SSC CHSL Tier-1 2021: Official Paper (Held On : 7 June 2022 Shift 1) (Previous Year Paper)

The correct answer is Plentiful.

Key Points

• The most appropriate antonym for the given word 'Meagre' is 'Plentiful'.
• The meaning of the word 'Meagre' is 'too small in amount'.
• The meaning of the word 'Plentiful' is 'available in large amounts or numbers'.
• Hence, the most appropriate answer is 'Plentiful.

Additional Information

• Let's understand the other options.
• Civilized- well organized; having a high level of social and cultural development.
• Miserable- unpleasant; making you feel unhappy.
• Sparse- small in quantity or amount.

The correct answer is Frail.

Key Points

• The most appropriate synonym for the given word 'Slender' is 'Frail'.
• The meaning of the word 'Slender' is '(used about a person or part of somebody’s body) thin in an attractive way'.
• The meaning of the word 'Frail' is 'weak or not healthy'.
• Hence, the appropriate answer is 'Frail'.

Additional Information

• Let's understand the other options.
• Lively- full of energy, interest, excitement, etc.
• Energetic- full of or needing energy and enthusiasm.
• Defame- to harm somebody by saying or writing bad or false things about him/her.

The correct answer is 'To be unsuccessful at eliciting a response'.

Key Points

• The most appropriate meaning of the given idiom ' To draw a blank' is 'To be unsuccessful at eliciting a response'.
• To draw a blank: to get no result or response.
• E.g. Detectives investigating the case have drawn a blank so far.
• Therefore, as per the points mentioned above, we find that the correct answer is Option 3.

Additional Information

• Let's look at some similar idioms.
• Fight a losing battle- to try hard to do something when there is no chance that you will succeed
• The police are fighting a losing battle against a rising tide of crime.
• Flog a dead horse- waste energy on a lost cause or a situation that cannot be changed. 
• He keeps trying to get it published but I think he's flogging a dead horse.
• Running on empty- have exhausted all of one's resources.
• He was running on empty and even the alcohol had worn off.

The correct answer is 'Plagiarise'.

Key Points

• The appropriate one-word substitution for 'Take and use the thoughts, inventions, etc. of another person as one’s own' is 'Plagiarise'.
• Let's understand the other options.
• ​Copyright- the legal right to be the only person who may print, copy, perform, etc. a piece of original work, such as a book, a song, or a computer program.
• Compose- to be the parts that together form something.
• Produce- to make something to be sold, especially in large quantities.

The correct answer is '“Is French your mother tongue?” Kavi asked Gina.'

Key Points

• The most appropriate option that expresses the sentence 'Kavi asked Gina if French was her mother tongue.' in direct speech is '“Is French your mother tongue?” Kavi asked Gina.'
• Direct speech is when we simply repeat what someone says, putting the phrase between speech marks.
• E.g. Paul came in and said, “I’m really hungry.”
• Hence, as per the above-mentioned points, the correct answer is Option 4.

Additional Information

• Let's understand Indirect speech.
• When we want to report what someone said without speech marks and without necessarily using exactly the same words, we can use indirect speech (also called reported speech).
• E.g. Direct speech: “We’re quite cold in here.”

        Indirect speech: They say (that) they’re cold.

The correct answer is "fallacy, subservient, symbiotic".

Key Points

• Fallacy means untrue notions.
• Example: The belief that the corner house is haunted is a fallacy.
• Subservient means acting as subordinate.
• Example: Even though Willy is talented, he acts as a subservient.
• Symbiotic means dependence on each other equally. 
• Example: Tina and her friend share a symbiotic relationship.
• Therefore, the appropriate answer is "fallacy, subservient, symbiotic".

Additional Information

• Frankness - being honest and open.
• Superior - in a higher rank or position.
• Disadvantageous - without any benefit.
• Accuracy - exactly to the point.
• Domineering - wanting to control other people with a strong character.
• Encumbering - a burden.
• Felicity - state of being very happy.
• Disobedient - refusal to listen to the rules.
• Hindering - troubling.

The correct answer is "inadequate, rigour". 

Key Points

• Inadequate means not sufficient.
• Example: The time was inadequate to finish the exam.
• Rigour means the quality of being careful and detailed. 
• Example: The detective examed the site rigorously for clues.
• Therefore, the appropriate option is "inadequate, rigour".

Additional Information

• Indefinite - not fixed.
• Stupor - almost unconscious
• Institutional - connected to an institution or body.
• Shiver - trembling.
• Inadvertent - an unintentional action.
• Snigger - to laugh in an unpleasant way.

The correct answer is pear.

Key Points

• The most appropriate homonym to fill in the blank is 'pear'.
• Considering the other food item that is mentioned in the sentence is an apple, the other item will automatically be a fruit as well.
• The word 'pear' means 'a fruit that has yellow or green skin and is white inside. Pears are thinner at the top than at the bottom'.
• Hence, the appropriate answer is 'pear'.

Additional Information

• Let's understand the other options.
• Prier- a curious or inquisitive person.
• Pair- two things of the same type that are used or worn together.
• Pare- to remove the thin outer layer of something.

The correct answer is b, d, a, c.

Key Points

• The most appropriate order for the sentences to make a meaningful and coherent paragraph is b, d, a, and c.
• When a person is talked about, then the correct order to describe is to mention the name and designation, appearance, and then qualities.
• So, according to the above-mentioned points, the paragraph will be as follows:
• Mrs Hima Raman used to teach us geography at school. She had beautiful eyes and a sharp nose. Though she was a woman of slim build, she was remarkably strong and energetic.

The correct answer is 'decisive'. 

Key Points

• The most appropriate antonym for the given word 'doubtful' is 'decisive'.
• The meaning of the word 'doubtful' is 'unlikely or uncertain'.
• The meaning of the word 'decisive' is 'making something certain of final.
• Hence, the most appropriate answer is 'decisive'.

Additional Information

• Let's understand the other options.
• Played- to take a part in.
• Adult- a person or an animal that is fully grown.
• Poverty- the state of being poor.

The correct answer is 'their'.

Key Points

• The most appropriate homonym for the given blank is 'their'.
• The meaning of the word 'their' is 'of or belonging to them'.
• Hence, the appropriate answer is 'their'.

Additional Information

• Let's understand the other options.
• They're- 'They're' is a contraction that means "they are."
• Dare- to have enough courage to do something
• There- used as the subject of ‘be’, ‘seem’, ‘appear’, etc. to say that something exists.

The correct answer is Discipline.

Key Points

• The most appropriate synonym for the given word 'Chastise' is 'Discipline'.
• The word 'Chastise' means 'to punish somebody physically'.
• The word 'Discipline' means 'train (someone) to obey rules or a code of behaviour, using punishment to correct disobedience'.
• Hence, the appropriate answer is 'Discipline'.

Additional Information

• Let's understand the other options.
• Order- the way in which people or things are arranged in relation to each other.
• Sever ties- to end a connection with someone or something.
• Chase- to run after somebody/something in order to catch him/her/it.

The correct answer is 'for'.

Key Points

• The most appropriate option to substitute the word 'to' is 'for'.
• The word 'To' is a preposition and a versatile little word that can be used to say many things. It can be used to indicate a goal or a direction of movement, as well as a place of arrival.
• The word 'for' is used 'to indicate the place someone or something is going to or toward'.

Additional Information

• Let's understand the other options.
• At- used to show where somebody/something is or where something happens.
• Towards- used for describing 'in the direction of, in relation to, or in contribution to.
• Since- used to describe proper time 'from a particular time in the past until a later time in the past or until now'.

The correct answer is 'fire'.

Key Points

• The most appropriate answer is 'fire'.
• The actual idiom is 'spread like wildfire' which means 'to become known very quickly'.
• A variation of the same idiom is given in the sentence.
• Hence, the appropriate answer is 'fire'.

The correct answer is 'Scholar'.

Key Points

• The most appropriate meaning of the given idiom 'Men of letters' is 'Scholar'.
• Men of letters- someone who is an expert in the arts and literature, and often a writer too
• Example: He is a man of great experience, a man of letters and of law.

Additional Information

• Let's understand the other options.
• Dancer- a person who dances, often as a job.
• Singer- a person who sings.
• Actor- a person who acts; whether in a movie or theatre.

The correct answer is Glory.

Key Points

• The most appropriate antonym for the given word 'Ignominy' is ' Glory'.
• The meaning of the word 'Ignominy' is 'public shame and embarrassment; a loss of honour'.
• The meaning of the word 'Glory' is 'fame or honour that you get for achieving something'.
• Hence, the appropriate answer is 'Glory'.

Additional Information

• Let's understand the other options.
• Beneficial- having a good or useful effect.
• Restorative- connected with treating the body or a part of it in order to repair it.
• Pejorative- expressing disapproval or criticism.

The correct answer is 'Start something too soon or act hastily'.

Key Points

• The most appropriate meaning of the given idiom 'Jump the gun' is 'Start something too soon or act hastily'.
• Jump the gun: to do something too soon, before the proper time.
• Example: They only met three weeks ago – isn't it jumping the gun to start talking about marriage?

Additional Information

• Let's look at some similar idioms.
• Time flies: Time passes extremely quickly
• Example: Look how fast our children grew up, how time flies.
• It's high time: It’s the right time to do something, or past the appropriate time to do something.
• Example: It’s high time he met with me to resolve this issue.
• Beat the clock: Finish something before time is up, before a deadline.
• Example: Although she was late to the exam, she managed to beat the clock and finished all of it 10 minutes before the end.

The correct answer is "It is proposed to build a dam for irrigation purposes."

Key Points

• The sentence given in the question is an active voice in a simple present tense (Subject+ first form of verb+ object).
• If the active sentence starts with ‘People think/acknowledge/know/consider/understand/believe/find/say/report/claim/propose....that he is’, it can be changed into passive form in two different ways.
• Use the dummy subject “it”:
• It was thought..... It was written.....
• It was said..... It was declared.....
• The subject of the noun clause in the active sentence is used as the subject of the passive form.
• Besides this ‘to’ is used.

​Hence, from the above explanation, we can say that the correct sentence is: "It is proposed to build a dam for irrigation purposes."

Additional Information

‘People say’ is replaced by ‘It is said’:

• Example:
• People believed that the earth was flat. (active)
• The earth was believed to be flat. (passive)
• It was believed that the earth was flat. (passive)

The correct answer is Brutish.

Key Points

• The most appropriate synonym for the given word 'Bestial' is 'Brutish'.
• The meaning of the word 'Bestial' is 'savagely cruel and depraved'. (वहशी, पाशविक)
• The meaning of the word 'Brutish' is 'cruel and unpleasant'. (पाशविक, पशु के समान)
• Hence, the most appropriate synonym is 'Brutish'.

Additional Information

• Let's understand the other options.
• Greedy: wanting more food, money, power, etc. than you really need. (लालची)
• High-minded: having strong moral principles. (उच्च आदर्शों वाला)
• Noble: belonging to the highest social class, honest; full of courage, and care for others. (उदार)

The correct answer is 'as soon as them noticed'.

Key Points

• The segment that contains the error is the 3^rd segment.
• In the segment, the word 'them' needs to be replaced with the word 'they'.
• The word 'them' is a third-person pronoun.
• 'Them' is used as the object of a verb or preposition.
• The word 'they' is used for 'the people or things that have been mentioned'.
• As per the above-mentioned options the error exists in the 3^rd segment.

The correct answer is Improvement.

Key Points

• In the given passage the correct option to be filled in the blank is Improvement.
• Improvement: Alterations that improve the character or state of someone or something.
• Example: We have seen some improvement in the condition of the slums.
• ​Therefore the correct option is Improvement.

​The complete sentence is: The improvement of roads in the 1700s and 1800s made the transportation of goods and people much easier.

Additional Information

• Stagnation refers to a circumstance where something remains unchanged and does not change and develop.
• Recovery refers to the process of healing from a disease or injury.
• Setback refers to something that takes place that hinders or delays the development of a process.

The correct answer is Transportation.

Key Points 

• In the given passage the correct option to be filled in the blank is Transportation.
• Transportation: The transfer of goods or persons between locations.
• Example: A bicycle is a cheap means of transportation.
• ​Therefore the correct option is Transportation.

​The complete sentence is: The improvement of roads in the 1700s and 1800s made the transportation of goods and people much easier.

Additional Information

• Traffic refers to the number of vehicles travelling along a road or the number of vehicles travelling by plane, rail, or ship.
• Delivery refers to the action of delivering items, correspondence, packages, etc. to people's homes or places of employment.
• Shipment refers to sending several items at once to a location or the act of sending them.

The correct answer is Invested.

Key Points 

• In the given passage the correct option to be filled in the blank is Invested.
• Invested: To invest time, money, effort, etc. in anything in order to gain a benefit or profit.
• Example: He has invested his money in the property market.
• ​​Therefore the correct option is Invested.

​The complete sentence is: Many nobles and businessmen invested their wealth in building bridges and tunnels.

Additional Information

• Donated refers to helping a person or group by giving money or goods.
• Supported refers to praising someone or something because you want them to be successful.
• Promoted refers to the act of persuading someone to like, support, utilise, or purchase something.

The correct answer is Remarkable.

Key Points

• In the given passage the correct option to be filled in the blank is Remarkable.
• Remarkable: Unusual or exceptional, hence startling and noteworthy.
• Example: Mother Teresa was a truly remarkable woman.
• ​​Therefore the correct option is Remarkable.

​The complete sentence is: John Metcalfe was one of the most remarkable road builders of this period. He was blind and felt the surface of the road.

Additional Information

• Credulous refers to being too trusting of what you are told and being so easily duped.
• Fascinated refers to something that is extremely interesting.
• Attentive refers to someone who is listening carefully.

The correct answer is Requirements.

Key Points 

• In the given passage the correct option to be filled in the blank is Requirements.
• Requirements: Something you have to accomplish or what you need.
• Example: Many jobs have a minimum requirement of a decent degree.
• ​​Therefore the correct option is Requirements.

​The complete sentence is: This was done to make sure that it met his requirements.

Additional Information

• Desire refers to having a strong interest in something.
• Wish refers to expressing your sorrow or regret over a current status or circumstance.
• Condition refers to the specific state that something or someone is in is described.

The correct mirror image of the given combination when the mirror is placed at MN is as shown below :-

Detailed Explanation :- 

• The line MN is the mirror.
• The word 

ends with  

. So, the mirror image will start with

 → Options 3 is eliminated.

• The first letter is

. So, the last letter in the mirror image will be

→ Options 4 is eliminated.

• The second letter is

. So, the second last letter in the mirror image will be

→ Options 1 is eliminated.

Hence, Option 2) is the correct answer.

Additional Information 

• In a mirror image Left changes to right and the right changes to leftwheretop and bottom remains the same.
• When placement of mirror not given, by default we will assume it in vertical direction.
• The starting letter word will be at last after the mirror image drawn with left changes to right and right changes to left

Given: A _ D K P A B _ K P A B F _ P A B _ K P

Let's check each option:

1) B P A G → A B D K P  - A B P K P - A B F A P - A B G K P 

2) B E K G → A B D K P - A B E K P - A B F K P - A B G K P 

• Here, we can observe a pattern.
• 3^rd letter is increasing by +1, rest letters are same.
• D + 1 = E; E + 1 = F; F + 1 = G

3) B C G D → A B D K P - A B C K P - A B F G P - A B D K P 

4) B D G E → A B D K P - A B D K P - A B F G P - A B E K P 

Hence, ‘B E K G ’ is the correct answer.

The figure from among the given options that can replace the question mark (?) in the following series is:

Explanation:

• The triangle in center is rotating 90° anti-clockwise at the same place.
• The arrow in the corner is moving clockwise from corner to corner and changing it's pointing direction from Down to Up and vice versa.

 Hence, option 1 is the correct answer.

The logic followed here is:

Second number ÷ 7 = First number

⇒15 : 105 → 105 ÷  7 = 15

⇒4 : 28 → 28 ÷ 7 = 4

Similarly,

⇒? : 196 → 196 ÷ 7 = 28

Hence, option 3 is the correct answer.

The option that represents the correct order of the given words as they would appear in an English dictionary is shown below:

1.Assignment

2.Assortment

4.Astrology

5.Astronaut

3.Asymmetric

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

The logic followed here is:-

The first three letters are increased by +1, +2, and +3 respectively, rest letters remain unchanged.

• DISEASE

• ​Therefore, code = EKVEASE

• FACULTY

• Therefore, code = GCFULTY

• Similarly, HELPFUL

• Therefore, code = IGOPFUL

Hence, "option 3" is the correct answer.

The logic followed here:

(Addition of the individual numbers of the first number) × 2 = Second number

1. 678 : 42 → 678 → 6 + 7+ 8 = 21 → 21 × 2 = 42

2. 546 : 30 → 546 → 5 + 4 + 6 = 15 → 15 × 2 = 30

3) 283 : 28 → 283 → 2 + 8 + 3 = 13 → 13 × 2 = 26 ≠ 28

4. 125 : 16 → 125 → 1 + 2 + 5 = 8 → 8 × 2 = 16

Hence, option 3 is the correct answer.

The logic followed here:

First number × (First number - Second number) = Third number

(43, 34, 387) → 43 × (43 - 34) = 43 × 9 = 387

(13, 10, 39) → 13 × (13 - 10) = 13 × 3 = 39

Similarly,

(18, 13, 90) → 18 × (18 - 13) = 18 × 5 = 90

Hence, option 1 is the correct answer.

Here, we need to find the pattern to get the missing number.

The logic here is: The odd terms are subtracted by 8 to get the next odd term and each even terms are added by 8 to get the next even numbers.

Hence, the missing number is "644".

Here, we need to find the pattern to get the correct answer.

The logic here is: The 1^st number is divided by 2^nd number and the answer is multiplied by 5 to get the 3^rd number.

So, (78, 13, 30): 78 $\div$ 13 = 6, 6 $\times$ 5 = 30

First we will check all the options one by one:

1) (56, 14, 80): 56 $\div$ 14 = 4, 4 $\times$ 5 = 20 $\ne$ 80. This is not true

2) (280, 70, 20): 280 $\div$ 70 = 4, 4 $\times$ 5 = 20. This is true

3) (360, 50, 40): 360 $\div$ 50 = 7.2, 7.2 $\times$ 5 = 36 $\ne$ 40. This is not true

4) (350, 17, 65): 350 $\div$ 17 = 20.58, 20.58 $\times$ 5 = 102.94 $\ne$ 65. This is not true.

Hence, the number pair '(280, 70, 20)' is the correct answer.

Here, the alphabets and their positions are shown as below:

The logic here is: Each odd term word has 1^st and last letter are interchanged, then 2^nd and 2^nd last letter are at their own place and the middle letters too interchange their positions.

For the word CHAISE : EHIASE, we have:

For the word MODULE : EOUDLM, we have:

Similarly for the word SLIDER : ?, we have:

Thus, for the given word SLIDER, the code language is: RLDIES

Hence, the code language is 'RLDIES' for the given word.

Confusion Point: Keep in mind the positions of all the letters.

Here, the alphabets and their positions are shown as below:

The logic here is: The first letter is added by 3 to get the next 1^st letter. Similarly the 2^nd letter by +7, 3^rd letter by +11 and the 4^th letter by +15.

Thus, we have:

Hence, the correct answer  is 'CORV'

Confusion Point: Keep in mind the positions of all the letters.

Here, we need to count number of circles.

First we will count all circles we can see directly:

Hence, the correct answer is  10

Here, we need to find the pattern to get the final output of missing number.

The logic here is: Each even term is completely divisible by each odd term.

So, 40 $\div$ 10 = 4, 112 $\div$ 14 = 8

First we will check all the options:

1. 187 $\div$ 17 = 11

2. 190 $\div$ 17 = 11.17

3. 162 $\div$ 17 = 9.52

4. 156 $\div$17 = 9.17

Thus, only option 1 is completely divisible by 17.

Hence, the missing number is 187.

Here, we have two dices and both have two faces in common.

Given:  

So, we will rotate the 2^nd dice in such a way that the common faces are in the same position as the 1^st one.

Thus, we can say that face 9 is opposite to face 6.

Hence, the number '9' will be on the face opposite to the one showing '6'.

Given: 12 January 2019 was on Monday.

The number of odd days between 14 December 1917 to 12 January 2019

Note:- Generally in 100 years, there are 5 odd days but when the century year is a leap year then 1 extra odd day is added and hence, the total odd days is 6.

Century years which are leap years:- 400, 800, 1200, 1600, 2000, 2024, and so on.

The number of odd days between 14 December 1917 to 14 December 2017 = 100 years = 6 odd days (2000 is a leap century year)

The number of odd days between 14 December 2017 to 14 December 2018 =  1 odd days

The number of odd days between 14 December 2018 to 12 January 2019 = 17 + 12 = 29 days

So, The number of odd days between 14 December 1917 to 12 January 2019 = 6 + 1 + 29 = 35 days = 36/7 = 5 weeks and 1 odd days.

So, 14 December 1917 will be = Monday - 1 = Sunday.

Hence, the correct answer is "Sunday".

Here, we have to find out the pattern used to get the odd pair out.

First we will check the options one by one as below:

1. 100 : 7 $\Rightarrow\sqrt{100}$ = 10 - 3 = 7

2. 25 : 4 $\Rightarrow\sqrt{25}$ = 5 - 3 = 2 but they have given 4. This is not true.

3. 169 : 10 $\Rightarrow\sqrt{169}$ = 13 - 3 = 10

4. 64 : 5 $\Rightarrow\sqrt{64}$ = 8 - 3 = 5

Hence, the correct answer is 25 : 4

Here, we are given some statements and we need to check which conclusion are true.

First we will see the venn diagram of each statements by one by:

1. All birds are parrots:

2) No parrot is a crow:

3) Some owls are crows:

Thus, combining all the statements, we will get,

Next, we will see the conclusion:

1. Some parrots are owls: Since they have not mentioned any relation between parrots and owls. This is not true.

2. No crow is a bird: From the above figure, we can say that, this is true. 

3. No owl is a bird: Since they have not mentioned any relation between parrots and owls. This is not true.

Hence, only conclusion 2 follows.

Here, we will substitute the signs given to get a balance equation.

Given: 75 * 25 * 40 * 63 * 92 * 91

First, we will check the options one by one:

1) ÷, ×, +, –, =

$\Rightarrow$ 75 ÷ 25 × 40 + 63 - 92 = 91

Applying BODMAS rule, we will get,

$\Rightarrow$ 3 × 40 + 63 - 92 = 91

$\Rightarrow$ 120 + 63 - 92 = 91

$\Rightarrow$ 91 = 91, which is possible. This is true.

2) ÷, +, –, ×, =

$\Rightarrow$75 ÷ 25 + 40 - 63 × 92 = 91

Applying BODMAS rule, we will get,

$\Rightarrow$ 3 + 40 - 63 × 92 = 91

$\Rightarrow$ 3 + 40 - 5796 = 91

$\Rightarrow$ -5753 = 91, which is not possible. This is not true.

3) –, +, ÷, ×, =

$\Rightarrow$ 75 - 25 + 40 ÷ 63 × 92 = 91

Applying BODMAS rule, we will get,

$\Rightarrow$ 75 - 25 + 0.63 × 92 = 91

$\Rightarrow$ 75 - 25 + 57.96 = 91

$\Rightarrow$ 107.96 = 91, which is not possible. This is not true.

4) –, ×, ÷, +, =

$\Rightarrow$ 75 - 25 × 40 ÷ 63 + 92 = 91

Applying BODMAS rule, we will get,

$\Rightarrow$ 75 - 25 × 0.63 + 92 = 91

$\Rightarrow$ 75 - 15.87 + 92 = 91

$\Rightarrow$ 151.13 = 91, which is not possible. This is not true.

Hence, the correct option is 1.

Confusion Point: Keep in mind to apply BODMAS rule, while solving these types of problems.

Here, the alphabets and their positions are shown as below:

The logic here is: Each 1^st letter is subtracted by 3 to get the next 1^st term. Similarly for all the letters.

Thus, we have:

Hence, the missing word is 'DLXI'.

Confusion Point: Keep in mind the positions of all the letters.

Here, we will substitute the signs given to get a balance equation.

Given: 17 * 3 * 48 * 42 * 14

First, we will check the options one by one:

1) +, −, ×, =

$\Rightarrow$17 + 3 - 48 × 42 = 14

$\Rightarrow$ 17 + 3 - 2016 = 14

$\Rightarrow$ -1996 = 14, which is not possible. This is not true.

2. =, +, −, ×

$\Rightarrow$17 = 3 + 48 - 42 × 14

$\Rightarrow$17 = 3 + 48 - 588 

$\Rightarrow$ 17 = -537, which is not possible. This is not true.

3) ×, −, =, ÷

$\Rightarrow$17 × 3 - 48 = 42 ÷ 14

$\Rightarrow$ 17 × 3 - 48 = 3

$\Rightarrow$ 51 - 48 = 3

$\Rightarrow$ 3 = 3, which is possible. This is true.

4) ÷, ×, =, −

$\Rightarrow$17 ÷ 3 × 48 = 42 - 14

$\Rightarrow$ 5.66 × 48 = 42 - 14

$\Rightarrow$ 272 = 42 - 14

$\Rightarrow$ 272 = 28, which is not possible. This is not true.

Hence, the correct option is 3.

Confusion Point: Keep in mind to apply BODMAS rule, while solving these types of problems.

Here, we have folded the paper two times and made a design by cutting it.

When we open the 1^st fold, we get,

So, we the same image in fig 2 as in fig 1.

Next, we open the last fold, we will get the same image in the next half too.

Thus, we have:

Hence, the correct answer is option 2.

Here, the alphabets and their positions are shown as below:

The logic here is: In each word, the odd letters are added by 2 and the even letters are subtracted by 2 to get the code language.

For the word UNDER, we have code language as WLFCT,

For the word WORDS, we have code language as YMTBU, 

Thus for the word LOFTY, we have:

Hence, the code language is 'NMHRA' for the given word.

Confusion Point: Keep in mind the positions of all the letters.

Here, we need to apply sign at the letters to get the answer.

Given: (17 B 4 ) A (29 B 3) C (85 D 17 ) A 26 C 13 A 52

Substituting the values of A as ‘+’, B as ‘×’, C as ‘−’ and D as ‘÷’, we will get,

= (17 × 4 ) + (29 × 3) - (85 ÷ 17 ) + 26 - 13 + 52 

Applying BODMAS rule, we will get,

= (17 × 4 ) + (29 × 3) - 5 + 26 - 13 + 52

= 68 + 87 - 5 + 26 - 13 + 52

= 233 - 5 - 13

= 233 - 18

= 215

Hence, the answer is 215 of the given equation.

Confusion Point: Keep in mind to apply BODMAS rule, while solving these types of problems.

Here, we are given the word and we need to find the mirror image of it.

First keep in mind that, in mirror image the first letter will be the last letter of the given word. Also, the size of the letters will not change i.e. capital letters will appear capital only.

The correct mirror image of the given combination when the mirror is placed at XY is as shown below :-

Detailed Explanation :- 

• The line XY is the mirror.
• The word  

ends with  

. So, the mirror image will start with

. → Options 2 and 4 are eliminated.

• The number-letter   

 is used . So, the mirror image will be  

. Also their positions must not interchanged → Options 1 is eliminated.

Hence, 'Option 3' is the correct answer.

Additional Information 

• In a mirror image Left changes to rightand theright changes to leftwheretop and bottom remains the same.
• When placement of mirror not given, by default we will assume it in vertical direction.
• The starting letter word will be at last after the mirror image drawn with left changes to right and right changes to left.

GIVEN:

Marked price = 30% more than Cost price

Discount  = 15%

FORMULA USED:

Discount % = (Discount / M.P.) × 100 

Discount = M.P. - S.P.                             

Where, M.P. = Marked price, S.P. = Selling price.

CALCULATION:

Let's assume the Cost price will be Rs100.

According to the question,

M.P. = 30% more than the cost price.

⇒ M.P. = ( 100 + 100 × 30/100 ) = Rs.130.

Now, discount%  = 15

⇒ Discount% =( Discount /M.P.) × 100

⇒ 15 = ( Discount / 130) × 100

⇒ Discount = Rs.19.5

Now, S.P. = ( M.P. - Discount ) =  ( 130 - 19.5 ) = Rs.110.5.

Now, S.P. = final price = Rs110.5 and Cost price = Rs.100

Difference = ( 110.5 -100) = 10.5 

Required percentage =( 10.5 / 100 ) × 100 =  10.5%.

Hence, the final price is 10.5% more than the Cost price.

Alternate MethodConcept used:

C.P/M.P = (100 - d%)/(100 + P%)

Calculation:

⇒ C.P/M.P = (100 - d%)/(100 + P%)

⇒ 10/13 = (100 - 15%)/(100 + x%)

⇒ 10/13 = 85/(100 + x%)

⇒ (100 + x%)  = (85 × 13)/10

⇒ (100 + x%) = 110.5

⇒ x% = (110.5 - 100) = 10.5%

∴ The correct answer is 10.5%.

Shortcut Trick

For any two numbers a and b, the Mean Proportion (M) is given by M = √(a × b).

To find the missing number, use the squared relation: b = M² ÷ a.

Given M = 50 and a = 20.

⇒ Required Number = 50² ÷ 20 = 2500 ÷ 20 = 125.

∴ The correct answer is 125.

Alternate Method

Given:

Mean proportional value = 50

One of the numbers = 20

Formula Used:

If x is the mean proportion between a and b, then a : x = x : b, which implies x² = ab.

Let the required number be n.

⇒ √(20 × n) = 50

Squaring both sides:

⇒ 20 × n = 50 × 50

⇒ 20 × n = 2500

⇒ n = 2500 ÷ 20

⇒ n = 125

∴ The correct answer is 125.

Additional Information

Third Proportional

If three numbers a, b, and c are in continued proportion (a:b = b:c), then c is the third proportional to a and b, calculated as c = b²/a.

Fourth Proportional

If four numbers a, b, c, and d are in proportion (a:b = c:d), then d is the fourth proportional, calculated as d = (b × c) / a.

Mean Proportional Property

The mean proportional between two numbers is always the positive square root of their product, also known as the Geometric Mean.

GIVEN:

The average run of 8 players = 6.5.

2 new players have added average increases = 1

FORMULA USED:

Average = Sum of values / No. of values.

CALCULATION:

The average run  of 8 players = sum/number of players  

⇒ 6.5 = sum / 8 

⇒ Sum =  52.

Now when two new players are added the average increases by 1 hence, it becomes 7.5

⇒ Average run of 10 players = sum/ number of  players

⇒ 7.5 =  sum/ 10 

⇒ Sum = 75.

The sum of a run of two new players = ( sum of run of10 players - sum of run of 8 players)

The sum of a run of two new players = ( 75 - 52) =  23.

Average run of new players = 23/2 = 11.5.

∴ The average run of new players is 11.5.

GIVEN:

Rate of increments = 5% , 2% and 6% 

Present population  = 56,763.

FORMULA USED:

Population after each increment = x × ( 100 + r) /100

Where, x = initial population, r = rate of increment.

CALCULATIONS:

Let the population of the city three years before be x, then

⇒ x × ( 105/100) × ( 102/100) × ( 106/100) = 56,763

⇒ x = 56763 × (20/21) × ( 50/51) × (50/53) 

⇒ x = 50000

∴ The initial population was 50000.

GIVEN:

(a + b) = √7 

(a - b) = √5 

FORMULA USED:

(a - b)2 = a2 + b2 - 2ab

(a + b)2 = a2 + b2 + 2ab

CALCULATION:

⇒ a + b = √7 

Squaring both sides of the equation:

⇒ (a + b)² = 7

⇒ a² + b² + 2ab = 7     ------ (1)

Now,

⇒ a - b = √5 

Squaring both sides of the equation:

⇒ (a - b)2 = 5 

⇒ a2 + b2 - 2ab = 5    ------ (2)

On adding (1) and (2) we get,

⇒ 2 × (a² + b²) = 12

⇒ (a2 + b2) = 6     ------ (3)

Putting the value of equation (3) in equation (1)

⇒ a2 + b2 + 2ab = 7

⇒ ab = 1/2

Putting the required value in the equation:

8ab × (a2 + b2) - (a - b)2

⇒ ( 8 × 1/2 × 6 ) - (√5)² 

⇒ ( 24 - 5) = 19.

∴ The required value is 19.

Given:

Sale in Outlet S = 26%

Calculation:

According to the question, 

From the options:

Option A,

⇒ P + Q = 14% + 10% = 24%

It is not more than S.

option B,

⇒ R + U = 18% + 12% = 30%

It is more than S 

∴ Option B is the correct answer.

GIVEN:

Triangle with sides 3 cm, 4 cm and 5 cm

FORMULA USED:

Area  = $\sqrt {s (s-a) (s-b)(s-c) }$

Where, s = semi-perimeter = $( a +b +c) \over 2$ 

and a, b, and c  are the respective sides.

CALCULATION:

Here, a = 3 cm , b = 4 cm , c = 5 cm

Now, s = ( 3+ 4 + 5) /2 = 12/2 = 6.

Area = $\sqrt{6 ( 6-3) (6-4) (6-5)}$ 

⇒ $\sqrt{ 6× 3× 2 × 1}$ = 6 cm2 

∴ The required area is 6 cm2.

Shortcut TrickCalculation:

Since 3,4 and 5 are popular triples of right angle triangle.

Here, the base (B) = 3, perpendicular (P) = 4, and hypotenuse (H) = 5

Area of triangle = (1/2) × B × P

⇒  (1/2) × 3 × 4

⇒ 6 cm²

∴ The correct answer is 6 cm2

GIVEN:

Distance = 475m

Time = 1 minute

FORMULA USED:

Distance = Speed × Time 

CALCULATION:

Distance = 475m =  475/1000 km 

Time = 1 min = 1/60 hours

Now, Speed = Distance ÷Time = ( 475/1000) ÷ ( 1/60)

⇒ ( 475/1000) × 60  =  28.5 km/h

According to the question:

She travelled at 1.2 times of current speed

New speed = 1.2 × 28.5 = 34.2 km/h  and New time = 1 h

Now, Distance =  34.2 km/h × 1 h = 34.2 km.

∴ Distance is 34.2 km.

GIVEN :

Population = 225000

Birth rate = 4.5%

Death rate = 2.5%

FORMULA USED:

The population after t years = P × $( 1 + R/100)^t$ 

Where, P = initial population , R = Rate, t = Time

CALCULATION:

According to the problem,

Net increased per year =  ( 4.5 -2.5)% = 2%

The population after 2 years = 225000 × $( 1 +2/100 )^2$ 

⇒ 225000 × 51/50 × 51/50 = 234090

Now, increase in population = ( population after 2 years - initial population)

⇒ ( 234090 - 225000) = 9090.

∴ The increase in population is 9090.

GIVEN:

cosec² θ + cot² θ = 5/3

FORMULA USED:

cosec2 θ = 1 + cot2 θ  

cot 60° = 1/√3

cot(180° - θ) = - cot θ

CALCULATION:

According to the question:

cosec2 θ + cot2 θ = 5/3

⇒ 1 + cot2 θ + cot2 θ = 5/3

⇒ 2 cot2 θ = ( 5/3 -1) = 2/3

⇒ cot2 θ = 1/3    

⇒ cot θ = 1/√3 

⇒ cot θ = cot 60°

⇒ θ = 60° 

Now, cot 2θ =  cot (2 × 60)

cot 120° = cot (180° - 60°) = - cot 60° = - 1/√3

∴ The required value is - 1/√3 .

Given:

The table shows the numbers of seats won in the local body election in a state by different political parties in the years 2019 to 2014.

Calculations:

The increase in the number of seats won by AGP in 2019 compared to 2014 is

⇒ 303 - 282

⇒ 21

The percentage increase in the number of seats won by AGP in 2019 compared to 2014 is

⇒ $\frac{(Increase \space in \space no. of \space seats \space won\space by \space AGP)}{No.\space of\space seats\space \space won\space by \space AGP \space \space in \space 2014}$× 100

⇒ $\frac{21}{282}$ × 100

⇒ 7.45 %

$\therefore$ The percentage increase in the number of seats won by AGP in the year 2019 is 7.45%.

Given:

Raghav and Aditya can complete the work in 3 days.

Aditya and Ishaan can complete the same work in 4 days.

Ishaan and Raghav can complete it in 6 days.

Calculations:

Raghav and Aditya's 1 day work = $\frac{1}{3}$ rd part of work

Aditya and Ishaan's 1 day work = $\frac{1}{4}$ th part of the work

Ishaan and Raghav's 1 day work = $\frac{1}{6}$ th part of work

Now, we have :

Raghav, Aditya and Ishaan all together 1 day work

= $\frac{1}{2}$ ( Raghav and Aditya's 1 day work + Aditya and Ishaan's 1 day work + Ishaan and Raghav's 1 day work)

Hence, Raghav, Aditya and Ishaan's together 1 day work = $\frac{(\frac{1}{3}+\frac{1}{4}+\frac{1}{6})}{2}$= $\frac{9}{24}$th part of work

Therefore, Raghav, Aditya and Ishaan took 24/9 days to complete the work.

∴ The time taken by all of them together to complete the work is $\frac{24}{9}$ = 2$\frac{2}{3}$ days.

Shortcut TrickCalculation:

Now,

Raghav + Aditya + Ishaan = (4 + 3 + 2)/2 = 9/2

Required number of days = 12 ÷ (9/2)

⇒ (12 × 2)/9 = 8/3 = 2$\frac{2}{3}$ days.

∴ The correct answer is 2$\frac{2}{3}$ days.

Concept used:

BODMAS

Calculations:

⇒ 96 $\div$ 48 $\times$ $29\over2$ + 52 - (1 + 2 + 3 + 4)

⇒ 96 $\div$ 48 $\times$ $29\over2$ + 52 - (10)

⇒ $2×\frac{29}{2}$ + 25 - 10

⇒ 29 + 25 - 10

⇒ 54 - 10

⇒ 44

∴ Required simplified value is 44.

Formula used:

The sum of (1 + 2 +.....+ n) = $\frac{n(n+1)}{2}$

Average = The sum of all number/(Total number)

Calculation:

The sum of odd numbers between 21 to 81,

21 + 23 + 25 + ..........+ 81

⇒ (21 + 0) + (21 + 2) + (21 + 4) +...........+ (21 + 60)

⇒ {21 + 21 + 21 +............(31 times)} + 0 + 2 + 4 + ...........+60

⇒ 31(21) + (0 + 2 + 4 + 6 + ...........+ 60)

⇒ 651 + 2(1 + 2 + 3 +......+ 30)

⇒ 651 + 2$[\frac{30(30+1)}{2}]$

⇒ 651 + 930

⇒ 1581

Average = The sum of all number/(Total number)

⇒ Average = (1581)/31

⇒ Average = 51

∴ The average of all odd numbers from 21 to 81 is 51.

Shortcut TrickConcept used:

If the series is in A.P, then

Average of the series = (First term + last term)/2

Calculation:

The consecutive odd numbers are:

21 + 23 + 25 + ..........+ 81

So this series is in A.P

Average of all odd numbers from 21 to 81 = (21 + 81)/2

⇒ 102/2 = 51

∴ The average of all odd numbers from 21 to 81 is 51.

Given:

Radius of solid cylinder = r cm

Height of Solid cylinder = r/2 cm

Formula used:

Total surface area of cylinder = 2πrh + 2πr²

Calculations:

Total surface area of solid cylinder

⇒ 2πrh + 2πr²

⇒ 2πr(h + r)

⇒ 2πr($\frac{r}{2}$+ r)

⇒ 2πr($\frac{3}{2}r$)

⇒ 3πr²

$\therefore$ The Required total surface area is 3πr².

Given:

Two successive discounts =10% and 5%

Concept Used:

Discounted Value = Actual Value(1 - Discount%)

Calculation:

Let the MP be 100

After 1^st discount of 10% price becomes (100 -10)%

⇒ 90

After 2^nd discount of 5% price becomes {90 - (5% of 90)}

⇒ 90 - $\frac{9}{2}$ = 90 - 4.5 = 86.45

∴ The net discount offered to the buyer is (100 - 86.45)

⇒ 14.5% 

∴ Net discount is 14.5%

Shortcut Trick For effective discount we can use, 

⇒ a + b - (a × b)/100,

where a and b are two discounts

⇒ 10 + 5 - (10 × 5)/100

⇒ 15 - 0.5

⇒ 14.5

 ∴ Net discount is 14.5%

Given:

Pulses of  rates Rs.80 per kg and Rs.95 per kg are mixed together to get pulse worth Rs.85 per kg.

Concept used:

Ratio of 1^st kind and 2^nd kind in mixture = (N - T) : (T - M)

Calculations:

So, the ratio of 1^st kind of pulse to 2^nd kind in mixture

⇒ 10 : 5 = 2 : 1

∴ The Required ratio is  2 : 1.

Given:

Discount offered on cash payment = 20%,

Discounts offered to ABC credit card holders = 8%.

Sandeep bought a laptop for Rs.35,000 by paying online with his ABC credit card.

Calculations:

Price after first 20% discount 

⇒ $\frac{100-20}{100}$× 35,000

⇒ $\frac{80}{100}$ × 35,000

⇒ Rs.28,000

Now, the price after second 8% discount on the card payment of Rs. 28,000

⇒ $\frac{100-8}{100}$ × 28,000

⇒ $\frac{92}{100}$× 28,000

⇒ 92 × 280

⇒ Rs.25,760

∴ Sandeep needs to be paid to buy the laptop is Rs.25,760.

Alternate MethodCalculation:

First discount = 20%; Second discount = 8%

Sandeep needs to pay to buy the laptop:

⇒ 35000 × 80% × 92%

⇒ Rs.25,760

∴ The correct answer is Rs.25,760.

Shortcut Trick

For similar triangles ΔABC and ΔDEF, the ratio of corresponding sides is equal.

Side Ratio: AB ÷ DE = BC ÷ EF

Substitute values: 6 ÷ 9 = 8 ÷ EF

2 ÷ 3 = 8 ÷ EF

EF = (8 × 3) ÷ 2 = 12 cm

∴ The correct answer is 12 cm.

Alternate Method

Given: AB = 6 cm, BC = 8 cm, DE = 9 cm, and ΔABC ∼ ΔDEF.

Formula Used: Ratio of corresponding sides of similar triangles: AB/DE = BC/EF = AC/DF.

Since ΔABC ∼ ΔDEF, we use the property of proportionality:

⇒ AB ÷ DE = BC ÷ EF

⇒ 6 ÷ 9 = 8 ÷ EF

⇒ 2 ÷ 3 = 8 ÷ EF

⇒ 2 × EF = 8 × 3

⇒ 2 × EF = 24

⇒ EF = 24 ÷ 2

⇒ EF = 12 cm

∴ The correct answer is 12 cm.

Additional Information

AA (Angle-Angle) Similarity

If two angles of one triangle are equal to two angles of another triangle, then the two triangles are similar.

Area Ratio Property

The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides: Area(Δ1)/Area(Δ2) = (Side1/Side2)².

Corresponding Parts

In similar triangles, corresponding angles are equal and corresponding sides are in the same ratio (proportional).

Given:

Number of puffs sold by 4 different bakeries in 3 different months

Calculations:

Number of puffs sold by bakeries A and B together in February

⇒ 109 + 87 

⇒ 196

Number of puffs sold by bakeries C and D together in February

⇒ 220 + 132

⇒ 352

The ratio between the number of puffs sold by bakeries A and B together in February to the total number of puffs sold by bakeries C and D together in the same month

⇒ 196 : 352

⇒ 49 : 88

∴ The required ratio is 49 : 88.

Given:

Selling price at 25% loss = ₹14,400

Gain wanted = 20%

Formula used:

S.P = $\frac{(100+gain\%)}{100}$× C.P

S.P = $\frac{(100-loss\%)}{100}$× C.P

Calculation:

According to the question, 

S.P at 25% loss = Rs. 14,400

⇒ $\frac{(100-25)}{100}$ × C.P = 14,400

⇒ C.P = 14,400 × $\frac{100}{75}$

⇒ C.P = 19,200

Hence,  C.P = Rs.19,200

Now, S.P at 20% gain 

⇒ $\frac{(100+20)}{100}$× 19,200

⇒ $\frac{120}{100}$ × 19,200

⇒ Rs.23,040

$\therefore$ To gain 20%, the item should be sold for Rs.23,040.

Concept used:

The number is divisible by 150  only if it is divisible by 3, 5 and 10.

Calculations:

According to the question, we have:

320550, 333300, 463750 and 201300

They all have the last digits 0 hence, they are all divisible by 10 and 5

Now we need to check the divisibility by 3

For this we need the sum of the digits:

320550, 3 + 2 + 0 + 5 + 5 + 0 = 15, which is divisible by 3,

333300, 3 + 3 + 3 + 3 + 0 + 0 = 12, which is also divisible by 3,

463750, 4 + 6 + 3 + 7 + 5 + 0 = 25, which is NOT divisible by 3

and 201300, 2 + 0 + 1 + 3 + 0 + 0 = 6, which is divisible by 3.

Hence, only 463750 is not divisible by 150.

$\therefore$ The number among the options that is not divisible by 150 is 463750.

Given:

The total surface area of a sphere is 400π cm2.

Formula used: 

Total surface area of sphere = 4πr2

Volume of sphere = (4/3) × πr³

Calculations:

According to the question,

Total surface area of sphere = 400π

⇒ 4πr2 = 400π 

⇒ r2 = 100

⇒ r = 10 cm

Now, Volume of sphere = 4πr³/3

⇒ $\frac{4}{3}$ × 10³ × π

⇒ $\frac{4000}{3}$π

∴ The Volume is  $\frac{4000}{3}$π cm³

Given:

x + y = 13

Formula used:

a³ + b³ = (a + b)³ - 3ab(a + b)

Calculations:

According to question, we have:

x + y = 13

if we put x = 8, and y = 5 then

⇒ x + y = 8 + 5

Equation is satisfied with these values.

So,

⇒ (x - 8) + (y - 5) = 0

From the question:

⇒ (x - 8)³ + (x - 5)³ 

⇒ {(x - 8) + (x - 5)}³ - 3(x - 8)(x - 5){(x - 8) + (x - 5)}

⇒ {(x - 8) + (y - 5)} [ {(x - 8) + (y - 5)}² - 3(x - 8)(x - 5) ]

⇒ 0 × [ {(x - 8) + (y - 5)}² - 3(x - 8)(x - 5) ]

⇒ 0 

∴ Required value is 0.

Given:

The product of three consecutive odd numbers is 693.

Calculation:

Let the three consecutive odd numbers be P , (P +2) and (P + 4).

Sum of the three consecutive odd numbers = P + (P +2 ) + (P + 4)

According to the question,

Product of three consecutive odd numbers = 693

⇒ P × (P + 2) × (P + 4) = 693

Let us take the prime factors of 693 i.e., 3, 3, 7, 11

Hence, the possible value can be 7, 9, 11

⇒ 7 × (7 + 2) × (7 + 4)

⇒ 7 × 9 × 11

⇒ 693

∴ The smallest of the three numbers is clearly 7.