The correct answer is 'Accompanied'.

Key Points

• The given sentence is in the past tense that can be identified by the usage of the second form 'went'.
• During the vacation, normally children wish to spend time with their parents. The same situation has been stated in the sentence.
• Accompany (verb) means 'to go somewhere with someone as a companion'
• Hence, the correct answer is Option 3.

Additional Information Let's understand the meaning of other options.

• Associate (verb) - to connect someone or something in your mind with someone or something else - He is glad to be associated with this project.
• Abandon (verb) - to leave something or someone usually forever -  The king abandoned his kingdom and spent the rest of his life as a saint.
• Isolate (Verb) - to separate something from other things with which it is connected - He isolated himself from the company of narrow-minded people.

The incorrect spelling is 'Failier'.

Key Points

• The accurate spelling of 'failier' is 'failure'.
• Failure (noun) means a lack of success in doing something.
• The meeting was a complete failure because no one was prepared.
• Hence, the correct answer is option 4.

Additional Information Let's understand the meaning of other options.

• Approval (noun) - official permission - They have received the approval to construct a building on this land.
• Commitment (noun) - a firm decision to do something - The students fulfilled their commitment to complete the project on time.
• Development (noun) - the process in which someone or something grows or changes and becomes more advanced - Nutritious diet is essential for the development of a healthy mind.

The correct answer is 'BADC'.

Key Points

• Whenever we try to arrange the sequence of the jumbled sentences, it's important to find out the first sentence.
• The sentence 'B' is the first one as it explains the situation perfectly. (When I was a street away from my house, I saw a huge banyan tree to my right.)
• The second in the sequence would be the sentence 'A' that states what I saw beneath the tree. (I saw a middle-aged man sitting beneath the tree with his knees drawn up to his chest.)**
• The third in the sequence would be the sentence 'D' that tells about the condition of that middle-aged man. (His head was bowed and his body was shivering continuously.)
• The sentence 'C' is the last one as it talks about how I felt at the end. ( My heart went out to him as he was crying bitterly.)

​Hence, the correct answer is option 2.

Additional Information

• Let's understand some important words given in the sentences.
• Shiver (verb) - to shake slightly or quickly because of feeling cold, ill, or frightened - She was shivering with the cold that's why she covered herself with the blanket.
• Bitterly (adverb) - in a way that shows deep anger and pain - He was bitterly disappointed when he couldn't get through the exam.

The correct answer is 'Astronomy.

Key Points

• 'Astronomy' is the study of objects and matter outside the earth's atmosphere and of their physical and chemical properties.
• For e.g.- Because Tim was fascinated with astronomy, he asked his parents to buy him a telescope.
• Hence, the correct answer is option 3.

Additional Information Let's understand the meaning of other words.

• Astrology - the study of the movements and positions of the sun, moon, planets, and stars in the belief that they affect the character and lives of people.
• Gemology - It is the science of studying, cutting, and valuing precious stones, but the essence lies in identifying the gemstones.
• Physiology - It is the scientific study of functions and mechanisms in a living system.

The correct answer is 'Alternatives',

Key Points

• The given sentence is about making choice out of four options. (For each question, four ______ are given as options.)
• Alternative means something that is different, especially from what is usual; a choice.
• ​I am left with no alternative but to leave the organization.
• ​Hence, the correct answer is option 1.​

Additional Information

Let's understand the meaning of other words.

• Altercation (noun) - a loud argument or disagreement - There should be no space for an altercation between the experienced employees.
• Alternate (noun) - a person or a thing that can take the place of another - Brad served as the alternate of Tom as he was too sick to come.
• Alteration (noun) - the action or process of changing or being changed - There should be some alterations required in the plan.

The correct answer is 'Seriousness'.

Key Points

• Severity (noun) means Seriousness or quality of being very unkind or unpleasant.
• In order to understand the severity of our financial problems, one has to undergo the same situation. (Seriousness)
• The severity of his comments surprised everyone. (Not kind)
• Hence, the correct answer is option 4.

Additional Information Let's understand the meaning of other words.

• Anguish (noun) - extreme sadness caused by physical and mental suffering - In his anguish, he ignored to answer the call of the customer.
• Pain (noun) - a feeling of physical or mental suffering  - People normally take heavy medicines to get instant relief from pain.
• Support (noun) - emotional or practical help - Dale gave me a lot of support when I faced financial crises.

The correct answer is 'The yoga instructor told us that doing yoga daily would help us to develop a healthy mind and body.'

Key PointsFollow some basic rules, whenever you have to convert the speech from direct to indirect.

• In the first part of the sentence (reporting speech), remember to change the verb according to the tense.
• Remove inverted commas using 'that'.
• In the second part of the sentence (reported speech), remember to change the verb according to the tense of the first part of the sentence (reporting speech)

On the basis of the above rules, change 'said to' into 'told' and 'will' into would' as the sentence is in the past tense.

The indirect speech would be 'the yoga instructor told us that doing yoga daily would help us to develop a healthy mind and body.'

Hence, the correct answer is option 3.

Additional Information Let's understand the concept with some more examples

• Patrick said to Sara, "I will meet you in the restaurant."
• Patrick told Sara that he would meet her in the restaurant.
• She said to me, "I will help you in English."
• She told me that she would help me in English.

The correct answer is 'All the topics in the syllabus should be covered by teachers.'

Key Points In order to convert from active to passive voice, we need to understand some basic rules.

• Start the sentence with the object. (All the topics in the syllabus - 'object')
• If a modal is used in the sentence, use 'be + verb 3rd form' with the given model. (should be covered - 'be + verb 3rd form')
• In the end, use 'by + subject (doer)' in order to show the relation between the action and subject. (by teachers - 'by + subject or doer')

Now if we follow the above rules, the sentence will be:

• All the topics in the syllabus should be covered by teachers

​Hence, the correct answer is option 2.

Additional Information Let's understand the concept with some more examples.

• The government should open more schools.
• ​More schools should be opened by the government.
• ​Smith can solve this sum.
• ​This sum can be solved by Smith.

The correct answer is 'Appear'.

Key Points

• Emerge (verb) means to appear by coming out of something. (किसी चीज से बाहर आकर प्रकट होना)
• The fact behind the conspiracy is confirmed to emerge eventually.
• Hence, the correct answer is option 1.

 Additional Information Let's understand the meaning of other words.

• Mingle (verb) - to mix or combine - It's easy for me to mingle with others especially if we have a common understanding of something. (मिलाना या मिलाना - मेरे लिए दूसरों के साथ घुलना-मिलना आसान है, खासकर अगर हमें किसी चीज़ की सामान्य समझ है)
• Withhold (verb) - to refuse to give something or to keep back something (कुछ देने या कुछ वापस रखने से इंकार करने के लिए) - Defense employees always withhold crucial information from everyone.
• Leave (verb) - to go away from someone or something (किसी से या किसी चीज से दूर जाना) - She left me alone in the dark.

The incorrect spelling is 'Seenary'.

Key Points 

• The accurate spelling of 'seenary' is 'scenery'.
• It means the general appearance of the natural environment.
• No one can ignore the spectacular view of mountain scenery.
• Hence, the correct answer is option 3.​

Additional Information

Let's understand a bit more about the word 'scenery'.

• The word 'scenery' is an uncountable noun.
• sceneries - wrong
• a scenery -  wrong

The correct answer is 'An unclear situation'.

Key Points

• Grey area means a situation that is not clear or where the rules are unknown. (ऐसी स्थिति जो स्पष्ट नहीं है या जहां नियम अज्ञात हैं)
• A lawyer tried his best to highlight many grey areas related to the case.
• Hence, the correct answer is **option 3.**​

Additional Information

Let's take some more examples to understand.

• I have to decide the right time to discuss this grey area with my aspirants.
• Making money in the stock market is always a grey area for outsiders.

The correct answer is 'was crying'.

Key Points The sentence is related to the past tense as it can be identified with the usage of 'could' & 'other combined sentence'.

• Has been crying - present perfect continuous tense - to use this tense it's essential to mention period or point of time in the sentence.
• Can be crying - the accurate way to use this format is 'model + be + verb 3rd form', so it's incorrect.
• Is been crying - again it's an inaccurate format.

Hence, the correct answer is option 1.

Additional Information Let's understand the concept with some more examples.

• He has been studying since morning. (present perfect continuous tense with a point of time)
• Food can be cooked in 10 minutes. (passive voice - model + be + verb 3rd form)

The correct answer is 'Gulp'.

Key Points

• Sip - to drink, taking only a very small amount at a time.
• Choke - to have severe difficulty in breathing due to the obstructed throat or a lack of air.
• Swish - to move quickly through the air making a soft sound.
• Gulp - to eat or drink liquid quickly by swallowing it in a large amount.

Hence, the correct answer is option 3.

Additional Information Let's understand the words with some examples.

• I always enjoy having sips of coffee early morning.
• Children can choke on peanuts.
• I heard the sword swish through the air.
• She swallowed her drink in one gulp.

The correct answer is 'Fluctuating'.

Key Points

• Constant (adjective) means: 
• Happening a lot or all the time.
• John was in constant trouble with his neighbor.
• Staying the same, not getting less or more.
• ​The demand for homemade food will always remain constant.
• The opposite of this term is Fluctuate which means to change or vary frequently between one level or thing and another.

Hence, the correct answer is option 4.

Additional Information Let's understand the meaning of other words.

• Competent (adjective) - able to do something well - John is competent at his work.
• Static - staying in one place without moving - Fuel prices have remained static for the last few weeks.
• Unchanging - not changing, not being different - Some people always say that the habit of drunkards is unchanging.

The correct answer is 'awkward'.

Key Points

• Graceful means moving in a smooth, relaxed, attractive way, or having a smooth, attractive shape.
• She presented herself in a graceful manner.
• The opposite of this term is awkward which means embarrassed or nervous; moving in a way that is not natural or attractive.
• No one was expecting such an awkward performance of the singer.
• Hence, the correct answer is **option 4.**​

Additional Information

Let's understand the meaning of other words.

• Attractive - very pleasing in appearance and sound - I still remember one of my classmates who was very attractive.
• Dangerous - able or likely to cause harm - It is really dangerous to be here at night.
• Pretty - quite, but not extremely; pleasant to look at - I have got such a pretty daughter.

The correct answer is 'to not know something others are aware of'.

Key Points

• To be in the dark means to be uninformed or unaware of something or someone. (बेख़बर होना या किसी चीज़ या किसी से अनजान होना)
• Till the end, she was in the dark about the notice period that had to be served after resignation.
• Hence the correct answer is option 1.

Additional Information Lets's understand this idiom with some more examples.

• ​Our manager tends to keep us in the dark especially when it's about the upcoming holiday.
• My brother kept me in the dark about his new business plan.

The correct answer is 'loose for me'.

Key Points

• The sentence is about the clothe i.e. shirt.
• Either it can be tight or loose.
• Hence, the correct answer is option 3.

Additional InformationLet's understand the meaning of other words.

• Lost - not knowing one's whereabouts - I lost my younger brother in a big 'Kumbh' fair.
• Loss - the process of losing something - He faced financial loss at an early age and gained experience to tackle such issues.

The correct answer is 'were warning'.

Key Points

• It can be easily understood that the sentence is in the past tense (passive voice).
• In passive voice, verb 3rd form is always used with the helping verb.
• That's why the format 'were warning' is incorrect.
• The accurate format should be 'were being warned' or 'were warned'.
• Hence, the correct answer is 'option 2'.

Additional Information Let's understand the concept with some more examples.

• The children were instructed not to play here as the floor was very slippery.
• Tourists were being informed not to go for tracking as the weather condition was not favorable.

The correct answer is ACDB

Key Points

• On reading the sentence, we can comprehend that the passage is all about the misinformation spread by the person.
• The first sentence will be sentence A as it tells us that the person is spreading rumors.
• The second sentence will be sentence C as it tells us that one evening the neighbors got arrested by the police.
• The third sentence will be sentence D as it tells us that after the investigation they were found innocent.
• The fourth sentence will be sentence B as it is the only sentence left.

So the correct passage is- He often spread rumors that his neighbors were thieves. One evening, some of them were arrested by the police. After the investigation, they were proven innocent.  After being released, one of them sued him for wrongly accusing them.

The correct answer is 'How many is'.

Key Points

• The sentence is related to the present tense where someone wants to know something.
• Here, the word 'fine' is a singular noun, it can't come with the determiner 'many'.
• Much is accurate with the word 'fine'.
• The sentence should be 'I'm sorry, sir. How much is the fine for returning the books late?'
• Hence, the correct answer is option 3.

Additional InformationLet's understand the concept of how much or how many.

• How much - can be used with an uncountable noun - sugar, time, money, milk, etc. - How much time will you take to get ready?
• How much - can be used with a countable noun to know the price - dress, jacket, etc. - How much is this jacket?
• How many - can be used with a countable plural noun - dresses, jackets, books, etc. - How many dresses have you bought?

The correct answer is 'Symbol'.

Key Points

 

• The passage talks about the various symbols used on garbage bins and the right ways to dispose of the waste.
• In the sentence, a kind of sign indicates the way to dispose of a particular type of item. (The wheeled-bin ______ which is crossed out indicates that the item______ be disposed of separately from household waste.)
• A kind of sign must be a symbol that can give an indication. Other options are not relevant as per the context.
• Hence, the correct answer is option 1.​

Additional Information

• Crossed out wheeled bins symbol reminds us that all electrical and electronic products and batteries must be taken to separate collection at the end of their working life.

The correct answer is 'shouldn't'.

 

Key Points

• The passage discusses the proper disposal methods for certain items, particularly focusing on those that need to be kept separate from household waste.
• The appropriate word should indicate that the item must not be mixed with household waste.
• "Shouldn't" fits well as it denotes that it is not proper to dispose of the item with household waste, aligning with the given instructions.
• Other options ("have", "can't", "won't") do not fit the context of describing proper waste disposal methods.

Therefore, the correct answer is 'Option 1'.

 

Complete Passage: These are the various symbols used on garbage bins. The wheeled-bin symbol which is crossed out indicates that the item shouldn’t be disposed of separately from household waste. The item should be handed in for recycling according to local environmental regulations for waste disposal. By separating a marked item from household waste, you will help reduce the volume of waste sent to landfills. It will also minimize any potential negative impact on human health and the environment. For more information, please contact your nearest civic official.

 

Additional Information

• Have (कचरा डालना): "Have" implies possession, which does not fit the context of discussing proper disposal methods.
• Can’t (नहीं कर सकता): "Can’t" means something that is not allowed, which is not as appropriate to use in this context as "shouldn’t".
• Won’t (नहीं होगा): "Won’t" means something that will not happen, which does not align with describing disposal rules.

The correct answer is 'according'.

Key Points

• Whenever "based on" some rules and regulations, we try to explain something, always use 'as per rules and regulations or according to the rules and regulations.
• In the sentence, as per local environmental regulations, it is mentioned that "what should be done" with the waste (The item should be handed in for recycling ______ to local environmental regulations for waste disposal.)
• Other options are not relevant as per the context.
• Hence, the correct answer is option 4.

Additional Information

• Let's try to understand the concept of 'according to' with some more examples.
• According to (preposition) used for saying which person or group provides a particular fact.
• According to a company spokesman, the firm is expected to make the highest profit this month.
• According to the world health organization, there have been 42,536,137 confirmed cases of COVID-19.

The correct answer is 'separating'.

Key Points

• The sentence talks about the segregation of marked items that will somewhere be beneficial. (By ______ a marked item from household waste, you will help reduce the volume of waste sent to landfills.)
• Apart from the word 'separating' none of the above-given options expresses segregation.
• Hence, the correct answer is option 1.

Additional Information

• Segregate (verb) means to keep one thing separate from another.
• By separating or segregating negative attitudes, one will be able to climb the ladder of success in a short period.
• Separate or segregate the odd one out from the given question.

The correct answer is 'minimise'.

Key Points

• All in all, for the benefits of human health and the environment, the passage talks about the various symbols used on garbage bins and the right ways to dispose of the waste.
• It's obvious that the awareness of symbols and waste disposal methods will reduce or minimise the negative impact. (It will also ______ any potential negative impact on human health and the environment.)
• Apart from the word 'minimise', the rest of the options aren't relevant as per the context.
• Hence, the correct answer is option 3.

Additional Information

• Many aspirants have confusion related to the spelling of Minimise or Minimize.
• Both the spellings are correct.
• 'Z' is used in American English.
• 'S' is used in British English.

Table show alphabet serial number –

The pattern followed is,

All follow the same pattern, except 'ASOJIB’.

Hence, “ASOJIB” is the odd one.

The pattern followed here is:

  

Hence, '121' is the correct answer.

 **Important Points:**Prime number series is 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41.

Here the next term of the series is obtained by adding the alternative prime numbers and skipping the adjacent one. Here prime number series started from 5.

For example:  5 added to 34 but 11 added to 39, skipped to add 7 and so on.

Note: Here 7 is not difference of 11 and 5.

The number of triangles in the given figure is:

 

So, there are a total of 8 triangles in the figure.

Hence, ‘8’ is the correct answer.

The table is alphabets place value:

The pattern followed here is:

Step1: All consonants are coded as the next alphabet.

• Consonants + 1

Step2: All vowels are coded as the previous alphabet.

• Vowel - 1

PAINT is written as QZHOU.

And,

BASK is written as CZTL.

Similarly,

Hence, 'MOVIE' is coded as "NNWHD".

The table is alphabets place value:

The pattern followed here is:

(Sum of the positional values of the letters)² = number.

ROHAN →.

R(18) + O(15) + H(8) + A(1) + N(14) = 18 + 15 + 8 + 1 + 14 = 56

(Sum of the positional values of the letters)² = number

=> (56)² = 3136

And,

SHYAM →

S(19) + H(8) + Y(25) + A(1) + M(13) = 19 + 8 + 25 + 1 + 13 = 66

(Sum of the positional values of the letters)² = number

=> (66)² = 4356

Similarly,

RAM →

R(18) + A(1) + M(13) = 18 + 1 + 13 = 32

(Sum of the positional values of the letters)² = number

=> (32)² = 1024

Hence, RAM will be written as “1024”.

Given :- p r _ b n _ r q _ n p _ q b _ p _ q _ n

By checking options and substituting accordingly.

Option (1) q, p, b, r, n, r, b → p r q b n - p r q b n - p r q b n - p r q b n

      ♦   Here p r q b n is repeated itself.

Option (2) q, b, p, n, r, n, r → p r q b n - b r q p n - p n q b r - p n q r n

Option (3) q, p, b, r, r, n, n → p r q b n - p r q b n - p r q b r - p n q n n

Option (4) q, r, n, p, b, r, n → p r q b n - r r q n n - p p q b b - p r q n n

     ♦   Option (1) gives a pattern of p r q b n - p r q b n - p r q b n - p r q b n.

Hence, ‘q, p, b, r, n, r, b’ is the correct answer.

The logic here is,

JOKERS : NKOAVO

Similarly,

ROMING : ?

Hence, "VKQERC" is correct answer.

The embedded part of this image is:

Hence, option (3) is the correct answer.

The pattern follows here is:

1. Star figure rotate upper left to lower right and vice-versa.

2. circle rotate an anti-clockwise direction of the square each corner.

The figure that will replace the question mark (?) in the following figure series is shown below:

Hence, ‘option 4’ is the correct answer.

The logic followed here is:

Spoon : Feeding → The spoon is used to feeding food.

Similarly,

Microscope : Magnifying → The microscope is used to magnify small objects.

Hence, 'Magnifying' is the correct answer.

Additional Information

• Radiating → linear accelerators or cobalt machines is used in radiation therapy.
• Grinding → Grinding machine used to grind any object.
• Heating → Heating devices like the heater is used to heat any object.

The Venn diagrams best represent the relationship between - Women, Gynaecologists, Doctors figures are shown below:

All Gynaecologists are doctors, some women are doctors and some women are Gynaecologists.

Hence, ‘option 2’ is the correct answer.

The correct mirror image of the given figure when the mirror is held at the right side is:

Hence, "option (1)" is the correct answer.

Additional Information 

In Mirror image left side and right side changed vice-versa where top and bottom remain same.

Reflection of an object into the water is its water image. It appears by inverting an object vertically i.e. upside down.

The water image of the figure looks like the mirror image of the figure in case the mirror is horizontally at the bottom of the figure.

Water image is just a reflection where top and bottom part of the images changed where left and right side of the image remain same.

The pattern followed here is:

(1^st number ÷ 6) × 9 = 2^nd number

Now follow the steps:

54 : 81

(1^st number ÷ 6) × 9

= (54 ÷ 6) × 9

= 9 × 9

= 81 = 2^nd number

Similarly,

6 : ?

(1^st number ÷ 6) × 9

= (6 ÷ 6) × 9

= 1 × 9

= 9 = 2^nd number

Hence, "9" is correct answer.

Given:

Three books coded as A, B and C.

1. The price of book A is twice the price of book B

=> A = 2B → eq. 1

2. The price of book A is one-third the price of book C

=> A = 1/3 C → eq. 2

3. Book C costs Rs. 84

Put the value in eq. 2

=> A = 1/3 × 84

=> A = 28

Put the value of A in eq 1;

=> A = 2B

=> 28 = 2B

=> B = 28 ÷ 2

=> B = 14

Hence, the costs of book A and book B, respectively “Rs. 28 and Rs. 14”.

The logical and meaningful order of the given words is as follows:

LOGIC: The words have been arranged according to the stage of vegetable cook.

3. Buy → Firstly we buy vegetables.

2. Rinse → Then we rinse vegetables.

4. Cut → After the rinse vegetables we cuts the vegetables.

5. Cook → Then after cutting we cook the vegetables.

1. Eat → After cooked vegetable we can eat.

Hence, "3, 2, 4, 5, 1" is the correct answer.

The image obtained when the paper is unfolded is,

Hence, "option 1" is the correct answer.

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.

Given:

From the dice X and Y: @ is common in both so we can rotate clockwise or anticlockwise of the given dice.

 

Here, Opposite of ! is %.

From dice Y and Z → ‘!’ is the common face

 

So,

1) ‘@’ is the opposite face of ‘*’.

2) ‘$’ is the opposite face of ‘%’

From the cube 'X' only ‘#’ is remaining

So the opposite face of ‘!’ is ‘#’.

From dice X and Z: % is common, so we can rotate clockwise or anticlockwise of the given dice.

 

Here, Opposite of ! is #.

So, comparing with all dices, opposite face of ‘!’ is ‘#’.

Hence, “#” is the correct answer.

The logic followed here is:

Given:

Circle : Arc → Arc is the part of Circle.

Similarly,

Flower : Petal → Petal is the part of Flower.

Hence, ‘Petal’ is the correct answer.

The logic followed here is:

Option (1) Scurvy → Scurvy is a disease resulting from a lack of vitamin C.

Option (2) Psoriasis → Psoriasis is the disease of skin problems.

Option (3) Vitiligo→ Vitiligo is the disease of skin problems.

Option (4) Eczema→ Eczema is the disease of skin problems.

All diseases are skin problems except Scurvy.

Hence, “Scurvy” is an odd one.

Decoding the information, 

Given:

15 C 7 B (24 D 8) A 16 C 4 B 21 D 3

After replacing the signs from left to right and using the BODMAS rule,

15 × 7 - (24 ÷ 8) + 16 × 4 - 21 ÷ 3

= 15 × 7 - 3 + 16 × 4 - 7

= 105 - 3 + 64 - 7

= 169 - 10

= 159

Hence, “159” is the correct answer.

Statements:

Some lights are wires.

All appliances are lights.

All bulbs are appliances.

The least possible diagram for the given statements is as follows

Conclusions:

I. Some lights are appliances → True (because all appliances are lights so some lights are also appliances)

II. Some wires are bulbs → False (It is possible but not definite)

III. All bulbs are lights → True (because all bulbs are appliances and all appliances are light so all bulbs are also lights)

Hence, “Both conclusions I and III follow”.

The pattern is following here,

First digit × last digit = middle digits

Option 1) 1055 → 1 - 05 - 5 → 1 × 5 = 5 = middle number

Option 2) 3124 → 3 - 12 - 4 → 3 × 4 = 12 = middle number

Option 3) 6457 → 6 - 45 - 7 → 6 × 7 = 42 ≠  middle number

Option 4) 4328 → 4 - 32 - 8 → 4 × 8 = 32 = middle number

All options follow the same pattern, except ‘Option 3’

Hence, "6457" is the correct answer.

Preparing the family tree using the following symbols,

Given:

1. U is the father of M.

2. V is the wife of K.

3. D is the mother of K's only brother M.

Hence, U is the "Husband" of D.

The Logic here is as follows:

(2^nd number - 1^st Number)² = 3^rd Number

In (11, 20, 81)

(2^nd number - 1^st Number)²

= (20 - 11)²

= 9²

= 81 = 3^rd Number

Now check the all options,

Option (1) (36, 28, 25)

(2^nd number - 1^st Number)²

= (28 - 36)²

= (- 8)²

= 64 ≠ 3^rd Number

Option (2) (25, 36, 121)

(2^nd number - 1^st Number)²

= (36 - 25)²

= 11²

= 121 = 3^rd Number

Option (3) (12, 30, 224)

(2^nd number - 1^st Number)²

= (30 - 12)²

= 18²

= 324 ≠ 3^rd Number

Option (4) (14, 29, 64)

(2^nd number - 1^st Number)²

= (29 - 14)²

= 15²

= 225 ≠ 3^rd Number

Hence, the correct answer is "(25, 36, 121)".

The Logic here is as follows:

(1^st number)² + 1^st number = 2^nd number

(2^nd number)² + 2^nd number = 3^rd number

In (1, 2, 6)

(1^st number)² + 1^st number

=> 1² + 1 = 1 + 1 = 2 = 2^nd number

(2^nd number)² + 2^nd number

=> 2² + 2 = 4 + 2 = 6 = 3^rd number

Now check the all options,

Option (1) (10, 20, 40)

(1^st number)² + 1^st number

=> 10² + 10 = 100 + 10 = 110 ≠ 2^nd number

(2^nd number)² + 2^nd number

=> 20² + 20 = 400 + 20 = 420 ≠ 3^rd number

Option 2) (7, 14, 49)

(1^st number)² + 1^st number

=> 7² + 7 = 49 + 7 = 56 ≠ 2^nd number

(2^nd number)² + 2^nd number

=> 14² + 14 = 196 + 14 = 210 ≠ 3^rd number

Option 3) (1, 2, 16)

(1^st number)² + 1^st number

=> 1² + 1 = 1 + 1 = 2 = 2^nd number

(2^nd number)² + 2^nd number

=> 2² + 2 = 4 + 2 = 6 ≠ 3^rd number

Option (4) (5, 30, 930)

(1^st number)² + 1^st number

=> 5² + 5 = 25 + 5 = 30 = 2^nd number

(2^nd number)² + 2^nd number

=> 30² + 30 = 900 + 30 = 930 = 3^rd number

Hence, the correct answer is "(5, 30, 930)".

Calculation:

Total number of production in 2015 and 2017 together = (600 + 750)

⇒ 1350

Total number of sales in 2018 and 2019 together = (400 + 516)

⇒ 916

The difference in the production in 2015 and 2017 taken together and the sales in 2018 and 2019 taken together = (1350 – 916)

⇒ 434

∴ The required difference is 434

Given:

θ ∶ 2√3 sin2 θ + cos θ – √3 = 0

Formula used:

sin²θ + cos²θ = 1

⇒ sin²θ = 1 – cos²θ 

Calculation:

2√3 sin2 θ + cos θ – √3 = 0

⇒ 2√3(1 – cos²θ) + cosθ – √3 = 0

⇒ 2√3 – 2√3cos²θ + cosθ – √3 = 0

⇒  2√3cos2θ – cosθ – √3 = 0

Let cosθ = x

Now,

⇒ 2√3x² – x – √3 = 0

⇒ 2√3x² – 3x + 2x – √3 = 0

⇒ √3x(2x – √3) + 1(2x – √3) = 0

⇒ (√3x + 1) (2x – √3) = 0

⇒ x = -1/√3, √3/2

So, cos √3/2 = cos30° 

⇒ θ = 30° 

∴ The required value of θ is 30° 

Alternate MethodExam approach -

Hit and trial -

Put θ = 30° 

2√3cos2θ – cosθ – √3 = 0

⇒ 2√3cos230° – cos30° – √3 = 0

⇒ 2√3(3/4) - √3/2 - √3 = 0

⇒ 3√3/2 - 3√3/2 = 0

⇒ 0 = 0

∴ The value of θ is 30°.

This method is useful if you have good command on value putting.

Given:

a + b + c = 4

ab + bc + ca = -14

abc = -18

Formula used:

(a + b + c)² = a² + b² + c² + 2(ab + bc + ca)

a³ + b³ + c³ – 3abc = (a + b + c) (a² + b² + c² – ab – bc – ca)

Calculation:

According to the question

 (a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca)

⇒ a² + b² + c² = (4)² – 2 × (-14)

⇒  a2 + b2 + c² = 16 – (-28)

⇒ a² + b² + c² = (16 + 28) = 44

Now,

The value of $√{4a^3+4b^3+4c^3-36}$

⇒ √4(a³ + b³ + c³) – 36

⇒ √4(a + b + c) (a2 + b2 + c2 – ab – bc – ca) + 3abc – 36

⇒ √4 × [4 × {44 – (-14) + 3 × (-18)}] – 36

⇒ √4 × [(4 × 58) – 54] – 36

⇒ √4 × (232 – 54) – 36

⇒ √(4 × 178) – 36

⇒ √712 – 36

⇒ √676

⇒ 26

∴ The required value is 26 

Alternate Method$√{4a^3+4b^3+4c^3-36}$

⇒ $√{4(a^3+b^3+c^3)-36}$

⇒ √4(a + b + c)((a + b + c)2 - 3(ab + bc + ca)) + 3abc – 36

⇒ √4 × [4{4 × 4 - 3 × (-14)} + 3 × (-18)] - 36

⇒ √16(16 + 42) - 4 × 54 - 36

⇒ √928 - 216 - 36

⇒ √676

⇒ 26

∴ The required value is 26

Given:

Total number of sheets = 800

A shopkeeper charges Rs. 1.50 to photocopy a sheet of paper

A discount of 5.5% is given on all photocopies done after 400 sheets

Calculation:

According to the question

Cost to photocopy next 400 sheets = Rs. (400 × 1.50) 

⇒ Rs. 600

Now,

Cost to photocopy after 400 sheets = [(400 × 1.50) × 94.5/100]

⇒ (600 × 94.5/100)

⇒ (6 × 94.5)

⇒ Rs. 567

Cost to photocopy 800 sheets of paper = Rs. (600 + 567)

⇒ Rs. 1,167

∴ The required cost is Rs. 1,167

Shortcut Trick

Radius (r) = 18 ÷ 2 = 9 cm.

Slant height (l) = CSA ÷ (π × r) = (2970 / 7) ÷ (22 / 7 × 9) = 15 cm.

In a cone, height (h), radius (r), and slant height (l) form a right-angled triangle.

Using the Pythagorean triplet (9, 12, 15), where r = 9 and l = 15, the height must be 12.

∴ The correct answer is 12 cm.

Alternate Method

Given:

Diameter of the base = 18 cm

Curved Surface Area (CSA) = 424 2/7 cm²

Formula Used:

1. Radius (r) = Diameter ÷ 2
2. Curved Surface Area of a cone = πrl
3. Slant height (l)² = r² + h²

Calculations:

⇒ Radius (r) = 18 ÷ 2 = 9 cm

⇒ CSA = 424 2/7 = (424 × 7 + 2) ÷ 7 = 2970 / 7 cm²

⇒ π × r × l = 2970 / 7

⇒ (22 / 7) × 9 × l = 2970 / 7

⇒ 198 × l = 2970

⇒ l = 2970 ÷ 198 = 15 cm

⇒ Height (h) = √(l² − r²)

⇒ h = √(15² − 9²)

⇒ h = √(225 − 81)

⇒ h = √144

⇒ h = 12 cm

∴ The correct answer is 12 cm.

Additional Information

Total Surface Area (TSA)

The Total Surface Area of a cone is the sum of the curved area and the base area: TSA = πr(l + r).

Volume of a Cone

The Volume represents the capacity of the cone: V = 1/3 × πr²h.

Pythagorean Relationship

In any right circular cone, the relationship between slant height, vertical height, and radius is l² = h² + r².

∴ The correct answer is 12 cm.

Calculation:

The total production of table fans on Tuesday and Wednesday together = (510 + 390)

⇒ 900

The total production of table fans on Thursday and Friday together = (150 + 300)

⇒ 450

The ratio of the total production of table fans on Tuesday and Wednesday together to that on Thursday and Friday together = (900 : 450)

⇒ 2 : 1

∴ The required ratio is 2 : 1

Given:

The ratio of boys and girls in a school = 6 : 7

The total number of students in the school = 3289

Calculation:

Let the ratio of boys and girls be 6x and 7x respectively.

According to the question

⇒ (6x + 7x) = 3289

⇒ 13x = 3289

⇒ x = (3289/13)

⇒ x = 253

Now,

The number of girls = 7x = (7 × 253)

⇒ 1771

∴ The required number of girls is 1771

Alternate Method(6 + 7) units = 3289

⇒ 13 units = 3289

⇒ 1 unit = 3289/13

⇒ 1 unit = 253

The number of girls = 7 units = 7 × 253 = 1771

∴ The required number of girls is 1771

Given:

The average of 5 numbers = 26.4

The first number is one-fifth of the sum of the remaining 4 numbers

Formula used:

Average = sum of observations/Number of observations

Calculation:

Let the 5 numbers be a, b, c, d and e respectively.

According to the question

The first number is one-fifth of the sum of the remaining 4 numbers

⇒ a = (b + c + d + e)/5

⇒ 5a = b + c + d + e

Now,

The average of 5 numbers = (a + b + c + d + e)/5 = 26.4

⇒ (a + b + c + d + e) = (26.4 × 5)

⇒ (a + b + c + d + e) = 132

⇒ b + c + d + e = 132 – a

Now,

⇒ 5a = 132 – a

⇒ 6a = 132

⇒ a = (132/6)

⇒ a = 22

∴ The first number is 22

Alternate MethodThe sum of all numbers = 26.4 × 5 = 132

First number ∶ Remaining 4 number = 1 ∶ 5

(1 + 5) units = 132

⇒ 6 units = 132

⇒ 1 unit = The first number = 22

∴ The first number is 22

Given:

∠ABC = 90° 

AB = 6 cm

BC = 8 cm

Formula used:

AC² = AB² + BC²

Calculation:

In ΔABC

AC² = AB² + BC²

⇒ AC² = (6)² + (8)²

⇒ AC² = 36 + 64

⇒ AC² = 100

⇒ AC = 10 cm

Now,

In ΔABC and ΔBDC, ∠B = ∠D = 90° 

BC = BC [common]

∠C = ∠C [common]

∴ ∠ABC ~ ∠BDC [By ASA criteria]

⇒ AC/BC = BC/DC

⇒ DC = BC²/AC

⇒ DC = (8)²/10

⇒ DC = 64/10

⇒ DC = 6.4 cm

And, AD = (AC – DC)

⇒ AD = (10 – 6.4) cm = 3.6 cm

Now,

The ratio of AD and DC = (3.6 : 6.4)

⇒ 9 : 16

∴ The required ratio is 9 : 16

Given:

The perimeter of a circle = 88 cm

Formula used:

Perimeter of circle = 2πr

Area of the circle = πr²

Calculation:

According to the question

Perimeter of circle = 2πr

⇒ 2πr = 88

⇒ (2 × 22/7 × r) = 88

⇒ 44r/7 = 88

⇒ r = (7 × 2) cm

⇒ r = 14 cm

Now,

Area of circle = πr²

⇒ (22/7 × 14 × 14) cm²

⇒ (22 × 28) cm²

⇒ 616 cm²

∴ The required area of the circle is 616 cm²

Given:

From a point P that is at a distance of 15 cm from centre O of a circle of radius 9 cm

A pair of tangents PQ and PR is drawn to the circle

Concept used:

The tangent at any point of circle is perpendicular to the radius through the point of contact.

Tangents through an external point to a circle are equal.

(Base)2 + (Perpendicular)2 = (Hypotenuse)2

Calculation:

Let P be a point at a distance of 15 cm from O.

Draw a pair of tangents, PQ and PR.

OQ = OR = radius = 9cm

And OP = 15 cm

We know that, tangent to at any point on the circle is perpendicular to the radius through point of contact.

Hence, we get

OQ ⏊ PQ and OR ⏊ PR

ΔPOQ and ΔPOR are right-angled triangles

Now,

Using Pythagoras theorem in ΔPQO

(Base)² + (Perpendicular)² = (Hypotenuse)²

⇒ (PQ)² + (OQ)² = (OP)²

⇒ (PQ)² + (9)² = (15)²

⇒ (PQ)² + 81 = 225

⇒ (PQ)² = (225 – 81)

⇒ (PQ)² = 144

⇒ PQ = 12 cm

Tangents through an external point to a circle are equal.

So,

 PQ = PR = 12 cm

Now,

The area of quadrilateral PQOR = Area of ΔPQO + Area of ΔPRO

⇒ (1/2 × OQ × PQ) + (1/2 × OR × PR)

⇒ (1/2 × 9 × 12) + (1/2 × 9 × 12)

⇒ (54 + 54) cm²

⇒ 108 cm²

∴ The required value is 108 cm²

Given:

a2 + 49b2 + c2 + 18 = 2(28b – c – a)

Formula used:

(a – b)² = a² + b² – 2ab

Calculation:

a2 + 49b2 + c2 + 18 = 2(28b – c – a)

⇒ a² + 49b² + c² + 18 = 56b – 2c – 2a

⇒ a² + 2a + 49b² – 56b + c² + 2c + 18 = 0

⇒ a² + 2a + 1 + 49b² – 56b + 16 + c² + 2c + 1 = 0

⇒ (a + 1)² + (7b – 4)² + (c + 1)² = 0

Now,

(a + 1) = 0 

⇒ a = -1

(7b – 4) = 0

⇒ b = 4/7

(c + 1) = 0

⇒ c = -1

Now, The value of (a + 7b – ​c) = [-1 + 7 × 4/7 – (-1)]

⇒ (-1 + 4 + 1)

⇒ (3 + 1)

⇒ 4

∴ The required value is 4

Alternate MethodDivide the coefficient of a , b and c in the right side by 2. and equal it with the left side respective expression.

a = -2/2 = -1

49b = 56/2 = 28

⇒ b = 4/7

c = -2/2 = -1

Now, The value of (a + 7b – ​c) = [-1 + 7 × 4/7 – (-1)]

⇒ (-1 + 4 + 1)

⇒ (3 + 1)

⇒ 4

∴ The required value is 4

Given:

Time taken to complete a work by P = 9 days

Time taken to complete a work by Q = 15 days

Formula used:

Work = Efficiency × Time

Calculation:

LCM of 9 and 15 is 45

Efficiency of P = (45/9) = 5 units/day

Efficiency of Q = (45/15) = 3 units/day

P and Q worked together for 3 days = [3 × (5 + 3)]

⇒ (3 × 8) = 24 units

Remaining work = (45 – 24) = 21 units

Now,

The remaining work completed by Q alone = (21/3)

⇒ 7 days

∴ The required days is 7

Given:

The difference between a number and its three-fifth = 274

Calculation:

Let the number be x

According to the question

⇒ (x – 3x/5) = 274

⇒ (5x – 3x)/5 = 274

⇒ 2x/5 = 274

⇒ 2x = 1370

⇒ x = (1370/2)

⇒ x = 685

Now,

20% of the number = (20/100 × 685)

⇒ 137

∴ The required number is 137

Alternate MethodLet the number be 5 units.

(5 - 3) units = 274

⇒ 2 units = 274

⇒ 1 unit = 137

⇒ The number = 5 units

20 % of the number = 20% of 5 units = 1 unit = 137

∴ The required number is 137

Given:

A number M is divided by 7, the remainder is 6

Formula used:

(a + b)² = a² + b² + 2ab

Calculation:

Let the number be K

Then,

Let M = 7k + 6

According to the question

⇒ (M)² = (7k + 6)²

⇒ (49k² + 36 + 84k)

Now,

After dividing it by 7, we get

⇒ (49k² + 36 + 84k)/7

⇒ [7k² + (7 × 5) + 1 + 12k]

Now, we can say that when M² is divided by 7, the remainder will be 1.

∴ The required remainder is 1

Alternate MethodLet M = 7 + 6 = 13

Now, M² = 169

⇒ 169/7 = 24 and Remainder = 1

∴ The required remainder is 1

Given:

x8 – 2599x4 + 1 = 0

Formula used:

(a + b)² = a² + b² + 2ab

(a – b)² = a² + b² – 2ab

Calculation:

x8 – 2599x4 + 1 = 0

Dividing the equation by x⁴ we get,

⇒ x⁴ – 2599 + 1/x⁴ = 0

⇒ x⁴ + 1/x⁴ = 2599

As we know,

(x² + 1/x²)² = x⁴ + 1/x⁴ + 2 × x² × 1/x²

⇒ (x2 + 1/x2)2 = x4 + 1/x4 + 2

⇒ (x2 + 1/x2)² = 2599 + 2

⇒ (x2 + 1/x2)² = 2601

⇒ x² + 1/x² = √2601

⇒ x² + 1/x² = 51

Again as we know,

(x – 1/x)² = x² + 1/x² – 2 × x × 1/x

⇒ (x – 1/x)2 = x2 + 1/x2 – 2

⇒ (x – 1/x)² = 51 – 2

⇒ (x – 1/x)² = 49

⇒ (x – 1/x) = √49

⇒ x – 1/x = 7

∴ The required value is 7

Given:

$\rm \sec\left(90^{\circ}-\frac{3θ}{2}\right)=√2$

Formula used:

sec(90 – θ) = cosecθ 

cosec 45° = √2

Calculation:

According to the question

$\rm \sec\left(90^{\circ}-\frac{3θ}{2}\right)=\sqrt2$

⇒ cosec 3θ/2 = cosec 45° 

⇒ 3θ/2 = 45° 

⇒ 3θ = 90° 

⇒ θ = 30° 

Now,

2sin θ + 4cos2θ = (2 × sin30° + 4 × cos60°)

⇒ (2 × 1/2 + 4 × 1/2)

⇒ (1 + 2)

⇒ 3

∴ The required value is 3

Shortcut Trick

Interest for the 1st year = 8% of 60,000 = ₹4,800.

Interest for the 2nd year = 4,800 + (8% of 4,800) = 4,800 + 384 = ₹5,184.

Total Compound Interest for 2 years = 4,800 + 5,184 = ₹9,984.

Since the sum matches the given interest exactly, the time period is 2 years.

∴ The correct answer is 2 years.

Alternate Method

Given: Principal (P) = ₹60,000, Rate (R) = 8% per annum, Compound Interest (CI) = ₹9,984.

Formula Used: Amount (A) = P + CI and A = P(1 + R/100)ⁿ

⇒ Amount (A) = 60,000 + 9,984 = ₹69,984

⇒ 69,984 = 60,000 × (1 + 8/100)ⁿ

⇒ 69,984 / 60,000 = (108/100)ⁿ

⇒ 11,664 / 10,000 = (1.08)ⁿ

⇒ 1.1664 = (1.08)ⁿ

⇒ (1.08)² = (1.08)ⁿ

⇒ n = 2 years

∴ The correct answer is 2 years.

Additional Information

Effective Interest Rate

For a rate R, the effective rate for 2 years in CI is given by (R + R + R×R/100)%. For 8%, it is 8 + 8 + 0.64 = 16.64%.

Difference between CI and SI

The difference between Compound Interest and Simple Interest for 2 years is P(R/100)².

Rule of 72

A quick way to estimate how long it takes for an investment to double: Time ≈ 72 ÷ Interest Rate.

Concept Used:       

Follow the BODMAS rule according to the table given below:

Calculation:

$(86÷20)-\frac{13}{8}\ of\ \left(\frac{1}{3}-\frac{2}{13}\right)+\left(\frac{1}{8}÷\frac{3}{7}\right)+\left(2-\frac{3}{10}\right)$

⇒ (43/10) – 13/8 of (13 – 6)/39 + (1/8 ÷ 3/7) + (2 – 3/10)

⇒ 43/10 – 13/8 of 7/39 + (1/8 ÷ 3/7) + (2 – 3/10)

⇒ 43/10 – 7/24 + (1/8 ÷ 3/7) + (2 – 3/10)

⇒ 43/10 – 7/24 + (1/8 × 7/3) + (2 – 3/10)

⇒ 43/10 – 7/24 + 7/24 + (2 – 3/10)

⇒ 43/10 – 7/24 + 7/24 + (20 – 3)/10

⇒ 43/10 – 7/24 + 7/24 + 17/10

⇒ 43/10 + 17/10

⇒ (43 + 17)/10

⇒ 60/10

⇒ 6

∴ The required value is 6

Calculation:

Total number of production of sugar by company P from the year 2015 to 2019 = (80 + 70 + 80 + 100 + 120)

⇒ 450

The average production of sugar by company P from the year 2015 to 2019 = (450/5)

⇒ 90

Total number of production of sugar by company R from the year 2015 to 2019 = (50 + 70 + 65 + 90 + 100)

⇒ 375

The average production of sugar by company R from the year 2015 to 2019 = (375/5)

⇒ 75

The ratio of the average production of sugar by company P from the year 2015 to 2019 to the average production of sugar by company R from the year 2015 to 2019 = (90 : 75)

⇒ 6 : 5

∴ The required difference is 6 : 5

Shortcut Trick

Apply Componendo and Dividendo: (sin θ + cos θ + sin θ − cos θ) ÷ (sin θ + cos θ − (sin θ − cos θ)) = (3 + 1) ÷ (3 − 1).

⇒ 2 sin θ ÷ 2 cos θ = 4 ÷ 2 ⇒ tan θ = 2.

Using Right Triangle: perpendicular = 2, base = 1, hypotenuse = √(2² + 1²) = √5.

sin⁴ θ − cos⁴ θ = (sin² θ − cos² θ)(sin² θ + cos² θ) = sin² θ − cos² θ = (2/√5)² − (1/√5)² = 4/5 − 1/5 = 3/5.

∴ The correct answer is 3/5.

Alternate Method

Given: (sin θ + cos θ) / (sin θ − cos θ) = 3

Formula Used: sin⁴ θ − cos⁴ θ = (sin² θ + cos² θ)(sin² θ − cos² θ); sin² θ + cos² θ = 1

⇒ sin θ + cos θ = 3(sin θ − cos θ)

⇒ sin θ + cos θ = 3 sin θ − 3 cos θ

⇒ 4 cos θ = 2 sin θ

⇒ tan θ = 2

⇒ sin θ = 2/√5 and cos θ = 1/√5

⇒ sin⁴ θ − cos⁴ θ = (sin² θ − cos² θ)(1)

⇒ (2/√5)² − (1/√5)² = 4/5 − 1/5 = 3/5

∴ The correct answer is 3/5.

Additional Information

Trigonometric Identities

Fundamental identities include sin² θ + cos² θ = 1, 1 + tan² θ = sec² θ, and 1 + cot² θ = cosec² θ.

Algebraic Difference of Powers

For even powers, a⁴ − b⁴ can be factored into (a² − b²)(a² + b²), which is very useful in trigonometric simplifications.

Componendo and Dividendo Rule

If a/b = c/d, then (a+b)/(a-b) = (c+d)/(c-d). This rule simplifies ratio-based trigonometric equations quickly.

Given:

Amount of rice bought = 840 kg

Profit in which a part is sold = 25%

Loss in which other part is sold = 10%

Total profit = 15%

Calculation:

Let the price of 1 kg rice be Rs. 1

Cost price of 840 kg rice = Rs. 840

Let x kg sold for 10% loss

Then,

(840 – x) kg sold for 25% profit

Now,

Net selling price = (840 × 115/100) = Rs. 966

Net amount on selling x kg rice at 10% loss = (x × 90%)

⇒ (x × 90/100) = 0.9x

Net amount on selling (840 – x) kg rice at 25% profit = [(840 – x) × 125/100]

⇒ [1.25 × (840 – x)]

Now,

⇒ 1.25 × (840 – x) + 0.9x = 966

⇒ 1050 – 1.25x + 0.9x = 966

⇒ 1050 – 0.35x = 966

⇒ 0.35x = 84

⇒ x = (84 × 100)/35

⇒ x = 8400/35

⇒ x = 240

∴ The required value is 240 kg

Alternate MethodLet the quantity sold at 10% loss be x kg.

According to the question

⇒ [(840 – x) × 125/100] + (x × 90/100) = (840 × 115/100)

⇒ [(840 – x) × 1.25] + 9x/10 = 966

⇒ 1050 – 1.25x + 0.9x = 966

⇒ 1050 – 0.35x = 966

⇒ 0.35x = 84

⇒ x = (84 × 100)/35

⇒ x = 240 kg

∴ The required value is 240 kg.

Alternate MethodBy mixture and allegation:

+25                -10

          +15

25         ∶         10

⇒ Ratio = 5 ∶ 2

(5 + 2) units = 840

⇒ 1 unit = 120

Quantity of rice sold at 10% loss = 2 units = 240 kg

∴ The required value is 240 kg.

Given:

Speed of man = 4 km/h

Time taken by man = 18 min

Formula used:

Speed = Distance/Time

1 km/hr = 5/18 m/s

1 min = 60 sec

Calculation:

Let the distance be x

Speed = Distance/Time

⇒ (4 × 5/18) = x/(18 × 60)

⇒ 20/18 = x/1080

⇒ 18x = 1080 × 20

⇒ 18x = 21,600

⇒ x = (21,600/18)

⇒ 1200 m

∴ The length of the tunnel is 1200 m

Given:

The length of the base of a triangle = 3 cm smaller than the length of its altitude

Area of triangle = 104 cm²

Formula used:

Area of triangle = 1/2 × base × height

Calculation:

Let the length of the base of the triangle be x cm.

The length of the base of a triangle is 3 cm smaller than the length of its altitude = (x + 3)

Now,

Area of triangle = [1/2 × x × (x + 3)] = 104

⇒ (1/2 × x² + 3x) = 104

⇒ x² + 3x = 208

⇒ x² + 3x – 208 = 0

⇒ x² + 16x – 13x – 208 = 0

⇒ x(x + 16) – 13(x + 16) = 0

⇒ (x – 13) (x + 16) = 0

⇒ x = 13, -16

Now,

The length of base of the triangle = x = 13 cm

∴ The required value is 13 cm

Alternate MethodArea of triangle = [1/2 × x × (x + 3)] = 104

⇒ x × ( x + 3) = 208

⇒ x × (x + 3) = 13 × 16

⇒ x × (x + 3) = 13 × (13 +3)

On comparing x = 13

The length of base of the triangle = x = 13 cm

∴ The required value is 13 cm

Calculation:

Total number of boys and girls in class A = (27 + 31) = 58

Number of students promoted in class A = 43

Number of failed students in class A = [(58 – 43)/58 × 100] 

⇒ (15/58 × 100)

⇒ (1500/58)

⇒ 25.86%

Now,

Total number of boys and girls in class B = (35 + 30) = 65

Number of students promoted in class B = 45

Number of failed students in class B = [(65 – 45)/65 × 100] 

⇒ (20/65 × 100)

⇒ (2000/65)

⇒ 30.77%

Now,

Total number of boys and girls in class C = (30 + 32) = 62

Number of students promoted in class C = 58

Number of failed students in class C = [(62 – 58)/62 × 100] 

⇒ (4/62 × 100)

⇒ (400/62)

⇒ 6.45%

Now,

Total number of boys and girls in class D = (33 + 34) = 67

Number of students promoted in class D = 61

Number of failed students in class D = [(67 – 61)/67 × 100]

⇒ (6/67 × 100)

⇒ (600/67)

⇒ 8.96%

∴ The highest percentage of failed students in class B

The correct answer is Baaram.

Key Points

• Baaram movie won the ‘Best Tamil Film’ award at the 66th National Film Awards.
• The 66th National Film awards were announced by Rahul Rawail, head of the Jury for feature films, almost Four hundred and nineteen films
  

competed for the awards this year.

Additional Information

• The national film awards are given in 31 categories.
• Best non-feature film: Son-Rise by Vibha Bakshi and The Secret Life of Frogs by Ajay and Vijay Bedi.
• Best Educational Film: Sarala Virala.
• Best Director: Uri: The Surgical Strike- Aditya Dhar.
• Best Feature Film: Hellaro is a Gujarati film directed by Abhishek Shah.
• Best Actor: Ayushmann Khuranna for Andhadhun and Vicky Kaushal for Uri: The Surgical Strike.
• Best Music Direction (Songs): Sanjay Leela Bhansali for Padmaavat.
• Best Female Playback Singer: Bindhu Malini for Mayavi Manave from Nathichirami (Kannada).
• Best Male Playback Singer: Arijit Singh for Bhinte Dhil.

The correct answer is Star topology.

Key Points

• A topology for a Local Area Network in which all nodes are individually connected to a central connection point like a hub or switch is called Star Topology.
• In a star topology, each device needs only one link and one I/O port to connect it to any number of other devices.
• Each device has a dedicated point-to-point link to a central controller known as a hub or switch.

Additional Information

• A multipoint connection is one in which more than two specific devices share a single link.
• A point-to-point connection provides a dedicated link between two devices. In mesh, star and ring topologies are point-to-point connection
• Mesh topology:
• In a mesh topology, every device has a dedicated point-to-point link to every other device.
• Bus Topology:
• In Bus Topology, one long cable acts as a backbone to link all the devices in a network.
• Ring topology:
• In a ring topology, each device has a dedicated point-to-point connection with only the two devices on either side of it; Each device is connected to its corresponding repeater.

The correct answer is Scanner.

Key Points

• The scanner is an input device, which works more like a photocopy machine.
• It is a device that captures images from photographic prints, posters, magazine pages.
• The scanner captures images from the source which are then converted into a digital form that can be stored on the disk.
• These images can be edited before they are printed.​

Additional Information

• A monitor: 
• It is an output device that is used to display images, text, video, and graphics information generated by a connected computer.
• It is an output device that displays information in pictorial form.
• It is also known as a video display terminal (VDT) or a video display unit (VDU).
• The first computer monitor was introduced on 1 March 1973, which was part of the Xerox Alto computer system.
• Projector:
• A projector or image projector is an optical device that projects an image onto a surface, commonly a projection screen.

The correct answer is Kamaicha.

Key Points

• The Kamaicha:
• It is a bowed lute played by the Manganiars of west Rajasthan.
• The whole instrument is one piece of wood, the spherical bowl extending into a neck and fingerboard; the resonator is covered with leather and the upper portion with wood.
• There are four main strings and a number of subsidiary ones passing over a thin bridge.
• It links the sub-continent to Western Asia and Africa and is considered by some scholars to be the oldest instrument, with the exception of the Ravana Hatta or Ravana Hasta Veena.

Additional Information

• The picture of Kamaicha is shown below:

The correct answer is European Commission.

Key Points

• European Commission has launched the 'United for Biodiversity' coalition made up of zoos, aquariums, botanical gardens, national parks, natural history and science museums from around the world, on World Wildlife Day 2020.
• The European Commission has put forward plans for the world's first "carbon border tax" on imports of carbon-intensive goods, including steel, cement, fertilizers, and aluminium, as part of a program to meet its new climate target.
• The border levy should be phased in from 2026.
• The measure is designed to protect European industries from competitors abroad.

Additional Information

• World Health Organization:
• World Health Organization (WHO) is a specialized agency of the United Nations (UN) established in 1948 to further international cooperation for improved public health conditions.
• Although it inherited specific tasks relating to epidemic control, quarantine measures, and drug standardization from the Health Organization of the League of Nations (set up in 1923) and the International Office of Public Health at Paris (established in 1907), WHO was given a broad mandate under its constitution to promote the attainment of "the highest possible level of health" by all peoples.
• WHO defines health positively as "a state of complete physical, mental, and social well-being and not merely the absence of disease or infirmity."
• Each year WHO celebrates its date of establishment, April 7, 1948, as World Health Day.
• With administrative headquarters in Geneva, governance of WHO operates through the World Health Assembly, which meets annually as the general policy-making body, and through an Executive Board of health specialists elected for three-year terms by the assembly.
• The WHO Secretariat, which carries out routine operations and helps implement strategies, consists of experts, staff, and field workers who have appointments at the central headquarters or at one of the six regional WHO offices or other offices located in countries around the world.

The correct answer is Kolkata.

Key Points

• The International Conference on Nano Science and Technology 2020 (ICONSAT) was held at Biswa Bangla Conventional Centre, Kolkata.
• The event was supported by the Department of Science and Technology (DST) and organized by S. N. Bose National Centre for Basic Sciences, Kolkata.
• The conference was held from March 5 to 7, 2020.

The correct answer is Two.

Key Points

• As of January 2021, India has won Two Olympic medals in badminton, all in women’s singles.
• Saina Nehwal became the first Indian to win an Olympic medal in badminton in 2012.
• PV Sindhu won silver in Rio 2016.
• PV Sindhu also won a bronze medal in the women's singles event at the Tokyo Olympics on August 01, 2021.

Additional Information

• India has won 7 medals in Tokyo Olympics 2021 - 1 Gold Medal, 2 Silver medals, and 4 Bronze medals.
• The 23-year old Neeraj Chopra won India's first-ever Gold in Athletics after finishing on top of the podium in the Javelin Throw.
• He also became only the second individual Gold medalist for the country at the Summer Olympics.
• Abhinav Bindra had won the country's first individual Gold after winning the 10m Air Rifle event at the 2008 Beijing Olympics.
• PV Sindhu wins bronze medal in women's singles shuttler PV Sindhu becomes first Indian woman to win two individual medals at Olympic Games.
• She had won the Silver at the 2016 Games held at Rio. She also became the first Indian player to win the World Badminton Championship and two Olympic medals across genders.
• She had won the World Championship in 2019.
• Ravi Kumar Dahiya gets India a Silver medal in the Tokyo Olympics.
• Lovlina Borogohain fetched a Bronze medal for India in Tokyo Olympics.
• Indian Men's Hockey team is also won the Bronze medal.

The correct answer is Australia.

Key Points

• Commonwealth Games 2018 was held on the Gold Coast, Australia.
• Officially known as 'XXI Commonwealth Games.
• Mascot: Borobi.
• Motto: Share the Dream.

Additional Information

• 71 Commonwealth Games Associations participated in this event.
• Open ceremony was inaugurated by Charles, Prince of Wales.
• Australia topped the medal table for the fourth time in the commonwealth games with 80 Gold medals.
• India made its 18th appearance at the Commonwealth Games.
• India finished third for the tournament with 26 Golds.
• First medal for India in Commonwealth Games 2018: Gururaja Poojary (Silver).
• First Gold medal for India in Commonwealth Games 2018: Mirabai Chanu.
• PV Sindhu was named flag-bearer of India for the opening ceremony in Gold Coast.
• Mary Kom carries India's flag at the closing ceremony in Gold Coast.
• The 2022 Commonwealth Games is scheduled to be held in Birmingham, England.