The correct answer is - Despite of the rain, the parade- the error lies in this part only.

Key Points

In the given sentence, the error lies in part A where Despite of is an incorrect usage.

• The sentence talks the Republic Day celebrations going on uninterrupted, even though it was raining. Thus, in simple words, the festivities continued without being influenced or hindered by the rain.
• ‘Despite’ means without taking any notice of or being influenced by. It is most appropriate in the context of the given sentence.
• It is important to note that **‘despite’**​ should be not be followed by ‘of’. Rather, it should be directly followed by the time-dependent clause which tells about the fact.

Thus, the correct sentence is:  Despite the rain, the parade went on uninterrupted which was followed by the President’s address and other​ formal festivities of the Republic Day.

• ‘In spite of’ is another expression that reflects the contrast between two things. Just like ‘despite’, ‘in spite of’ means without being prevented by. However, ‘of’ is a part of the expression ‘in spite of’ itself and not that of the clause following it. Example:
• ​Despite her dedicated effort, she failed.
• In spite of the dedicated effort, she failed.​

Additional Information

• Both despite and in spite of require a clause to show the flip of that as mentioned in the fact.
• Both of the mentioned preposition expressions are synonymous to ‘notwithstanding’, ‘regardless of’, ‘even though’.

The correct answer is -Lisa is more stronger than- the error lies in this part only.

Key Points

In the given sentence, the error is part A where more stronger than is an incorrect usage.

• Here, the coach says that Lisa is stronger than her opponent. There is a comparison between Lisa and her opponent and thus a comparative adjective stronger is used.
• The adjective ‘strong’ when used in a comparative form becomes ‘stronger’. There is no need of using more along with this comparative adjective. Therefore, usage of ‘more stronger’ is a repetition mistake or redundancy.

Thus, the correct sentence is: “Lisa is stronger than her opponent”, said the coach during the press briefing ahead of the Asian Games.

Additional Information

• Comparative form of the adjectives with three or more syllables consists of ‘more’ in front of the adjective. Similarly, the superlative form of such adjective consists of ‘most’ in front of the adjective.​
• Examples of the adjectives with ‘more’ and ‘most’ in their comparatives and superlatives:
  

The correct answer is Option 1 i.e. A.

• According to the rule, before possessives, determiners such as ‘all’, ‘both’, half’, etc. are used.
• Let’s see an example-

1. She loves both her daughters equally and distributed the property evenly between them.

• Hence, ‘all my documents’ should be used instead of ‘my all documents’ to make the sentence correct.

 So, the correct sentence is - “I lost the bag in which I had all my documents, certificates, and academic records. I have a job interview tomorrow where I need all these things, and I have no clue what will happen. I lodged a police complaint, but within this short time, nothing is possible.”

The correct answer is Option 1 i.e. A.

• According to the rule, if ‘as…..as’ is used in a sentence, the adjective or adverb used in-between ‘as’ should always be in the Positive Degree.
• Let’s see an example-

1. He is as brave as his father, who is a police officer. 

2. He is as bravest as his father, who is a police officer. 

• Hence, ‘as soft as’ should be used to make the sentence correct.
  

 So, the correct sentence is- “The fabric is as soft as cotton, but it is not pure cotton. That's why she got so many allergic reactions on her face after using that mask and is now under proper medication and care.”

The Correct answer is option D

• Error is in part D of the sentence.
• The word 'sudden' is giving additional information regarding 'Dropping cases'
• Here we need to use the adverb of 'Sudden' i.e 'Suddenly'

Correct answer - After the rise, the cases started dropping suddenly.

The correct answer is '(D)'.

Key Points

Reading the sentence we find that:

• The adverbial phrase for 2005 used in part D is incorrect.
• We don’t use for  with a point in time (2005).
• The sentence can be made correct if we use since.

The correct sentence will be: Kiva has loaned out nearly a quarter of a billion dollars to small and medium businesses since 2005. 

Additional Information

• In adverbial phrases that tell us for how long,
• for is always followed by an expression of duration - I stayed in Manali for three days.
• since is always followed by an expression of a point in time - There has not been a more exciting discovery since last century.

The sentence mentions ‘tense and dynamic period that affected society on all levels’, therefore, ruling-out words like ‘significant’ and ‘advantage’ as these terms do not fit the context.

The word ‘successfully’ disturbs the meaning of the sentence.

The word ‘beginning’ that means 'to start' fits the blank best.

The correct answer is option 1.

Key Points

• The word ‘damper’ cannot be used with respect to 'war', as mentioned in the sentence.
• The words 'subsequent' and 'arming' are grammatically incorrect and therefore making ‘preceded’ as the best fit to fill the blank.
• Let us look at the meaning of the words:
• Preceded: to happen, come or go before somebody/something. (किसी अन्‍य व्‍यक्ति या वस्‍तु से पहले होना, जाना या आना, पूर्ववर्ती होना (स्‍थान, समय या क्रम में))
• Damper: a little wet (सीलनभरा)
• Subsequent: coming after or later (बाद का या बाद में होने या आने वाला; परवर्ती या उत्तरवर्ती)
• Arming: the act of taking arms or providing with arms; (असलह)
• Static: not moving, changing or developing (थमा हुआ, स्थिर (जिसमें कोई गति, परिवर्तन या विकास न हो रहा हो))

The sentence mentions ‘Communism and Democracy’, which should be used as a hint while picking up the word fitting the blank.

As the sentence indicates a negative remark, ‘public’ and ‘radical’ gets omitted.

The word ‘politically’ is grammatically incorrect.

The word ‘paranoia’ fits the blank along with appropriately conveying the meaning of the sentence too.

The correct answer is 'Simultaneously'.

Key Points

• The words 'separated' means to become divided or detached and 'hiding' means a severe defeat, thus, are grammatically incorrect.
• The word ‘warheads’ refers to the explosive head of a missile, torpedo, or similar weapon, which do not make a strong option to fit the blank as it doesn't fit the context of the sentence.
• The word ‘simultaneously’ means existing or occurring at the same time and hence, makes the best fit for the blank as it conveys the most appropriate meaning.
• Therefore, the correct answer is option 3.

The words ‘behind’ and 'repressive' gets omitted due to being grammatically incorrect.

The word ‘retrospect’ does not fit the context of the sentence.

‘Expansion’ not just carries the required message fitting the sense of the statement, but also make the sentence meaningful.

The misspelled word is 'conclutions'.

Key Points

• The correct spelling is Conclusions.
• Conclusion means an end to something (समाप्ति, समापन)
• Example- Let us hope the peace talks reach a successful conclusion.
• Let us look at the meanings of the other words:
• Analysis: the careful examination of the different parts or details of something (विश्‍लेषण)
• Deeper: (it is a comparative adjective) going a long way down from the surface (गहरा, सतह से नीचे की ओर लंबाई में जाने वाला)
• Gain: to obtain or win something, especially something that you need or want (वस्‍तु तक पहुँचना या प्राप्‍त करना, विशेषतः अपेक्षित या अभीष्‍ट वस्‍तु; पाना)
• Hence, the correct answer is option 4.

The misspelled word is 'techneeque'.

Key Points

• The correct spelling is 'technique'.
• Technique means a particular way of doing.
• Example- He’s a naturally talented runner, but he needs to work on his technique.
• Let us look at the meaning of the other words:
• practise- to do an activity or train regularly so that you become very good at something (in the above sentence, the word practise is being used as a verb.)
• Improve: to become or to make something better.
• Players: a person who plays a game or sport
• Hence, the correct answer is option 4.

​

Additional Information

Difference between practice and practise:

• In British English, practice is a noun, and practise is a verb.
• used as an uncountable noun
• Practice- involves doing something regularly in order to improve your ability at it.
• Examples-
• Your skiing will get better with practice.
• He has to do a lot of music practice.
• used as a countable noun
• A practice is something that is done regularly, for example as a custom.
• Examples-
• Our usual practice is to keep a written record of all meetings.
• The ancient practice of yoga is still popular today.
• used as a verb
• If you practise something, you do it or take part in it regularly.
  

Examples-

• I had been practising the piece for months.
• His family practised traditional Judaism.
• In American English, the spelling `practise' is not normally used. The verb and noun are both spelled practice.
• Example- I practiced throwing and catching the ball every day.

The misspelled word is 'previaled'.

Key Points

• The correct spelling is 'prevailed'.
• Prevail means to exist or be common in a particular place or at a particular time. (स्‍थान-विशेष या समय-विशेष में (किसी बात का) विद्यमान या प्रचलन में होना)
• Example- Those beliefs still prevail among certain social groups.
• Let us look at the other words given in the options:
• Admired: to respect or like somebody/something very much; to look at somebody/something with pleasure (किसी के प्रति आदर व प्रशंसा का भाव रखना; किसी को प्रिय दृष्टि से देखना)
• Creativity: the ability to make or produce new things using skill or imagination (सृजन-क्षमता)
• Writer: a person who writes, especially one whose job is to write books, stories, etc. (पुस्‍तक आदि का) लेखक
• Hence, the correct answer is option 3.

The misspelled word is 'intented'.

Key Points

• The correct spelling is 'intended'.
• Intend means to plan or mean to do something (कुछ करने की योजना बनाना या इरादा करना)
• Example- I did not intend to be rude.
• Let us look at the meanings of the other words given in the options:
• Encourage-  to give hope, support or confidence to somebody (किसी को) प्रोत्‍साहित करना; (किसी की) हिम्‍मत बढ़ाना
• More- a larger number or amount of people or things; something extra as well as what you have (व्‍यकि्तयों या वस्‍तुओं की अधिक बड़ी संख्‍या या मात्रा; जो है वह भी (और) साथ ही और भी, से अधिक)
• Distraction- something that takes your attention away from what you were doing or thinking about (काम से ध्यान बँटाने वाली वस्‍तु, एकाग्रता भंग करनेवाली वस्तु)
• Hence, the correct answer is option 1.

The misspelled word is 'defennded'.

Key Points

• The correct spelling is 'defended'.
• Defend means to protect somebody/something from harm or danger (संकट से किसी की) रक्षा करना
• Example- She defended herself successfully in court, and was found innocent of the charges against her.
• Let us look at the meanings of the words given in the options:
• Country: an area of land with its own people, government, etc. (किसी भूक्षेत्र में रहनेवाले लोग, उनकी सरकार आदि, देश)
• Against: (preposition) being an opponent to somebody/something in a game, competition, etc., or an enemy of somebody/something in a war or fight. (के विरुद्घ (खेल आदि में) या (युद्ध में) शत्रु)
• Invaders:  someone who enters by force in order to conquer. (कोई है जो जीतने के लिए बलपूर्वक प्रवेश करता है।)
  
• Hence, the correct answer is option 1.

The correct answer is: Confinement. 

Key Points

Let's look at the meaning of the correct answer. 

• Confinement: The action of confining or the state of being confined.
• The given sentence talks about state of confinement people experience while staying home.

Therefore the correct answer is Confinement**.**

The correct answer is: All of the above. 

Key Points

Reading the given passage we find the following lines:  

• 'It has been hypothesized that the causative mechanism for many of the neurological conditions due to COVID-19 may be the direct invasion of the nervous system by the virus, an increased tendency to blood clotting or an exaggerated immune response by the body.'
• Thus from the given points, we find that direct invasion of the nervous system, increased tendency to blood clotting, and an exaggerated immune response by the body all arise due to the neurological conditions due to COVID-19.

Therefore the correct answer is All of the above.

The correct answer is: Smoking and consumption of alcohol decreased due to prolonged quarantine. 

Key Points

Reading the passage we find that:  

• **'**There was a steep increase in the amount of alcohol consumed by regular drinkers. Persons who had stopped smoking and consuming alcohol resumed their habit in disconcerting numbers.'

Here from the given sentence, it is clear that the statement given in the option is false. 

Therefore the correct answer is Smoking and consumption of alcohol decreased due to prolonged quarantine.

The correct answer is: Both 1 and 3.

Key Points

Reading the passage we find that:  

• 'Remote working disrupts a healthy-work life balance. Face to face contact and human interactions which were considered so essential for emotional well-being has taken a backseat. Lack of comforting physical contact like shaking hands and hugging friends is stressful and disconcerting.'

Therefore the correct answer is Both 1 and 3 as we see both the points are mentioned in the passage.

The correct answer is: The imposed virtual learning has increased the mental stress and fatigue in students. 

Key Points

Reading the sentence we find that:  

'Mental stress and fatigue have increased manyfold due to the rigours imposed by virtual learning.'

Thus from the given line, it is clear that virtual learning has increased mental stress and fatigue in students. 

All the other points mentioned in the options are wrong and is not mentioned in the passage.

The correct answer is Operate. 

Key Points

Let's look at the meaning of the given word and the correct option: 

• Function: Work or operate in a particular way.
• Operate: Control the functioning of something.

Thus from the given meaning, it is clear that the correct answer is Operate. 

Additional Information

• Conjugate: Become temporarily united (biological term).
• Impede: Delay or prevent by obstructing.

The correct answer is: Enormous 

Key Points

Let's look at the meaning of the given word. 

• Gargantuan: Enormous.

Thus from the above meaning, it is clear that the correct answer is Enormous. 

Additional Information

• Puny: small and weak.
• Miniscule: extremely small, tiny.
• Tepid: slightly warm; lukewarm.
• Opulent: costly and luxurious.

The correct answer is: The wide range of mental and neurological disorders in patients with milder symptoms.  

Key Points

Reading the given passage we find that: 

'However, what is alarming is the wide gamut of mental and neurological disorders seen even in those with milder symptoms.'

Thus from the given sentence, it is clear that the correct answer is option 4.

The correct answer is Agreement. 

Key Points

Let's look at the meaning of the given word.

• Accord: Be harmonious or consistent with.
• Agreement: Having the same opinion about something.

Thus from the given meanings, it is clear that the correct answer is Agreement.  

Additional Information

Transpose: Cause two things to exchange places

The correct answer is D

Key Points

Reading the given sentences we find that: 

• The paragraph starts by introducing the Nuclear Power Corporation of India Limited, and my mentioning what it is; which is D.
• Then statement A provides us more information regarding NPCIL that it is a dividend-paying company.
• This is soon followed by statement C which elaborates on what NPCIL does, its responsibilities.
• This is elaborated using the second statement that is the overriding priority given to safety as mentioned in E.
• The paragraph ends by concluding the present operation of NPCIL i.e the number of power reactors and it's capacity, which is B.

Therefore the correct sequence is DACEB.

The correct answer is A.

Key Points

Reading the given sentences we find that: 

• The paragraph starts by introducing the Nuclear Power Corporation of India Limited, and my mentioning what it is; which is D.
• Then statement A provides us more information regarding NPCIL that it is a dividend-paying company.
• This is soon followed by statement C which elaborates on what NPCIL does, its responsibilities.
• This is elaborated using the second statement that is the overriding priority given to safety as mentioned in E.
• The paragraph ends by concluding the present operation of NPCIL i.e the number of power reactors and it's capacity, which is B.

Therefore the correct sequence is DACEB.

The correct answer is C. 

Key Points

Reading the given sentences we find that: 

• The paragraph starts by introducing the Nuclear Power Corporation of India Limited, and my mentioning what it is; which is D.
• Then statement A provides us more information regarding NPCIL that it is a dividend-paying company.
• This is soon followed by statement C which elaborates on what NPCIL does, its responsibilities.
• This is elaborated using the second statement that is the overriding priority given to safety as mentioned in E.
• The paragraph ends by concluding the present operation of NPCIL i.e the number of power reactors and it's capacity, which is B.

Therefore the correct sequence is DACEB.

The correct answer is E. 

Key Points

Reading the given sentences we find that: 

• The paragraph starts by introducing the Nuclear Power Corporation of India Limited, and my mentioning what it is; which is D.
• Then statement A provides us more information regarding NPCIL that it is a dividend-paying company.
• This is soon followed by statement C which elaborates on what NPCIL does, its responsibilities.
• This is elaborated using the second statement that is the overriding priority given to safety as mentioned in E.
• The paragraph ends by concluding the present operation of NPCIL i.e the number of power reactors and it's capacity, which is B.

Therefore the correct sequence is DACEB.

The correct answer is B. 

Key Points

Reading the given sentences we find that: 

• The paragraph starts by introducing the Nuclear Power Corporation of India Limited, and my mentioning what it is; which is D.
• Then statement A provides us more information regarding NPCIL that it is a dividend-paying company.
• This is soon followed by statement C which elaborates on what NPCIL does, its responsibilities.
• This is elaborated using the second statement that is the overriding priority given to safety as mentioned in E.
• The paragraph ends by concluding the present operation of NPCIL i.e the number of power reactors and it's capacity, which is B.

Therefore the correct sequence is DACEB.

Concept used:

Calculation:

? = 40% of 320 + 4³ ÷ 16 × 108 ÷ 8

⇒ ? = 128 + 64 ÷ 16 × 108 ÷ 8 

⇒ ? = 128 + 4 × (27/2)

⇒ ? = 128 + 54 = 182 

∴ The required answer is 182

Given  

35% of 180 + 182 = (27)5/3 + ?²

Concept Used 

Follow the BODMAS rule according to the table given below:

Calculation 

35% of 180 + 182 = (27)5/3 + ?²

⇒ 63 + 324 = 3⁵ + ?²

⇒ ? = √ (324 + 63 - 243) = 12

∴ The required answer is 12

Given 

38 + 41 × (441 ÷ 21) – 172 = ?

Concept used 

Follow the BODMAS rule according to the table given below:

Calculation 

38 + 41 × (441 ÷ 21) – 172 = ?

⇒ 38 + 41 × 21 - 289 = ? 

⇒ 38 + 861 - 289 = ?

⇒ ? = 610 

∴ The required answer is 610

Given 

(252 – 106) ÷ 3 – 132 + 35 = ?

Concept used 

Follow the BODMAS rule according to the table given below:

Calculation 

(252 – 106) ÷ 3 – 132 + 35 = ?

⇒ (625 - 106) ÷ 3 - 169 + 35 = ?

⇒ 519 ÷ 3 - 169 + 35 = ? 

⇒ 173 - 169 + 35 = ?

⇒ ? = 39 

∴ the required answer is 39

Mistake Points ⇒ 173 - 169 + 35 = ?

there is no btacket after - sign before 169 so the calculation can't come -204.

Given 

215 + 369 – 60% of 900 + 5 = ?²

Concept Used 

Follow the BODMAS rule according to the table given below:

Calculation

215 + 369 – 60% of 900 + 5 = ?2

⇒ √(215 + 369 - 540 + 5) = ?

⇒ ? = √(589 - 540) = 7

∴ The required answer is 7

Given

40% of 820 + 60% of 390 – 511 = 49 + ?

Concept Used 

Follow the BODMAS rule according to the table given below:

Calculation 

40% of 820 + 60% of 390 – 511 = 49 + ?

⇒ 4 × 82 + 6 × 39 - 511 - 49 = ? 

⇒ ? = 328 + 234 - 560 

⇒ ? = 2 

∴ The required answer is 2

Alternative method:

We can also solve it by fraction method

As we know fraction value of 40% = 2/5

And, 60% = 3/5

40% of 820 + 60% of 390 – 511 = 49 + ?

⇒ 2/5 × 820 + 3/5 × 390 – 511 – 49 = ?

⇒ ? = 328 + 234 - 560 

⇒ ? = 2 

∴ The required answer is 2

Concept Used:

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

​

Calculation:

39.87 + 56.83 – 19.11 × 3.99 + 7.84 = ?

⇒ 40 + 57 – 19 × 4 + 8 = ?

⇒ 97 – 76 + 8 = ?

⇒ 105– 76= ?

⇒ 29 = ?

∴ The value of (?) is 29

Given 

17 × 18 ÷ √324 × 11 + 48 – 10 = ?²

Concept used 

Follow the BODMAS rule according to the table given below:

Calculation 

17 × 18 ÷ √324 × 11 + 48 – 10 = ?²

⇒ 17 × 18 ÷ 18 × 11 + 48 - 10 = ?²

⇒? = √(17 × 1 × 11 + 38)

⇒ ? = √(187 + 38) = 15   

∴ The required answer is 15

Given 

? × 22 = 2740 ÷ 20 - [(100/9)% of 729 – 10]

Concept Used 

Follow the BODMAS rule according to the table given below:

Calculation 

? × 22 = 2740 ÷ 20 - [(100/9)% of 729 – 10]

⇒ ? × 22 = 137 - [81 - 10]

⇒ ? × 22 = 137 - 71 

⇒ ? = 66/22 = 3 

∴ The required answer is 3

Given:

?2/3 = 64% of 150 + 7 × 3 – 9²

Concept Used:

Follow the BODMAS rule according to the table given below:

Calculation:

?2/3 = 64% of 150 + 7 × 3 – 9²

⇒ ?^2/3 = 96 + 21 - 81 

⇒ ?^2/3 = 117 - 81 

⇒ ?2/3 = 36

⇒ ?2/3× 1/2 = √36

⇒ ?1/3 = 6

⇒ ?1/3× 3 = 6³

⇒ ?1 = 216

⇒ ? = 216

∴ The required answer is 216

Given: 

Small Pizzas sold by A = 44

Small Pizzas sold by B = 56

Small Pizzas sold by D = 34

Total number of Pizza sold by C = 88

Solution: 

Difference between total number of small sized pizzas sold from shop A, B and D together and total number of pizza sold from Shop C = (44 + 56 + 34) - 88

⇒ Difference = 46

∴ Difference between total number of small sized pizzas sold from shop A, B and D together and total number of pizza sold from Shop C is 46.

Given:

Total number of Pizza sold from shop D = 62

Total number of Pizza sold from shop A = 80

Solution:

62 × 100/80 = 77.5

∴ Total number of pizzas sold from shop D is 77.5 % of total number of pizzas sold from shop A.

Given: 

Total number of pizzas sold from shop C = 88

Total number of pizzas sold from shop B = 96

Solution: 

Ratio between total number of pizzas sold from shop C to that of shop B = 88/96 = 11/12

∴ Ratio between total number of pizzas sold from shop C to that of shop B is 11:12.

Given:

Number of medium pizzas sold by A = 36

Number of medium pizzas sold by B = 40

Number of medium pizzas sold by C = 48

Number of medium pizzas sold by D = 28

Formula used: 

Average = Sum of all observations/number of observations 

Solution:

Average = (36 + 40 + 48 + 28)/4

⇒ Average = 152/4 = 38

∴ Average of total number of medium sized pizzas sold from all the shops together is 38.

Given:

The number of small sized pizzas sold from shop C = 40

Solution: 

Number of large Pizza sold from shop C = 40 × 20/100 = 8

Number of medium sized Pizzas from shop C = 48

The number of small sized pizzas sold from shop C = 40

Total number of Pizzas sold from shop C = 40 + 48 + 8 = 96

∴ Total number of pizzas sold from shop C is 96.

Calculation:

The series follows the following pattern:

⇒ 12 + 2 = 14 

⇒ 14 + 4 = 18 

⇒ 18 + 6 = 24

⇒ 24 + 8 = 32 

⇒ 32 + 10 = 42 

⇒ 42 + 12 = 54 

∴ The wrong number is 23

Calculation:

The series follows following pattern: 

⇒ 38 + 1 = 39 

⇒ 39 + 4 = 43 

⇒ 43 + 9 = 52 

⇒ 52 + 16 = 68

⇒ 68 + 25 = 93 

⇒ 93 + 36 = 129 

∴ The wrong number in the series is 70

Calculation:

The series follows following pattern:

⇒ 18 + 17 = 35 

⇒ 35 + 34 = 69 

⇒ 69 + 68 = 137 

⇒ 137 + 136 = 273 

⇒ 273 + 272 = 545 

∴ The wrong number in the series is 136

Calculation:

The series follows following pattern:

⇒ 48 – 7 = 41 

⇒ 41 – 7 = 34 

⇒ 34 – 7 = 27 

⇒ 27 – 7 = 20

⇒ 20 – 7 = 13 

⇒ 13 – 7 = 6 

∴ The wrong number in the series is 21

Calculation:

The series follows following pattern:

⇒ 87 + 1³ = 87 + 1 = 88 

⇒ 88 – 2² = 88 – 4 = 84

⇒ 84 + 3³ = 84 + 27 = 111

⇒ 111 – 4² = 111 – 16 = 95 

⇒ 95 + 5³ = 95 + 125 = 220 

∴ The wrong number in the series is 110

Shortcut Trick

Volume of water from pipe in 1 hour = π × r² × speed = (22/7) × 0.07 × 0.07 × 5000 = 77 m³.

Required volume in tank = Length × Breadth × Height = 50 × 44 × 0.07 = 154 m³.

Time taken = Required Volume ÷ Flow rate per hour = 154 ÷ 77 = 2 hours.

∴ The correct answer is 2 hours.

Alternate Method

Given:

Speed of water = 5 km/h = 5000 m/h

Diameter of pipe = 14 cm ⇒ Radius (r) = 7 cm = 0.07 m

Tank dimensions: L = 50 m, B = 44 m, Required Rise (h) = 7 cm = 0.07 m

Formula Used:

Volume of cylinder = πr²h | Volume of cuboid = L × B × H

Calculations:

⇒ Volume of water required in tank = 50 × 44 × 0.07

⇒ Volume = 50 × 44 × (7/100) = 154 m³

⇒ Volume of water flowing through pipe per hour = π × (0.07)² × 5000

⇒ Flow rate = (22/7) × 0.0049 × 5000 = 22 × 0.0007 × 5000 = 77 m³/h

⇒ Time = Total Volume ÷ Flow Rate per hour

⇒ Time = 154 ÷ 77 = 2 hours

∴ The correct answer is 2 hours.

Additional Information

Rate of Flow Concept

Volume of water flowing through a pipe in time 't' is given by Area of Cross-section × Speed × Time.

Unit Conversion

Always ensure all dimensions are in the same unit (meters) before calculation. 1 km = 1000 m and 1 cm = 0.01 m.

Volume of Water in Tank

The volume of water for a specific rise in level is simply Area of base × Rise in height (L × B × h).

Shortcut Trick

Efficiency ratio A : B = 3 : 1

Time ratio A : B = 1 : 3 (Inverse of efficiency)

Difference in time units = 3 − 1 = 2 units → 60 days

1 unit = 30 days. So, A takes 30 days and B takes 90 days.

Together (XY / X+Y) = (30 × 90) ÷ (30 + 90) = 2700 ÷ 120 = 22.5 days.

∴ The correct answer is 22.5 days.

Alternate Method

Given: Efficiency of A is 3 times B. Time difference is 60 days.

Calculation:

⇒ Let time taken by B = x days, then A = x − 60 days.

⇒ Ratio of time A : B = 1 : 3

⇒ (x − 60) / x = 1 / 3

⇒ 3x − 180 = x

⇒ 2x = 180 ⇒ x = 90 days (Time for B)

⇒ Time for A = 90 − 60 = 30 days.

⇒ Total Work = LCM(30, 90) = 90 units.

⇒ Combined Efficiency = 3 + 1 = 4 units/day.

⇒ Time taken together = 90 ÷ 4 = 22.5 days.

∴ The correct answer is 22.5 days.

Additional Information

Efficiency and Time Relation

Efficiency is inversely proportional to the time taken to complete a task. If efficiency ratio is x:y, the time ratio is y:x.

Work from Efficiency

Total Work = Efficiency × Time. This is the fundamental unit for solving all Time and Work problems.

Combined Work Formula

For two people taking x and y days respectively, the time taken together is (x × y) ÷ (x + y).

Shortcut Trick

Total Capacity (LCM of 8, 6) = 24 units.

Efficiency of A = 3, Efficiency of B = 4.

Work done by (A + B) in 2 hours = (3 + 4) × 2 = 14 units.

Remaining work = 24 − 14 = 10 units.

Time taken by B = 10 ÷ 4 = 2.5 hours.

∴ The correct answer is 2.5 hr.

Alternate Method

Given:

Time taken by Pipe A = 8 hours

Time taken by Pipe B = 6 hours

Duration both pipes are open = 2 hours

Calculations:

⇒ Combined efficiency of (A + B) = 3 + 4 = 7 units/hr

⇒ Work completed in 2 hours = 7 × 2 = 14 units

⇒ Remaining work = Total work − Completed work = 24 − 14 = 10 units

⇒ Time taken by Pipe B to fill remaining tank = Remaining work ÷ Efficiency of B

⇒ Time = 10 ÷ 4 = 2.5 hours

∴ The correct answer is 2.5 hr.

Additional Information

Pipes & Cisterns Basics

If a pipe fills a tank in x hours, its 1-hour work is 1/x. If an outlet pipe empties it in y hours, its efficiency is negative (-1/y).

Total Work Concept

Always take the LCM of individual times as the total capacity of the tank to simplify calculations into integers.

Remaining Work

Remaining Work = Total Work − (Efficiency × Time already spent). Time to complete = Remaining Work ÷ Efficiency of remaining pipes.

Shortcut Trick

Initial Ratio = 2 : 3 (Difference = 1 unit)

Final Ratio = 5 : 7 (Difference = 2 units)

Make differences equal: Multiply initial ratio by 2 → 4 : 6. Difference now is 2 units.

Change in units: 5 − 4 = 1 unit. Given 1 unit = 4.

Difference between numbers = 6 − 4 = 2 units ⇒ 2 × 4 = 8.

∴ The correct answer is 8.

Alternate Method

Given: Ratio of two numbers = 2 : 3. Increment = 4. New ratio = 5 : 7.

Let the numbers be 2x and 3x.

⇒ (2x + 4) / (3x + 4) = 5 / 7

⇒ 7(2x + 4) = 5(3x + 4)

⇒ 14x + 28 = 15x + 20

⇒ 15x − 14x = 28 − 20

⇒ x = 8

Difference between numbers = 3x − 2x = x.

⇒ Difference = 8

∴ The correct answer is 8.

Additional Information

Ratio Balancing Method

When the same value is added to or subtracted from both terms, the difference between the ratio parts should remain constant. Multiply the ratios to equalize these differences.

Cross Multiplication Method

For a : b changing to c : d after adding k: Value of 1 unit = (k × (d − c)) / (ad − bc). This works even if added values are different.

Duplicate Ratio

The duplicate ratio of a : b is a² : b², and the sub-duplicate ratio is √a : √b.

Shortcut Trick

Ratio of Principal (P) to Simple Interest (SI) = 10 : 3

Let Principal = 10 units and Interest = 3 units.

Rate (R) = 6% p.a.

Time (T) = (SI × 100) ÷ (P × R) = (3 × 100) ÷ (10 × 6) = 300 ÷ 60 = 5 years.

∴ The correct answer is 5 years.

Alternate Method

Given:

Ratio of Money (Principal) : Interest = 10 : 3

Rate of Interest (R) = 6% per annum

Formula Used:

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

Calculations:

⇒ Let Principal (P) = 10x and Simple Interest (SI) = 3x

⇒ 3x = (10x × 6 × T) ÷ 100

⇒ 3 = (60 × T) ÷ 100

⇒ 300 = 60 × T

⇒ T = 300 ÷ 60

⇒ T = 5

∴ The correct answer is 5 years.

Additional Information

Simple Interest Components

Simple Interest is calculated only on the Principal amount. Amount = Principal + Simple Interest.

Rate and Time Relationship

For a fixed Principal, Simple Interest is directly proportional to both the Rate of interest and the Time period.

Annual Rate Conversion

If time is given in months, divide by 12 to convert to years. If given in days, divide by 365.

From the Statement 1

Total student in college A and B = 220 

Statement 2 

Ratio of student in college A and B = 6 : 5 

So, Number of student in college A = (220/11) × 6 = 120 

Number of student in college B = 220 - 120 = 100 

Number of student in college B from Mumbai = 30% of 100 = 30 

Statement 3 

Number of student of Mumbai in college B = 75% of Number of student of Patna in college A 

Number of student of Patna in college A = (30/75) × 100 = 40 

Statement 4 

Number of students from Delhi  in college B = 62.5% of the number of students from Patna  in college A

Number of student from Delhi in college B = (5/8) × 40 = 25

Number of student from Patna in college B = 100 - 30 - 25 = 45 

Ratio of students from Patna in college B and number of students from Mumbai who studies in college A =  9 : 10.

So, Number of student from Mumbai in college A = (45/9) × 10 = 50

Number of student from Delhi in college A = 120 - 40 - 50 = 30 

Ratio of student from Delhi in college A and college B = 30 : 25 

⇒ 6 : 5 

∴ The required answer is 6 : 5

From the Statement 1

Total student in college A and B = 220 

Statement 2 

Ratio of student in college A and B = 6 : 5 

So, Number of student in college A = (220/11) × 6 = 120 

Number of student in college B = 220 - 120 = 100 

Number of student in college B from Mumbai = 30% of 100 = 30 

Statement 3 

Number of student of Mumbai in college B = 75% of Number of student of Patna in college A 

Number of student of Patna in college A = (30/75) × 100 = 40  

Required Percentage = (40)/100 × 100 = 40% 

∴ Number of students from Patna in college A is 40% of total number of students in college B

From the Statement 1

Total student in college A and B = 220 

Statement 2 

Ratio of student in college A and B = 6 : 5 

So, Number of student in college A = (220/11) × 6 = 120 

Number of student in college B = 220 - 120 = 100 

Number of student in college B from Mumbai = 30% of 100 = 30 

Statement 3 

Number of student of Mumbai in college B = 75% of Number of student of Patna in college A 

Number of student of Patna in college A = (30/75) × 100 = 40 

Statement 4 

Number of students from Delhi  in college B = 62.5% of the number of students from Patna  in college A

Number of student from Delhi in college B = (5/8) × 40 = 25

Number of student from Patna in college B = 100 - 30 - 25 = 45 

Ratio of students from Patna in college B and number of students from Mumbai who studies in college A =  9 : 10.

So, Number of student from Mumbai in college A = (45/9) × 10 = 50

Number of student from Delhi in college A = 120 - 40 - 50 = 30 

Total student from Patna = 40 + 45 = 85 

Total student from Delhi = 25 + 30 = 55

Required Difference = 85 - 55 = 30

∴ Difference between total number of students from Patna to that of Delhi is 30

From the  Statement 1

Total student in college A and B = 220 

Statement 2 

Ratio of student in college A and B = 6 : 5 

So, Number of student in college A = (220/11) × 6 = 120 

Number of student in college B = 220 - 120 = 100 

Number of student in college B from Mumbai = 30% of 100 = 30 

Statement 3 

Number of student of Mumbai in college B = 75% of Number of student of Patna in college A 

Number of student of Patna in college A = (30/75) × 100 = 40 

Statement 4 

Number of students from Delhi  in college B = 62.5% of the number of students from Patna  in college A

Number of student from Delhi in college B = (5/8) × 40 = 25

Number of student from Patna in college B = 100 - 30 - 25 = 45 

Ratio of students from Patna in college B and number of students from Mumbai who studies in college A =  9 : 10.

So, Number of student from Mumbai in college A = (45/9) × 10 = 50

Number of student from Delhi in college A = 120 - 40 - 50 = 30

Total student from Mumbai in both college = 50 + 30 = 80  

Total student from Patna = 40 + 45 = 85 

Total student from Delhi = 25 + 30 = 55

So, The highest number of student from Patna in both colleges 

∴ The most number of students studying in both colleges is Patna

From the  Statement 1

Total student in college A and B = 220 

Statement 2 

Ratio of student in college A and B = 6 : 5 

So, Number of student in college A = (220/11) × 6 = 120 

Number of student in college B = 220 - 120 = 100 

Number of student in college B from Mumbai = 30% of 100 = 30 

Statement 3 

Number of student of Mumbai in college B = 75% of Number of student of Patna in college A 

Number of student of Patna in college A = (30/75) × 100 = 40 

Statement 4 

Number of students from Delhi  in college B = 62.5% of the number of students from Patna  in college A

Number of student from Delhi in college B = (5/8) × 40 = 25

Number of student from Patna in college B = 100 - 30 - 25 = 45 

Ratio of students from Patna in college B and number of students from Mumbai who studies in college A =  9 : 10.

So, Number of student from Mumbai in college A = (45/9) × 10 = 50

Number of student from Delhi in college A = 120 - 40 - 50 = 30

Total Number of student from Delhi and Mumbai in college A = 30 + 50 = 80 

∴ The required answer is 80

Shortcut Trick

Change in profit percentage for A = 15% − 12% = 3%.

According to the question, 3% of A's capital = Rs. 270.

100% of A's capital = (270 ÷ 3) × 100 = Rs. 9,000.

Profit sharing ratio A : (B + C) = 9/10 : 1/10 = 9 : 1.

Since Investment ratio = Profit ratio, total capital of B and C = 9000 ÷ 9 = Rs. 1,000.

B and C share equally ∴ Capital of B = Capital of C = 1000 ÷ 2 = Rs. 500.

∴ The correct answer is Rs. 500, Rs. 500.

Alternate Method

Given → A's share = 9/10, B and C share equally. Income increase = Rs. 270. Formulas: Profit = Investment × Rate | Change in Income = Capital × (R₂ − R₁)%

⇒ Remaining profit = 1 − 9/10 = 1/10. ⇒ Share of B = Share of C = (1/10) ÷ 2 = 1/20. ⇒ Ratio of shares A : B : C = 9/10 : 1/20 : 1/20 = 18 : 1 : 1. ⇒ Let A's capital be K. Change in income = K × (15% − 12%) = 270. ⇒ K × 3/100 = 270 ⇒ K = 9000. ⇒ Since 18 units = 9000, then 1 unit = 9000 ÷ 18 = 500. ⇒ B's capital = 1 unit = Rs. 500; C's capital = 1 unit = Rs. 500.

∴ The correct answer is Rs. 500, Rs. 500.

Additional Information

Partnership Investment

In a partnership, if the time period is the same for all partners, the profit sharing ratio is directly proportional to the capital invested.

Income and Profit %

Total Income = Capital × Profit Rate. Therefore, an increase in income is equal to the Capital multiplied by the difference in profit percentages.

Shortcut Trick

Passing Marks = Obtained marks + Failing marks = 190 + 35 = 225

As per percentage, Passing Marks = 36% of Total Marks

36% → 225

100% → (225 ÷ 36) × 100 = 6.25 × 100 = 625

∴ The correct answer is 625.

Alternate Method

Given:

Passing percentage = 36%

Marks obtained = 190

Shortfall to pass = 35 marks

Calculations:

⇒ Required Passing Marks = 190 + 35

⇒ Required Passing Marks = 225

⇒ Let Total Marks be 'x'

⇒ 36% of x = 225

⇒ (36 ÷ 100) × x = 225

⇒ x = (225 × 100) ÷ 36

⇒ x = 22500 ÷ 36

⇒ x = 625

∴ The correct answer is 625.

Additional Information

Percentage to Value Conversion

To find the total value when a percentage part is known, use: Total = (Value ÷ Percentage) × 100.

Passing Marks Concept

Passing Marks = Obtained Marks + Marks by which failed, OR Passing Marks = Obtained Marks − Marks in excess of passing.

Successive Percentage Change

If a value changes by a% then b%, net change = (a + b + ab/100)%.

Shortcut Trick

Net increase in population = 16300 − 15000 = 1300.

Assume all 15000 are males, increase = 15000 × 8% = 1200.

Assume all 15000 are females, increase = 15000 × 10% = 1500.

Apply Alligation: (1500 − 1300) : (1300 − 1200) = 200 : 100 = 2 : 1.

Number of females = (1 / 3) × 15000 = 5000.

∴ The correct answer is 5000 females.

Alternate Method

Given: Initial Population = 15000, Final Population = 16300, Male increase = 8%, Female increase = 10%.

Formula Used: Total Increase = (Male % × Males) + (Female % × Females)

⇒ Total increase in value = 16300 − 15000 = 1300

⇒ Total percentage increase = (1300 / 15000) × 100 = 8.666...% or 26/3%

⇒ Using Alligation for Ratio (M : F):

⇒ (10 − 26/3) : (26/3 − 8)

⇒ (4/3) : (2/3)

⇒ 4 : 2 = 2 : 1

⇒ Number of females = [1 / (2 + 1)] × 15000

⇒ Number of females = (1 / 3) × 15000 = 5000

∴ The correct answer is 5000 females.

Additional Information

Alligation Rule

It is a rule that enables us to find the ratio in which two or more ingredients at their respective prices/percentages must be mixed to produce a mixture of a specified price/percentage.

Percentage Change

Percentage change = [(New Value − Old Value) / Old Value] × 100. Always keep the base as the original value.

Population Problems

If population P increases at r% per annum, population after n years = P(1 + r/100)ⁿ.

Shortcut Trick

Weight of New Player = Weight of Replaced Player + (Total Players × Increase in Average)

Weight of New Player = 55 + (12 × 1/3)

Weight of New Player = 55 + 4 = 59 kg

∴ The correct answer is 59 kg.

Alternate Method

Given:

Number of players (n) = 12

Weight of player replaced = 55 kg

Average weight increase = 1/3 kg

Calculations:

⇒ Total weight increase = Number of players × Increase in average

⇒ Total weight increase = 12 × 1/3 = 4 kg

⇒ Weight of new player = Weight of replaced player + Total weight increase

⇒ Weight of new player = 55 + 4 = 59 kg

∴ The correct answer is 59 kg.

Additional Information

Net Change in Sum

When one member is replaced, the Total Sum changes by the difference between the new value and the old value: (New Value − Old Value) = n × (Change in Average).

Average Concept

Average = Sum of all observations ÷ Number of observations. If the average increases, the new value must be greater than the replaced value.

Shortcut Trick

Difference in discount percentage = 6% − 5% = 1%.

This 1% difference in Marked Price (MP) results in Rs. 15 less profit.

Since Profit decreases as Discount increases, 1% of MP = Rs. 15.

Therefore, 100% of MP = 15 × 100 = Rs. 1500.

∴ The correct answer is Rs. 1500.

Alternate Method

Given: First discount = 5%, Second discount = 6%, Decrease in profit = Rs. 15.

Formulas: SP = MP × (100 − Discount%) ÷ 100 | Profit = SP − CP.

⇒ Let the Marked Price (MP) be x.

⇒ First Selling Price (SP₁) = x × (100 − 5) ÷ 100 = 0.95x.

⇒ Second Selling Price (SP₂) = x × (100 − 6) ÷ 100 = 0.94x.

⇒ Difference in Profit = SP₁ − SP₂ = 0.95x − 0.94x = 0.01x.

⇒ 0.01x = 15 ⇒ x = 15 ÷ 0.01 = 1500.

∴ The correct answer is Rs. 1500.

Additional Information

Relationship between SP and MP

The Selling Price is calculated by subtracting the Discount from the Marked Price. SP = MP − Discount.

Impact of Discount on Profit

For a fixed Cost Price, any increase in the discount percentage directly reduces the profit by the same monetary amount. Change in Profit = MP × (Difference in Discount%).

1. R sits second to the right of V.

2. Only one person sits between R and W.

3)  P is not an immediate neighbor of W and does not sit at corner. 

4)Q faces S who sits immediately to the left of U. (This eliminates case 2) 

Hence, U sits third to the left of T.

1. R sits second to the right of V.

2. Only one person sits between R and W.

3) P is not an immediate neighbor of W and does not sit at corner. 

4) Q faces S who sits immediately to the left of U. (This eliminates case 2)

Hence, four people sit between R and S, when counted in a clockwise direction from S.

1. R sits second to the right of V.

2. Only one person sits between R and W.

3. P is not an immediate neighbor of W and does not sit at corner.

4. Q faces S who sits immediately to the left of U. (This eliminates case 2)

Hence, both 1) and 2) are true.

1. R sits second to the right of V.

2. Only one person sits between R and W.

3. P is not an immediate neighbor of W and does not sit at corner.

4. Q faces S who sits immediately to the left of U. (This eliminates case 2)

Person who sits immediately to the right of S is W, R sits second to the left of W.

Hence, R sits second to the left of the person who sits immediate right of S.

1. R sits second to the right of V.

2. Only one person sits between R and W.

3. P is not an immediate neighbor of W and does not sit at corner.

4. Q faces S who sits immediately to the left of U. (This eliminates case 2)

All are sitting at the corner of the table except Q.

Hence, Q does not belong to that group.

Hence, code for 'economic' is 'py'.

Hence, 'su' is the code for focus.

Code for growth is 'om'.

Code for 'is important' is 'ta nx'

Hence, code for 'growth is important' is 'om ta nx'.

Code for 'important' is either 'ta' or 'nx'.

Hence, answer is cannot be determined.

Hence, 'wr' is the code for greater.

Digits are arranged in descending order within the number:

793 → 973

689 → 986

957 → 975

495 → 954

879 → 987

Hence, "879" is the correct answer.

1) G goes on Friday.

2) One person goes between G and C.

3) D goes on the second day of the week.

4) Three persons go between D and F.

5) The number of persons goes after C is equal to the number of persons go before G. 

Here, case 2 will be cancelled.

6. A goes on one of the days before C.

7) B does not go on Monday or Thursday.

Hence, A goes on Monday.

1) G goes on Friday.

2) One person goes between G and C.

3) D goes on the second day of the week.

4) Three persons go between D and F.

5) The number of persons goes after C is equal to the number of persons go before G. 

Here, case 2 will be cancelled.

6. A goes on one of the days before C.

7) B does not go on Monday or Thursday.

Hence, three persons go for movie after E.

1) G goes on Friday.

2) One person goes between G and C.

3) D goes on the second day of the week.

4) Three persons go between D and F.

5) The number of persons goes after C is equal to the number of persons go before G. 

Here, case 2 will be cancelled.

6. A goes on one of the days before C.

7) B does not go on Monday or Thursday.

Hence, the number of persons go for movie before C is the same as the number of persons who go for movie after G.

1) G goes on Friday.

2) One person goes between G and C.

3) D goes on the second day of the week.

4) Three persons go between D and F.

5) The number of persons goes after C is equal to the number of persons go before G. 

Here, case 2 will be cancelled.

6. A goes on one of the days before C.

7) B does not go on Monday or Thursday.

Hence, F goes on Saturday.

1) G goes on Friday.

2) One person goes between G and C.

3) D goes on the second day of the week.

4) Three persons go between D and F.

5) The number of persons goes after C is equal to the number of persons go before G. 

Here, case 2 will be cancelled.

6. A goes on one of the days before C.

7) B does not go on Monday or Thursday.

Hence, "C" goes for the movie just before E.

Given number: 81247563

Sum of all even digit: 8 + 2 + 4 + 6 = 20

Sum of all odd digit: 1 + 7 + 5 + 3 = 16

Difference between the sum of all even and sum of all odd digit = 20 - 16 = 4

Hence, "4" will be the difference between the sum of all the even digits and the sum of all the odd digits of the given number ‘81247563’.

Statements

Only a few animal are cat → Some part of Animal are overlapping with Cat and some part of animal are not cat

Some animal are dog → Some part of animal are overlapping with dog 

Venn diagram for the given statements are follows.

Conclusions

I. All Cat are animal → False ( some part of animal are not cat but remaining part of the animal can be cat so, this possible statement not definite hence false)

II. Some cat are Dog → False( some dog are cat or not is definite it can be a possible case but not definite)

Hence Neither I nor II follow is the correct answer.

Statement:

Only a few Sea are River → Some parts of Sea are River and Some parts of sea are not River.

All River are Water bodies → All river will be part of Waterbodies

The least possible venn diagram will be.

Conclusion :

I. Some Sea are Water bodies → True ( Some parts of Sea are River and All River are water bodies hence some sea are water bodies)

II. All sea are River → False ( Some parts of Sea are River and Some parts of the sea are not River hence all sea are river is False )

Hence,Only I follow.