" suggests a surface placement, but "applied to" is more precise and commonly used.
• "Upon" is an elevated, somewhat archaic form of "on" and doesn't fit modern usage with "applied".
• "Over" implies covering something, which is not the intended meaning in this context.

The correct answer is Option 2)

Key Points

• "Also" is used to indicate that something is in addition to something else, fitting seamlessly into this sentence.
• The context implies that multiple items in the film studio used animal fats, so "also" appropriately conveys the additional inclusion.
• Using "also" makes it clear that the lipstick wasn’t the only product made with animal derivatives, reinforcing the argument of widespread indirect cruelty.
• The pre-existing flow of the sentence discusses one item (the lipstick) and then moves on to mention other items, making "also" the logical connector for addition.
• "Also" ensures the sentence retains its intended meaning, suggesting that animal fats were commonly used across various items in the studio.
• By emphasizing the word, readers understand the extent of animal-derived materials used, thus highlighting the irony of the showbiz environment concerning vegan actors.

Therefore, the correct answer is 'Option 2'.

Additional Information

• "Long" suggests duration or extent, which is irrelevant here.
• "Too" is informal for this specific construction and less precise compared to "also".
• "Least" connotes minimal availability or extent, which contradicts the idea of additional items being involved.

The correct answer is Option 4)

Key Points

• "Confessed" is the simple past tense of the verb "to confess," indicating a completed action in the past.
• The passage is in past tense, as seen with phrases like "were harmed," "was applied," and "were used." Thus, "confessed" maintains this consistency.
• "Confessed" accurately reflects that the actors' admissions about being vegan occurred before the current context of being unaware of their indirect involvement in cruelty.
• The structure of the sentence suggests that the confession is a point of fact that happened in the past, harmonizing with the past-tense narrative.
• Using "confessed" ensures clarity and maintains the coherence and flow of the passage.
• The simple past tense is typically used in narratives to recount completed actions, making "confessed" the most appropriate for historical statements.

Therefore, the correct answer is 'Option 4'.

Additional Information

• "Are confessing" implies ongoing action, which is unsuitable given the past context.
• "Had confessed" is the past perfect tense, which indicates an action completed before another past action; this adds unnecessary complexity here.
• "Were confessing" suggests a continuous action in the past, which does not fit the point-in-time admission being described.

The correct answer is Option 1)

Key Points

• " To" is used to indicate effect or relation, which is suitable in this context to show how something negatively impacts something else.
• The phrase “detrimental to” correctly expresses harm or damage towards something, in this case, the ecosystem.
• "To" accurately connects the cause (plastic becoming part of the animal food chain) and effect (detriment to the ecosystem) in a cause-effect relationship.
• This usage fits well within the passage's structure, maintaining clarity and grammatical correctness.
• The term "detrimental to" is a common collocation, meaning it is often used together in similar contexts to indicate harmful effects.
• By using "to," the sentence succinctly conveys the overall negative impact without ambiguity.

Therefore, the correct answer is 'Option 1'.

Additional Information

• "In" suggests location or position, which doesn't express the cause-effect relationship needed here.
• "For" implies purpose or benefit, which is contrary to the intended negative connotation.
• "On" indicates a surface or topic but does not correctly convey the relationship of harm or impact in this context.

The correct answer is Option 2)

Key Points

• The word "custom" means a traditional and widely accepted way of behaving or doing something that is specific to a particular society, place, or time. (रिवाज)
• Example: It is a custom in many cultures to celebrate the New Year with fireworks.
• "Habit" refers to a regular tendency or practice, especially one that is hard to give up. (आदत)
• Example: Brushing your teeth twice a day is a good habit to maintain oral hygiene.

Hence, we can infer that "habit" is a more suitable word for the given sentence as it refers to a regular practice.

Additional Information

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

• Oddity (विचित्रता): A strange or peculiar person, thing, or trait.
• Example: His habit of wearing mismatched socks is considered an oddity by his friends.
• Addiction (लत): The fact or condition of being addicted to a particular substance, thing, or activity.
• Example: His addiction to video games is affecting his studies.
• Perfection (पूर्णता): The condition, state, or quality of being free or as free as possible from all flaws or defects.
• Example: She strives for perfection in everything she does.

The correct answer is Option 4)

Key Points

• The word "important" means something of great significance or value. (महत्वपूर्ण)
• Example: It is important to attend the meeting on time.
• "Trivial" refers to something of little value or importance; not significant. (तुच्छ)
• Example: She was upset over a trivial matter that didn't really affect anything.

Therefore, the correct answer is: Option 4.

Additional Information

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

• Option 1: Choose the right colour to make your bike stand out! (अपनी बाइक को अलग दिखाने के लिए सही रंग चुनें!)
• Explanation: This sentence talks about choosing a colour to make the bike noticeable, which is unrelated to importance.
• Option 2: Namita also makes some very salient points in her newly revised preface. (नमिता अपने नए संशोधित प्राक्कथन में कुछ बहुत महत्वपूर्ण बातें भी करती हैं।)
• Explanation: The word "salient" means important or prominent, which is a synonym rather than an antonym of "important".
• Option 3: I have some urgent questions for you. (मेरे पास आपके लिए कुछ आवश्यक प्रश्न हैं।)
• Explanation: The word "urgent" implies something that needs immediate attention and is important, not the opposite of important.

The correct answer is Option 2)

Key Points

• The word "Pronounciation" is incorrectly spelt. The correct spelling is "Pronunciation". (उच्चारण)
• Example: The pronunciation of some English words can be challenging for non-native speakers.
• "Pronunciation" refers to the way in which a word is pronounced. (उच्चारण)
• Example: Her pronunciation of French words is impeccable.

Therefore, the correct answer is: Option 2.

Additional Information

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

• Clandestine (गुप्त): Something that is done in secret or kept hidden.
• Example: They held a clandestine meeting to plan the surprise party.
• Dissociation (विच्छेदन): The disconnection or separation of something from something else.
• Example: There was a clear dissociation between her professional and personal lives.
• Denunciation (निंदा): Public condemnation of someone or something.
• Example: The mayor's denunciation of corruption was well-received by the citizens.

The correct answer is Option 3)

Key Points

• The word "covering" means to put something over or on top of something else to protect or conceal it. (ढंकना)
• Example: She used a blanket for covering herself during the cold night.
• "Exposing" refers to making something visible by uncovering it; to reveal something that is usually hidden. (उघाड़ना)
• Example: The photographer was exposing the film to capture the image.

Hence, we can infer that the opposite of 'covering' is 'exposing'.

Additional Information

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

• Expecting (उम्मीद करना): To think or believe something will happen.
• Example: She is expecting a parcel in the mail today.
• Expounding (व्याख्या करना): To explain or describe something in detail.
• Example: The professor was expounding on the principles of physics.
• Expanding (विस्तार करना): To increase in size, number, or importance.
• Example: The company is expanding its operations overseas.

The correct answer is Option 3)

Key Points

• The word "tomorow" is the incorrect spelling of "tomorrow". It refers to the day after today. (कल)
• Example: I am in a hurry so I will see you tomorow.
• "Tomorrow" is the correct spelling. It refers to the day following the present day. (कल)
• Example: I have a meeting scheduled for tomorrow.

Therefore, the correct spelling is: 'tomorrow'.

Additional Information

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

• tomoorrow (टूमॉर्रो): This is an incorrect spelling of "tomorrow".
• Example: Incorrect: I will meet you tomoorrow.
• tomoorow (टूमॉरो): This is an incorrect spelling of "tomorrow".
• Example: Incorrect: Let's plan for tomoorow.
• toomorow (टूमोरो): This is an incorrect spelling of "tomorrow".
• Example: Incorrect: The event is scheduled for toomorow.

The correct answer is Option 2)

Key Points

• The word "Abundance" means a very large quantity of something; plentifulness. (प्रचुरता)
• Example: The garden was filled with an abundance of flowers, creating a beautiful and vibrant scene.
• "Scarcity" refers to the state of being in short supply; a situation in which something is not easy to find or obtain. (कमी)
• Example: During the drought, there was a scarcity of water in the village.

Hence, we can infer that the opposite of 'Abundance' is 'Scarcity'.

Additional Information

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

• Excitement (उत्साह): A feeling of great enthusiasm and eagerness.
• Example: The excitement in the air was palpable as the concert began.
• Fortune (भाग्य): A large amount of money or assets; luck.
• Example: She made her fortune in the stock market.
• Prosperity (समृद्धि): The state of being successful and having a lot of money.
• Example: The country is enjoying a period of peace and prosperity.

The correct answer is: Option 1.

Key Points

• The word "advanced" means to move forward in a purposeful way, especially in a military context. (आगे बढ़ना)
• Example: The soldiers advanced towards the enemy lines with determination.
• "Retreated" refers to the act of moving back or withdrawing, especially to avoid confrontation or danger. (पीछे हटना)
• Example: After facing heavy resistance, the army retreated to a safer position.

Hence, we can infer that the opposite of 'advanced' is 'retreated'.

Additional Information

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

• Protruded (बाहर निकला हुआ): To extend beyond or above a surface.
• Example: The rock protruded from the ground, making it a tripping hazard.
• Commuted (यात्रा करना ): To travel some distance between one's home and place of work on a regular basis.
• Example: He commuted daily from the suburbs to the city for work.
• Arose (उठना): To emerge or become apparent.
• Example: A new problem arose during the meeting, requiring immediate attention.

The correct answer is Option 4)

Key Points

• The word "spacious" means having ample space; large in area or extent. (विशाल)
• Example: The spacious garden allowed the children to run and play freely.
• "Roomy" refers to having plenty of room; spacious. (कक्षयुक्त)
• Example: The roomy car was perfect for the long family road trip.

Hence, we can infer that the word 'spacious' can be substituted with 'roomy'.

Additional Information

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

• Cramped (संकीर्ण): Feeling or causing someone to feel uncomfortably confined or hemmed in by lack of space.
• Example: The cramped apartment made it difficult to move around freely.
• Tiny (छोटा): Very small in size.
• Example: The tiny house was cozy but lacked sufficient space for a large family.
• Cozy (आरामदायक): Giving a feeling of comfort, warmth, and relaxation.
• Example: The cozy cabin in the woods was perfect for a weekend getaway.

The correct answer is Option 4)

Key Points

• The word "Sceptical" means having doubts or reservations about something; not easily convinced. (संदेहपूर्ण)
• Example: She was sceptical about the effectiveness of the new diet plan.
• "Incredulous" refers to a state of being unwilling or unable to believe something; showing disbelief. (अविश्वासी)
• Example: He gave an incredulous look when he heard the news of the sudden promotion.

Hence, we can infer that the synonym of 'sceptical' is 'incredulous'.

Additional Information

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

• Stoic (संयमी): A person who can endure pain or hardship without showing their feelings or complaining.
• Example: Despite the harsh conditions, he remained stoic and focused on his mission.
• Garrulous (बातूनी): Excessively talkative, especially on trivial matters.
• Example: The garrulous old man kept us entertained with his endless stories.
• Insensitive (असंवेदनशील): Showing or feeling no concern for others' feelings.
• Example: His insensitive remarks hurt her feelings deeply.

The correct answer is Option 2)

Key Points

• The phrase "keeps a low profile" means to avoid attracting attention or publicity. (ध्यान आकर्षित करने से बचना)
• Example: Despite his fame, the actor keeps a low profile and rarely appears in public.
• "Even though she’s a celebrity, she doesn’t draw any attention towards herself." implies that she avoids the limelight and public attention. (वह खुद पर ध्यान आकर्षित करने से बचती है)
• Example: Even though she’s a celebrity, she keeps a low profile and doesn’t draw any attention towards herself.

Therefore, the correct answer is: 'keeps a low profile'.

Additional Information

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

• Keeps hot under the collar (गुस्से में रहना): To be angry or agitated.
• Example: He keeps hot under the collar whenever someone criticizes his work.
• Keeps up with the Joneses (दूसरों की बराबरी करना): To try to match the lifestyle of one's neighbors or peers.
• Example: She buys new gadgets just to keep up with the Joneses.
• Is hard to come by (दुर्लभ होना): To be rare or difficult to obtain.
• Example: In this remote area, fresh vegetables are hard to come by.

The correct answer is Option 2)

Key Points

• The word "celebrated" means widely known and praised, often for some achievement or contribution. (प्रसिद्ध)
• Example: William Shakespeare is a celebrated author whose works are studied worldwide.
• "Inglorious" refers to someone or something that is not famous, or is infamous; lacking glory or honor. (अपमानजनक)
• Example: The general's inglorious defeat was a blot on his otherwise distinguished career.

Hence, we can infer that the opposite of 'celebrated' is 'inglorious'.

Additional Information

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

• Laureate (पुरस्कार विजेता): A person who is honored with an award for outstanding creative or intellectual achievement.
• Example: The Nobel laureate delivered a lecture on climate change.
• Illustrious (प्रसिद्ध): Well known, respected, and admired for past achievements.
• Example: The illustrious scientist was invited to speak at the conference.
• Acclaimed (सराहनीय): Publicly praised; celebrated.
• Example: The acclaimed director's new film received rave reviews.

The correct answer is Option 1)

Key Points

• In the given sentence, the verb form should match the conditional structure.
• The sentence uses a future conditional structure "If it is sunny tomorrow," which should be followed by "will" + base form of the verb.
• Hence, the correct form is "will go" instead of just "go."

Hence, the correct statement: If it is sunny tomorrow, we will go for a picnic.

Additional Information

• The future conditional structure in English often follows the pattern "If + present simple, will + base verb."
• Example: If it rains, we will stay indoors.

The correct answer is '4' i.e. among the three families.

Key Points

• In the given sentence, the underlined segment "between the three families" is incorrect because the preposition "between" is typically used when referring to two entities.
• When referring to more than two entities, the correct preposition is "among".
• Therefore, the correct phrase should be "among the three families".

Hence, the correct answer is option 4.

Correct sentence: There is an old rivalry among the three families for ages.

Additional Information

• The preposition "between" is used to indicate a relationship involving two people or things. For example: "The book is between the two shelves".
• The preposition "among" is used for relationships involving more than two people or things. For example: "She is popular among her friends".

The correct answer is Option 4)

 

Key Points

• The verb "pay" is commonly used with the noun "attention" to form the phrase "pay attention."
• The sentence is instructing students to focus on the instructions given, which fits the usage of "pay attention."
• Options 1, 2, and 3 are grammatically incorrect in this context.

Therefore, the correct answer is "The teacher asked the students to pay attention towards the instructions given for the project."

 

Additional Information

• Option 1: "make" is incorrect because we do not "make" attention.
• Option 2: "had" is incorrect because it does not fit the sentence structure appropriately.
• Option 3: "keen" is incorrect as "keen attention" is not a standard phrase and does not fit grammatically.

The correct answer is Option 3)

Key Points

• The word "compete" means to strive to gain or win something by defeating or establishing superiority over others. (प्रतिस्पर्धा करना)
• Example: Many athletes compete in the Olympics to win gold medals.
• "Support" means to give assistance to, especially financially; to enable to function or act. (समर्थन करना)
• Example: Parents often support their children in their education and career choices.

Hence, we can infer that the opposite of "compete" is "support".

Additional Information

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

• Pervert (विकृत करना): To alter something from its original course, meaning, or state to a distortion or corruption of what was first intended.
• Example: He was accused of attempting to pervert the course of justice.
• Attack (आक्रमण करना): To take aggressive action against a place or enemy forces with weapons or armed force.
• Example: The soldiers prepared to attack the enemy at dawn.
• Impede (बाधा डालना): To delay or prevent someone or something by obstructing them; hinder.
• Example: The heavy traffic might impede our progress to the meeting.

The correct answer is Option 4)

Key Points

• The phrase "a bolt from the blue" means a sudden and unexpected event or piece of news. (आकस्मिक घटना या समाचार)
• Example: The news of his resignation came as a bolt from the blue.
• "A gift from my teacher on the eve of the new year was a complete surprise." This sentence suggests that the gift was unexpected and sudden.
• Example: The sudden announcement of the bonus was a bolt from the blue for all the employees.

Therefore, the correct answer is: a bolt from the blue.

Additional Information

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

• Like a cat on hot bricks (बेचैन): Extremely nervous or restless.
• Example: She was like a cat on hot bricks waiting for the exam results.
• Like striking one’s colours (हार मानना): To surrender or give up.
• Example: After a long debate, he finally struck his colours and agreed to the terms.
• Spilling of beans (राज़ खोलना): To reveal a secret.
• Example: He accidentally spilled the beans about the surprise party.

The logic followed here is :-

From the given two different cubes the adjacent sides are as shown below :

As J is common on both the dice, it is clear that K, P, L, and E are adjacent to it, and the remaining i.e., M will be opposite to it.

Opposite pairs:

P → E

K → L

J → M

So, the opposite side of "M" will be side "J".

Hence, the correct answer is "J".

The image embedded in the given figure is as shown below :

∴ Here, the given figure is embedded in option Figure - 4.

Hence, the correct answer is "Option 4".

Logic : Squares of odd number series are added subsequently.

Hence, "233" is the correct answer.

The logic followed here is:

Logic: (1^st number)² × (2^nd number)² = 3^rd number.

Now,

For, (2, 3, 36)

⇒ (2)² × (3)²

= 4 × 9 = 36.

For, (3, 5, 225)

⇒ (3)² × (5)²

= 9 × 25 = 225.

Similarly, for (1, 7, 49)

⇒ (1)² × (7)²

= 1 × 49 = 49.

Hence, the correct answer is "Option 2".

Decoding the Symbols:

Given: P + Q ÷ R × S − T 

P + Q → P is the sister of Q.

Q ÷ R  → Q is the wife of R.

R × S → R is the father of S.

​

S − T → S is the brother of T.

Here, P is the maternal aunt or mother's sister of T.

Hence, the correct answer is "Option 1".

The image embedded in the given figure is as shown below :

∴ Here, the given figure is embedded in option Figure - 2.

Hence, the correct answer is "Option 2".

Given: ABC_C_CC_DCBG_CA  

By checking options :

1. DCEE → ABCDCCCCEDCBGECA → (It follows the pattern of) : 

 

2. ECDC → ABCECCCCDDCBGCCA → (It doesn't Follow the pattern)

3. DCED → ABCDCCCCEDCBGDCA → (It doesn't Follow the pattern)

4. EDCE → ABCECDCCCDCBGECA → (It doesn't Follow the pattern)

So, out of all the options "Option 1" follows the pattern.

Hence, "DCEE" is the correct answer.

Given : 47 + 10 × 3 - 32 ÷ 8 = ? 

According to the question, after replacing the signs :

‘+’ and ‘-’ are interchanged 

So,​​

47 - 10 × 3 + 32 ÷ 8 = ?

47 - 10 × 3 + 4 = ?

47 + 4 - 30 = ?

51 - 30 = ?

21 = ?

Hence, "21" is the correct answer.

Given word: 'ENGLISH'

After arranged in alphabetical order:

 

Now,

there is One alphabet "E" will remain unchanged if each of the letters in the word 'ENGLISH' is arranged in English alphabetical order.

Hence, the correct answer is "Option 4".

The faces opposite to each other are shown below:

⇒ As the alternate positions become opposite to each other, the remaining two faces become opposite to each other.

So, opposite pairs are:

11 → 12

15 → 16

13 → 14

Therefore, '15' is the opposite of '16'.

Hence, "15" is the correct answer.

Given : 20 - 80 × 16 ÷ 5 + 15 = ? 

According to the question, after replacing the signs :

‘+’ and ‘-’ are interchanged 

‘×’ and ‘÷’ are interchanged

So,​​

20 + 80 ÷ 16 × 5 - 15 = ?

20 + 5 × 5 - 15 = ?

20 + 25 - 15 = ?

45 - 15 = ?

30 = ?

Hence, "30" is the correct answer.

The correct mirror image of the given figure is:

Hence, the correct answer is "Option 3".

Given Equation: 100 N 80 G 40 Y 20 M 10 = ?

BODMAS Rule:

Decoding the given information:

 

Now replacing the sign from left to right using BODMAS Rule, we get:

⇒ 100 × 80 - 40 ÷ 20 + 10 = ?

⇒ 100 × 80 - 2 + 10 = ?

⇒ 8000 - 2 + 10 = ?

⇒ 8010 − 2 = 8008.

Hence, the correct option is "Option 3".

Logic: ​

Option (1): EBD

Option (2): LIK

Option (3): ROS

Option (4): PMO

Thus, out of all the options "ROS" is the odd one out.

Hence, "Option 3" is the correct answer.

Logic : Consecutive multiples of (8) are added subsequently.

Hence, "209" is the correct answer.

Logic: (4) is added to the position values according to the English alphabetic series.

​​So,

Hence, "Option 2" is the correct answer.

The number of rectangles in the given figure is shown below :

Here, as marked there are a total of 6 rectangles.

Hence, "6" is the correct answer.

The logic followed here is: No specific pattern is followed here, random digits are assigned to each letter of the word.

'BILLION' is coded as '3264581'

And,

'MILLION' is coded as '3249581'

Therefore it can be concluded that :

M is coded as → 9

So, the code for 'M' is '9'.

Hence, "Option 3" is the correct answer.

The logic followed here is: √(1^st number - 1) = ∛(2^nd number + 1)

So,

10 : 26

√(10 - 1) = ∛(26 + 1)

√9 = ∛27

3 = 3 (LHS = RHS)

Similarly,

50 : ?

√(50 - 1) = ∛(? + 1)

√49 = ∛(? + 1)

(7)³ - 1 = ?

343 - 1 = ?

342 = ?

Hence, "Option 3" is the correct answer.

Logic : (16) is added to each number subsequently.

Hence, "88" is the correct answer.

The least possible Venn diagram for the given statements is as shown below :

Conclusions:

I. Some charts are files → Does not follow (As some charts are notebooks and some notebooks are files. So it is possible but not definite)

II. All papers being notebooks is a possibility → Follow (As all papers are charts and some charts are notebooks. As whole papers comes in charts which has some parts common with notebooks therefore all papers can be notebooks is true.)

∴ Here, Only conclusion II follow.​

Hence, the correct answer is "Only conclusion II follows"

The logic followed here is:

Logic: Synonyms

Here,

Engage and Involve are synonyms, meaning they have similar meanings.

Similarly,

Diverse and Varied are synonyms, meaning they have similar meanings.

Hence, the correct answer is "Option 1".

The logic followed here is :

1. First box alternate series → Bottom element interchange positions and rest of the elements interchange positions diagonally.

2. Second box alternate series → First column elements shift in the clockwise direction, rest elements shift in an anticlockwise direction, and the bottom right corner element is replaced by a new element.

Thus, the final series is :

Hence, "Option 3" is the correct answer.

Given: 19 February 2004 was Thursday.

Now,

2004 to 2019 = 15 Years (11 Ordinary Years and 4 Leap Years).

And, In 15 Years = 4 Leap years and 11 Ordinary Years.

So, 4 Leap Years have 8 odd days,

And, 11 Ordinary Years have 11 odd days.

Total odd days = 8 + 11 = 19.

19 odd days → 19/7 = 2 weeks and 5 odd days.

then, 19 February 2019 will be Thursday + 5 = Tuesday.

Now, the number of days between 19 February 2019 to 2 March 2019

= 9(February) + 2(March) = 11 days.

= 11 days → 11/7 = 1 week and 4 odd days.

So, 2 March 2019 will be Tuesday + 4 = Saturday.

Hence, the correct answer is "Option 4".

Logic: Increasing number series is subtracted from the position values according to the English alphabetic series.

​​So,

JNLO is related to ILIK

​ 

​And,

NRPS is related to MPMO

​ 

​Similarly,

LPNQ is related to

​ 

Hence, "Option 4" is the correct answer.

Given:

A trader buys 500 kg cotton for Rs. 8,000. 10% of this cotton is spoiled due to rain. He wants to earn a 20% profit.

Formula Used:

Profit Percentage (P%) = (Profit / Cost Price) × 100

Selling Price (SP) = Cost Price (CP) + Profit

Calculation:

Total cotton = 500 kg

⇒ Cost Price (CP) = Rs. 8,000

⇒ Spoiled cotton = 10% of 500 kg = 0.10 × 500 = 50 kg

⇒ Usable cotton = 500 kg - 50 kg = 450 kg

⇒ Desired Profit = 20%

⇒ Desired Profit Amount = 20% of Rs. 8,000 = 0.20 × 8,000 = Rs. 1,600

⇒ Total Selling Price (SP) = CP + Profit = Rs. 8,000 + Rs. 1,600 = Rs. 9,600

⇒ Selling Price per kg = Total SP / Usable cotton

⇒ Selling Price per kg = Rs. 9,600 / 450 kg

⇒ Selling Price per kg = Rs. 21 (1/3)

∴ The correct answer is option 1.

Formula Used:

N = ap × bq × cr

The total number of factors = (p + 1) × (q + 1) × (r + 1)

Calculation: 

When 732 is divided by a positive integer x, the remainder is 12. So, 

732 – 12 = 720

So 720 will be completely divisible by x

720 = 24 × 32 × 51

Total number of factors of 720 = (4 + 1) × (2 + 1) × (1 + 1) = 5 × 3 × 2 = 30

Number of factors 12 or less than 12 are (10) = 1, 2, 3, 4, 5, 6, 8, 9, 10, 12

So x cannot have these values because x is greater than 12

So, we can say that there are 30 - 10 = 20 possible values of x

Shortcut Trick

For a covered box, outer dimensions = inner dimensions + (2 × thickness).

Outer L, B, H = (128+11), (90+11), (25+11) = 139, 101, 36 cm.

Volume of wood = Outer Volume − Inner Volume.

Volume = (139 × 101 × 36) − (128 × 90 × 25) = 505404 − 288000.

∴ The correct answer is 217404 cm³.

Alternate Method

Given:

Inner Length (l) = 128 cm, Inner Breadth (b) = 90 cm, Inner Height (h) = 25 cm.

Thickness of wood (t) = 5.5 cm.

Formula Used:

Volume of wood = (Outer Length × Outer Breadth × Outer Height) − (Inner Length × Inner Breadth × Inner Height)

Calculations:

⇒ Total increase in each dimension = 2 × 5.5 = 11 cm

⇒ Outer Length (L) = 128 + 11 = 139 cm

⇒ Outer Breadth (B) = 90 + 11 = 101 cm

⇒ Outer Height (H) = 25 + 11 = 36 cm

⇒ Inner Volume = 128 × 90 × 25 = 288000 cm³

⇒ Outer Volume = 139 × 101 × 36 = 505404 cm³

⇒ Volume of Wood = 505404 − 288000 = 217404 cm³

∴ The correct answer is 217404 cm³.

Additional Information

Volume of a Cuboid

The volume of a rectangular cuboid is calculated as Length × Breadth × Height.

Open vs. Closed Box

For a closed box, add 2 × thickness to all dimensions. For an open box, add 2 × thickness to L and B, but only 1 × thickness to the Height.

Total Surface Area

The total surface area of a cuboid is 2(lb + bh + hl), where l, b, and h are its dimensions.

Calculation:

Sum of all categories in 1989 = 46 + 31 + 73 = 150

Sum of all categories in 1990 = 47 + 39 + 77 = 163

Sum of all categories in 1991 = 45 + 45 + 80 = 170

Sum of all categories in 1992 = 44 + 50 + 80 = 174

In 1991 is increase the revenue from 1989 and 1990

In 1992 is increase revenue from 1990, 1991, and 1992

According to the question,

1991 and 1992 was an increase the revenue from at least two categories. 

∴ The required answer is 2.

Calculation:

The average of demand of buses of all companies 

⇒ (150 + 145 + 160 + 165 + 155)/5

⇒ 155

According to the question,

The number of companies whose production of buses is equal to or more than the average demand of buses of all five companies

Companies A, C, and D are equal and more than average demand of buses of all five companies. 

∴ The correct answer is 3.

Given:

Lateral surface area of a cube = 144 cm²

Concept:

The lateral surface area of a cube is given by 4a², where 'a' is the length of a side of the cube.

Formula Used:

Volume of a cube = a³

Calculation:

We have,

⇒ 4a² = 144 cm²

⇒ a² = 144 cm² / 4

⇒ a² = 36 cm²

⇒ a = √36 cm

⇒ a = 6 cm

Volume of the cube,

⇒ a³ = 6³ cm³

⇒ a³ = 216 cm³

∴ The volume of the cube is 216 cm³.

Shortcut Trick

Let T be the total duration of the work (time Hari worked).

Fractional work equation: (Rohan time ÷ Rohan total) + (Hari time ÷ Hari total) = 1.

(3 ÷ 12) + (T ÷ 16) = 1

1/4 + T/16 = 1 ⇒ T/16 = 3/4.

T = (3 × 16) ÷ 4 = 12 days.

∴ The correct answer is 12 days.

Alternate Method

Given: Rohan alone = 12 days, Hari alone = 16 days. They work together for 3 days.

Formula: Efficiency = Total Work ÷ Time taken.

⇒ Total Work = LCM of 12 and 16 = 48 units.

⇒ Combined efficiency of Rohan and Hari = 4 + 3 = 7 units/day.

⇒ Work done in 3 days = 7 × 3 = 21 units.

⇒ Remaining work = 48 − 21 = 27 units.

⇒ Time taken by Hari alone to finish remaining work = 27 ÷ 3 = 9 days.

⇒ Total time to complete work = Initial 3 days + Hari's 9 days = 12 days.

∴ The correct answer is 12 days.

Additional Information

Work and Efficiency Relationship

Efficiency is inversely proportional to time. If a person is twice as efficient as another, they take half the time to complete the same work.

Work and Wages

Wages are always distributed according to the ratio of the actual work done by each individual (Efficiency × Time).

Pipes and Cisterns

This follows the same logic as Time and Work, where an outlet pipe (leak) has negative efficiency and reduces the total work done.

Shortcut Trick

Sum of digits of 6428A83 = 6 + 4 + 2 + 8 + A + 8 + 3 = 31 + A.

According to the Divisibility Rule of 9, the sum of digits must be a multiple of 9.

The nearest multiple of 9 after 31 is 36.

31 + A = 36 ⇒ A = 5.

∴ The correct answer is 5.

Alternate Method

Given number: 6428A83

Property: A number is divisible by 9 only if the sum of its digits is divisible by 9.

⇒ Sum = 6 + 4 + 2 + 8 + A + 8 + 3

⇒ Sum = 31 + A

⇒ For the number to be divisible by 9, (31 + A) ÷ 9 must leave a remainder of 0.

⇒ Multiples of 9 are 9, 18, 27, 36, 45, ...

⇒ Since A is a single digit (0 to 9), the only possible value for 31 + A is 36.

⇒ 31 + A = 36

⇒ A = 36 − 31

⇒ A = 5

∴ The correct answer is 5.

Additional Information

Divisibility Rule of 3

Similar to 9, a number is divisible by 3 if the sum of its digits is a multiple of 3.

Divisibility Rule of 11

A number is divisible by 11 if the difference between the sum of digits at odd places and the sum of digits at even places is either 0 or a multiple of 11.

Digital Root Concept

The digital root of a number is the single-digit sum obtained by adding digits repeatedly. For any number divisible by 9, the digital root is always 9.

Shortcut Trick

Ratio of Radii (R : r) = 3 : 1

Ratio of CSA (C₁ : C₂) = 350 : 100 = 3.5 : 1

Ratio of Heights (H : h) = (C₁/R) : (C₂/r) = (3.5/3) : (1/1) = 3.5 : 3

Ratio of Volumes (V₁ : V₂) = (R² × H) : (r² × h) = (3² × 3.5) : (1² × 3) = 31.5 : 3

Required percentage = (3 ÷ 31.5) × 100 = (1 ÷ 10.5) × 100 ≈ 9.52%

∴ The correct answer is 9.52.

Alternate Method

Given:

⇒ Radius ratio of Larger (R) to Smaller (r) cylinder = 3 : 1

⇒ CSA of Larger cylinder (C_L) = 350% of CSA of Smaller cylinder (C_S)

Formula Used:

⇒ Curved Surface Area (CSA) = 2πrh

⇒ Volume (V) = πr²h

Calculations:

⇒ Let R = 3x and r = x

⇒ C_L = 3.5 × C_S

⇒ 2πRH = 3.5 × 2πrh

⇒ 3x × H = 3.5 × x × h

⇒ H/h = 3.5/3 = 7/6

⇒ Volume of Larger Cylinder (V_L) = πR²H = π(3x)²(7/6)h = π(9x²)(7/6)h = 10.5πx²h

⇒ Volume of Smaller Cylinder (V_S) = πr²h = πx²h

⇒ Percentage = (V_S / V_L) × 100

⇒ Percentage = (πx²h / 10.5πx²h) × 100 = 100 / 10.5

⇒ Percentage = 1000 / 105 ≈ 9.52%

∴ The correct answer is 9.52.

Additional Information

Cylinder Properties

Total Surface Area (TSA) of a cylinder = 2πr(h + r). It includes both the curved surface and the two circular bases.

Volume and CSA Relationship

The volume of a cylinder can also be expressed as Volume = (CSA × r) ÷ 2. This is useful when CSA and radius are known.

Ratio Scaling

If radius is scaled by 'k' and height by 'm', the CSA scales by (k × m) and the volume scales by (k² × m).

Shortcut Trick

Assume the third number is 100.

Then the first number becomes 130 and the second number becomes 160.

The required ratio is 130 : 160.

Simplified ratio ⇒ 13 : 16.

∴ The correct answer is 13  ∶  16.

Alternate Method

Given:

Increase in first number = 30%

Increase in second number = 60%

Let the third number be x.

⇒ First number = x + 30% of x = 1.3x

⇒ Second number = x + 60% of x = 1.6x

⇒ Ratio = First number / Second number

⇒ Ratio = 1.3x / 1.6x

⇒ Ratio = 13 / 16

∴ The correct answer is 13  ∶  16.

Additional Information

Percentage Increase Formula

New Value = Original Value × (1 + Rate/100). In this case, the third number acts as the original base.

Ratio Simplification

To simplify a ratio a : b, divide both terms by their Highest Common Factor (HCF) to get the simplest form.

Comparing Percentages

When multiple values are compared to a common reference, that reference is often assumed as 100 for easier calculation.

Given:

Tea worth Rs. 27 per kg and Rs. 31 per kg

Selling price of the mixture to gain 25% = Rs. 36 per kg

Concept:

We use the concept of alligation to find the ratio in which two varieties must be mixed.

Formula Used:

Alligation rule:

If two ingredients are mixed, then the ratio of the quantities of the two ingredients is given by:

⇒ (C₁ - C_m) : (C_m - C₂)

where C₁ and C₂ are the costs of the two ingredients, and C_m is the mean cost of the mixture.

Calculation:

Let the cost price of the mixture be C_m.

Given selling price of mixture = Rs. 36 per kg

Gain = 25%

⇒ Cost price of mixture (C_m) = Selling price / (1 + Gain)

⇒ C_m = 36 / (1 + 0.25)

⇒ C_m = 36 / 1.25

⇒ C_m = 28.8

Using the alligation rule:

⇒ (C₁ - C_m) : (C_m - C₂)

⇒ (31 - 28.8) : (28.8 - 27)

⇒ 2.2 : 1.8

⇒ 11 : 9

∴ The correct answer is option 4 (11 ∶ 9).

Calculation:

Export of Unit Li-ion = 20000 × 30% 

⇒ 6000

Export of Unit Sodium = 20000 × 2%

⇒ 400

Export of Unit M-Air = 20000 × 20%

⇒ 4000

Export of Unit Lead Acid = 20000 × 35%

⇒ 7000

Export of Unit S - Capacitor = 20000 × 13%

⇒ 2600

Revenue of Li-ion = 2500000 × 35%

⇒ 875000

Revenue of Sodium = 2500000 × 5%

⇒ 125000

Revenue of M-Air = 2500000 × 20%

⇒ 500000

Revenue of Lead Acid = 2500000 × 25%

⇒ 625000

Revenue of S - Capacitor = 2500000 × 15%

⇒ 375000

According to the question,

Revenue of battery per unit export 

Li-ion = 875000/6000 = 145.83

Sodium = 125000/400 = 312.5

M-Air = 500000/4000 = 125

Lead Acid = 625000/7000 = 89.28

S - Capacitor = 375000/2600 = 144.23

∴ The highest revenue per unit of export is Sodium.

Given:

10% of the voters did not cast their votes and 5% of the votes polled were found invalid. The successful candidate got 52.5% of the valid votes and won by a majority of 1710 votes.

Concept Used:

Calculate the total number of voters enrolled based on the given percentages and majority votes.

Calculation:

Let the total number of voters enrolled be x .

10% of the voters did not vote:

⇒ Voters who did not vote = 0.10x

⇒ Voters who voted = x - 0.10x = 0.90x

5% of the votes polled were invalid:

⇒ Invalid votes = 0.05 × 0.90x = 0.045x

⇒ Valid votes = 0.90x - 0.045x = 0.855x

The successful candidate got 52.5% of the valid votes:

⇒ Votes received by successful candidate = 0.525 × 0.855x = 0.448875x

Let the votes received by the other candidate be y .

⇒ Total valid votes = Votes received by successful candidate + Votes received by the other candidate

⇒ 0.855x = 0.448875x + y

⇒ y = 0.855x - 0.448875x = 0.406125x

The majority is 1710 votes:

⇒ 0.448875x - 0.406125x = 1710

⇒ 0.04275x = 1710

⇒ x = $\frac{1710}{0.04275}$

⇒ x = 40000

∴ The number of voters enrolled on the voters list was 40000.

Given:

In a 2 km linear race, if P completes the race in 200 second and Q in 220 seconds

Formula Used:

Speed = Distance/Time

Calculation:

Distance = 2000m or 2 km

Speed of P = 2000/200 

⇒ 10 m/sec

Speed of Q = 2000/220

⇒ 100/11 m/sec

Distance cover by P in 10 Sec

D = 10/11 × 200 = $181 \frac{9}{11}$ meters

∴ The correct answer is $181 \frac{9}{11}$ m.

Given:

The marked price (MP) of an item is 1.4 times the cost price (CP).

To earn a 23.2% profit, we need to find the discount percentage.

Concept:

Profit percentage (Profit%) = (Selling Price (SP) - Cost Price (CP)) / CP × 100

Discount percentage (Discount%) = (Marked Price (MP) - Selling Price (SP)) / Marked Price (MP) × 100

Calculation:

Let the Cost Price (CP) be 100 units.

⇒ Marked Price (MP) = 1.4 × CP

⇒ MP = 1.4 × 100 = 140 units

Profit% is 23.2%:

⇒ Profit = (SP - CP) / CP × 100

⇒ 23.2 = (SP - 100) / 100 × 100

⇒ 23.2 = SP - 100

⇒ SP = 123.2 units

Now, we calculate the discount percentage:

⇒ Discount% = (MP - SP) / MP × 100

⇒ Discount% = (140 - 123.2) / 140 × 100

⇒ Discount% = 16.8 / 140 × 100

⇒ Discount% = 0.12 × 100

⇒ Discount% = 12%

∴ The correct answer is option 4.

Shortcut Trick

Let initial Income be 100, so Savings = 45 and Expenditure = 55.

New Income = 100 + 200 = 300.

New Savings = 5 × 45 = 225.

New Expenditure = 300 − 225 = 75.

% Increase in Expenditure = (75 − 55) / 55 × 100 = 20 / 55 × 100 ≈ 36.4%.

∴ The correct answer is Increased, 36.4%.

Alternate Method

Given:

Initial Savings = 45% of Income

Income increase = 200%

Final Savings = 5 × Initial Savings

Formula Used:

Income = Expenditure + Savings

Percentage Change = (Final − Initial) / Initial × 100

Calculations:

⇒ Let Initial Income = 100

⇒ Initial Savings (S₁) = 45% of 100 = 45

⇒ Initial Expenditure (E₁) = 100 − 45 = 55

⇒ New Income (I₂) = 100 + (200% of 100) = 100 + 200 = 300

⇒ New Savings (S₂) = 5 × 45 = 225

⇒ New Expenditure (E₂) = 300 − 225 = 75

⇒ Increase in Expenditure = 75 − 55 = 20

⇒ Percentage Increase = (20 / 55) × 100

⇒ Percentage Increase = 400 / 11 ≈ 36.36% ≈ 36.4%

∴ The correct answer is Increased, 36.4%.

Additional Information

Income-Expenditure Relationship

The fundamental relation is Income = Expenditure + Savings. Any change in one variable must be balanced by the others.

Percentage Increase vs "Increase by X times"

An increase of 200% means the new value is 300% of the original (Multiplier = 3). "Increases by 5 times" can sometimes be interpreted as the new value being 5 times the old one or adding 5 times the old value to itself.

Successive Percentage Change

If a value changes by a% then by b%, the net change is [a + b + (ab/100)]%, though in Income-Expenditure problems, simple linear addition of components is used.

Shortcut Trick

When two circles with radii R and r touch each other externally, the length of their direct common tangent (LM) is given by the formula: LM = √(4 × R × r) Substituting the given values: 12 = √(4 × 18 × r) ⇒ 12 = √(72 × r) Squaring both sides: 144 = 72 × r ⇒ r = 2 cm.

∴ The correct answer is 2 cm.

Alternate Method

Given: ⇒ Radius of the bigger circle (R) = 18 cm ⇒ Length of the common tangent (LM) = 12 cm ⇒ The two circles touch each other externally.

Formula Used: For two circles touching each other externally, the distance between their centres is d = R + r. The length of their direct common tangent (LM) is: LM = √(d2 − (R − r)2)

Calculations: Substituting d = R + r into the tangent formula: ⇒ LM = √((R + r)2 − (R − r)2) Since (a + b)2 − (a − b)2 = 4ab, the expression simplifies to: ⇒ LM = √(4 × R × r) Now, substitute the known values LM = 12 cm and R = 18 cm: ⇒ 12 = √(4 × 18 × r) ⇒ 12 = √(72 × r) Squaring both sides of the equation to eliminate the square root: ⇒ 122 = 72 × r ⇒ 144 = 72 × r Solving for r (radius of the smaller circle): ⇒ r = 144 ÷ 72 ⇒ r = 2 cm

∴ The correct answer is 2 cm.

Additional Information

Direct Common Tangent (DCT) The length of the direct common tangent for two circles with radii R and r separated by center distance d is given by √(d2 − (R − r)2).

Transverse Common Tangent (TCT) The length of the transverse common tangent is given by √(d2 − (R + r)2), which only exists when the circles do not overlap (d > R + r).

Circles Touching Externally When two circles touch externally, d = R + r. In this configuration, there are exactly three common tangents: two direct common tangents of equal length √(4Rr), and one transverse common tangent of length zero at the point of contact.

Given:

Chords AB and CD intersect at point L.

AL = 9 cm, LB = 7 cm, LD = 3 cm

Concept:

When two chords intersect inside a circle, the products of the lengths of the segments of each chord are equal.

Formula Used:

If two chords AB and CD intersect at L, then:

AL × LB = CL × LD

Calculation:

We have,

⇒ AL = 9 cm, LB = 7 cm, LD = 3 cm

⇒ AL × LB = CL × LD

⇒ 9 × 7 = CL × 3

⇒ 63 = 3 × CL

⇒ CL = 63 ÷ 3

⇒ CL = 21 cm

∴ The correct answer is option 2.

Given:

Principal (P) = Rs. 7,200

Amount (A) = Rs. 8,928

Rate of Interest (R) = 8% per annum

Concept:

Simple Interest (SI) is calculated using the formula:

SI = P × R × T / 100

Here, we need to find the time (T) in years.

Formula Used:

SI = A - P

SI = P × R × T / 100

By rearranging the formula to find T:

T = (SI × 100) / (P × R)

Calculation:

We have,

⇒ SI = A - P

⇒ SI = 8,928 - 7,200

⇒ SI = 1,728

Now, using the formula for T:

⇒ T = (SI × 100) / (P × R)

⇒ T = (1,728 × 100) / (7,200 × 8)

⇒ T = 172,800 / 57,600

⇒ T = 3

∴ The correct answer is option 2, i.e., 3 years.

Given:

The hypotenuse of a right triangle is 6 m more than twice the shortest side. The third side is 2 m less than the hypotenuse.

Concept:

In a right triangle, the relationship between the sides is given by the Pythagorean theorem: a² + b² = c², where c is the hypotenuse.

Formula Used:

Pythagorean theorem: a² + b² = c²

Area of the triangle: (1/2) × base × height

Calculation:

Let the shortest side be x m.

The hypotenuse = 2x + 6 m

The third side = (2x + 6) - 2 = 2x + 4 m

Using the Pythagorean theorem:

⇒ x² + (2x + 4)² = (2x + 6)²

⇒ x² + (4x² + 16x + 16) = (4x² + 24x + 36)

⇒ x² + 4x² + 16x + 16 = 4x² + 24x + 36

⇒ 5x² + 16x + 16 = 4x² + 24x + 36

⇒ x² - 8x - 20 = 0

Solving the quadratic equation x² - 8x - 20 = 0:

⇒ x = [8 ± sqrt((8)² - 4 × 1 × (-20))]/2 × 1

⇒ x = [8 ± sqrt(64 + 80)]/2

⇒ x = [8 ± sqrt(144)]/2

⇒ x = [8 ± 12]/2

⇒ x = 10 m (taking the positive value)

Hence, the shortest side is 10 m.

The hypotenuse = 2x + 6 = 2 × 10 + 6 = 26 m

The third side = 2x + 4 = 2 × 10 + 4 = 24 m

Area of the triangle:

⇒ (1/2) × base × height

⇒ (1/2) × 10 × 24

⇒ 120 m²

∴ The area of the triangle is 120 m².

Given:

The angles of the triangle are in the ratio 2 ∶ 4 ∶ 6 and its circumradius is 12 cm.

Concept:

For a triangle with circumradius R and angles A, B, C , the sides opposite to these angles a, b, c can be found using the formula:

Formula Used:

a = 2R sin A

b = 2R sin B

c = 2R sin C

Calculation:

First, find the angles of the triangle:

⇒ Let the angles be 2x, 4x, 6x

⇒ 2x + 4x + 6x = 180° 

⇒ 12x = 180° 

⇒ x = 15° 

Thus, the angles are:

⇒ A = 2x = 30° 

⇒ B = 4x = 60° 

⇒ C = 6x = 90° 

Now, use the circumradius R = 12 cm to find the sides:

⇒ a = 2 × 12 × $\sin 30$° 

⇒ a = 24 × 1/2

⇒ a = 12 cm

⇒ b = 2 × 12 × sin 60° 

⇒ b = 24 × √3/2

⇒ b = 12√3 cm

⇒ c = 2 × 12 × sin 90° 

⇒ c = 24 × 1

⇒ c = 24 cm

∴ The lengths of the sides of the triangle are 12 cm, 12√3 cm, and 24 cm.

Given:

Illiterate female count in state C = 4,40,000

Illiterate ratio (M : F) in state C = 3 : 2

Concept:

Use the given ratio to find the total number of illiterate people, then use the literacy percentage to find the total population.

Formula Used:

Total illiterate population = Illiterate male + Illiterate female

Total population = Total illiterate population / (1 - Literacy percentage)

Calculation:

We have, illiterate female count = 4,40,000

Illiterate ratio (M : F) = 3 : 2

⇒ Let the number of illiterate males be 3x and females be 2x

⇒ 2x = 4,40,000

⇒ x = 4,40,000 / 2

⇒ x = 2,20,000

⇒ Number of illiterate males = 3x = 3 × 2,20,000

⇒ Number of illiterate males = 6,60,000

⇒ Total illiterate population = 6,60,000 + 4,40,000

⇒ Total illiterate population = 11,00,000

Literacy percentage in state C = 78%

⇒ Illiteracy percentage = 100% - 78% = 22%

⇒ Total population = Total illiterate population / Illiteracy percentage

⇒ Total population = 11,00,000 / 0.22

⇒ Total population = 50,00,000

∴ The total population in state C is 50,00,000.

Shortcut Trick

For a cuboid, the Total Surface Area (TSA) is equal to twice the sum of the areas of its three adjacent faces.

Adjacent face areas (x, y, z) = 5 cm², 15 cm², and 27 cm².

Total Surface Area = 2 × (x + y + z)

Total Surface Area = 2 × (5 + 15 + 27) = 2 × 47 = 94 cm².

∴ The correct answer is 94 cm².

Alternate Method

Given:

Area of face 1 (length × width) = 5 cm²

Area of face 2 (width × height) = 15 cm²

Area of face 3 (length × height) = 27 cm²

Formula Used:

Total Surface Area of a cuboid = 2(lw + wh + lh)

Calculations:

⇒ Let the three adjacent face areas be A₁, A₂, and A₃.

⇒ A₁ = 5 cm², A₂ = 15 cm², A₃ = 27 cm²

⇒ Total Surface Area = 2 × (A₁ + A₂ + A₃)

⇒ Total Surface Area = 2 × (5 + 15 + 27)

⇒ Total Surface Area = 2 × 47

⇒ Total Surface Area = 94 cm²

∴ The correct answer is 94 cm².

Additional Information

Volume from Face Areas

The volume (V) of a cuboid with adjacent face areas x, y, and z is given by V = √(x × y × z).

Diagonal of a Cuboid

The length of the longest diagonal is calculated using the formula D = √(l² + w² + h²).

Lateral Surface Area

The Lateral Surface Area (LSA), which excludes the top and bottom faces, is given by 2h(l + w).

Shortcut Trick

Divide the first term by sin α to convert it into cot α.

(P cot α − Q) ÷ (P cot α + Q) = (P × (P/Q) − Q) ÷ (P × (P/Q) + Q) = (P² − Q²) ÷ (P² + Q²).

The total expression becomes [(P² − Q²) ÷ (P² + Q²)] − [(P² − Q²) ÷ (P² + Q²)] + 3.

The identical fraction terms cancel each other out, leaving only the constant.

∴ The correct answer is 3.

Alternate Method

Given: cot α = P/Q

Formula Used: cot α = cos α ÷ sin α

⇒ Let the expression be E = [(P cos α − Q sin α) ÷ (P cos α + Q sin α)] − [(P² − Q²) ÷ (P² + Q²)] + 3

⇒ Divide the numerator and denominator of the first term by sin α:

⇒ Term 1 = [P(cos α ÷ sin α) − Q(sin α ÷ sin α)] ÷ [P(cos α ÷ sin α) + Q(sin α ÷ sin α)]

⇒ Term 1 = (P cot α − Q) ÷ (P cot α + Q)

⇒ Substitute cot α = P/Q into Term 1:

⇒ Term 1 = [P × (P/Q) − Q] ÷ [P × (P/Q) + Q]

⇒ Term 1 = [(P² − Q²) ÷ Q] ÷ [(P² + Q²) ÷ Q]

⇒ Term 1 = (P² − Q²) ÷ (P² + Q²)

⇒ Substitute Term 1 back into the original expression E:

⇒ E = [(P² − Q²) ÷ (P² + Q²)] − [(P² − Q²) ÷ (P² + Q²)] + 3

⇒ E = 0 + 3 = 3

∴ The correct answer is 3.

Additional Information

Trigonometric Ratio Identities

Fundamental identities include tan α = sin α ÷ cos α and cot α = cos α ÷ sin α = 1 ÷ tan α.

Pythagorean Identity

For any angle α, sin²α + cos²α = 1, which implies cos α = P ÷ √(P²+Q²) and sin α = Q ÷ √(P²+Q²) based on the right triangle.

Componendo and Dividendo Rule

If a ÷ b = c ÷ d, then (a + b) ÷ (a − b) = (c + d) ÷ (c − d). This is often used to simplify ratio-based trigonometric equations.

Shortcut Trick

Sum of Length (L) and Breadth (B) = Perimeter ÷ 2 = 110 ÷ 2 = 55 m.

Difference between Length and Breadth (L − B) = 15 m.

To find the larger value (Length), use the formula: (Sum + Difference) ÷ 2.

⇒ Length = (55 + 15) ÷ 2 = 70 ÷ 2 = 35 m.

∴ The correct answer is 35 m.

Alternate Method

Given:

Perimeter of the rectangular park = 110 m

Length (L) exceeds Breadth (B) by 15 m → L = B + 15

Formula used:

Perimeter of a rectangle = 2 × (Length + Breadth)

Calculations:

⇒ 2 × (L + B) = 110

⇒ L + B = 110 ÷ 2

⇒ L + B = 55

⇒ Substituting L = B + 15 in the equation:

⇒ (B + 15) + B = 55

⇒ 2B + 15 = 55

⇒ 2B = 55 − 15

⇒ 2B = 40

⇒ B = 20 m

⇒ Length (L) = B + 15 = 20 + 15 = 35 m

∴ The correct answer is 35 m.

Additional Information

Area of Rectangle

The total space occupied by the rectangle is given by Area = Length × Breadth. For this park, Area = 35 × 20 = 700 m².

Diagonal of Rectangle

The distance between opposite corners is calculated using the Pythagoras theorem: Diagonal = √(L² + B²).

Semi-Perimeter

The sum of one length and one breadth (L + B) is known as the semi-perimeter, which is exactly half of the total perimeter.

The correct answer is a secular state

Key Points

• The Preamble of the Constitution of India describes the country as a sovereign, socialist, secular, and democratic republic.
• The term secular indicates that the state has no official religion and treats all religions equally.
• This reflects the commitment of the Indian Constitution to maintain religious neutrality and ensure freedom of religion for all citizens.
• The Preamble serves as an introduction to the Constitution and sets forth the guiding principles and philosophy of the document.

Additional Information

• The Constitution of India was adopted by the Constituent Assembly on 26^th November 1949 and came into effect on 26^th January 1950.
• It establishes the framework for the political principles, structures, procedures, powers, and duties of government institutions, and sets out fundamental rights, directive principles, and the duties of citizens.
• The Preamble reflects the aspirations and values of the people of India, including justice, liberty, equality, and fraternity.
• The inclusion of the word "secular" in the Preamble was made through the 42^nd Amendment Act of 1976.
• The Preamble is considered a part of the Constitution and is used to interpret ambiguous areas of the law.

The correct answer is Ministry of Petroleum and Natural Gas

Key Points

• Oil India Limited (OIL) is under the administrative structure of the Ministry of Petroleum and Natural Gas.
• The Ministry of Petroleum and Natural Gas is responsible for the exploration, production, refining, distribution, marketing, import, export, and conservation of petroleum, natural gas, and petroleum products.
• OIL is a government-owned company that plays a crucial role in the energy sector of India, focusing on the exploration, development, and production of crude oil and natural gas.
• The Ministry oversees various public sector undertakings (PSUs) related to petroleum and natural gas, ensuring the energy security of the country.

Additional Information

• The Ministry of Petroleum and Natural Gas was formed in 1947 and has since played a significant role in the development of the petroleum industry in India.
• The Ministry's responsibilities include policy formulation, coordination, and regulation of the petroleum and natural gas industries in India.
• It works towards ensuring the availability of petroleum products at reasonable prices and promotes the conservation of petroleum products.
• The Ministry is also involved in international cooperation and partnership in the energy sector to enhance India's energy security.
• OIL, under the Ministry's guidance, has expanded its operations both domestically and internationally, contributing significantly to India's energy needs.

The correct answer is Supreme Court

Key Points

• The Supreme Court of India emphasized that the country cannot have a parallel judicial system - one for the rich and the other for the poor.
• This statement underscores the importance of equality before the law and the need for a uniform judicial system that serves all citizens equally, regardless of their socio-economic status.
• The Supreme Court is the highest judicial forum and final court of appeal under the Constitution of India, and it has the power of judicial review.
• The Court's decision reflects its role in upholding the Constitution and ensuring justice is accessible to everyone.

Additional Information

• The Supreme Court of India was established on 28^th January 1950, two days after the Constitution of India came into effect.
• It comprises the Chief Justice of India and a maximum of 33 other judges, appointed by the President of India.
• The Supreme Court's primary function is to interpret the Constitution and adjudicate disputes between the central government and state governments or between two or more states.
• The Court also has the authority to hear appeals against the judgments of lower courts and tribunals.
• Through its judgments, the Supreme Court plays a crucial role in the development of constitutional law and the protection of fundamental rights in India.

The correct answer is Uday Shankar

Key Points

• Uday Shankar is known as the Father of Modern Dance in India.
• He was a pioneer in adapting Western theatrical techniques to Indian classical dance forms, creating a new genre of modern Indian dance.
• Uday Shankar's innovative approach combined elements of Indian classical dance, folk traditions, and Western ballet, making dance accessible to a broader audience.
• His contributions significantly influenced the development of contemporary dance in India.

Additional Information

• Uday Shankar was born on 8^th December 1900, in Udaipur, Rajasthan, India.
• He studied at the Royal College of Art in London, where he was introduced to Western art forms.
• In 1930, he established the Uday Shankar India Cultural Centre in Almora, which became a hub for training and innovation in Indian dance and music.
• He was awarded the Padma Vibhushan, India's second-highest civilian award, in 1971 for his contributions to the arts.
• Uday Shankar's legacy continues to inspire dancers and choreographers in India and around the world.

The correct answer is Urbain-Jean-Joseph Le Verrier

Key Points

• Urbain-Jean-Joseph Le Verrier calculated the approximate location of the planet Neptune by studying gravity-induced disturbances in the motion of Uranus.
• Le Verrier's calculations were based on Newton's laws of gravitation, which predicted the presence of another planet affecting Uranus's orbit.
• His work led to the discovery of Neptune on September 23, 1846, by Johann Gottfried Galle and Heinrich d'Arrest at the Berlin Observatory.
• Le Verrier's prediction and the subsequent discovery of Neptune stand as a monumental achievement in the field of astronomy.

Additional Information

• John Couch Adams independently made similar calculations around the same time, but Le Verrier's work led to the actual observational discovery.
• Neptune is the eighth planet from the Sun and is known for its deep blue color caused by the absorption of red light by methane in its atmosphere.
• The discovery of Neptune was a major milestone in the validation of Newtonian mechanics.
• Le Verrier's methods of celestial mechanics continue to influence modern astronomy and space navigation.

The correct answer is Sinho commission

Key Points

• The Supreme Court upheld the 10% reservation for the Economically Weaker Sections (EWS) in November 2022.
• This EWS reservation was granted based on the recommendations from the Sinho Commission.
• The Sinho Commission was specifically constituted to identify and recommend measures for the upliftment of economically weaker sections.

Additional Information

• The reservation for EWS was introduced through the 103^rd Constitutional Amendment Act, 2019.
• The amendment added Articles 15(6) and 16(6) to the Constitution, enabling the state to make special provisions for the advancement of economically weaker sections.
• The EWS quota is in addition to the existing reservations for Scheduled Castes (SC), Scheduled Tribes (ST), and Other Backward Classes (OBC).

The correct answer is Indus

Key Points

• The river Indus is known as 'Singi Khamban' in Tibet.
• 'Singi Khamban' translates to the "Lion's Mouth" in Tibetan language, referring to the river's origin in the Tibetan plateau.
• The Indus River is one of the longest rivers in the world, flowing through China (Tibet), India, and Pakistan.
• It plays a crucial role in the agricultural and economic activities of these regions.

Additional Information

• The Indus River originates in the Tibetan plateau near Lake Mansarovar.
• It flows through the Ladakh region of India and then into Pakistan, where it eventually drains into the Arabian Sea.
• The river is a key water source for the Indus Valley Civilization, one of the world's oldest civilizations.
• The Indus Basin is shared by India and Pakistan, making it a significant geopolitical feature in South Asia.
• The river supports diverse ecosystems and is home to various species of fish and other aquatic life.

The correct answer is 17.64%

Key Points

• India's population growth rate during the period 2001-2011 was 17.64%.
• This growth rate is calculated based on the census data collected in 2001 and 2011, showing the percentage increase in the population over the decade.
• The census is conducted every ten years by the Office of the Registrar General and Census Commissioner under the Ministry of Home Affairs, Government of India.
• Population growth rates are crucial for planning and development policies, as they impact resources, infrastructure, and services.
• The growth rate reflects various factors including birth rates, death rates, and migration patterns during the decade.

Additional Information

• The census data provides comprehensive information on demographic, social, and economic parameters.
• The population growth rate is a key indicator of demographic trends and is used for various analytical purposes including economic forecasting and infrastructure development.
• India's total population as per the 2011 census was approximately 1.21 billion.
• The decadal growth rate witnessed a decline from the previous decade (1991-2001), indicating a slowdown in the population increase.
• Understanding population dynamics is essential for the effective implementation of government schemes and initiatives aimed at improving the quality of life for citizens.

The correct answer is 943

Key Points

• According to the Census of India-2011, the sex ratio of India is 943 females per 1000 males.
• The sex ratio is an important demographic indicator that shows the number of females per 1000 males in a population.
• A higher or balanced sex ratio is indicative of better gender equality in the society.
• Various government policies and programs aim to improve the sex ratio by addressing issues such as female infanticide, gender-based abortions, and discrimination against girls.

Additional Information

• The Census of India is conducted every ten years and is one of the most comprehensive sources of demographic data in the country.
• The 2011 Census was the 15^th National Census of the country since 1871.
• Key parameters measured in the Census include population size, sex ratio, literacy rate, and employment statistics, among others.
• The data collected from the Census helps in the formulation of policies and planning for socio-economic development.