SSC CHSL Tier-1 2024: Official Paper (Held On: 01 Jul, 2024 Shift 1) (Previous Year Paper)

The correct answer is ‘3’ i.e. until the last house.

Key Points

• The phrase 'until the last house' is incorrect in this context.
• The correct phrase should be 'up to the last house.'
• The other segments are grammatically correct.
• 'The couple' correctly refers to two people acting together.
• 'Preferred to walk' correctly indicates their choice of activity.
• 'Of the town' correctly indicates the location in question.

Hence, the correct answer is option 3.

Correct sentence: The couple preferred to walk up to the last house of the town.

Additional Information

• Using 'until' often implies a continuation of action up to a point in time, while 'up to' is more appropriate for physical distances or locations.
• Example: We walked up to the park entrance.

The correct answer is ‘2’ i.e. violent when.

Key Points

• The phrase 'violent when' is incorrect in this context.
• The correct phrase should be 'violently when.'
• This is because 'violently' is the adverb that correctly modifies the verb 'behaving.'
• The other segments are grammatically correct:
• 'Passengers started behaving' correctly sets the subject and verb phrase.
• 'they were asked' correctly indicates the action done to the passengers.
• 'to leave the bus station' correctly completes the action that the passengers were asked to do.

 

Hence, the correct answer is option 2.

Correct sentence: Passengers started behaving violently when they were asked to leave the bus station.

Additional Information

• Adverbs often end in '-ly' and are used to modify verbs, adjectives, or other adverbs, providing more information about how an action is performed.
• Example: She sang beautifully.

The correct answer is ‘4’ i.e. I will be twenty five next Sunday.

Key Points

• The sentence 'I will be twenty five next Sunday' is in the future tense.
• The use of 'will be' indicates an event that is certain to happen in the future.
• The other options are not in the future tense:
• Option 1: 'I could be twenty five next Sunday' uses 'could,' which indicates possibility but not a certain future event.
• Option 2: 'I should be twenty five next Sunday' uses 'should,' which indicates obligation or expectation, not a certain future event.
• Option 3: 'I have been twenty five next Sunday' is grammatically incorrect because it mixes present perfect tense with a future time reference.

 

Hence, the correct answer is option 4.

Additional Information

• Future tense in English can be formed using 'will' followed by the base form of the verb.
• Example: She will arrive tomorrow.

The correct answer is ‘2’ i.e. fed up with.

Key Points

• The phrase 'down with' is incorrect in the given context.
• The correct phrase should be 'fed up with.'
• This is because 'fed up with' accurately conveys the feeling of being tired or annoyed with something.
• The other options do not fit the context:
• Option 1: 'passed out with' indicates fainting or losing consciousness, which does not make sense in the context of complaints.
• Option 3: 'held down with' implies being physically restrained or burdened, which is not appropriate here.
• Option 4: 'looked down with' implies viewing with disapproval or disdain but is not idiomatically correct.

 

Hence, the correct answer is option 2.

Correct sentence: I am fed up with her complaints.

Additional Information

• Idioms like 'fed up with' are used to express specific feelings or situations in a figurative manner.
• Example: She is fed up with the constant noise.

The correct answer is 'eating'.

 

Key Points

• The passage describes Paul having his supper, which means he is consuming food.
• The word "eating" is a commonly used term for consuming food during a meal.
• "Eating" fits well as it accurately conveys the action of having supper.
• Other options ("grazing", "churning", "feeding") do not accurately describe the action of having supper in a typical context.

Therefore, the correct answer is 'Option 4'.

The correct answer is 'asked'.

 

Key Points

• The passage describes Aunt Jenny interacting with Paul by posing questions.
• The word "asked" accurately conveys the action of posing questions to someone.
• "Asked" fits well as it naturally describes the act of inquiring or seeking information.
• Other options ("submitted", "demanded", "allowed") do not appropriately fit the context of posing questions.

Therefore, the correct answer is 'Option 4'.

The correct answer is 'talent'.

 

Key Points

• The passage suggests that Aunt Jenny has a special ability to pose deceitful and meaningful questions to trap Paul.
• The word "talent" denotes a natural aptitude or skill, fitting well with Aunt Jenny's special ability.
• "Talent" fits well as it conveys the idea of a unique skill or ability.
• Other options ("technique", "purpose", "weakness") do not accurately describe a natural ability or skill.

Therefore, the correct answer is 'Option 4'.

The correct answer is 'suspicion'.

 

Key Points

• The passage describes Paul feeling uneasy due to Aunt Jenny's deceitful questions.
• The word "suspicion" reflects a state of doubt or mistrust, aligning with Paul's discomfort.
• "Suspicion" fits well as it accurately conveys Paul's uneasy feeling.
• Other options ("guess", "view", "drop") do not appropriately describe an uneasy or mistrustful feeling.

Therefore, the correct answer is 'Option 4'.

The correct answer is 'searched'.

 

Key Points

• The passage depicts Paul looking at Aunt Jenny's face to find any clues about her intentions.
• The word "searched" accurately describes the action of looking for information or clues.

Here are the options:

• chased - This implies a physical pursuit, which does not fit the context of looking at someone's face.
• pursued - This also suggests following something physically or pursuing a goal, which again doesn't fit the context.
• ruffled - This means disturbed or flustered, which would not make sense in terms of looking at someone's face.
• searched - This means looking carefully in an attempt to find something, which fits the context of examining Aunt Jenny's face for information.

Therefore, the correct answer is 'Option 4'.

The correct answer is: Option 4.

Key Points

• The word "conspicuous" means something that is clearly visible or noticeable; it stands out and attracts attention. (स्पष्ट रूप से दिखाई देने वाला)
• Example: The red umbrella was conspicuous among the sea of black ones.
• "Noticeable" refers to something that is easily seen or noticed; it is prominent and attracts attention. (ध्यान देने योग्य)
• Example: There was a noticeable improvement in his performance.
• Hence, we can infer that "conspicuous" and "noticeable" are synonymous.

Therefore, the correct answer is: Option 4.

Additional Information

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

• Charming (आकर्षक): Pleasant or attractive.
• Example: The charming village was a perfect holiday destination.
• Faint (मंद): Weak or barely perceptible.
• Example: She gave a faint smile before leaving.
• Obscure (अस्पष्ट): Not clearly expressed or easily understood.
• Example: The message was obscure and difficult to interpret.

The correct answer is: Option 3 i.e. In writing.

Key Points

• The idiom "black and white" refers to something that is written down or printed, making it clear and unambiguous. (लिखित में)
• Example: The terms of the agreement were laid out in black and white.
• "In writing" means something that is documented or recorded in text. (लिखित में)
• Example: She made sure to get the contract in writing before starting the project.

Therefore, the correct answer is: Option 3 i.e. In writing.

Additional Information

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

• Doubtful (संदेहपूर्ण): Not certain or confident about something.
• Example: He was doubtful about the success of the new venture.
• In dispute (विवाद में): Subject to disagreement or argument.
• Example: The ownership of the land was in dispute for many years.
• A false invention (झूठी आविष्कार): Something that is fabricated or not true.
• Example: The story about the haunted house was just a false invention.

The correct answer is: Option 3 i.e. refute.

Key Points

• The word "support" means to give assistance to, or to back someone or something. (समर्थन करना)
• Example: She always supports her friends during tough times.
• "Refute" means to prove a statement or theory to be wrong or false; to disprove. (खंडन करना)
• Example: The lawyer refuted the allegations against his client with strong evidence.
• Hence, we can infer that the opposite of 'support' is 'refute'.

Therefore, the correct answer is: Option 3 i.e. refute.

Additional Information

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

• Disclaim (त्याग करना): To refuse to acknowledge or deny any connection with.
• Example: He disclaimed any responsibility for the error.
• Document (दस्तावेज़): To record something in written, photographic, or other form.
• Example: She documented all her travels in a journal.
• Establish (स्थापित करना): To set up on a firm or permanent basis.
• Example: They established a new company to market their product.

The correct answer is: Option 4 i.e. Sold quickly and in large numbers.

Key Points

• The idiom "sold like hot cakes" means something that is sold very quickly and in large quantities. (बहुत तेजी से और बड़ी मात्रा में बेचा गया)
• Example: The new smartphone model sold like hot cakes on the first day of its release.
• "Sold quickly and in large numbers" refers to items being sold at a rapid pace and in significant quantities. (बहुत तेजी से और बड़ी मात्रा में बेचा गया)
• Example: The concert tickets sold quickly and in large numbers, leaving many fans disappointed.

Therefore, the correct answer is: Option 4 i.e. Sold quickly and in large numbers.

Additional Information

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

• Sold illegally (अवैध रूप से बेचा गया): Items being sold in a manner that is against the law.
• Example: The black market goods were sold illegally to avoid taxes.
• Sold innovatively (नवीन तरीके से बेचा गया): Items being sold using new and creative methods.
• Example: The startup sold its products innovatively through social media campaigns.
• Sold with great difficulty (बहुत कठिनाई से बेचा गया): Items being sold with a lot of effort and challenges.
• Example: The outdated technology products were sold with great difficulty in the modern market.

The correct answer is: Option 2.

Key Points

• The word "Encraoch" is incorrectly spelt. The correct spelling is "Encroach". (अतिक्रमण करना)
• Example: The new construction encroaches on the park's land.
• "Encroach" means to intrude on (a person's territory, rights, personal life, etc.). (अतिक्रमण करना)
• Example: The weeds encroach upon the garden every spring.

Therefore, the correct answer is: Option 2.

Additional Information

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

• Illusion (भ्रम): A thing that is or is likely to be wrongly perceived or interpreted by the senses.
• Example: The magician's performance was full of fascinating illusions.
• Delegate (प्रतिनिधि): A person sent or authorized to represent others, in particular, an elected representative sent to a conference.
• Example: Each country sent a delegate to the summit.
• Obtain (प्राप्त करना): To get, acquire, or secure (something).
• Example: She managed to obtain a visa for her trip.

The correct answer is ‘2’ i.e. exceptional.

Key Points

• The phrase 'leaders of exceptional ability' is the most appropriate because 'exceptional' describes someone who is outstanding or superior in ability.
• This phrase indicates that the leaders have abilities far above the norm.
• The other options do not fit as well in this context:
• Option 1: 'compelling' refers to something that evokes interest, attention, or admiration but does not necessarily relate to ability.
• Option 3: 'powerful' describes someone with great power or influence but does not specifically highlight their ability.
• Option 4: 'almighty' refers to having complete power, often used in a divine context, and is not typically used to describe human ability.

 

Hence, the correct answer is option 2.

Correct sentence: In both countries we have leaders of exceptional ability.

Additional Information

• Choosing the right adjective to describe a noun helps convey the exact quality being emphasized.
• Example: She has an exceptional talent for painting.

The correct answer is ‘1’ i.e. No substitution required.

Key Points

• The phrase 'when he burnt his fingers' is correct and does not require substitution.
• The past tense 'burnt' matches with the past tense 'cried,' maintaining the grammatical consistency of the sentence.
• The other options are incorrect:
• Option 2: 'when he burns his fingers' uses present tense 'burns,' which is inconsistent with the past tense 'cried.'
• Option 3: 'while he burn his fingers' is grammatically incorrect because 'burn' should be 'burns' for the present tense or 'burned/burnt' in the past tense.
• Option 4: 'as he burning his fingers' is grammatically incorrect because it is missing an auxiliary verb and should be 'as he was burning his fingers.'

 

Hence, the correct answer is option 1.

Correct sentence: The little boy cried with pain when he burnt his fingers.

Additional Information

• Maintaining verb tense consistency in a sentence is crucial for clarity and grammatical accuracy.
• Example: She laughed when she heard the joke.

The correct answer is: Option 1.

Key Points

• The word "Glory" means high renown or honor won by notable achievements. (महिमा)
• Example: The athlete basked in the glory of his Olympic victory.
• "Shame" refers to a painful feeling of humiliation or distress caused by the consciousness of wrong or foolish behavior. (शर्म)
• Example: He felt deep shame after being caught cheating on the exam.
• Hence, we can infer that the opposite of 'Glory' is 'Shame'.

Therefore, the correct answer is: Option 1.

Additional Information

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

• Delight (आनंद): Great pleasure.
• Example: The children screamed with delight when they saw the ice cream truck.
• Honour (सम्मान ): High respect; great esteem.
• Example: He received an award in honor of his contributions to the field.
• Gluttony (पेटूपन): Habitual greed or excess in eating.
• Example: His gluttony at the buffet was embarrassing to watch.

The correct answer is ‘2’ i.e. pair.

Key Points

• The word 'pair' is the most appropriate option because it correctly denotes two of something, in this case, apples.
• The phrase 'a pair of apples' indicates that you ate two apples for dinner.
• The other options are incorrect:
• Option 1: 'pare' means to trim off the outer skin of something and does not make sense in this context.
• Option 3: 'pier' refers to a structure projecting into the water, often where boats dock, and is unrelated to apples.
• Option 4: 'pear' is a type of fruit and is not the correct word for indicating two apples.

 

Hence, the correct answer is option 2.

Correct sentence: Yesterday, I ate only a pair of apples for my dinner.

Additional Information

• Choosing the correct homophone is important for clarity in writing.
• Example: I bought a new pair of shoes.

The correct answer is: Blissful.

Key Points

• The word "joyless" means lacking joy or happiness; feeling or expressing no joy. (उदासीन)
• Example: She felt joyless after hearing the bad news.
• "Blissful" refers to being extremely happy; full of joy. (आनंदमय)
• Example: The couple had a blissful honeymoon in the Maldives.
• Hence, we can infer that the opposite of 'joyless' is 'blissful'.

Therefore, the correct answer is: Blissful.

Additional Information

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

• Dubious (संदेहपूर्ण): Hesitating or doubting.
• Example: He was dubious about the success of the new project.
• Rapt (मग्न): Completely fascinated by what one is seeing or hearing.
• Example: The audience was rapt during the entire performance.
• Beaming (मुस्कुराते हुए): Smiling broadly; grinning.
• Example: She was beaming with joy after winning the award.

The correct answer is: Option 2.

Key Points

• The word "Trivial" means something that is of little value or importance. (तुच्छ)
• Example: She often gets upset over trivial matters.
• "Essential" refers to something that is absolutely necessary or extremely important. (आवश्यक)
• Example: Water is essential for all forms of life.
• Hence, we can infer that the opposite of 'Trivial' is 'Essential'.

Therefore, the correct answer is: Option 2.

Additional Information

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

• Lavish (शानदार): Rich, elaborate, or luxurious.
• Example: They threw a lavish party for their anniversary.
• Vain (अभिमानी): Having or showing an excessively high opinion of one's appearance, abilities, or worth.
• Example: He is so vain that he checks his reflection in every mirror he passes.
• Liable (उत्तरदायी): Responsible by law; legally answerable.
• Example: The company is liable for any damages caused by their product.

The correct answer is: Option 2.

Key Points

• The word "antique" means something that is old and often valuable because of its age. (प्राचीन)
• Example: She collects antique furniture from the 18^th century.
• "Ancient" refers to something belonging to the very distant past and no longer in existence. (प्राचीन)
• Example: The ancient pyramids of Egypt are a marvel of engineering.
• Hence, we can infer that the synonym of 'antique' is 'ancient'.

Therefore, the correct answer is: Option 2.

Additional Information

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

• Contemporary (समकालीन): Belonging to the same period of time as something else.
• Example: She enjoys contemporary art.
• Obsolete (पुराना): No longer produced or used; out of date.
• Example: Typewriters have become obsolete in the digital age.
• Modern (आधुनिक): Relating to the present or recent times.
• Example: Modern technology has revolutionized the way we communicate.

The correct answer is: Option 2.

Key Points

• The word "guard" means to keep watch over something to protect or control it. (रक्षा करना)
• Example: The soldiers guard the border diligently.
• "Guards" is the simple present tense of "guard" and is used to indicate a habitual action or a general truth. (रक्षा करता है)
• Example: The security guard guards the building every night.

Therefore, the correct answer is: Option 2.

Additional Information

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

• Option 1: is guarding the nest at night (रात को घोंसले की रक्षा कर रही है): This is in the present continuous tense, which indicates an action that is currently ongoing.
• Example: She is guarding the nest at night.
• Option 3: does guard the nest in night (रात में घोंसले की रक्षा करती है): This is an emphatic form of the simple present tense, but "in night" is incorrect; it should be "at night."
• Example: She does guard the nest at night.
• Option 4: guarded the nest at night (रात को घोंसले की रक्षा की): This is in the past tense, indicating an action that happened in the past.
• Example: She guarded the nest at night last year.

The correct answer is: Option 3 i.e. severe.

Key Points

• The word "strong" means having great physical power and ability; it can also describe something intense or forceful. (मजबूत)
• Example: He has a strong grip, which makes him a good wrestler.
• "Severe" refers to something very intense or serious, often used to describe pain or weather conditions. (तीव्र)
• Example: She was rushed to the hospital due to severe chest pain.
• Hence, we can infer that the most appropriate word to replace "strong" in the context of pain is "severe".

Therefore, the correct answer is: Option 3 i.e. severe.

Additional Information

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

• Strict (सख्त): Demanding that rules concerning behavior are obeyed and observed.
• Example: The teacher is very strict about homework deadlines.
• Deep (गहरा): Extending far down from the top or surface.
• Example: The lake is very deep in the middle.
• High (ऊँचा): Of great vertical extent.
• Example: The mountain is very high.

The correct answer is ‘3’ i.e. This is the best book.

Key Points

• The phrase 'This is the best book' is the most appropriate option because 'the best' is the superlative form of 'good,' which is needed here to indicate that this book stands out as the best among all.
• The other options are incorrect:
• Option 1: 'This is good book' has a missing article 'a' before 'good,' which makes it grammatically incorrect.
• Option 2: 'This is very good book' also lacks the article 'a' and doesn't convey the superlative degree needed to indicate this book is outstanding among others.
• Option 4: 'This is very best book' is incorrect because 'very' should not be used directly before a superlative adjective.

 

Hence, the correct answer is option 3.

Correct sentence: This is the best book for children to read.

The correct answer is ‘3’ i.e. to reconcider.

Key Points

• The word 'reconcider' is incorrectly spelled. The correct spelling is 'reconsider.'
• Here are the correct segments:
• Option 1: 'he refused to yield.' — This segment is correct.
• Option 2: 'I begged him' — This segment is correct.
• Option 4: 'the decision but' — This segment is correct.

Hence, the correct answer is option 3.

Correct sentence: I begged him to reconsider the decision but he refused to yield.

Additional Information

• Correct spelling is crucial for effective written communication.
• Example: Please reconsider your decision.

The logic followed here is,

DFG: IKL

MOP: RTU

Let's check each option,

1. PST: KHG

2. WYZ: GIJ

3. FHI: EGH

4. TVW: YAB

 

⇒ Follows the logic.

Hence, the correct answer is "TVW: YAB".

The logic followed here is:

Logic: 1^st number ÷ 6 = 2^nd number.

Now,

For, 96 : 16

⇒ 96 ÷ 6 = 16.

For, 156 : 26

⇒ 156 ÷ 6 = 26.

Similarly, for 228 ∶ ?

⇒ 228 ÷ 6 = 38.

Hence, the correct answer is "Option 2".

The logic followed here is,

Here, we can see that the code for 'N' is 7.

Hence, the correct answer is "7".

The logic followed here is,

Hence, the correct answer is "Option 1".

The logic followed here is:

Logic: (1^st number - 2^nd number) × 4 = 3^rd number.

Now,

For, (10, 5, 20)

⇒ (10 - 5) × 4 = 5 × 4 = 20.

For, (14, 7, 28)

⇒ (14 - 7) × 4 = 7 × 4 = 28.

Now let's check the options:

Option 1: (48, 24, 58)

⇒ (48 - 24) × 4 = 24 × 4 = 96 ≠ 58.

Option 2: (54, 18, 72)

⇒ (54 - 18) × 4 = 36 × 4 = 144 ≠ 72.

Option 3: (22, 11, 44)

⇒ (22 - 11) × 4 = 11 × 4 = 44.

Option 4: (33, 11, 44)

⇒ (33 - 11) × 4 = 22 × 4 = 88 ≠ 44.

Hence, the correct answer is "Option 3".

Opposite surface of the open dice can be found by the below methods: -

• Alternate surfaces are opposite to each other.
• No two opposite surface are touched by side or by corners.

So, by using the above rule we can find the opposite surface of open dice.

Below are the opposite surfaces: -

Here, we can see that the symbol on the opposite side of '≠' is '%'.

Hence, the correct answer is "%".

The correct mirror image of the given figure is:

Hence, the correct answer is "Option 2".

The least possible venn diagram is shown below,

Conclusions: 

(I) No rock is a key → False (Some keys are chains, all chains are locks and no lock is a rock implies that some rock can be key. This is possible but not definite).

(II) At least some keys are locks → True (Some keys are chains, all chains are locks implies that some keys which are chains are also locks).

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

Opposite surface of the open dice can be found by the below methods: -

• Alternate surfaces are opposite to each other.
• No two opposite surface are touched by side or by corners.

So, by using the above rule we can find the opposite surface of open dice.

Below are the opposite surfaces: -

Here, we can see that the letter on the opposite side of 'Y' is 'Z'.

Hence, the correct answer is "Z".

The correct mirror image of the given figure is:

Hence, the correct answer is "Option 3".

Let's check each option,

1. MVC

2. OXC

 

⇒ Different from others.

3. ENU

4. AJQ

Hence, the correct answer is "OXC".

Preparing the family tree using the following symbol,

Given equation: T × X ÷ Y + Z

The family tree can be drawn using the given information,

Here, we can see that T is the father of Z.

Hence, the correct answer is "Father".

Given: If the year is NOT a leap year

Then, 

In non-leap year the number of days = 365 days

In, 365 days → 52 week and 1 odd day,

So, the week starts on any day will same for the next odd day after that week,

Therefore, The first and last day will be same in a non leap year.

Hence, the correct answer is "Option 1".

Given equation: 74 – 52 + (39 ÷ 13) × 16 + (14 ÷ 2) = 106

Let's check each option,

1) 74 and 52

→ 52 – 74 + (39 ÷ 13) × 16 + (14 ÷ 2) = 106

→ 52 – 74 + 3 × 16 + 7 = 106

→ 52 – 74 + 48 + 7 = 106

→ 107 – 74 = 106

→ 33 ≠ 106

→ LHS ≠ RHS

2) 52 and 39

→ 74 – 39 + (52 ÷ 13) × 16 + (14 ÷ 2) = 106

→ 74 – 39 + 4 × 16 + 7 = 106

→ 74 – 39 + 64 + 7 = 106

→ 145 – 39 = 106

→ 106 = 106

→ LHS = RHS ⇒ Satisfies the equation.

3) 14 and 52

→ 74 – 14 + (39 ÷ 13) × 16 + (52 ÷ 2) = 106

→ 74 – 14 + 3 × 16 + 26 = 106

→ 74 – 14 + 48 + 26 = 106

→ 148 - 14 = 106

→ 134 ≠ 106

→ LHS ≠ RHS

4) 14 and 16

→ 74 – 52 + (39 ÷ 13) × 14 + (16 ÷ 2) = 106

→ 74 – 52 + 3 × 14 + 8 = 106

→ 74 – 52 + 48 + 8 = 106

→ 130 – 52 = 106

→ 78 ≠ 106

→ LHS ≠ RHS

Hence, the correct answer is "52 and 39".

Given word: 'VIRTUAL'

After arranged in alphabetical order:

 

Now,

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

Hence, the correct answer is "Option 3".

According to the given information,

Here, we can see that the code for 'strong' is "tk".

Hence, the correct answer is "tk".

Given Equation: 13 T 26 U 13 D 24 B 7 = ?

BODMAS Rule:

Decoding the given information:

 

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

⇒ 13 - 26 ÷ 13 × 24 + 7 = ?

⇒ 13 - 2 × 24 + 7 = ?

⇒ 13 - 48  + 7 = ?

⇒ 20 - 48 = -28.

Hence, the correct option is "Option 3".

The logic followed here is:

Given Sequence: A _ A _ C A B _ B _ A _ _ B C A B A _ C

Now, putting the letters in the blank spaces given in the option one by one:

Option 1) B, A, B, A, C, B, A → A B A A C / A B B B A / A C B B C / A B A A C

Option 2) B, B, A, B, B, C, B → A B A B C / A B A B B / A B C B C / A B A B C

Option 3) B, B, A, C, A, B, B → A B A B C / A B A B C / A A B B C / A B A B C

Option 4) B, B, A, C, B, A, B → A B A B C / A B A B C / A B A B C / A B A B C

Here, 'Option 4' followed a pattern of 'ABABC'.

Hence, the correct answer is "Option 4".

BODMAS Table: 

Given equation: 162 × 9 - 452 + 7 ÷ 9 = ?

Now, if ‘+’ and ‘-‘ and ‘×' and '÷’ are interchanged, then:

⇒ 162 ÷ 9 + 452 - 7 × 9 = ?

⇒ 18 + 452 - 7 × 9 = ?

⇒ 18 + 452 - 63 = ?

⇒ 470 - 63 = 407.

Hence, the correct answer is "Option 2".

In first and second dice,

Logic: If two dice have the same face value in the given image then their clockwise or anticlockwise wise number are known as opposite numbers in dice.

In the first dice and second dice. The number 3 is common.

The left numbers will be opposite each other writing them anticlockwise starting from 3.

 

So, the number opposite to 6 is 3.

Hence, the correct answer is "3".

Let's count the number of triangles,

Hence, the correct answer is "14".

The logic followed here is,

Hence, the correct answer is "28".

The logic followed here is:

LBXF: SYCM

TGFY: AGHF

Similarly,

ZDMK: ?

Hence, the correct answer is "GNER".

The logic followed here is,

Hence, the correct answer is "RBN".

The logic followed here is,

Hence, the correct answer is "74".

Shortcut Trick

Remaining percentage after expenses and rent = 100% − (60% + 20%) = 20%.

Out of this 20%, he donated 80%, so 20% was left: 20% × 20% = 4% of total salary.

4% of Salary = ₹20,000 ⇒ 1% = ₹5,000.

100% Salary = ₹5,00,000.

∴ The correct answer is ₹5,00,000.

Alternate Method

Given:

Household Expenses = 60% | Rent = 20% | Remaining = 100% − 80% = 20%.

Donation = 80% of Remaining | Saving = ₹20,000.

Calculations:

⇒ Let total Salary be S.

⇒ Remaining Salary after expenses = S × (100 − 60 − 20)% = 0.20S.

⇒ Final Saving = Remaining Salary × (100 − 80)% = 0.20S × 0.20.

⇒ 0.04S = 20,000.

⇒ S = 20,000 ÷ 0.04.

⇒ S = 5,00,000.

∴ The correct answer is ₹5,00,000.

Additional Information

Successive Percentage Change

When values change sequentially on the remaining balance, the effective factor is product of individual factors: Final = Initial × (1−r₁/100) × (1−r₂/100).

Base Change Property

Always identify if the percentage is applied to the Total Salary or the Remaining Salary before calculating.

Shortcut Trick

Use the direct formula for two people working together: Time = (X × Y) ÷ (X + Y).

Here X = 10 days and Y = 40 days.

Combined Time = (10 × 40) ÷ (10 + 40) = 400 ÷ 50 = 8 days.

∴ The correct answer is 8 days.

Alternate Method

Given: A = 10 days, B = 40 days.

Formula Used: Total Work = LCM of individual days; Efficiency = Total Work ÷ Days.

⇒ Total Efficiency of (A + B) = 4 + 1 = 5 units/day.

⇒ Time taken together = Total Work ÷ Total Efficiency

⇒ Time taken = 40 ÷ 5 = 8 days.

∴ The correct answer is 8 days.

Additional Information

Work and Efficiency Relation

Efficiency is inversely proportional to the Time taken to complete a work. If the ratio of time is a:b, the ratio of efficiency is b:a.

Pipes and Cisterns

This concept is identical to Time and Work, where an inlet pipe does positive work and a leakage/outlet pipe does negative work.

Work and Wages

Wages are always distributed in the ratio of the Work Done by the individuals, which is usually the ratio of their Efficiencies if they work for the same duration.

Given:

Length of the first chord = 12 cm

Length of the second chord = 20 cm

Radius of the circle = 5√13 cm

Calculation:

OB = OD = 5 √13 cm

AB = 12 cm, CD = 20 cm, AM = MB = 12/2 = 6 cm and CN = ND = 20/2 = 10 cm

In Δ MBO

OB2 = MB2 + MO2

⇒ (5 √13)2 = 62 + OM2

⇒ OM2 = 325 – 36 = 289

⇒ OM = √289 = 17

In Δ NDO

OD2 = ND2 + NO2

⇒ (5 √13)2 = 102 + NO2

⇒ ON2 = 325 – 100 = 225

ON = √225 = 15

As we know,

OM = MN + ON

⇒ 17 = MN + 15

⇒ MN = 17 – 15 = 2 cm

∴ The correct answer is option (4).

Calculation:

Manufacturing capacity of plant A = 420 + 140 = 560

Manufacturing capacity of plant B = 350 + 150 = 500

Manufacturing capacity of plant C = 360 + 120 = 480

Manufacturing capacity of plant D = 440 + 80 = 520

Manufacturing capacity of plant E = 440 + 110 = 550

So,

Plant A has the highest manufacturing capacity.

In Plant A:

Local Quality = 420

Export Quality = 140

Thus, 

Local quality : Export quality

⇒ 420 : 140 = 3 : 1

∴ The correct answer is option (1).

Given:

Surface area of a cube = 486 cm²

Formula Used:

Surface area of a cube = 6a²

Volume of a cube = a³

Calculation:

Surface area of a cube = 6a²

⇒ 486 = 6a²

⇒ a² = 486 / 6

⇒ a² = 81

⇒ a = √81

⇒ a = 9 cm

Volume of the cube = a³

⇒ Volume = 9³

⇒ Volume = 729 cm³

The volume of the cube is 729 cm³.

Given:

Perimeter of ∆ABC = 24 cm

Perimeter of ∆DEF = 9 cm

DE = 3 cm

Formula Used:

Ratio of areas of similar triangles = (Ratio of perimeters)²

Calculation:

Ratio of perimeters = 24 / 9

Ratio of perimeters = 8 / 3

Ratio of areas = (8 / 3)²

Ratio of areas = 64 / 9

The ratio between the area of ∆ABC and that of ∆DEF is 64 : 9.

Calculation:

Option 1: Equal chords are equidistant from the centre of the circle but not always subtend equal angle at centre of the circle.

This statement is incorrect as equal chords subtend equal angles at the centre of the circle.

Option 2: If two circles touch each other, the point of contact lies on the line joining the two centres.

This statement is correct as the point of contact must lie on the line joining the centres of two touching circles.

Option 3: Angles subtended by the arc in the same segment of the circle are in ratio of 2:1.

This statement is incorrect as angles subtended by the same arc are equal.

Option 4: The sum of the angles of a cyclic quadrilateral is always 180º.

This statement is incorrect as the sum of the angles of a cyclic quadrilateral is always 360º.

The correct statement is Option 2.

Given:

5-digit number: 627x5

Concept used:

Divisibility rule for 9: A number is divisible by 9 if the sum of its digits is divisible by 9.

Calculation:

Sum of digits of 627x5 = 6 + 2 + 7 + x + 5

Sum of digits = 20 + x

For 627x5 to be divisible by 9: (20 + x) must be divisible by 9.

from the option:

x = 7, 

Sum = 20 + x = 20 + 7 = 27, it is divisible by 9.

So, the least value of x = 7

Hence, the correct answer is option 3.

Given:

Ratio of diameters of two spheres = 1 : 4

Number of identical spheres made from the larger sphere = 125

Number of identical spheres made from the smaller sphere = 27

Ratio of the volume of each of the 125 identical spheres to the volume of each of the 27 identical spheres = 1 : m

Formula Used:

Volume of a sphere = $\frac{4}{3}\pi r^3$

Volume ratio of spheres = $\left(\frac{d_1}{d_2}\right)^3$

Calculation:

Let the diameter of the smaller sphere be d. Then the diameter of the larger sphere is 4d.

Let the radius of the smaller sphere be r. Then the radius of the larger sphere is 4r.

Volume of the smaller sphere = $\frac{4}{3}\pi r^3$

Volume of the larger sphere = $\frac{4}{3}\pi (4r)^3$

⇒ Volume of the larger sphere = $\frac{4}{3}\pi (64r^3)$

⇒ Volume of the larger sphere = $\frac{256}{3}\pi r^3$

Volume of each of the 125 identical spheres = $\frac{\frac{256}{3}\pi r^3}{125}$

⇒ Volume of each of the 125 identical spheres =$\frac{256\pi r^3}{375}$

Volume of each of the 27 identical spheres = $\frac{\frac{4}{3}\pi r^3}{27}$

⇒ Volume of each of the 27 identical spheres = $\frac{4\pi r^3}{81}$

Ratio of the volume of each of the 125 identical spheres to the volume of each of the 27 identical spheres = $\frac{\frac{256\pi r^3}{375}}{\frac{4\pi r^3}{81}}$

⇒ Ratio = $\frac{256\pi r^3}{375} \times \frac{81}{4\pi r^3}$

⇒ Ratio = $\frac{256 \times 81}{375 \times 4}$

⇒ Ratio = $\frac{20736}{1500}$

⇒ Ratio = 1728/125

⇒ Ratio = 1 : m

⇒ m = $\frac{125}{1728}$

The correct answer is Option 3).

Given:

First part distance = 60 km

First part speed = 40 km/h

Second part distance = 90 km

Second part speed = 45 km/h

Formula Used:

Average speed = Total distance / Total time

Calculation:

Time taken for the first part = Distance / Speed = 60 / 40

Time taken for the first part = 1.5 hours

Time taken for the second part = Distance / Speed = 90 / 45

Time taken for the second part = 2 hours

Total distance = 60 km + 90 km

Total distance = 150 km

Total time = 1.5 hours + 2 hours

Total time = 3.5 hours

Average speed = Total distance / Total time

Average speed = 150 km / 3.5 hours

Average speed = $\frac{150}{3.5}$

Average speed = $\frac{1500}{35}$

Average speed = 42 $\frac{6}{7}$ km/h

The overall average speed of the motorcycle is 42 $\frac{6}{7}$ km/h.

Given:

Simplify the following expression: 3 + 28 ÷ 35 × 15 + 4 - 3 × 4

Formula Used:

Order of Operations (PEMDAS/BODMAS): Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

Calculation:

Start with the expression: 3 + 28 ÷ 35 × 15 + 4 - 3 × 4

Step 1: Division and Multiplication from left to right.

⇒ 3 + (28 ÷ 35) × 15 + 4 - 3 × 4

⇒ 3 + (0.8) × 15 + 4 - 3 × 4

⇒ 3 + 12 + 4 - 12

Step 2: Addition and Subtraction from left to right.

⇒ (3 + 12) + 4 - 12

⇒ 15 + 4 - 12

⇒ 19 - 12

⇒ 7

The simplified value of the given expression is 7.

Given:

Total number of students = 5000

Total number of girls = 1550

Percentage of girls enrolled in Craft = 22%

Calculations:

Number of girls enrolled in Craft = 22% of 1550

⇒ Number of girls enrolled in Craft = 0.22 × 1550

⇒ Number of girls enrolled in Craft = 341

Percentage of the total number of students in the school:

⇒ Percentage = (Number of girls enrolled in Craft / Total number of students) × 100

⇒ Percentage = (341 / 5000) × 100

⇒ Percentage = 6.82%

∴ The number of girls enrolled in Craft forms 6.82% of the total number of students in the school.

Given:

In right-angled triangle ABC, ∠B = 90º and angle A and angle C are acute angles.

cosecA = 2√2

Formula Used:

sinA . cosC + cosA . sinC = sin(A + C)

In a right-angled triangle, A + C = 90º

sin(A + C) = sin(90º) = 1

Calculation:

Given cosecA = 2√2

⇒ sinA = 1 / (2√2)

Since A + C = 90º, C = 90º - A

⇒ cosC = cos(90º - A) = sinA

⇒ sinC = sin(90º - A) = cosA

Now, sinA . cosC + cosA . sinC = sinA . sinA + cosA . cosA

⇒ (1 / (2√2)) . (1 / (2√2)) + cosA . cosA

⇒ (1 / (8)) + cosA . cosA

Since sin²A + cos²A = 1

⇒ cos²A = 1 - sin²A

⇒ cos²A = 1 - (1 / (8))

⇒ cos²A = 7 / 8

⇒ sinA . cosC + cosA . sinC = (1 / 8) + (7 / 8)

⇒ 1

The value of sinA . cosC + cosA . sinC is 1.

Given:

Equation of line p: x + y = 5

Equation of line q: x - y = 3

Formula Used:

To find the coordinates of the intersection point, solve the system of equations:

1. x + y = 5
2. x - y = 3

Calculation:

Adding equations 1 and 2:

x + y + x - y = 5 + 3

⇒ 2x = 8

⇒ x = 8 / 2

⇒ x = 4

Substituting x = 4 into equation 1:

4 + y = 5

⇒ y = 5 - 4

⇒ y = 1

Coordinates of the point common to both lines:

(4, 1)

Given:

PQ and PR are the two tangents to a circle with center O.

∠QOR = 150º.

Formula Used:

The angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line segment joining the points of contact at the center.

i.e. ∠QOR + ∠QPR = 180

Calculation:

∠QOR + ∠QPR = 180

⇒ 150° + ∠QPR = 180

⇒ ∠QPR = 180 - 150

⇒ ∠QPR = 30º

The correct answer is option 4.

Given:

Markup percentage = 40%

Faulty machine measures 15% less

Discount given = 32%

Formula Used:

Profit/Loss percentage = $\left(\frac{\text{Selling Price} - \text{Cost Price}}{\text{Cost Price}}\right) \times 100 \%$

Calculation:

Let Cost Price (CP) = 100

Marked Price (MP) = 100 + 40% of 100

⇒ MP = 100 + 40

⇒ MP = 140

Due to faulty machine, the quantity measured is 15% less, hence the quantity sold is 85%

⇒ Selling Price (SP) before discount = 140

Discount given = 32% of 140

⇒ Discount = 32% × 140

⇒ Discount = 0.32 × 140

⇒ Discount = 44.8

SP after discount = 140 - 44.8

⇒ SP = 95.2

Effective quantity sold = 85% of CP = 85% of 100

⇒ Effective quantity sold = 85

Profit/Loss = SP - Effective CP

⇒ Profit/Loss = 95.2 - 85

⇒ Profit = 10.2

Profit percentage = $\left(\frac{10.2}{85}\right) \times 100 \%$

⇒ Profit percentage = 12%

The profit percentage is 12%.

Given:

The marks obtained by Mohan in different subjects are as follows:

Physics (300 marks): 80%

Maths (300 marks): 60%

Music (100 marks): 70%

Hindi (100 marks): 95%

Botany (200 marks): 80%

Calculations:

The actual marks obtained by Mohan in each subject.

Physics: $80\% \text{ of } 300 = \frac{80}{100} \times 300 = 240 \text{ marks}$

Maths: $60\% \text{ of } 300 = \frac{60}{100} \times 300 = 180 \text{ marks}$

Music: $70\% \text{ of } 100 = \frac{70}{100} \times 100 = 70 \text{ marks}$

Hindi: $95\% \text{ of } 100 = \frac{95}{100} \times 100 = 95 \text{ marks}$

Botany: $80\% \text{ of } 200 = \frac{80}{100} \times 200 = 160 \text{ marks}$

Total marks obtained by Mohan = 240 + 180 + 70 + 95 + 160 = 745 marks

Maximum marks = 300 + 300 + 100 + 100 + 200 = 1000 marks

⇒ Percentage = $\left(\frac{745}{1000}\right) \times 100$

⇒ Percentage = 74.5%

∴ Mohan obtained 74.5% marks.

Mistake Points 

The total maximum marks are different for all subjects. Marks are given in the percentage.

For example, Mohan's marks in Physics = 80 it's mean 80% of maximum marks = 80% of 300 = 240

Same as, Mohan's marks in Music = 70% of maximum marks of music = 70% of 100 = 70

​So,

Total maximum marks = 1000

and

Marks achieved by Mohan = 745

So,

%Marks = (745/1000) * 100 = 74.5%

Shortcut Trick

Value ratio of coins = (₹5 × 3) : (₹10 × 5) : (₹20 × 7) = 15 : 50 : 140

Total value units = 15 + 50 + 140 = 205 units

205 units = ₹1845 ⇒ 1 unit = ₹9

Total worth of smallest coin (₹5) = 15 units = 15 × 9 = ₹135

∴ The correct answer is ₹135.

Alternate Method

Given:

Total amount = ₹1,845

Denominations = ₹5, ₹10 and ₹20

Ratio of number of coins = 3 : 5 : 7

Total Cheque Value = ₹1845

₹5 Ratio: 3x Value: 15x

₹10 Ratio: 5x Value: 50x

₹20 Ratio: 7x Value: 140x

Total Value = 15x + 50x + 140x = 205x 205x = 1845 → x = 9 → ₹5 Value = 15(9) = ₹135

Calculations:

⇒ Let the number of ₹5, ₹10 and ₹20 coins be 3x, 5x and 7x respectively.

⇒ Total worth of ₹5 coins = 5 × 3x = 15x

⇒ Total worth of ₹10 coins = 10 × 5x = 50x

⇒ Total worth of ₹20 coins = 20 × 7x = 140x

⇒ Total amount = 15x + 50x + 140x = 205x

⇒ Given total amount = 1845

⇒ 205x = 1845

⇒ x = 1845 ÷ 205

⇒ x = 9

⇒ The smallest coin is ₹5.

⇒ Total worth of ₹5 coins = 15x = 15 × 9 = ₹135

∴ The correct answer is ₹135.

Additional Information

Coins and Denomination Rule

Total Value of Coins = Value of one coin × Number of coins. Always convert the ratio of the number of coins to the ratio of their total values to equate with the total amount.

Ratio & Proportion

When parts of a whole are given in a ratio (a : b : c), the actual values can be written as ax, bx, and cx where x is a common multiplier. Summing these parts directly connects the ratio to the absolute total quantity.

Shortcut Trick

When Simple Interest equals Principal, the product of Rate and Time must be 100%.

Rate (R) = 2 6/7% = 20/7% per annum.

Time (T) = 100 ÷ R = 100 ÷ (20/7)

⇒ T = 100 × 7 ÷ 20 = 5 × 7 = 35 years.

∴ The correct answer is 35 years.

Alternate Method

Given:

Simple Interest (SI) = Principal (P)

Rate (R) = 2 6/7% = (2 × 7 + 6)/7 % = 20/7 % per annum.

Formula Used:

SI = (P × R × T) ÷ 100

Calculations:

⇒ P = (P × (20/7) × T) ÷ 100

⇒ 1 = (20 × T) ÷ (7 × 100)

⇒ 1 = (20 × T) ÷ 700

⇒ 700 = 20 × T

⇒ T = 700 ÷ 20

⇒ T = 35 years.

∴ The correct answer is 35 years.

Additional Information

Simple Interest Concept

Interest calculated only on the initial principal amount throughout the entire period: SI = (P×R×T)/100.

Total Amount

The final value after adding interest to the principal: A = P + SI = P[1 + (R×T)/100].

Interest as a Fraction

If SI is 1/n of the Principal, then the time period T can be directly calculated as 100 / (n×R).

Shortcut Trick Other = 48%

We have two options: PG + Phd OR PG + M.phil

PG + Phd = 39 + 9 = 48%

PG + M.phil = 39 + 4 = 43%

So, Others = PG + Phd = 48%

∴ The correct answer is Option 2).

Given:

Percentage of students in various categories:

M.Phil = 4%

Ph.D. = 9%

PG = 39%

Other = 48%

Other1 = 34%

Entrepreneur = 14%

Calculation:

Let's check each combination:

1. M.Phil + Ph.D = 4% + 9% = 13%
2. M.Phil + PG = 4% + 39% = 43%
3. M.Phil + Other = 4% + 48% = 52%
4. M.Phil + Other1 = 4% + 34% = 38%
5. M.Phil + Entrepreneur = 4% + 14% = 18%
6. Ph.D + PG = 9% + 39% = 48%
7. Ph.D + Other = 9% + 48% = 57%
8. Ph.D + Other1 = 9% + 34% = 43%
9. Ph.D + Entrepreneur = 9% + 14% = 23%
10. PG + Other = 39% + 48% = 87%
11. PG + Other1 = 39% + 34% = 73%
12. PG + Entrepreneur = 39% + 14% = 53%
13. Other + Other1 = 48% + 34% = 82%
14. Other + Entrepreneur = 48% + 14% = 62%
15. Other1 + Entrepreneur = 34% + 14% = 48%

⇒ The two categories that combined have the same number of students as other are:

Ph.D + PG = Other

∴ The correct answers are Ph.D + PG.

Given:

Initial salary of Arun = S

Decrease in salary = 50%

Subsequent increase in salary = 50%

Formula Used:

Final Salary = Initial Salary × (1 - Decrease%) × (1 + Increase%)

Percentage Loss = $\frac{(Initial Salary - Final Salary)}{Initial Salary} \times 100$

Calculation:

Decrease in salary = 50% of S = 0.5S

New salary after decrease = S - 0.5S = 0.5S

Subsequent increase = 50% of 0.5S = 0.25S

Final salary after increase = 0.5S + 0.25S = 0.75S

Percentage Loss = $\frac{(S - 0.75S)}{S} \times 100$

Percentage Loss = $\frac{0.25S}{S} \times 100$

Percentage Loss = 0.25 × 100

Percentage Loss = 25%

Arun lost 25% of his salary.

Given:

Marked price increase = 40%

Formula Used:

Discount percentage required =$\left( \frac{\text{Increase Percentage}}{100 + \text{Increase Percentage}} \right) \times 100$

Calculation:

Increase Percentage = 40%

Discount percentage required = $\left( \frac{40}{100 + 40} \right) \times 100$

Discount percentage required = $\left( \frac{40}{140} \right) \times 100$

Discount percentage required = $\left( \frac{2}{7} \right) \times 100$

Discount percentage required = 28.57%

Discount percentage required = 28 (4/7)%

The discount percentage required is 28 (4/7)%.

Shortcut Trick

For the largest sphere inside a cube, the diameter of the sphere = side of the cube.

Side = 14 cm ⇒ Radius (r) = 7 cm.

Volume of sphere = (4/3) × π × r³ = (4/3) × (22/7) × 7 × 7 × 7.

Volume = (4 × 22 × 49) / 3 = 4312 / 3 = 1437 (1/3) cm³.

∴ The correct answer is 1437 (1/3) cm³.

Alternate Method

Given: Side of cube (a) = 14 cm.

Formula Used: Volume of Sphere = (4/3)πr³; Radius of inscribed sphere = a/2.

⇒ Side of the cube (a) = 14 cm.

⇒ Diameter of the largest sphere = 14 cm.

⇒ Radius (r) = 14 / 2 = 7 cm.

⇒ Volume = (4/3) × (22/7) × 7³

⇒ Volume = (4/3) × (22/7) × 343

⇒ Volume = (4/3) × 22 × 49

⇒ Volume = 4312 / 3

⇒ Volume = 1437 (1/3) cm³.

∴ The correct answer is 1437 (1/3) cm³.

Additional Information

Cube properties

Total Surface Area = 6a² and Volume = a³, where 'a' is the side length.

Sphere properties

Surface Area = 4πr² and Volume = (4/3)πr³, where 'r' is the radius.

Cube and Sphere Relationship

For a sphere circumscribing a cube, the diameter is equal to the diagonal of the cube (√3 a).

Shortcut Trick

For a constant distance, Speed is inversely proportional to Time.

Time 1 (Walk) = 3 h 45 min = 225 min | Time 2 (Cycle) = 2 h 10 min = 130 min

Time Ratio (Walk : Cycle) = 225 : 130 = 45 : 26

Speed Ratio (Walk : Cycle) = 26 : 45

If 26 units = 5 km/h, then 45 units = (5 ÷ 26) × 45 = 225/26 = 8 17/26 km/h.

∴ The correct answer is 8(17)/(26) km/h.

Alternate Method

Given: Walking speed = 5 km/h, Walking time = 3 h 45 min, Cycling time = 2 h 10 min.

Formula Used: Distance = Speed × Time; Speed = Distance ÷ Time

⇒ Walking time = 3 + 45/60 = 3 + 3/4 = 15/4 hours

⇒ Distance = Speed × Time = 5 × (15/4) = 75/4 km

⇒ Cycling time = 2 + 10/60 = 2 + 1/6 = 13/6 hours

⇒ Cycling Speed = Distance ÷ Cycling time = (75/4) ÷ (13/6)

⇒ Cycling Speed = (75/4) × (6/13) = (75 × 3) / (2 × 13) = 225/26

⇒ Cycling Speed = 8 17/26 km/h

∴ The correct answer is 8(17)/(26) km/h.

Additional Information

Speed-Time Relation

When distance is constant, Speed₁ × Time₁ = Speed₂ × Time₂.

Unit Conversion

To convert minutes to hours, divide by 60. To convert km/h to m/s, multiply by 5/18.

Average Speed

For the same distance covered at speeds x and y, Average Speed = 2xy/(x + y).

Shortcut Trick

Net multiplier for 12% and 15% increase = 1.12 × 1.15 = 1.288

Sale two years ago = Present Sale ÷ Net Multiplier

Sale = 1,28,800 ÷ 1.288 = 1,00,000

∴ The correct answer is ₹1,00,000.

Alternate Method

Given:

Present Sale = ₹1,28,800

Increase in 1^st year (r₁) = 12%

Increase in 2^nd year (r₂) = 15%

Formula Used:

Final Value = Initial Value × (1 + r₁/100) × (1 + r₂/100)

Initial (x)

+12%

Year 1

+15%

1,28,800

Growth Timeline over 2 Years

Calculations:

⇒ Let the sale two years ago be x.

⇒ Sale after 1^st year = x × (1 + 12/100) = 1.12x

⇒ Sale after 2^nd year = 1.12x × (1 + 15/100) = 1.12x × 1.15

⇒ 1.288x = 1,28,800

⇒ x = 1,28,800 ÷ 1.288

⇒ x = 1,00,000

∴ The correct answer is ₹1,00,000.

Additional Information

Successive Percentage Change

If a value changes by a% and then by b%, the net effective change is (a + b + ab/100)%.

Reverse Percentage Calculation

To find the original value after an increase, divide the final value by (1 + r/100). For multiple years, divide by the product of multipliers.

Fractional Equivalent

12% = 3/25 (Multiplier 28/25) and 15% = 3/20 (Multiplier 23/20). Initial = 1,28,800 × (25/28) × (20/23).

The correct answer is Difference between imports and exports

Key Points

• The balance of trade of a country is the difference between its imports and exports.
• If a country exports more than it imports, it has a trade surplus; if it imports more than it exports, it has a trade deficit.
• The balance of trade is a significant component of a country's current account, indicating whether a country is a net exporter or importer of goods.
• It is a critical economic indicator used to assess the health of a country's economy and its trade relationships with other nations.

Additional Information

• A positive balance of trade (trade surplus) can contribute to a country's economic growth, while a negative balance of trade (trade deficit) might indicate economic challenges.
• The balance of trade can be influenced by various factors such as exchange rates, competitiveness, trade policies, and global economic conditions.
• Countries often aim to achieve a favorable balance of trade to boost their economic performance and maintain financial stability.
• The balance of trade is one part of the broader balance of payments, which also includes financial transfers and capital flows.

The correct answer is West Bengal

Key Points

• Bhatiali folk music is traditionally associated with the state of West Bengal.
• This form of music is predominantly sung by fishermen as they navigate the rivers, reflecting the life and culture of the riverine communities.
• The songs often depict the daily life, struggles, and emotions of the fishermen.
• Bhatiali music is characterized by its melodic and soulful tunes that resonate with the rhythm of the flowing river.

Additional Information

• West Bengal has a rich tradition of various forms of folk music, including Baul, Bhawaiya, and Jhumur, besides Bhatiali.
• The state is known for its cultural heritage and contributions to Indian music, literature, and art.
• Folk music in West Bengal often serves as a medium to preserve and transmit local history, folklore, and social values.
• Efforts are being made to preserve and promote these traditional forms of music in the face of modern influences.

The correct answer is 1981

Key Points

• The growth rate of India's population has been declining since 1981.
• This decline is attributed to various factors including government policies on family planning, increased literacy rates, and improved healthcare services.
• Efforts to control population growth have included the promotion of contraceptive use, education about family planning, and incentives for smaller families.
• The decline in the growth rate is a positive indicator of the effectiveness of these policies and the changing socio-economic conditions in the country.

Additional Information

• India's population policy aims to stabilize the population by the middle of the 21^st century.
• In 1952, India became the first country in the world to launch a national program, emphasizing family planning to the extent necessary for reducing birth rates to stabilize the population at a level consistent with the requirements of the national economy.
• Population growth rate is a crucial factor in planning for economic and social development.
• The Total Fertility Rate (TFR) has also been on a decline, indicating fewer children per woman.
• Various states in India have different rates of population growth, with some states achieving replacement-level fertility.

The correct answer is Parliament

Key Points

• The power to regulate the right of citizenship in India is vested in the Parliament.
• According to the Constitution of India, the Parliament has the authority to make laws regarding the acquisition and termination of citizenship and all other matters related to citizenship.
• Article 11 of the Indian Constitution grants Parliament the power to regulate the right of citizenship by law.
• Over the years, Parliament has enacted several laws to govern citizenship, including the Citizenship Act of 1955.

Additional Information

• The Citizenship Act, 1955 provides for the acquisition and determination of Indian citizenship.
• The Act has been amended multiple times, with significant amendments in 1986, 1992, 2003, 2005, and 2019.
• Citizenship can be acquired by birth, descent, registration, naturalization, or incorporation of territory.
• The Constitution of India, adopted on 26^th November 1949 and effective from 26^th January 1950, laid the foundation for the legal framework of citizenship in India.

The correct answer is Africa

Key Points

• The peninsular plateau of India was once a part of the ancient supercontinent known as Gondwana.
• Gondwana included regions that are now part of Africa, South America, Antarctica, Australia, and the Indian subcontinent.
• Over millions of years, the tectonic plates drifted apart, leading to the present-day geographical formations.
• This separation and movement of the tectonic plates is explained by the theory of continental drift proposed by Alfred Wegener.

Additional Information

• The concept of continental drift was further developed into the theory of plate tectonics, which explains the movement of Earth's lithospheric plates.
• India's collision with the Eurasian plate led to the formation of the Himalayas.
• The peninsular plateau is characterized by its stable geological structure and is one of the oldest landmasses on Earth.
• The plateau is rich in minerals and has significant geological and ecological importance.

The correct answer is 1923

Key Points

• Johannes Nicolaus Bronsted and Thomas Martin Lowry proposed the fundamental concept of acids and bases in 1923.
• The Bronsted-Lowry theory defines an acid as a proton donor and a base as a proton acceptor.
• This theory expanded the understanding of acid-base reactions beyond the limitations of the Arrhenius theory.
• It is applicable to a broader range of chemical reactions, including those in non-aqueous solutions.

Additional Information

• The Bronsted-Lowry theory was independently proposed by both scientists in the same year.
• This theory is fundamental in the field of chemistry and is widely taught in academic institutions.
• The concept of conjugate acid-base pairs is also a significant aspect of the Bronsted-Lowry theory.
• Johannes Nicolaus Bronsted was a Danish physical chemist, while Thomas Martin Lowry was a British chemist.

The correct answer is Sikkim

Key Points

• Sakewa is a significant religious festival celebrated by the Kirat Khambu Rai community.
• This festival is primarily observed in the state of Sikkim.
• Sakewa is a time when the community comes together to offer prayers and perform rituals to honor nature and their ancestors.
• The festival holds great cultural and spiritual importance among the Kirat Khambu Rai people.

Additional Information

• Sikkim is a state in northeastern India, known for its diverse cultural heritage and vibrant traditions.
• The Kirat Khambu Rai community is one of the indigenous communities of Sikkim, with a rich history and cultural legacy.
• Besides Sakewa, Sikkim is home to various other festivals and cultural events that reflect its multi-ethnic society.
• Sakewa is also known as the “Ubhauli” festival in some regions, marking the beginning of the farming season.