The correct answer is option 2 i.e. a public speaker, especially one who is skilled.

Explanation:

• The passage is about the great Swami Vivekananda.
• The sentence in the passage containing the above word is: "His mastery over the English language helped him to be an eloquent orator."
• Here, 'eloquent' means fluent. An orator is a public speaker who is skilled in his/her ability to deliver their thoughts.
• Vivekanand was one of the most fluent speakers due to his mastery over the English language.

Therefore, the correct answer is option 2.

The correct answer is option 2 i.e. Ramakrishna Mission.

Explanation:

• The passage is about the great Swami Vivekananda
• The following is stated in the passage: "Swami Vivekananda is one of the greatest monks of India and the founder of Ramakrishna Mission."

Therefore, the correct answer is option 2.

The correct answer is option 1 i.e. Sri Ramakrishna Paramhansa.

Explanation:

• The passage is about the great Swami Vivekananda
• The following is stated in the passage: "He went to Dakshineswar Kali temple to meet Sri Ramakrishna Paramhansa to find out whether God really existed or not... Vivekananda was greatly inspired by Sri Ramakrishna and became his follower."

Therefore, the correct answer is option 1.

The correct answer is option 1 i.e. felt favourably towards someone or something.**

Explanation:

• The passage is about the great Swami Vivekananda.
• The sentence in the passage containing the above word is: "Since childhood, Vivekananda was inclined towards spiritualism."
• This means that he was always had a preference for spiritualism.
• Example: "She was inclined to accept their offer."

Therefore, the correct answer is option 1.

The correct answer is option 2 i.e. Sanyasi.

Explanation:

• The passage is about the great Swami Vivekananda
• The following is stated in the passage: "Vivekananda became a 'Sanyasi' (monk) and took up the name 'Swami Vivekananda.'"

Therefore, the correct answer is option 2.

The correct answer is option 4 i.e. all except 3.

Explanation:

• The passage is about the great Swami Vivekananda.
• The following is stated in the passage: " In 1880 Vivekananda joined the Arts faculty of Presidency College and studied English, Mathematics, History, Psychology, Philosophy and Logic for his graduation."

Therefore, the correct answer is option 3.

The correct answer is option 3 i.e*.*** living forever; never dying or decaying.

Explanation:

• The passage is about the great Swami Vivekananda
• The sentence in the passage containing the above word is: "He left behind an immortal legacy for the youth of India."
• Here, it means that Vivekananda's legacy and work will be remembered forever.

Mistake Point:

• Although gods and goddesses(option 1) are often considered to be immortal beings, this is contextually incorrect here.

Therefore, the correct answer is option 3.

The correct answer is option 3 i.e. Maharaja of Khetri.

Explanation:

• The passage is about the great Swami Vivekananda
• The following is stated in the passage: "With the financial help from Maharaja of Khetri he attended the World Parliament of Religions in 1893 in Chicago..."

Therefore, the correct answer is option 3.

The correct answer is option 3 i.e.1863.

Explanation:

• The passage is about the great Swami Vivekananda.
• The following is stated in the passage: "Vivekananda was born as Narendranath Dutta to Visvanath Dutta and Bhubaneshwari Devi on 12 January 1863 in Kolkata."

Therefore, the correct answer is option 3.

The correct answer is income level

Key Points

• Financial inclusion is aimed at providing access to financial services to everyone, regardless of their income level.
• This means that people who are traditionally underserved by the financial system, such as low-income households, can access services like savings accounts, loans, and insurance.

The correct answer is financial.

Key Points

• Financial inclusion is about providing access to financial services, so the answer is financial.
• Providing access to financial services can help promote economic growth and reduce poverty, as people can use these services to save money, invest in their education or business, and protect themselves against financial shocks.

The correct answer is technological

Key Points

• One of the challenges to achieving full financial inclusion is a lack of technological infrastructure, particularly in developing countries where many people do not have access to the internet or mobile phones.
• This can make it difficult to provide financial services to people in remote or rural areas.

The correct answer is Money.

Key Points

• Financial education is important to ensure that people can make informed financial decisions, manage their money effectively, and avoid financial pitfalls.
• Without financial education, people may not know how to save money, manage debt, or invest in a way that aligns with their financial goals.

The correct answer is financial

Key Points

• The answer is financial, as the financial system is what policymakers and financial institutions are working to make more inclusive.
• By providing access to financial services to more people, policymakers and financial institutions can help to promote economic growth, reduce poverty, and create more opportunities for everyone.

The correct answer is Option 1 i.e., ‘Reading storybooks and watching movies- is’- the error lies in this part only.

 

• The error lies in the wrong usage of the verb ‘is’ in Part A.

• ‘Is’ should be replaced by ‘are’ because a plural verb is used when two gerunds used as subjects of a sentence are joined by the coordinating conjunction ‘and’.

• Let’s see a few examples-

• Baking chocolate cakes and decorating the house are my duties for tomorrow's event. 

• Baking chocolate cakes and decorating the house is my duties for tomorrow's event. 

• Singing classical songs and attending concerts have helped me to overcome the loss of my pet dog. 

• Singing classical songs and attending concerts has helped me to overcome the loss of my pet dog. 

Therefore, the plural verb ‘are’ should be used instead of the singular verb ‘is’ to make the sentence correct.

So, the correct sentence is:

“Reading storybooks and watching movies- are my two favourite hobbies- and these two hobbies have helped me prosper more as an individual and be a better person.” 

 

• Gerunds are the verb that ends with '-ing' and does the work of a noun.

• A singular verb is used when gerunds are subjects of a sentence.

• For example-

• Swimming in the dirty pond was a ridiculous stunt by Rohit. 

• Swimming in the dirty pond were a ridiculous stunt by Rohit. 

• Playing the synthesizer has been my wish since childhood. 

• Playing the synthesizer have been my wish since childhood.

The correct option is 4) i.e. B.

Key Points

• This statement shows the possibility that 'we work hard to please our CEO' but we don't know whether CEO is pleased or not.
• Thus, this statement/situation shows the possibility we use 'may', in such cases where we try to state that an event can or cannot occur, we use 'may'.   
• ​Example: 'It can be a holiday tomorrow.' (Incorrect) ❌

                                      'It may be a holiday  tomorrow*.'* (Correct) ✔️

Additional Information

USE OF

• May: Permission to do something
• ​Example: May I take that newspaper?
• Can: Offer something
• ​Example: I can lend you my scooter till next week.

 

Correct sentence: 'We work hard so that we may please our CEO to promote us to the post of Manager or at least a raise would be nice for a change.'✔️

The correct answer is option 2 i.e. B

Key Points​​​

• ​We use 'who' in relative clauses to refer to people, and sometimes to pet animals.
• ​As per the rule given above, 'who' will be used instead of 'which' in the 2^nd part of the sentence.
• Here "Young girl" is the noun, hence we will use 'who'.
• "Who" is used for the noun/pronouns in nominative case i.e. I, we, you, he, she, it, they.

Additional Information  ​

• The pronouns that connect a clause or phrase to a noun or a pronoun, is called a relative pronoun.
• The most common relative pronouns are:
• who, whom, whose, which, that.
• Example:
• We don’t know the person who donated this money.

​Correct Sentence: "The front-page story was about a young girl who had hurt herself while saving a puppy in an accident. She single-handedly took the initiative and saved the life of that disowned puppy, took care of all its medical expenses and even went to see a medical veteran."

The correct Answer is Option 4.

Key Points

• The error is in part D of the sentence, due to the wrong spelling of uncountable noun.

• Furniture is an uncountable noun and is not used in a plural sense.

• Plural of furniture is also furniture.​

• NOT furnitures.

• The word furniture is always used along with a singular verb.

 

Correct sentence: "In my neighbourhood there lived an old couple; they led the simplest kind of lives, and studied and wrote; they grew their own food, built their own houses and furniture."

Additional Information

• Uncountable nouns are nouns that come in a state or quantity that is impossible to count.
• Uncountable nouns are always considered to be singular. Hence, require singular verbs according to Subject Verb agreement.
• To refer to one or more quantities of an uncountable noun, expressions such as a bit of, a piece of, an item of or words for containers and measures must be used:
• He bought a very expensive piece of furniture for his new apartment.

The correct answer is 'Option 4 (D)'.

 

Key Points

• The error is in part D, where the phrase "in the venue" is used.
• The preposition "at" is used with a specific place or location when referring to an event or activity taking place there.
• Therefore, "at the venue" is the correct expression instead of "in the venue."
• Options 1, 2, and 3 do not contain any grammatical error.

Therefore, the correct answer is Option 4.

 

Complete Sentence: "A vast number of people greeted the politician on her arrival at the venue."

 

Additional Information

• Option 1 (A): "A vast number" is grammatically acceptable because "a vast number of" is used to refer to a large quantity of countable people or things.
• Option 2 (B): "of people greeted" is grammatically correct and appropriately connects the subject with the verb.
• Option 3 (C): "the politician on her arrival" is grammatically correct and clearly indicates when the politician was greeted.
• Option 4 (D): "in the venue" is incorrect in this context. The correct preposition is "at", making the phrase "at the venue."

The correct answer is option 4 i.e. A-B

We can look at the sentence in the following way:

Molly said she wanted to _______ (A) the new _______ (B) but Mark was _______ (C) it. 

• Restaurant: A place where people sit and pay to eat meals. 'Restaurant' is not a verb or an action that one can 'do'.
• Visit: Go to see or spend time somewhere. 'Visit' is a verb and we have to replace it with a noun.
• Against: To be opposition to something

Hence A and B need to be interchanged in order to make the sentence contextually correct.

Correct Sentence: Molly said she wanted to visit (A) the new restaurant (B) but Mark was against (C) it.

The correct answer is option 2 i.e. C-A

We can look at the sentence in the following way:

Sally wanted to _______ (A) in the _______ (B) but she was _______ (C).

• Confused: Refers to a state of not being able to think clearly. The preposition 'to' cannot precede the past tense of a verb. Only the base form of the verb can come after 'to'.
• Startup: A newly established business.
• Invest: To put money into financial plans for a profit. The past tense verb 'was' cannot precede the base verb form 'invest'.

Hence, A and C need to be interchanged in order to make the sentence contextually correct.

Correct answer: Sally wanted to invest (A) in the startup (B) but she was confused (C).

The correct answer is option 2 i.e. B-C

We can look at the sentence in the following way:

_______ (A) struck the electric _______ (B) as soon as it started _______ (C). 

• Lightning: A natural phenomenon of a large release of energy in the sky that emits powerful light and sound
• Raining: Pouring of water from the clouds in the sky to the ground. We can't use an adjective like 'electric' to describe it. We have to replace 'raining' with a noun.
• Pole: A long, slender piece of metal which usually has one end in the ground as support. 'Pole' is a noun and blank C requires an action/verb. 

Hence, we need to interchange B and C in order to make the sentence contextually correct

Correct Sentence: Lightning (A) struck the electric pole (B) as soon as it started raining (C).

The correct answer is option 2 i.e. B-A

We can look at the sentence in the following way:

The _______ (A) was usually _______ (B) but the _______ (C) had brought everyone out.

• Empty: Refers to something that does not contain anything. 'Empty' is an adjective and needs to be followed by a noun. It has to be replaced with a noun.
• Library: A building or a room containing a collection of books. A 'library' is not an adjective that can be used to describe something.
• Submission: The act of presenting some kind of work that one has done. 

Hence, we need to interchange B and A in order to make the sentence contextually correct

Correct Sentence: The library (A) was usually empty (B) but the submission (C) had brought everyone out.

The correct answer is option 3 i.e. B-C

We can look at the sentence in the following way:

The _______ (A) were a long _______ (B) coming, it was time to _______ (C) up. 

• Protests: Organized public demonstrations expressing strong objection to official policies or courses of action.
• Speak: The action of talking about something. The verb 'speak' cannot be preceded by the adjective 'long'(it would have been correct if it was 'speech').
• Time: The arrangement or schedule of when something should have happened. We have to use a verb here in order to make the sentence grammatically correct.

Hence, we need to interchange B and C in order to make it contextually correct.

Correct Sentence: The protests (A) were a long time (B) coming, it was time to speak (C) up. 

Note- 

• 'Speak up' is a phrasal verb meaning 'express one's opinions frankly and publicly'.
• 'A long time coming' means '1. Something that's long overdue. 2. Something that should've happened a long time ago'.

The correct answer is option 4.

Key Points

The correct phrase is 'as fast as originally'.

• As + adjective + as is a correlative conjunction and it is used to compare things that are similar in proportion.
• For Example -
• My car is as expensive as his bike.
• She is as tall as her brother.
• Thus, 'than' given in the sentence should be replaced with 'as'.
• Thus, the correct sentence after phrase replacement would be - The industry's automated vehicle segment has not rolled out as fast as originally expected as the technology has proven tough to master.

 

Additional Information

Let's understand some more correlative conjunctions -

• Either…or -
• It is used for two positive options that carry equal value.
• For Example -
• You can either get a ride home now or walk home later.
• Neither...nor -
• It is used for two or more things that are not true or that do not happen.
• For Example -
• My brother neither like mangos nor apples.
• No sooner...than -
• It is used to show that one thing happens immediately after another thing.
• For Example -
• No sooner had the motivational speaker finished her speech than the lights went out.
• Both...and -
• It is used for emphasizing that each of two things is true.
• For Example -
• The crowd both applauded, and stood up for the great performance of the actors.
• Rather...than -
• It is used to give more importance to one thing when two alternatives or preferences are being compared.
• For Example -
• She took the blame rather than blaming everyone else because she did not want to create a scene.

The correct answer is option 2.

Key Points

The correct phrase is 'a significant form of'.

• The use of the article 'an' before 'significant' is incorrect and it should it replaced with the article 'a' because the article 'a' is used before nouns that begin with a consonant sound, and the noun 'significant' has a consonant sound.
• Thus, the correct sentence after phrase replacement would be - Postpartum depression is a significant form of depression that can begin after childbirth, with symptoms that vary from person to person.

​ 

Additional Information

Use of articles a, an, and the - 

• Article 'a' is used before nouns that begin with a consonant sound.
• For Example -
• I have a book in my purse.
• (Here, article 'a' is used before the noun 'book' because it begins with a consonant sound)
• Article 'an' is used before nouns that begin with a vowel sound.
• For Example -
• Do you want an apple for breakfast?
• (Here, the article 'an' is used before the noun 'apple' because it begins with a vowel sound)
• Article 'the' is used before both singular and plural nouns when the noun is specific.
• For Example -
• I saw the play you are talking about.
• ​​(Here, the article 'the' is used before the noun 'play' because it is the specific play that is being talked about)

The correct answer is option 3.

Key Points

The correct phrase is 'Republican to challenge former'.

• The underlined phrase is incorrect because here, after the preposition 'to' the verb 'challenge' is given as its present participle which is incorrect, and as per English grammar rules, after the preposition 'to' we use the base form of the verb.
• Hence 'challenging' should be replaced with 'challenge'.
• Also, the use of the adverb 'formerly' is incorrect and it should be replaced with the adjective 'former' because it is used to describe the quality of the noun 'U.S. President'.
• Thus, the correct sentence after phrase replacement would be - Prominent Indian-American politician Nikki Haley launched her presidential campaign, becoming the first Republican to challenge former U.S. President Donald Trump in his 2024 bid for the White House.

The correct answer is '​Both A and B.'

Key Points

• The word 'Revised' can be defined as both a verb and an adjective.
• As a verb, the word 'Revised' means To reconsider and amend something, especially in the light of further evidence or to reflect a changed situation.
• Example: In order to progress their project smoothly, they revised the plan several times.
• As an adjective, the word 'Revised' means (Of written or printed matter) having been altered or corrected.
• Example: The code is presently under review and a revised edition will be published later this year.
• Thus, understanding the meaning of the word 'Revised' we can say that both sentences A and B are correct.

Hence, the only possible answer is option 4.

Additional Information

• In sentence C, the correct word to be used will be 'Reviled' instead of 'Revised'.
• The word 'Reviled' means To criticize in an abusive or angrily insulting manner.
• ​Example: A hundred bad writers misrepresented him and reviled him.

The correct answer is 'Both B and C.'

Key Points

• The word 'Lead' as a verb means To have something as a result.
• The word 'Lead' as a verb means To have a particular type of life.
• In sentence A, the word 'Lead' is inappropriately used and doesn't fit the context of the sentence.
• In sentence B, the word 'Lead' has been correctly used as a verb as the sentence is talking about having all sorts of health problems on eating too much sugar.
• In sentence C, the word 'Lead' has been correctly used as a verb as the sentence is talking about having or living a busy life.

Hence, the only possible answer is option 4.

The correct answer is 'Both A and C.'

Key Points

• The word 'Goal' as a noun means The area between two posts into which the ball must be kicked, hit, etc. for a point or points to be scored.
• The word 'Goal' as a noun means The object of a person's ambition or effort; an aim or desired result.
• In sentence A, the word 'Goal' has been correctly used as a noun as the sentence is talking about a center forward heading the ball into the area between two posts.
• In sentence B, the word 'Goal' is inappropriately used and doesn't fit the context of the sentence.
• In sentence C, the word 'Goal' has been correctly used as a noun as the sentence is talking about achieving a person's ambition or aim.

Hence, the only possible answer is option 4.

As we know that BODMAS is used of simplifying a mathematical problem.

According to BODMAS first we have to solve ‘brackets’ followed by ‘of’ then ‘division’ then ‘multiplication’ and later ‘addition’, ‘subtraction’.

L.H.S

157/100 × 360 + 66/100 × 275

565.2 + 181.5 = 746.7

R.H.S

Let ‘x’ be the final answer

30/100 × x

Now, cross multiplying

x = (746.7 × 100)/30 = 2489.

As we know that BODMAS is used of simplifying a mathematical problem.

According to BODMAS first we have to solve ‘brackets’ followed by ‘of’ then ‘division’ then ‘multiplication’ and later ‘addition’, ‘subtraction’.

∴ 142 × 1.56 = 221.52

 221.52 + 423 = 644.52

Now, cross multiplying 2 from R.H.S to L.H.S

644.52/2 = 322.26

Concept used:

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

Calculation:

28% of 450 + 45% of 280 = ?

⇒ (28/100) × 450 + (45/100) × 280 = ?

⇒ 126 + 126 = ?

⇒ 252 = ?

∴ The value of ? is 252

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

Step-1: Parts of an equation enclosed in 'Brackets' must be solved first and in the bracket,

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

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

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

12³ × 6⁴ ÷ 432 = ?

12³ × 3 = ?

? = 5184.

Follow BODMAS rule to solve this question, as per the order given below,Step - 1 - Parts of an equation enclosed in 'Brackets' must be solved first,Step - 2 - Any mathematical 'Of' or 'Exponent' must be solved next,Step - 3 - Next, the parts of the equation that contain 'Division' and 'Multiplication' are calculated,Step - 4 - Last but not least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated

⇒ 16 × 2 – 5 + 6

⇒ 32 – 5 + 6

∴ 38 – 5 = 33

Convert the data into mathematical form,

⇒ 630 × (4/7) × (60/100) = ?

⇒ 90 × 4 × 0.6 = ?                                      

⇒ ? = 216

Given:

(7/19) of 1064 = (?)2 × 2

Concept Used:

Follow the BODMAS rule according to the table given below:

(7/19) of 1064 = (?)2 × 2

⇒ 392 = (?)² × 2

⇒ 392 ÷ 2 = (?)²

⇒ 196 = (?)²

⇒ 14 = ?

∴ The value of ‘?’ Is 14.

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

Step – 1 – Parts of an equation enclosed in the ‘BRACKETS’ must be solved first

Step – 2 – Any mathematical ‘OF’ or ‘EXPONENTS’ must be solved next

Step – 3 – Next the part of the equation that contains ‘DIVISION; and ‘MULTIPLICATION’ are calculated

Step – 4 – Last but not least, the parts of the equation that contains ‘ADDITION’ and ‘SUBTRACTION’ should be calculated

Now, the given expression:

⇒ 9672 ÷ 156 – 5 × 3.2 = √(?)

⇒ 62 – 5 × 3.2 = √(?)

⇒ 62 – 16 = √(?)

⇒ 46 = √(?)

⇒ (46)² = ?

⇒ 2116 = ?

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

Step-1: Parts of an equation enclosed in the ‘BRACKETS’ must be solved first

Step-2: Any mathematical ‘OF’ or ‘EXPONENTS’ must be solved next

Step-3: Next the part of the equation that contains ‘DIVISION; and ‘MULTIPLICATION’ are calculated

Step-4: Last but not least, the parts of the equation that contains ‘ADDITION’ and ‘SUBTRACTION’ should be calculated

Now, the given expression:

\( {5\frac{1}{9}} + 7 {\frac{2}{5}} - 11 {\frac{3}{{45}}} = ?\)

⇒ \(\frac{46}{9}\) + \(\frac{37}{5}\) - \(\frac{498}{45}\) = ?

⇒ (230 + 333 - 498)/45 = ?

⇒ 65/45 = ?

∴ ? = 13/9.

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

Step-1: Parts of an equation enclosed in the ‘BRACKETS’ must be solved first

Step-2: Any mathematical ‘OF’ or ‘EXPONEMTS’ must be solved next

Step-3: Next the part of the equation that contains ‘DIVISION; and ‘MULTIPLICATION’ are calculated

Step-4: Last but not least, the parts of the equation that contains ‘ADDITION’ and ‘SUBTRACTION’ should be calculated

Now, the given expression:

⇒ ?² + √1024 = 561

⇒ ?² + 32 = 561

⇒ ?² = 561 – 32

⇒ ?² = 529

⇒ ?² = (23)²

⇒ ? = 23

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

Step-1: Parts of an equation enclosed in the ‘BRACKETS’ must be solved first

Step-2: Any mathematical ‘OF’ or ‘EXPONENTS’ must be solved next

Step-3: Next the part of the equation that contains ‘DIVISION; and ‘MULTIPLICATION’ are calculated

Step-4: Last but not least, the parts of the equation that contains ‘ADDITION’ and ‘SUBTRACTION’ should be calculated

Now, the given expression:

⇒ 937 + (9)³ ÷ 27 × (3)⁴ = ?

\(\Rightarrow 937; + ;\frac{{{{\left( 9 \right)}^3}}}{{27}}; \times ;{3^{4;}}; = ;?\)

⇒ 937 + (9)³ × 3 = ?

⇒ 937 + 729 × 3 = ?

⇒ 937 + 2187 = ?

⇒ 3124 = ?

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

Step-1∶ Parts of an equation enclosed in 'Brackets' must be solved first and in the bracket,

Step-2∶ Any mathematical 'Of' or 'Exponent' must be solved next,

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

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

⇒ 5 + (5 × 5) – 5 + 5

⇒ 5 + 25 – 5 + 5

⇒ 30

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

Step 1: Parts of an equation enclosed in 'Brackets' must be solved first, and in the bracket,

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

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

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

Given expression is,

⇒ {(3654 + 1346) × 2} ÷ 100 = ?

⇒ {(5000) × 2} ÷ 100 = ?

⇒ ? = 10000 ÷ 100

⇒ ? = 100

Given:

A batsman’s 16^th innings score = 60 runs

The average increases by = 3

Calculation:

Let the average after 16^th innings be x

The average after 15^th innings = (x – 3)

∴ According to the question:

⇒ 16x = 15 (x – 3) + 60

⇒ 16x = 15x – 45 + 60

⇒ 16x – 15x = 15

⇒ x = 15

∴ the batsman’s average after his 16^th innings is 15 runs.

Given:

Speed of train = 54 km/h

Time train takes to cross a tree = 13 sec

Length of a platform = 75 m

Formula used:

Speed = Distance/Time

Calculation:

Speed of the train in m/sec = 54 × (5/18) = 15 m/sec

⇒ Length of the train = 15 × 13 = 195 m

Time taken to cross the platform = (195 + 75)/15

⇒ Time taken to cross the platform = 270/15 = 18 sec

∴ The time train will take to cross the platform is 18 sec.

Total produced units = 300 + 450 + 400 + 500 + 420 = 2070

Total sold units = 180 + 300 + 350 + 320 + 360 = 1510

⇒ required difference = 2070 – 1510 = 560

Units produced by A = 300

So, units produced by company F = 300 × 110/100 = 330

Units sold by company C = 350

So, units sold by company F = 350 × 80/100 = 280

Unsold unit of company F = 330 – 280 = 50

Unsold unit of company A = 120

Unsold unit of company B = 150

Unsold unit of company C = 50

Unsold unit of company D = 180

Unsold unit of company E = 60

Average unit remain unsold = (120 + 150 + 50 + 180 + 60)/5 = 112

Unit produced by Company C = 400

Units sold by Company B = 300

⇒ Required percent = (400 -300)/300 × 100 = 33.33%

Unsold unit of company E = 420 – 360 = 60

Unsold unit of company D = 500 – 320 = 180

Unsold units of Company E and D together = 180 + 60 = 240

Sold units of company A = 180

Sold units of company B = 300

Sold units of company A and B together = 180 + 300 = 480

⇒ required ratio = 240 : 480

⇒ 1 : 2

Given:

⇒ Speed upstream = 35/7 = 5kmph

⇒ Speed of stream = 20kmph

⇒ Speed of boat in still water = 20 + 5 = 25 kmph

⇒ Speed downstream = 25 + 20 = 45 kmph

∴ Required time = 45/45 + 20/5 = 5 hours

Given:

The difference in selling price of an article when sold at 21% profit and 10% loss is Rs. 589

Formula used:

Selling Price = Cost Price (100% ± Profit or Loss) [ + for Profit and - for loss ]

Calculation:

let cost price be 100x,

Selling Price at 21% profit = 100x (100% + 21%)

= \(100x \times \frac{121}{100}\)

= 121x

Selling Price at 10% loss = 100x (100% - 10%)

= \(100x \times \frac{90}{100}\)

= 90x

The difference in selling price of an article when sold at 21% profit and 10% loss is Rs. 589,

121x - 90x = 589

31x = 589

x = 589/31

x = 19

Cost price = 100x

= 100 × 19

= 1900

Selling Price at 25% profit = 1900 (100% + 25%)

= \(1900 \times \frac{125}{100}\)

= 19 × 125

= 2375

Selling price at 25% profit is Rs. 2375

Answer is Rs. 2375.

Alternate MethodGiven:

The difference in selling price of an article when sold at 21% profit and 10% loss is Rs. 589

Formula used:

Selling Price = Cost Price (1 ± Profit or Loss) [ + for Profit and - for loss ]

Calculation:

let 100% be cost price,

Difference in selling price,

21% - (-10%) = 589

21% + 10% = 589

31% = 589

1% = 19

Cost price = 100%

= 100 × 19

= 1900

Selling Price at 25% profit = 1900 (1 + 25%)

= \(1900 \times \frac{125}{100}\)

= 19 × 125

= 2375

Selling price at 25% profit is Rs. 2375

Answer is Rs. 2375.

Given:

Sum of money becomes 6 times of itself in 7 years

Formula used:

SI = PRT/100

Where, P = principal

R = rate

T = time

A = SI + P

Where, A = Amount

SI = simple interest

Calculation:

Let the principal be P.

For 7 years,

SI = (P × R × 7)/100

⇒ 7PR/100

A = SI + P

⇒ 6P = 7PR/100 + P

⇒ 5P = 7PR/100

⇒ R = 500/7

For 42 years,

SI = (P × R × 42)/100

⇒ {P × (500/7) × 42}/100

⇒ 30P

A = SI + P

⇒ A = 30P + P

⇒ A = 31P

∴ In 42 years, amount will become 31 times of principal.

Given:

The ratio of the present ages of A and B = 5 : 8

The ratio of the present ages of C and B = 3 : 2

The sum of their ages = 100 years

Calculation:

As per the question, the ratio of A and B is given and the ratio of C and B is given, so on equalizing the ratio of B in both ratios:

A and B = 5 : 8      ----(1)

C and B = 3 : 2      ----(2)

After multiplying 4 in equation (2), B become equal in both the equations:

A : B : C = 5 : 8 : 12

The sum of their present ages ratio = 5 + 8 + 12

⇒ 25 units

Value of 25 units = 100 years

Value of 1 unit = 4 years

So. the present age of A = 5 units

⇒ 5 × 4

⇒ 20 years

 ∴ The present age of A is 20 years.

Given:

A and B invested Rs. 8000 for 2 years and 3 years respectively

B withdrew 60% of his amount after one year of investing

Formula used:

Ratio of profit is the product of capital and time

Calculation:

Effective investment of A

⇒ 8000 × 2 = Rs. 16000

Effective investment of B

⇒ 8000 × 1 + (40/100) × 8000 × 2 = 8000 + 6400 = 14400

∴ Ratio of their profits = 16000 : 14400 = 10 : 9

Given:

13860, 6930, ?, 462, 66, 6

Calculation:

The Series follows the following pattern

13860 ÷ 2 = 6930

6930 ÷ 3 = 2310

2310 ÷ 5 = 462

462 ÷ 7 = 66

66 ÷ 11 = 6

∴ The Required term in the series will be 2310

Note: this series divide by a prime number like 2, 3, 5, 7, 11

Calculation:

The series follows following pattern:

⇒ 7

⇒ 7 + (2)² = 11

⇒ 11 + (3)² = 20

⇒ 20 + (4)² = 36

⇒ 36 + (5)² = 61

⇒ 61 + (6)² = 97

∴ The missing number in place of ‘?’ is 20.

Given:

The number series:

900, 890, 870, 830, 750, ?

Concept Used:

Number series following a fixed pattern.

Calculation;

The given number series follows the pattern:

900 – (10 × 2⁰) = 890

890 – (10 × 2¹) = 870

870 – (10 × 2²) = 830

830 – (10 × 2³) = 750

750 – (10 × 2⁴) = 590

∴ The Missing Number in the given number series is 590

This series follows following pattern:

⇒ 171 + 2 = 173

⇒ 173 – 3 = 170

⇒ 170 + 5 = 175

⇒ 175 – 7 = 168

⇒ 168 + 11 = 179

∴ The value of ? is 168

The given series follows the given pattern,

1³ + 1 = 2

2³ + 2 = 10

3³ + 3 = 30

4³ + 4 = 68

5³ + 5 =130

6³ + 6 = 222       

∴ The missing term in the series is 30.

Tabulation Solution :

 

 

 

 

 

∴ Required difference = 1080 – 560 = 520

Alternate Method

Let total number of word type by Mr. A in four days = x

The number of words type by Mr. A in Sunday = x × 30/100 = 0.3x

The number of words type by Mr. A in Monday = (x – 0.3x) × 3/9 = 0.7x/3

The number of words type by Mr. A in Tuesday = (x – 0.3x) × 4/9 = 2.8x/9

The number of words type by Mr. A in Wednesday = (x – 0.3x) × 2/9 = 1.4x/9

Given that,

1.4x/9 = 560

⇒ x = 560 × 9/1.4 = 3600

The number of words type by Mr. A in Sunday = 0.3x = 0.3 × 3600 = 1080

The number of words type by Mr. A in Wednesday = 560 (Given)

So, required difference = 1080 – 560 = 520

Tabulation Solution :

 

 

 

 

 

∴ Required average = (1080 + 1120 + 560)/3 = 920

Alternate Method

Let total number of word type by Mr. A in four days = x

The number of words type by Mr. A in Sunday = x × 30/100 = 0.3x

The number of words type by Mr. A in Monday = (x – 0.3x) × 3/9 = 0.7x/3

The number of words type by Mr. A in Tuesday = (x – 0.3x) × 4/9 = 2.8x/9

The number of words type by Mr. A in Wednesday = (x – 0.3x) × 2/9 = 1.4x/9

Given that,

1.4x/9 = 560

⇒ x = 560 × 9/1.4 = 3600

The number of words type by Mr. A in Sunday = 0.3x = 0.3 × 3600 = 1080

The number of words type by Mr. A in Monday = 0.7x/3 = 0.7 × 3600/3 = 840

The number of words type by Mr. A in Tuesday = 2.8x/9 = 2.8 × 3600/9 = 1120

The number of words type by Mr. A in Wednesday = 1.4x/9 = 1.4 × 3600/9 = 560

∴ required average = (1080 + 1120 + 560)/3 = 920

Shortcut Trick

Ratio of words typed on Monday, Tuesday and Wednesday = 3: 4: 2

Given 2 unit = 560

∴ 3 unit  = 840 = words typed by A on Monday

Given that ratio between words typed by A and Y, on Monday = 2: 3

So, Here 2 unit = 840 = words typed by A on Monday

∴ 1 units = 840/2 = 420

∴ 3 unit = 420 × 3 = 1260 words types by Y on Monday.

Tabulation Solution :

 

 

 

 

 

∴ The total words type by Mr. ‘Y’ on Monday = 840 × 3/2 = 1260

Alternate Method

Let total number of word type by Mr. A in four days = x

The number of words type by Mr. A in Sunday = x × 30/100 = 0.3x

The number of words type by Mr. A in Monday = (x – 0.3x) × 3/9 = 0.7x/3

The number of words type by Mr. A in Tuesday = (x – 0.3x) × 4/9 = 2.8x/9

The number of words type by Mr. A in Wednesday = (x – 0.3x) × 2/9 = 1.4x/9

Given that,

1.4x/9 = 560

⇒ x = 560 × 9/1.4 = 3600

The number of words type by Mr. A in Sunday = 0.3x = 0.3 × 3600 = 1080

The number of words type by Mr. A in Monday = 0.7x/3 = 0.7 × 3600/3 = 840

The number of words type by Mr. A in Tuesday = 2.8x/9 = 2.8 × 3600/9 = 1120

The number of words type by Mr. A in Wednesday = 1.4x/9 = 1.4 × 3600/9 = 560

∴ The total words type by Mr. ‘Y’ on Monday = 840 × 3/2 = 1260

Tabulation Solution :

 

 

 

 

 

∴  Required ratio = 1080 : 840 = 9 : 7

Alternate Method

Let total number of word type by Mr. A in four days = x

The number of words type by Mr. A in Sunday = x × 30/100 = 0.3x

The number of words type by Mr. A in Monday = (x – 0.3x) × 3/9 = 0.7x/3

The number of words type by Mr. A in Tuesday = (x – 0.3x) × 4/9 = 2.8x/9

The number of words type by Mr. A in Wednesday = (x – 0.3x) × 2/9 = 1.4x/9

Given that,

1.4x/9 = 560

⇒ x = 560 × 9/1.4 = 3600

The number of words type by Mr. A in Sunday = 0.3x = 0.3 × 3600 = 1080

The number of words type by Mr. A in Monday = 0.7x/3 = 0.7 × 3600/3 = 840

The number of words type by Mr. A in Tuesday = 2.8x/9 = 2.8 × 3600/9 = 1120

The number of words type by Mr. A in Wednesday = 1.4x/9 = 1.4 × 3600/9 = 560

The total words typed by Mr. ‘X’ on Sunday = 1120 × 75/100 = 840

So, required ratio = 1080 : 840 = 9 : 7

Tabulation Solution :

 

 

 

 

 

∴ Required % = (3600 – 2520)/3600 × 100 = 30%

Alternate Method

Let total number of word type by Mr. A in four days = x

The number of words type by Mr. A in Sunday = x × 30/100 = 0.3x

The number of words type by Mr. A in Monday = (x – 0.3x) × 3/9 = 0.7x/3

The number of words type by Mr. A in Tuesday = (x – 0.3x) × 4/9 = 2.8x/9

The number of words type by Mr. A in Wednesday = (x – 0.3x) × 2/9 = 1.4x/9

Given that,

1.4x/9 = 560

⇒ x = 560 × 9/1.4 = 3600

The number of words type by Mr. A in Sunday = 0.3x = 0.3 × 3600 = 1080

The number of words type by Mr. A in Monday = 0.7x/3 = 0.7 × 3600/3 = 840

The number of words type by Mr. A in Tuesday = 2.8x/9 = 2.8 × 3600/9 = 1120

The number of words type by Mr. A in Wednesday = 1.4x/9 = 1.4 × 3600/9 = 560

The total words typed by Mr. ‘Z’ = 840 × 3 = 2520

So, required % = (3600 – 2520)/3600 × 100 = 30%

Eight people P,Q,R,S,T,U,V, and W

1)  Only two-person lives between R and S.

2. S lives on an odd-numbered floor below the sixth floor. 

3) Only one person lives between R and P who lives immediately below T. 

4)  V lives on an odd-numbered floor but not on the lowermost floor. 

 

5) The number of people living between Q and U is the same as the number of people between U and P. Q lives below U but not immediately.

6. Q lives below U but not immediately.

7. Therefore Case II and Case III are invalid.

So, the final arrangement is,

 

Hence, S lives on the fifth floor.

Eight people P,Q,R,S,T,U,V, and W

1)  Only two-person lives between R and S.

2. S lives on an odd-numbered floor below the sixth floor. 

3) Only one person lives between R and P who lives immediately below T. 

4)  V lives on an odd-numbered floor but not on the lowermost floor. 

 

5) The number of people living between Q and U is the same as the number of people between U and P. Q lives below U but not immediately.

6. Q lives below U but not immediately.

7. Therefore Case II and Case III are invalid.

So, the final arrangement is,

 

Therefore, 4 people live between P and W.

Hence, the correct answer is 4.

Eight people P,Q,R,S,T,U,V, and W

1)  Only two-person lives between R and S.

2. S lives on an odd-numbered floor below the sixth floor. 

3) Only one person lives between R and P who lives immediately below T. 

4)  V lives on an odd-numbered floor but not on the lowermost floor. 

 

5) The number of people living between Q and U is the same as the number of people between U and P. Q lives below U but not immediately.

6. Q lives below U but not immediately.

7. Therefore Case II and Case III are invalid.

So, the final arrangement is,

 

Hence, W lives on the lowermost floor.

Eight people P,Q,R,S,T,U,V, and W

1)  Only two-person lives between R and S.

2. S lives on an odd-numbered floor below the sixth floor. 

3) Only one person lives between R and P who lives immediately below T. 

4)  V lives on an odd-numbered floor but not on the lowermost floor. 

 

5) The number of people living between Q and U is the same as the number of people between U and P. Q lives below U but not immediately.

6. Q lives below U but not immediately.

7. Therefore Case II and Case III are invalid.

So, the final arrangement is,

After rearrangement in alphabetical order from bottom to top,

Hence, the correct answer is One.

Eight people P,Q,R,S,T,U,V, and W

1)  Only two-person lives between R and S.

2. S lives on an odd-numbered floor below the sixth floor. 

3) Only one person lives between R and P who lives immediately below T. 

4)  V lives on an odd-numbered floor but not on the lowermost floor. 

 

5) The number of people living between Q and U is the same as the number of people between U and P. Q lives below U but not immediately.

6. Q lives below U but not immediately.

7. Therefore Case II and Case III are invalid.

So, the final arrangement is,

Except T, all lives on the even number floor.

Hence, the correct answer is T.

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

Conclusions:

I. Some water can be Fire → True (as there is no relation between water and Fire, so it is possible. Hence, Some water can be Fire is true).

II. Some Fire is water → False (as there is no relation between Fire and water so it is possible nut it's not definite. Hence, Some Fire is water is false).

Hence, Only I follow is the correct answer.

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

Conclusions:

I. Some Mobiles are Bags → False (As No Mobile is Bag, no part of Mobile will be Bag. So, it is false)

II. All Mobiles are Bags → False (As No Mobile is Bag, no part of Mobile will be Bag. So, it is false)

Hence, Neither conclusion I nor II follows.

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

Conclusions:

I. Some Pens are Book → True (because Only a few Pens are Book → Some Pens are Book and Some Pens are not Book. So, It is true)

II. Some Pens are not Book → True (because Only a few Pens are Book → Some Pens are not Books and Some Pens are Book. So, It is true)

Hence, Both conclusions I and II follow.

Given series:

Left Side A C B @ K I 9 D L 4 © 5 2 T $ M 4 J # U 3 1 A δ K 5 V W 6 % F Q 7 H P Right Side

Alphabets which are immediately preceded by an alphabet and followed by a symbol:

Required order is: Alphabet → Alphabet → Symbol

A C B @ K I 9 D L 4 © 5 2 T $ M 4 J # U 3 1 A δ K 5 V W 6 % F Q 7 H P

Hence, there is only one alphabet which is immediately preceded by an alphabet and followed by a symbol: C B @.

Given series:

Left Side A C B @ K I 9 D L 4 © 5 2 T $ M 4 J # U 3 1 A δ K 5 V W 6 % F Q 7 H P Right Side

Required order: First A → → Consonant → Number → Consonant → → W

A C B @ K I 9 D L 4 © 5 2 T $ M 4 J # U 3 1 A δ K 5 V W 6 % F Q 7 H P 

Hence, there are 2 such numbers.

Given series:

Left Side AC B @ K I 9 D L 4 © 5 2 T $ M 4 J # U 3 1 A δ K 5 V W 6 % F Q 7 H PRight Side

Vowels which are immediately followed by a symbol but not immediately preceded by a number:

required order is: Not number → Vowel → Symbol

A C B @ K I 9 D L 4 © 5 2 T $ M 4 J # U 3 1 A δ K 5 V W 6 % F Q 7 H P

Hence, there is no vowel which are immediately followed by a symbol but not immediately preceded by a number.

Hence, the correct answer is none.

Given series:

Left Side A C B @ K I 9 D L 4 © 5 2 T $ M 4 J # U 3 1 A δ K 5 V W 6 % F Q 7 H P Right Side

15^th from the left → $

15^th from right → 3

Terms between $and 3 are M 4 J # U

Therefore, J is exactly in middle of $and 3.

Hence, J is exactly in middle between the fifteenth from the left end and the fifteenth from the right end in the above arrangement.

Given series:

Left Side A C B @ K I 9 D L 4 © 5 2 T $ M 4 J # U 3 1 A δ K 5 V W 6 % F Q 7 H P Right Side

As, Right – Right = Right

6^th from the Right – 5^th from the Right = 1^st from the Right

Clearly, 1^st from the Right is P.

Hence, P is the fifth to the right of the sixth element from the right end of the above arrangement$.

So, we get HI, GH, ST, and EG

Hence, we have 4 pairs of letters as in the English alphabetical series.

Given words: NGX      FHZ      TJU      DOU      WCM

1. Replacing first and last letter to immediate preceding letter:

MGW   EHY   SJT   COT   VCL

2. Clearly, there are two words EHY and COT which have only one vowel.

Note: In English alphabetical series there are 5 vowels i.e. A, E, I, O, U else all are consonants.

Hence, two words have only one vowel after rearrangement.

Given words: NGX      FHZ      TJU      DOU      WCM

1. Replacing each consonant to 2^nd preceding letter:

LEV   DFX   RHU   BOU   UAK  

2. Clearly, two words BOU and UAK have two vowels.

Note: In English alphabetical series there are 5 vowels i.e. A, E, I, O, U else all are consonants.

Hence, two words have two vowels after rearrangement.

Given words: NGX      FHZ      TJU      DOU      WCM

1. Sum of WCM → 23 + 3 + 13 = 39

Hence, 39 is the sum of WCM.